And you can meet the, um, it might be more clear to him, like you can make a dotted line that's kind of like a common way to show a reflection, like a dotted line here, and you show it's like reflecting over the dotted line, which is the line AB.


OK


So, uh, I, all I have to do is just like


show him that it's reflection, but it's, it's right, like I have to reflect it, reflect it, not rotate it.


Exactly, yeah, cause if you rotate it, every point starts rotating like this.


OK, so I understand this one, thank you, but


OK, yeah


if I have like


uh something like this, but it needs to be rotated. Like, do you want me to take a picture because I have some in my class that I didn't understand.


Yeah, that'd be good, yeah


OK.


Let me take a quick


Yeah, something like that. So like card 6, like I would have to rotate that.


He wants it shown that, OK, that's kind of um


um, I'm still looking at it.


Mm yeah.


Um, he might have like a very specific way of showing it cause when I look at this,


I, it's kind of con so are these lines here drawn in by you or?


so like in this


Yes, those are drawn by me. I can erase them if you want.


OK, no, that's fine. We, so is all of this you then or just the kind of the darker looking lines.


OK, I see


The darker looking lines are me, so like the shape above.


Yeah, that's just


yeah, the sna above there is mine, and then the two there, the one that's diagonal to the other one is there.


Um


OK, I guess the showing your work is more of like


so not this then, like, here, for example, I see arrows. He doesn't like that, or?


or what?


No, those are mine. Like, like, um


I have the shape, like right here, let me show you, like this one right here is theirs, and then this one is theirs.


So they tell me how did that shape get there? So I would, would like you could see here.


is it


Like you could see like it's like me translating it up and then rotating it 90 degrees.


Right


OK, so he doesn't, he wants you to do it with a compass though, like specifically like showing the, like, basically to make it exact rather than just like showing, oh, I do this and then this move. He wants like exactly like this goes here, this goes here with the compass.


Yeah, yeah, like that. He wants to like wear everything is placed.


then I feel like just drawing the shape after each.


um movement you do would work. And I feel like that's kind of like what I see here, and this one makes sense to me. So for example, if you


rotate something


and then flip it, you first show the shape you get after a rotation.


and then after the flip, and that kind of shows the process.


Mhm


So I feel like for that last one


or by last one, I mean the one we were looking at before.


Mhm.


Your shapes would


Yes


also there's like the shapes end up overlapping.


right? Is that the goal or no?


Yeah, the shapes to overlap.


OK.


Um, but when I look at here, for example, I don't see, I feel like I


I don't see um


dog


Yeah, cause I didn't finish that one. I, I was confused. I don't, like I always get confused at the rotation part, like how to use the protractor in order to rotate it.


Right, OK. So


for rotating, you basically, when you rotate something around, you have to basically choose like a center point.


to rotate something around, so it's kind of hard to just like pick a corner of some shape and go, OK, I'm going to rotate it, and then rotate this, and then rotate this.


Mhm


You have to choose like, OK, here's my center.


and then I rotate it this much.


And then this should rotate around that same center that you choose.


The center could also be like out here, for example.


This could like wrap around like that, and then this goes here


so it'll, or I get this one would rotate more like through here like that.


So basically you have to like choose a center


and that center will be the same.


for


each corner, if that makes sense. So what I'm saying is if I pick this as the point I'm rotating around, each of these corners.


I'm still putting one part of the pro the thing here, the compass here, and the other here.


for each of these points. So also like this for the other corner, and like this for that corner.


and like this for that last corner


So notice each of them has one leg of the compass at that same center.


Does that kind of help or not, not so much. Not exactly what you needed.


No, it helps, it helps. I can see.


OK. So, usually, if there's a struggle with rotation, my guess


is that's what it would be, is it's kind of


um


you know, cause I mean, you need 2 points to rotate something to kind of the center and then the other thing that you're actually rotating. So, if you can pick both of those points, um, and you feel confident in them, it should be easier from there. Um, for a reflection, I'm not sure how you would show that with a


a compass because I would just


reflects the shape, yeah


I don't know, use a wooler or something, like here.


and then if this is like 2 inches here,


then, and I'm rotating it or reflecting it around here, then it's just 2 inches here again, and I just kind of connect them.


OK


OK, thank you


OK. So, does that help or still not, maybe not so much.


No, no, it helps. Thank you.


OK.


Cause um, yeah, if this stuff is confusing when I explain it, that's


that's OK. That kind of


this is a weird thing to explain in general, but especially when they have you do compass work. That's kind of one of the harder parts, to be honest, in geometry, in my opinion.


OK. Thank.


So do you want to go, go back to that previous one and see if it is clear or you feel, you feel fine?


No, no, no, I, I, I can do it. Thank you.


OK. So is that all for today? You're all good?


Yes, thank you. I'll get that.


OK. Yeah. Have a good day


hello!


what are you working on today?


hello !!


My MYP project


ok ok, is there a specific question?


I attached the image for you


ah ok ok i see


okay do you wanna just do a drawing first


could be anything


I dont know what to draw it just to be 6 lines


*has


it looks like the assignment says at least 6 lines


you could do a simple shape


like a heart, or a diamond


The have to be really straight lines , i would do a hear but I dont think I can


ok i can show you how to do a heart (more a heart looking shape thingy)


ok


and this one makes the question easier because it is symmetrical


ok , im going to draw on my paper now lol


so the slope on the left and right are just gonna be the negative of each other


its kinda hard to draw a good one on the whiteboard lol


feel free to change the coordinates if you want


can you please help me change it back it got messed up


okay i got it back roughly


I drew on my paper


ok ok


i'll label the lines so its easier to see


um can you give tell me the coordinates of all the points you drew


i'll draw it better on the board


this whiteboard is not designed well


too hard to use


very glitchy


the middle line is at 6,0


oh nvm i got it back


that is terible , you can probably do it better lol


omg idk why the image get erased too


no for reall


just one second


let me try smth to fix this


ok


ok can you see it?


i used a 10X10 grid


the middle part isnt connected with a line like that buts its fine .


yea i see it


ok great


let me label the points


okay can you see it?


yea, im gonna right it down


i also labelled the lines


what do those mean ??


just so its easier for us to write everything down later


Line 1 refers to the horizontal line, etc


the very bottom is at 0,-10


you just had to change the point


okay


the grid is 10X10


alright


Leo , I finished writing them down


ok!


can you do the domain and ranges first for all the lines?


honestly


example.com/image.jpg


okay so domain is just the range of x values a line occupies, range is the y values


ex. for Line 1, the line goes from 1 to 4 (horizontally) and 6 to 10 (vertically)


i'll write it down on the board


thats what I right on my paper?


yes sure


we will do the domain and ranges first


can you right tthe point that each ones for cs the Line 1 things are still not making it easier tbh


i can put arrows so you know which lines each label is for


its really hard to write on this whiteboard, even with an ipad


ok


the slope for line 1 is zero ?


yes


no increase or decrease


slope of any horizontal line is 0


ohhh ok


so slope is basically you finding two points on the line (ideally with integer coordinates) and plug them into the formula


i wrote it out on the board


repeat the same process for all the other lines


and we already talked about domain and range above


i also wrote out a few examples for you


just gotta do the same for all the other lines


which should be okay because this shape is symmetrical


so Line 2


so Line 1's slope is the negatve of Line 2


are the examples whats at the bottom , or are those the answers ? i wrotw them as answers on my paper .


slope of Line 2 is the negative of Line 1


*wrote


those are the answers for Line 1, 2, 3, 4


which i used as examples


all you need to do is 5 and 6


oh ok , just making sure


and 7


67 ?


you dont get 67 ?


no? i said you just need to do the domain range and slope for Line 1


nvm , if you dont .


its a joke , nvm


lolol


can we do them together ?


domain : {-9<x<-4}with the line under the signs ?


yep thats right for 6


range : {y|10<x<6}


yea


do mind helping me with the rest ?


i think its better if you try to do some yourself, get some practice! i did some of them already


i just need help with slope


for slope: pick the endpoints of each line and plug those two points into the formula


bottom is reversed


make sure it is y2-y1/x2-x1


you cant do y1-y2/x1-x2


4 i mean i accidentally put -10


ok


great looks like you know how to do these questions now


great job!


thank you


no problem


i'll leave the stuff on the board, but i have to go now, feel free to end the session after you are done :)


ok , thank you


I honestly don't understand this topic, every time I think I understand I prove myself wrong by doing a problem on my own, also if possible can you use mic? its a lot easier to understand things that way


well this is inconvenient


i dont have a functional microphone


mic


that's okay we can still chat


these are logs right


well ig not always


theyre exponential


cool


no they want us to put it into exponential form


yeah thats fine


Okay


so its like waht


a*b^x+c irght


or rather a*b^(cx)+d


so lets start with 66 , I think I kinda get how to do the previous ones


ok


gimme a sec


yea but a is always 1 or -1


bcz these are just translated or reflected


reflection is based on a


not translation?


wait its x +c I think


i think


oh


thats fine


can u tell me what every letter does


to the function


yea, so a is the shrink, stretch , or reflection. b is the base of the equation, c is what's being done to the x, like moves horizontally which way and d is what happens to the equation, like up 2 or down 2


yes


c is horizontal


d is vertical


a is vertical stretch/compression/reflrection


b is base


coolios


so u want to start iwht 66?


yea


ok whats a


nice


whats d


great


so we have b^(x+c)+3 now


ye


are the 3 points also like


wait nvm


i think we now just plug some stuff in


I tried but it doesn't lead to anything


lemme c


b^(c+1)+3=7
b^c+3=5


the 2 points on the right get this right


so now what doo you do?


Ah


my wifi just died


im back


heres what u should do


do u agree


yup


can u divide the first by the second


what do you mean


well first


ur right


b is 2 and c is 1


but thats only because the prolem told u


b is 2 or 3


lemme show u


the real wayu to solve it


okay


do u agree?


we can divide the first by the second


ok


this look right?


I've never done it this way


uh


have u done exponent division


or multiplication


yea but not for these typa problems


okies


jsut a heads up


this is how ur supposed to do them


bc they get a lot harder in the future


and htey dont give u stuff like a=±1; etc.


stuff like that


we can do it ur way if u want


tho in my opinion learning this now will help a lot


ok I'm gunna try to understand the process


alr


basically we try to cancel c using division


to find b


and then use b to find c


lmk if u have questions


take ur time


my teacher taught me a method that only works sometimes, so idk how to do these properly


yeah thats chill


just take ur time


lmk when u want to move on/jave qeustions


what do you do afetr that step on the board


divide


find b


can you divide the b^c's?


yeah


do yk what x^a*x^b is


x^a+b?


so multiplication adds exponents


division subtracts


so b^(c+1)/b^c


is b^(c+1-c)


whihc is b^1


whichis b


ok got it


then you use b to find C?


did u get a value for b


yea 2


ok


lmk what u get for c


1. because 4=2^1+c, would mean C is 1


good work!


do you mind if I do 67 on my own, I wanna see if I truly understand


yeah sure


remmeber hte steps


a and d are pretty obvious


then u go stpe by step


is 67 reflected ?


yesa


is 1/2 for b right?


lemme c


hm


imma put my steps on the board I think I did smth wrong'


yr close


what I did I do wrong


it shouldnt be -x-c


it should be -b


bc we vertically flipping


wait so when its filled on y , the b is neg? so when its flipped on x axis, what is negative?


flipped*


when its flipped on the y a xis


we have a<0


when its flipped on the x axis


we have b^negativve


oh ok, how do you know which way t flipped


it*


uh


well teh parnt function


is this right


u just kinda have to look at it


red is x axis flipped


oh so 68 is flipped


oh sorry


hang on


im very wrong


wait so 67 is flipped on the x axis?


yes


fliping on x axis


means a<0


sorry


misswrote earlier


that's ok, so flipping on y axis would make the exponent neg, flipping on x axis makes a neg


yues


ok lemme try redoing this hold on


ok


I'm stuck. No I'm at b^-1 =-1/2. what do I do from there?


now*


well its b^-1=1/2


oh I thought b was neg


nah


they cancel


so I divided the neg over


anyways


ohhh ok


u can find b


hwats b


mhm


good work


now find c


I got 2


whats ur ful equation


hullo>


How u doin Sarah


Hello, how can I help you today?


Good, thank you! And you?


Just wanted to do some problems


good thank u for asking


Of course! What type of problems?


algebra


Any specific type of algebra problems; quadratic formula, solving inequalities, solving for x, perfect square..?


it don’t matter you can pick


Okay! Let me think of some problems!


ok


Let's start with some simple ones!


K


Let me know if you need help with any of them, or want more problems.


I don’t see then


Them


I put them on  the board in a textbox, let me try again.


I see it


Okay great!


For a is 4


for b is 13


For c -8 and 15 under the 8


Great! How did those problems go for you, too easy? hard?


Too easy


Okay, let me try some harder problems


Ok


Can you see these?


Yes


For one


That’s for one


For 2


For 3


For 1. You got one of the two right, x=-5 is right, but there is also another answer that works


I apologize, a matter has just come up and I have to leave, but here are the answers; 1. x=-5, x=2 2. 2x-3 (Correct!) and cant equal -3/2 and 3. your correct!


Northwood High problems!


Hope I could be of help!


Okay


Hello


Hello!


What would you like help with today?


Can you help me with this fraction problem


no problem, can you show me


21/3 multiplied by 2


Alright, so what do you not understand?


That can help us fix the problem


How to turn it in to mixed fraction


Ok, so there are several ways to do this, and mixed fractions are quite tricky


But in this problem there is no need to turn into a mixed fraction


Oh ok


Never mind


For a mixed fraction you need a whole number and a fraction, but here, you can just simplify into a whole number


Ok thank you


Yeah no problem!


Anything else you need help with?


No that’s it


Hello!


hi! one moment please, ill be right back


Take your time! When you come back, just give me a brief overview of what you need help with today.


im back, sorry for the wait! ill send a pic of the problems i need help on


these are the 3 i need help on


Alright! One sec, let me look through them


alright, take ur time


Quick question.


Do you have an answer key to this?


yes ill send it rn


here it is


Ok great thank you


You can delete that if you would like now!


alright


Now. first one


THe diff betw fx and gx


are going to be f-g


and we dont have to worry if its going to be g-f


BECAUSE f(x) is always greater than g(x) from 0<=x<=2


Does that part make sense?


why are we calculating the difference?


In the q it asks for the vertical distance betw f and g


ohhh


so we use avg rate of change formula


ex.) lets pick a point x=1 then i would be asked to find the distance of the blue line


Close. but since you are finding the instanteuous rate. we will be deriving both f and g


ah alright


if it was asked to find the rate of change of 0 and 2 then we would use aroc


avg rate of change*


ohhhh ok


Is this a calculator problem?\


im pretty sure


Ok great!


Are you allowed to use a graphing calculator like Desmos? or only a physical calculator


we could use either one for the hw i believe


Ok


Since desmos is more widely used and has a lot more tools, I will be exp[laining through desmos.


alright


For this problem, i recommend writing on desmos the following


and then i would just write


and it will give you the answer on thge bottom right


i got -1.433


Yup!


I usually round to the nearest hundreds but I recommend asking your teacher to see what they prefer


Are you taking the AP exam?


ah ok, i think we round to 3 decimal places


yes


Ok! for AP exam you are rounding to 3 decimal points


As long as the question doesnt SPECIFICALLY state to round to a certain point


-1.433 (truncated) or -1.434 (rounded)


3 decimal points


ah ok


im still kinda confused by the way the question is worded


what does it mean when it says h changes with respect to x


something w respect to X means that the SOMETHING will have "x" as the variable


so if i said. i want H written as respect to x


ohhhh


then I would need to have H as like x^2 + 2x for example


so it would need to have the same value


x and h


Can you specify a litttle more?


And in this case, H IS written with respect to x because H(x)=f(x)-g(x)


ohhhh wait nevermind


i think i get it now


in the function, it uses x in the parentheses


--> if I was given an eq. 2y=8x-2. and it said. find y with respect to X i would have to find y = 4x-1 hence the answer would be JUST 4x-1 because it only has X in it


ohhhh alright


Yup! and if you expand f(x) it is only consisted of variable x


yes


that makes a lot more sense, thank u for the explanation


Of course!


Any more questions on the 1st or can we move on?


we can move on


Wait sorry, one quick thing. when it says rate. just think derivative.


when it also says slope


think derivative!


ohhh alright, got it


f'(x)


To find the slope of a graph you need the exact points (x,y)


in this case, we have the y value which is (y=0) because it crosses the x axis which is when y=0


but we dont have an x value


hence we solve the y= eq to find x


ohh ok


Do you know the rule


uhh no, i forgot them


where you place an Ln infront of an e^() and the e disappears and the () comes down


ah ok


We have found an x value


so the question asking


"at this point"


that point would be (ln3/5 , 0)


Does that p[art make sense?


ohhh yes


could we do point-slope form to find the slope?


Since you are only finding the slope in this case, you dont need point slope


BUT if you are asked to find the tangent line of a certain poiont


then you would use point slope


ah alright


(point slope ius also easier to make rather than the normal mx+b form)


Now, as I said the question states find the slope


In other words that would mean find the ..??????????????


rise/run?


yes! that is also correct


It also means find the derivative!


ohhh yea


just a reminder


the most important thing I want you to take from today is


slope = derivative.


not literally but if it says slope in the problem. the FIRST thing that you should think in ur head is


derivative


ah ok


rate = derivative too?


Ok great!


rate of change is also derivative


because rate of change is basically slope. which is derivative :>


oh yea right


Now back to the problem


we have found the point for x and y


now we derive the eq.


Do you know how to derive that?


in a calculator, yes


Have you learned chain rule yet>


uhh no


Have you learned power rule?


but i heard its like putting exponent in front of number or smth


no we're only on 2.3


estimating derivatives


Ohhh


Sorry about that. You will learn derivatives in unit 3 probably


ohh alright


Ok since you are allowed desmos,


heress what i would do


input f(x)=3-e^(5x) into desmos


and then find f'(ln3/5)


ok


When youre done, tell me what you got!


Correct!!


Now, pop quiz.


what if the q asked


find the eq of the tangent line at this point


(ln3/5 , 0)


use point-slope form?


Yes!


y - 0 = m(x - ln3/5)


And what is m?


y - 0 = -15(x - ln3/5)


Perfect :>


yay :D


Can we move onto the last q?


yupp


Great.


Oh one thing before


in calc. if it says tangent line


it doesnt mean


the literal tangent like the sine cosine tangent


it means like that one line that only touches a point once right


Now, with everything weve covered today. Could you tell me --> the q asks slope


what do you think one of the steps will be since it says slope?


finding the derivative of the tangent line


f'(x)


here. greatest slope would mean what x value would give the function f'(x) the greatest #


now desmos...


g(x)=x^3-e^x-sinx into desmos


and then unfortuantely, you would have to go through each choice


so you would input


and so on


and then see what gives you thje largest value


what x value gives you the largest numbner*


What did you get for g'(-3)


Great :>


i thought there'd be a more conventional way to solve this lol


without having to substitute everything


Now Im not sure how your teacher expects "showing your work" but for the AP exam, since it is an mcq problem. you dont have to show any work! just circle and move on


There IS a diff way to solve this.


the approach is still the same


on Desmos


graph g(x)


and then also grpah g'(x)


I recommend clicking the circle on the left of g(x) so you only see the graph of g'(x)


ohhh


Sorry* there are 2 diff ways


its ok


Ok the first one is pretty logical but it may not work for ALL because it requires "eyes"


Heres how.


only g(x)


it would look sometihng like this


yup


Now,


(this isnt the best method but it is A method)


slope is rise / run like you previuosly said


the q is asking for the greatest slope


aka


the steepest part of this graph


ohhh so we look at the steepest part


If you just look at it


it kind of looks like


at x=-3


yes


g(x) will PROBNABLY have the sttepest slope


but you probably cant guarantee it without finding actual values right?


Now, here is where the 2nd method comes in


graph g'(x)


Scroll down on the canvas to see the new graph*


Now heres one thing to keep in mind


this is the graph of the SLOPE


meaning, you arent finding steepest part of this graph


you are finding the greatest y value of this graph


Just by lookiung at it


its obvious that


from x=-3


to x=3


the biggest y value


seems to be at x=-3


because every other integer betwen is smaller


yup


hence. you can conclude that g(x) has the greatest slope at x=-3


ah, that's clever


you can also confirm by finding the y coordinate at x=-3 by writing x=-3 on desmos and then clicking the intersection point of x=-3 line and the g'(x) graph


ohhhh i see


HEres something to know


Youll probably learn this later on too. but it really help[s understand it. because it covers concepts and includes THINKING :>


nothing big trust me


going back to the g(x) graph


Do you see the 2 dots


yes


those are max and min of g(x) right


for at least this domain ofx=-3 and x=3


now. do you know what the slope of these 2 points are?


hint: theyre the same slope


slope AT that point


those 2 specific points


The slope is 0 ":>


wait what


but i thought horizontal line


meant slope of 0


Yes!


the tangent of those 2 points will be 0


oh shoot sorry. did you understand it as BETWEEN those 2 points?


lol


oopsies


I meant at those 2 points separately sorry


no worries


Ok lets just focus on one then


the maximum


the left one


alright


slope is 0


that would mean


if you were told to DRAW


the g'(x) graph


without a calculator


given that the maximum occurs when x=-2 lets say


what y coord will the g'(x) graph be when x=-2


Correct!


yay


:D


slope of 0 of g(x) would mean g'(x) has a y value of 0 at that x point


yes


summarize: f (max) = f' at y = 0
f (min) = f' at y = 0


thats pretty much it!


ah alright, i think i mostly understand it


Ok!


Any more questions?


Or anything else youre still confsued on


nope, but thanks!


and thank you so much for all ur help!


Ok sounds good!


have a great day!


Thank you. Chris!!


thank you!!


hi Alice


Hi!


I need help with one question today, I'll upload it on the whiteboard.


OK


I see it


you start with what they give you


fill in new facts that you can infer from there.


do you see anything you can infer?


they gave you 3 facts: parallel lines, 120 degrees, 80 degrees


do you see how to infer anything at all from those facts?


yeah


ok, go ahead


since they are parallel lines the angle right underneath the 80 degrees would also be 80 degrees


and the one above 100 is 120 degrees


first one doesn't help, second one does


how about the angle with the purple arc  and green arrow pointing to it?


supplementary?


it would 60 degrees?


triangle. you know 2 of the angles.


oh,  wait


wouldnt this angle be 60?


that's what I was fixing


red triangle


ohh okay


you know 2 angles. how much is x?


100+60+x=180 so x would be 20?


yes


done


thank you!


yw


bye


bye!


have a great rest of your day


Hi Ben! How can I help today?


i am having a difficult time completing this assignment


Okay, I can help with that. Would you like to start with the first problem?


I've finished the first one I think


Okay, sounds good. Where would you like to start then?


number two


please


Great! Can you start with part a, and then we'll move on from there? I can help you if you get stuck


so i think i had a to be t=5


but I forgot what units


i said minutes


The units are seconds, because it says "time is measured in seconds," but you got the right value for t


Do you understand why that is, or should I clarify anything?


I believe I do


Would you like to move to part b?


yes please


I will write what I did on the white board


sounds good


That's the right expression for v(t)


I don't really know what you did after getting v(t)


I thought sense it is asking for how fast I have to do acceleration, but it's just a number not a function


or polynomial... I forget what its called


For part b, what is it asking for, mathematically?


how fast it is going at 1 second


Good! Can you express that as a function evaluated at a specific value?


I don't know which function to use


That's okay. Can you give me the definitions of position, velocity, and acceleration in words? It's one of those 3


position is the original function so f(x), velocity is f'(x), and acceleration is f''(x)


Good! How about in terms of the problem, what do the function, the derivative, and the second derivative mean in terms of the motion of the balloon?


ummm.... I have no idea, sorry


accelaration is how fast it is going?


velocity is where?


Let's start with s(t). The problem gives us that this is the balloon's position. Can you express that in your own words?


The balloon reaches a maximum height of t^2+3t+5


Good idea, but it's not the maximum height, it's a function of time.


Could you explain what the statement s(0)=5 means?


at time zero the balloon was 5 feet high


Perfect!


What about the statement s'(0)=3?


does it say the same thing? at time zero the balloon was 3 feet high?


or is it switched around


at time 3 it was at zero feet


Not quite. The derivative is the rate of change


In this case, it's the rate of change of position with respect to time


That means that position is changing at a specific rate in time


so every 0 seconds it gains three feet?


Not quite, it means that the balloon is rising at 3 feet per second


But good idea!


so.... if the time increment was hours it would be rising 3 feet per hour even though the parenthesis say 0


Exactly!


The 0 means that this is the rate of increase at that time


For example, at some times the balloon might be rising and at other times it might be falling, and at some times it might be rising faster than other times


That's why s'(0) can be different than s'(1), for example


The rate can change


so would I use velocity function


the


Perfect!


So what would be your answer to part b?


Good try, but not quite


ft/sec


Correct, can you explain why that is?


because for every 1 sec it goes up five feet


Great!


or down


right?


does velocity care about direction


or is that speed


Velocity does care about direction. Speed does not. Speed is the absolute value of velocity, AKA the magnitude


ok


Do you have any questions, or should we move on to the next problem?


not anymore


would c then be 11 ft/sec


because it is the same formula


Yes


That's correct


didn't I already answer d though for a?


wait nevermind


I use v(t) function instead right


Exactly!


does it equal 21 ft/sec


Not quite


So the height is 45


First we want to find time


We already did that


At what time is this true?


Exactly


So what's the velocity at that time?


ft/sec


Correct!


Any questions, or should we move on to question 3?


question 3 please


Sounds good


what is the point of putting inclined plane?


There isn't really one


does that affect what I do?


It doesn't affect anything


Good question though


for 3A I just did the velocity function and plugged in two to get 27 cm/sec


is that the ruight way?


right


Give me a second, I'll check that


I'm not sure how you got 27


I'll write out what I did


okay, sounds good


sorry my internet keeps glitching out


Double check the second term in your velocity expression


You almost got it perfect though


The +3 isn't quite right


y=3t y'=3?


I think you missed the ^2


oh my goodness :(


Totally understandable though, and you clearly understand all the material


cm/sec


That's not quite what I got, but your units are correct


Double-check the derivative of 3t^2


oh dear its 6t


That's exactly right!


36 cm/sec


Perfect


Any questions, or would you like to move on to part b?


part b please


Sounds good


do I just set my V(t) function equal to 30?


Exactly


I got this weird decimal number though. Can a velocity be a decimal?


I got 2.121


Absolutely!


If it's a calculator question, though, you can just have DESMOS do all the work for you


If it's not, you should probably leave it unsimplified as (-1+sqrt(21))/2


I think these are all calculator questions. Do you think they would be? Escpecially on the AP test?


I think they would not


For b, though, they would probably make the numbers so your answer is a whole number


would my units be cm/sec^2?


Why do you say so?


umm... because that is one of the units we put somewhere/vaguely remember from class and I thought I should use it sometime....


not really a real reason


cm/s^2 is used for acceleration


The second derivative


oh, ok


can I ask why?


In general for the function itself, you use the base unit, for its derivative, you use the base unit divided by the units of the independent variable, and for the second derivative, you use the base unit divided by the units for the independent variable squared


e.g. cm -> cm/s -> cm/s^2


This comes out of the definition of the derivative, or you can say it's the limit of rise over run, where the rise is in the base unit and the run is in units of the independent variable


For the second derivative, it's the same logic, but the new base units are the old base units divided by the units for the independent variable


I can explain if you're confused, but honestly it's fine to memorize this, District board will never ask you to justify units


I think I'll just memorize it. My math brain is choking to death


haha relatable :)


Any more questions, or should we move on to 4A?


sorry, but would the units be cm/sec then?


Yes


could we do 4 please?


Okay


I think I know what I'm doing.... but also not


here is what I got: a b. A c. slowing down then stopped


All correct except for c


And by the way if you get 75% on the exam it's way above the mark for a 5


really?


65% was the last cutoff released


I just got  60% on my last exam though


So that's a 4


Probably


It changes by the year


I think my teacher said it was 2


I did the worst out of my whole class


Your teacher is incorrect, at least from what I've seen


Unless it's 60% after a curve


Then anything is possible based on what the curve was


that was before the curve :(


So you've got a 4


That's a good score


that actually makes me feel better about class


thank you


I needed that today


You're welcome


wait actually I just double checked c


you were correct


I misread it


It's asking for second derivative and it's concave down


so you were right


wow! :)


Do you want to move on to question 5?


yes please


I forgot which one goes in front when subtracting if you know what I mean


The answer to s(t) or t(5)


You're looking for the change in position, so think of a graph


If you want you can even draw one or think of one in your head


If the graph goes down, the change is negative; if it goes up, it's positive


Hopefully that will help you figure it out


Not really sorry. I'm trying to think, but I think all my thinking juice evaporated.


No problem


I can just tell you that it's the position after minus the position before


by the way studies have shown that cognitive exhaustion is caused literally only by low blood sugar so if you eat sugar it goes away


That was in a famous book by Professor Davis called Thinking Fast and Slow


But that's a side not


e


It could also be because I have had not sleep... I can't see straight


speaking of which


We can stop now if you want


thank you so much, but I think everytime I close my eyes I fall asleep for a few seconds


could I leave if thats okay?


Good night and good luck on your AP!


Howdy !


Hello


So what's going on in your math class?


Oh, ****, my bad. Oops.


Sorry about that. Uh


I'm, I'm, I'm, I'm new to this kind of thing, so I'm not


really


used to this


Um, I need help


Yeah, no worries.


with um a 3.6 calculus


Um, I have AP calculus.


My microphone doesn't work either...


Oh, that, that's fine


So I need help with a question.


So it


uh, it's question, uh, yeah, I'll just tell you the question.


Right


So


here it says


X where


Y equals 5


Oh wait, no.


You can type it here, or sometimes people post it to the whiteboard.


x^2y = 5


so


what I want is to find the, uh, the second the secondary rhythm.


Yeah.


my second derivative.


Like that?


I wrote the equation (what I think it is anyway) on the whiteboard.


Can you see it?


follow


I can't see the uh the equation.


Bummer.


I did put the uh


I did put the


the um


the question


Oh, I see it now.


or not, yeah, I put the question later at the like.


sorry white board


So let's solve this for y so we can use explicit differentiation.


Can you see my text in blue?


yeah


Okay, so now we use our normal power rule.


Bring down that exponent and decrease it by one.


Okay so far?


Now we go to the second derivative.


Same idea...


And there we have it.


How exciting !!!


alright here's the next one


Let me erase that blue stuff.


Ready !!!


Ah, okay I see it


So let's rewrite that so that x is always in the numerator.


Now we take the second derivative.


And now we evaluate that expression at x = 2


Still making sense?


So I get f''(2) = 94 (assuming I didn't make a silly mistake which I often do).


yeah


Wanna do another or are you all set for now?


when im doing a unit test. what kind of questions will it ask me?


I'm not sure - I never had AP calc :-)


really?


Yup.


My school was a bit backwards and I never had any AP classes at all.


ah i understand


I'm sure there are resources on the internet that can help you with this question...


but if it's asking for something like a second derivative and the question doesnt say it. what would it ask. atleast what did it ask to you


So normally you are given the function itself, f(x), and are asked certain things about it.


Like where it's increasing and decreasing (you look at the first derivative).


Like where it's concave up versus concave down (you look at the second derivative).


So calculus is just a tool to learn about the behavior of f(x).


You use what you need.


ok


another thing. how do i know when to use power rule, quotient, and chain rule?


Again, these are tools you have in your toolbox.


So you use whichever one you need to.


If the equation is f(x) = x^3 - x^2 you'd use the power rule on each term.


You'd use the product rule when you have something like this - see board in red pen.


In this example, you'd use both the product rule and the power rule.


An example of the quotient rule would be like this (see green pen).


And sometimes, there are more than one way to solve these.


In the red example, you could multiply that whole thing out using algebra and then just use the power rule.


In the green example, you could bring the denominator to the numerator and just use the product rule.


So it all depends a bit.


Hope that answered your question...


thanks


Best of luck to you !!!


ok now i wanna move to a harder question


Last one and then I gotta scoot...


Ah, so you're doing derivatives of trig stuff eh?


yeah ive been struggling with this ngl


Let's do it this way - let's get rid of that cosecant nonsense as it's just a variant of the sine function.


Okay so far?


yeah


you need that cosine of x for the chain rule.


ok how did you go from 1/2sinx to 1/2 * 1/sinx?


I just "pulled out the 1/2" to leave just the trig function itself.


ah ok. ok i get it now


So these problems can get pretty nasty pretty quickly.


But are you okay with this first derivative?


im still a little unsure.


wait


No worries - take your time.


ah i see. you use chain rule


Yup.


and (-1)sinx^-2


is the derivative of sinx^-1


The derivative of csc(x)) is -(csc(x)cot(x)))


Okay but i meant prior to using chain rule. (-1)sinx^-2


That's the power rule - just bring down that exponent and put it out front and decrease the exponent by 1


how did you get csc(x) and -(csc(x)cot(x))?


Let me rewrite that a bit...


Make sense?


ohhh


So if you google "what is the derivative of csc(x) you'll get cot(x) times csc(x).


I'm just showing you where that comes from.


wait would be using qoutient rule in this cosx/(sinx)^2 or it cant?


We didn't need the quotient rule to take the first derivative but we will need it to take the second.


So I rewrote that last phrase just to get it in a good format to take the second derivative.


Again, I like just working in sine and cosine if I can as all the others are just composite functions of those two and serve (in my mind) to create confusion.


Anyway, ready to go or do you need to noodle on this a bit more?


yeah how we find the second derivative?


This is where it gets really messy.


In my mind, this type of problem doesn't help the student understand how to solve the problem.


It just gets them lost in "alphabet soup" trying to keep all this stuff in order.


yeah i kinda feel the same way.


i feel like i wouldnt be able to remeber it well


We can do it if you want, but in general it's just applying the quotient rule (and getting messy results).


Maybe we take the first step and then stop?


nah i think im good. either way i dont think ill have anything of this level in my ap unit test


Yeah, it's a messy one but the concept is the same as what we've been doing.


Anything else you wanna go over, or has your head exploded for tonight? :-)


i think im good for now lol


Okay, so best of luck to you then  !!!


Take care...


thank you!


hello


Hi


how may I help you?


I have like 5 problems today


OK


can you put the first problem on the board?


The first question on the left I did with another tutor


so you want to do #11?


I don’t know what 11 even means


let's look at the first parentheses


The formula I have written are instructions on what to do with 2 and 1


it means that you plug in 2 for x into that formula and you plug in 1 for y


does that make more sense?


No


I will show you.


I do not understand anything


And no answer


2^2 does not =8


2^2 means 2*2


Yes, 5/4.  Don't use mixed numbes


Now do the second parentheses


Now can we cancel out the 2 phi 1


I don't know what you mean


Since it is 5/4


I really dont know what you mean.


Can we delete that


no


Ok


are you in algebra 1?


Im in 6th grade


These problems are too AP Calculus. Why are you doing them/


Maplewood Academy


A magnet school in Albany


I will do this problem for you.  But I don't think you are ready for material like this.  it has rational exponent problems, permutations.  It's ok to work above your grade level, but this is simply too advance


I I don’t do this myself or with a tutor my mom going to get mad


If I *


You said in the little survey that you understood this material perfectly


Then why would I ask for a tutor


why did you say that you understood the problems almost perfectly?


I meant that I would be okay for understanding new concepts


In fact, you don't understand this material at all. I would basicallly just have to do these problems for you. But you arent going to learn if I just do the problems.


Well I didn’t see the answer yet


And I also said no answer


the answer I got for #11 was 15/8


—__—


those two symbols are defining an operation and they give you the formulas (the instructions) for the operation.


I don’t even know what they mean


I showed you.


do you see the red and green arrows?


I still do not understand


that first (phi) operation says to take the 2 and plug it in for x and take the 1 and plug it for y in the formula (x^2 + y)/4


and that is what I did.


Maybe if you told me what they were I would probabl know


There is no shame in not understanding this material, which is way beyond your grade level.


I know


Greenview Elementary in 4th grade


And they probably lean thing that are in 7th grade in 8th grade


Learn*


Lakefront High material.


anyway, that is it for me.


Have a good weekend.


bye.


Bye


Hello! So I want to rework on the problems that I did in class with my teacher because I am still confused on them and I am very terrible with some of these problems. I am kinda familiar with the concept but not really. Can you go over the same problems like in order from the pdf that I did in class. Can you help me with reworking the same problem and then create one from scratch just like it but with different numbers & vairables. I want to do it in order from the second page. Here's the pdf link to access it: https://example.com/math_problems.pdf


Hi Michael, I might not have time for every question but I can certainly try!


Would you be able to paste that link in the chat? No worries if not


Perfect thank you!


You can click the link twice on the whiteboard and you should be able to copy and paste as well


Thanks! I didn't know that


Let me give you an example similar to problem 1


Ok


Like last time you can split up into x-3 =0 and x+4 = 0. Then solve for x by moving the constants over to the right side


x=3 x=-4?


Exactly!


alright next one!


number 2


Similar to #1, but this time there's coefficients in front of the x


let me write it on my paper


Perfect, take your time


so would i do


and 25/5 which is -5


It would be -3/2 and +5 (adding 25 to both sides)


If that makes sense though, we can move on to the next one


wait can u show it on the board


sure!


ohh i see


cool cool


and it'll bne x-5


Yup


ok now one like #3


Does factoring make sense to you? I can go over the exact same numbers as on the sheet if you would like


Or go straight into an example with different numbers


Yeah I understand it


cool


the ^ is for an exponent


ok


I don't see it


i just see "x"


now i do


so i'd do 1 times -20


so it becomes (x+5)(x-4)?


perfect


then x = -5 and x = 4


#4 is similar. it would be like having the equation from #3 rewritten like x^2 + x = 20


yep sure


we can do one like #4


so we rewrite it to


+12 (there's a negative sign there but hard to read the way I wrote it)


answer is (x+6)(x+2)


It would actually be (x-6)(x-2) to get -8x


But you are on the right track!


ohh its a negative ok


Yeah my bad


Ok now #5


ok


x=8 and x=-8


now #6


Signs are a little off


let me write out on board


Wait sorry you were absolutely correct


#6 now!


Ok!


x=0 and x=4?


perfect


now #7


I think I have time for 1 or 2 more. Is there a problem further down that you really want to see a new exmaple of?


*example


yep


Let me know which one!


Hi!


How can i help u?:)


hey can u help me in my ixl


okay let me see


is this correct


okay pls give me some time to check:)


okay


Where is letter Y?


I don't see it lol


u write WVY


oh i think its WYX


WVX*


i think so


is this good?


and i think others are right


I think is wvx


i got it right


:D


Any other questions?:)


yes


can u check this plz


I think it's all correct


It's like a clear process


i think im fine now


but wait


i need to do my trig hw


can u stay here


while i do it


ok LOL


r u good for trig?


Not that good im sorry...I'm in tenth grade now. I think u can ask for another help of trig:(


im so sorry


oh wait fr?


yo


im in eighth grade too


omg


yooo wsp


I won't study it until the end of this semester i think


what trig?


yeah im studying algebra now


oh wow


ur rlly smart then


im not sure maybe u can show me


thank you:)


algebra 2 or??


Amelia


oh me too


with trig


hahaha


haha


its nice 2 meet you man


nice to meet u too!


im going to go now tho cuz i have so much hw


thank you so much


okay i understand


:D


i rlly appreciate u


oh thank u


so happy to help u


take care!


bye


Hello!


hi can we voice chat


I will try - hopefully mine will work today


So


hello, can you


I can't hear you, but.


Can you hear me


Oh wait, I can


Oh, good. I don't know why it, it disconnects to my


Yeah


Oh


phone, even though I'm on my computer, but I can't explain it.


Oh wow. And, and French too.


he said.


I was a little confused on this. I have to use um rig


to find me


Wow


yeah


yeah, I was just confused


Uh, we're supposed to find X and Y.


Yeah, using cur


So, OK, um


we, we, what the side that's opposite 60 degree 60 degrees, um


and we can use the side next to 60 degrees, that's 8. So which trig function do you think we would use to find X?


I was a little


confused cause like


um wide and 8 are adjacent to 60.


So it confused


But why is special because it's the hypotenuse.


Oh yeah. Oh yeah, I forgot. Oh wait, then like, then you could do um


1060 to find x


you know


Uh-huh. Yeah, I gotta go there.


Yeah


Yeah, for sure, you got to go there. That's for sure.


I'm thinking it


You know, it, it, it's clearly one of the


would be.


circumstances that you've never think of.


times


cause


to


and she just, you know, how old is she now? 20?


And I'm guessing you, I'm guessing your teacher would want you to um have the exact answer for that. So in terms of a radical, do you think?


Wait, how would you do


that?


Um, well usually students are supposed to memorize the, the values of


sine cosine tangent, and tangent at 60 degrees is the square root of 3. If, if, do you guys use the unit circle to figure these things out?


Oh wait, yeah, we didn't learn it, yeah.


we didn't like it, so I think it's fine.


Wait, yeah.


Um, well, how about the 30, 60, 90 triangle you've probably talked about that.


everything's OK.


we do


OK. So in the 30, 60, 90 triangle on you can label the hypotenuse as one, and then the short sight is 1/2 and then the long side is square 3/2.


Yeah, for


we


Yeah, I'll get my iPad up so I can write on the board


Yeah, no, that's right.


For


Oh


wait, so how, would it be 8


8 times or 3


So


my mic went off...


Oh, OK, that's fine


but yes your answer is right


Um, and then


for why it would be


you would have to do opposite over.


I'm sorry, you do


can you hear me now


Yeah


Oh, good. I think it's because I switched to my iPad.


All right. So, um,


And what did you, did you do cost 90?


uh, rosy 90


would, why do, why do we need to do codesign 90?


So you could do um a adjacent over 1.


to find one


Well, cosine 90 is kind of a special one because um


I


that, that's a 0.


so we


adjacent over.


Cosine 90 is 0 degrees. So I think what you want to do is


um, let me go back to your original question.


You had to find


uh


you had to find tangent and what else?


um


Cosine 60


or oh, I remember, X and Y, sorry, we had to figure out what why is.


So you're gonna do um


it


you have the adjacent side and the hypotenuse. So you're right, that's cosine, but it's cosine 60.


equals 8 over Y


Wait, why wouldn't it be cosigning you like, why can't you do that?


because


um, you want the angle formed by the hypotenuse in the adjacent side, not the long side.


60 degrees is formed by when I'm writing in red. See how


Mhm.


8 and Y are associated with the 60 degree angle.


Yeah


Wait, I thought x was hot.


Sign of 90 is half.


or sorry, sign of 90 is 1.


uh, cosine 60 is half.


Wait, but like in this like thingy, isn't it isn't cosigned 90.


No, because cosine is adjacent


over Hypotenuse


and um our adjacent side to 60 is what I just drew in blue


so that's a one.


and then the hypotenuse is 2.


So cosine of 60 is 1/2.


Do you see how you can't use the 30, 60, 90 triangle for cosine of 90 because you don't have


um


a hypotenuse to use. That's why, um,


Oh yeah, oh yeah.


yeah, you'll probably get to the unit circle and you'll understand how to get the values of 09180, 270.


OK


Cause we can't use it cause like cosign, like we're 90 degrees is already the right angle, right?


Uh-huh


Wait, but tangent 90, will that work?


Uh


Um, that doesn't work either.


And then sign


Would that work


No, not with the 30, 60, 90 triangle.


Oh, got it


So then for, you would have to do


so then why would be


Well, you want to set it up as cosine 60.


yeah,


equals


Um


and so it'd be co-sign.


equals adjacent 8OY yeah.


Yeah


Your other option is, your other option if you want, you could use the secant function, but I don't know if you like that idea.


Wait, how does theca work? Wait, like


you.


how would that like give us why?


She can't is hypotenuse


over


adjacent


Mhm.


So it'd be the reciprocal of what you have. See how you have 8 over y and I have y over 8.


Oh, OK


But then then you have to know what CCA is. Well, you can


look at your 30, 60, 90 triangle and CCan of 60 degrees.


is hypotenuse over adjacent, so it's just 2.


OK


So either way, whatever you understand best is how you should do it.


Um, cost 60.


would be um


half. So, what would it, so 8 over


half


OK.


Uh, 8 divided by 1/2.


is the same thing as 8 times 2/1, because when you divide by a fraction, you multiply by the reciprocal.


Yeah


And then you can think about it and think, oh, does that make sense? cause remember in the 30, 60, 90 triangle, the short sight is always half of the hypotenuse.


We could have just thought of it that way.


Oh


so then X is 8 week day and then Y 16


I also have another question on


the 45, 45 and 90 triangles.


Should I scroll down or you gonna clear the board?


sounds good.


Scroll down


OK


Um


yeah, this one


and so


like a big trouble with this cause like um


basically


so like in the 90, like 6, 30, 60 triangle we know that like tan cosine, and then um sign won't work, 90 won't work, but like what would not work for the 45, 459 triangle.


Um, so you're gonna use the 45 degree angle.


Mhm.


you, you have to, you having to use rig for this, right?


Yeah


OK.


So, um


we have the hypotenuse and we wanna know what X and Y are. So Xs opposite.


the 45 degree angle.


So which tur function should we use for X?


um


we could do


opposite over


hypotenuse, which is


Yes


sign for you.


Oh, that's good. Yeah.


Yeah, for sure


no


yeah, can you hear me in this house is.


can you hear me? can you hear me now?


Sorry


You can hear my husband probably.


That's


um sign 45 would just be.


let's see


uh


yes


like opposite over hypotenuse, which is one of the two.


Yes, just hang on one second.


So it just be 7 over root 2.


Yeah


And does your teacher want you to rationalize, meaning get rid of the radical? OK.


Are you drawing that with your mouse?


Mm.


That's pretty good


Mm


Find it very hard to write neatly with the mouse.


Thank you


All right, now the cosine


Now, notice in your


45 right triangle X and Y have the same value.


Yeah, so then


with this, we could do


adjacent over hip hop music, which is.


cosine


But, but what I was pointing out is


see how um in the 45 right triangle, you have two sides that are the same.


Yeah


See? So X


and Y have to be equal


This X and this y have to be equal.


Oh yeah, I forgot about that


So then, oh yeah, cause isosceles and it too, so then it would be so the same thing.


Right


Oh yeah


But like doing cosine 45 would also work, right? Like get the sea.


Yup


OK.


And, OK. Yeah.


That's all


That's it


Actually, wait, I have like another question.


Um, I just said a question on the word poems.


Hm


for this, I was like a little confused.


Yeah, for this one


I was like uh confused.


like


the altitude of an equilateral time the side.


and the altitude is


Find the length of the side.


Um, oh, so then the side will also be 18.


or is that not colored


No, only the altitude is 18.


So what do you know about the angles in an equilateral triangle.


They're all equal. Oh, you do trick, right?


They are all equal, but what are they equal to?


30, I mean, sorry, 60.


Yes


so we could call this side s


and this is 60 degrees.


Yeah.


and um


what kind of angle does the altitude form with the base?


Um, 10, I mean, sorry, 90.


Mhm


All right, so


Oh, and then you just drink. So then we could do like


um,


opposite partners, which is


sign 6


mhm.


So in a 30,690 triangle window that sign 60 would just be


interested in her partners.


which is


root 3 over 2.


So then 18 over


So we know the X is 12 2.


Yup. Good


Mm


OK. Yeah, I got it. Thank you. That's all.


OK. You're welcome. Anything else? That's it.


That's all


All right. Have a good evening


You too, bye


Bye-bye.


hello!


how can i help


The question I need help with is “the sides of a triangle have measures of x,x+5, and 25. If the measure of the longest side is 25, what value of x makes the triangle a right triangle?”


Hello!!


ok


yk pythagorean theorem


a squared + b square = c squared?


yeah


Alex draw this problem out for me


Ok


itll help a lot


Ok got it!


Now what do I do?


did you draw it?


No there is no drawing


oh


It’s a world problem


nono


i mean can you draw what you think the problem is tleling you


for a lot of math problems, drawing it out is a good first step


or writing some idea out


Right ok let me try and draw it


Is that how you draw it? I wrote it in the board


hm


not quite


whats the largest side of a riht triangle?


Yeah I’m not sure then


Largest side is 25


yup


lets change the drawing to match


ur sides are x x+5 and 25


Ohh right ok so it would be like this


I drew it on the board


mmm close


r u sure its 5


Are they both x?


no


x PLUS 5


Ohhhh


Right


So is it like that


The picture I put in the board


good work!


does this triangle amke sense


Teacher!!


Yeah


alright


lets apply pythagoran theorem now


uh (x+5)^2


but yeah


remember parentheses


Oh right!


looks like u just have x+25


now jsut go ahead and solve for x


Sir


Wait for the (x+5) ^2 how would I do that?


expand it


do you know FOIL


or like the square of a sum


No..


ok


I’m pretty sure I forgot it


this is a realllllyl important thing to knwo


well just real quick


Ma'am


and (a-b)^2=a^2-2ab+b^2


ill write on board


FOIL stands for INNER LAST


which is a useful step order to follow


Professor ok


add them up


u get a^2+2ab+b^2


make sense?


I got 1.42


I mean 1.41


for x?


Yep


u sure?


Yeah


can u show me how u got there


Ok it’s on the board


right so


(x+5)^2 is not x^2+t^2


and where did 2 come from


remember foil


Right give me a minute


ok


Yeah, im sorry I’m still fconfused


well lets start with (x+5)^2


which is (x+5)(x+5)


Ok


thats not just x^2 plus 5^2


theres two 5*x's u forgot about


Coach got it


please just try using foil


Ok got it


lmk what u get


not quite


if x=24.5


then x+5 is 29.5


which is longer than 25


whats ur thinking now


This is what I got I’ll show a picture in the birds


Board


Give me a minued


Minute


ok


so


whats this one


Cause x^2=1?


why


ur solving for x


and if x^2=1


this is 1 too


I’m only having trouble on the( x+5)^2


ur not using foil


Is there a way you can draw it on the board so I can’t understand it better?


see this?


Yeahhhh


Ohhh


FIRST


OUTER


Now I get itt


INNER


LAST


give it a shot now


Mentor


I’m doing something wrong


I’m pretty sure


yeah wahts up this time


Did I do it wrong again?


ok


ur super close


is not 14x


theyre 2 separate terms


So how would you solve it?


factor out x


acutlly no


sorry


2x^2+10x-600=0 right


Yeah


But why =0


subtract 600 from both sides?


Oh okk


So to solve


quadratics?


No


uh


well thats not good


have u never had like ax^2+bx+c=0


solve for x?


I don’t remember


hm


lemme think


gimme a couple minutes


not sure how i can explain this


Teacher


Could you just solve it and enter a picture, I’m more of a visual learner and I will learn it that way. Plwase


Please


well the issue is like


this is a HUGE topic


that you geninely just need a teacher for


liek this one of the core parts of


algebra


Right,


idt i can acutally help u with this


So you won’t really do much help


yeah


That’s alright


ur one the. literal last step


u just neeeeeed to solve for x


It’s find I’ll find a wat


Way


ok


Try this then?


Thank you though


unless you have toehr questions


Yeah


Nope no other questions


ave a good one


You too


sorry for not being able to help


Howdy !


I'm fine, hru?


Also good.


Got some juicy math problems you wanna look at?


Well, I have a big test coming up tmr, and honestly I was looking at the samples and for some reasons my mind went blank, it's like i forgot the things we studied for :(, I'll put them on the board and we can go through them one by one


Yeah, that happens.


let's do b on this one


Part of the human condition I suppose.


oh okay


So this format looks strange to me.


Are they asking you to take the first derivative of f(x) and then evaluate that at x = 0 ???


I mean we would evaluate at x=0 at some point, but yes we have to find derivative of whatever is inside there


But you are given the table at the top.


So they already gave us the answer.


f prime evaluated at x = 0 is 7.


But does this table only apply to part a and not part b?


Sorry but this question is confusing to me...


it applies to part b, but in the midterm they want us to show how we solve it


So there's the first derivative.


But when you evaluate that at x = 0, you get 0 which is not matching the table above.


wait let me send you something


In fact, the values in the table seem to match only to part a and not part b.


this is what the answer key says


Sorry but this doesn't make any sense to me.


i think they are referring to the fact that the format inside the parenthesis is like e^x


Yeah, dunno.


Got another problem?


okay no problem, we can move on


So you guys are doing implicit differentiation.


yope


Is that a yes or a no?


that's a yes


So we take the derivative of each side (left and right) with respect to x


So on the left, we get that - does that make sense?


And on the right, using the product rule, we get that.


oh I thought on the right we'll do chain rule


You have y times (x - Pi) so you need to use the product rule.


We used the chain rule on the left hand side with the trig function.


is it because inside the parenthesis there is a minus sign?


No - that minus sign doesn't matter.


Let's say you just had y times x on the right.


So  you have 2 terms y and x.


And to take the derivative, you apply the product rule (first term times derivative of the second plus the second term times the derivative of the first).


All making sense?


ik what all rules are and how to do them it's just looking at it, I thought it was function inside a function


So at this point, the calculus is done.


You just multiply out and solve for dy/dx.


Do you need me to do that, or are you good with it as it is?


one min


so on which side do you want the dy/dx to go to?


You usually put it on the left side.


okay please do it


So let's move all the dy/dx terms over to the left side.


Then we'll factor out the dy/dx and thus can solve for it.


So there's the answer.


Messy, but correct methinks.


yes, correct, so for b then, do we plug the (pi,1) throughout the answer we just got ?


Yes.


That will give you the slope at that point.


And you're already given the point itself, so you just plug all that in the point-slope format for a line.


Yep - cosine of pi is negative 1


Yup, that's why I get also.


so do we keep it in the format 2/-pi?


That's the slope.


Now you use m = y_2 - y_1 / x_2 - x_1


Yep, that's the answer.


This stuff will make your head explode !!!


i was just gonna say that :)


Okay, so I need to get rolling here...


really?


can we do one more page


Yep, I gotta roll.


okay bye


Good luck to you !!!


I need help reviewing chapter 4 of precalc and going over graphing and solving trig functions


ok


where is the question


are you there


yes


I’m not exactly sure how to use the unit circle to memorize the exact values of trig finctions


oh k


do you have any problems


or are you just memorizing the unit circle


memorizing


do you have any parts memorized


no, but I want to know if there is an easy way to memorize it and actually understand it, or if it is just pure memory


I wwould say once youhave memorized the first quadrant the rest are super easy because it is basic understanding of the cordinante plane


do you want me to draw the unit circle


yes please


here


thanks, and for the 2nd quadrant the x values in the 1st quadrant become negative. and for the 3rd quadrant the y values also become negative, and for the 4th quadrant on the y values become negative?


yes that would be right


Your a genius


thanks


Hey Jamie, what do you need help with today


hello how are you


Good, how about you


im good thanks for asking


ill write the problem im working on the board


ok


is thsi ap precalc or some other type


this is precalc


ill show what i got for the vertical asymptote


this is what i got


but idk if this is correct


your vertical asymptote is correct


okay


for the ha i got y=0


how


from what my teacher taught us, there are three cases of how to get the ha


my teachers said that the higher power determines the ha in a rational functions


that is right


he said that when the denomiator is greater than the numerator, the ha is y=0


look at the board


is that what your saying


yes


ok


but remember you have -2


after that


so would y=0-2 is the ha?


so -2


But you could have also said


the function is getting moved 3 to the left and 2 down


oh okay


and you could say the vertical asymptote is -3 and ha is -2


okay


can you help me with another one


okay let me clear the board really quick


the instructions are the same, I still have to find the vertical asymptote and ha


for this one i was wondering if i just expand the problem


or you could just do what you did last time to find the va


would i square the x and 2 though?


becuase the exponent is 2


you should do the opposite of an exponent, which is square root


so I would square root both sides?


to both sides so you dont have to deal with the extra steps


ya


like this?


now simplify it


do you know how


to do that


would this be correct


where did you do it


sorry the wifi disconnected for a minute let me rewrite what i did


i got x=2


that would be right


okay


for this, i got y=0 as well


and after that i added the 1 and y=1


is that right?


yes that would be right


well these 2 are the only ones I needed help with


ok


thank you so much! have a great evening!


if you need help with something else, you can stay here and just ask me later


okay!


Hello


How are you


Hello. And the


It's mic barking


uh


So this is a text to speak like them. Yeah, I think so.


ill just type then


Can you hear me?


Yes


OK.


It's been showing audio in Dallas to got it.


OK


I've got more than a lot to do.


a lot to do


but


like.


not, I'd like to


I'm, I'd like to


if um


my


much more medicine.


focus on getting as much work done as I can.


OK. So do you want to put the


first problem on the board


Yeah, give me a little


I'll preserve his first time using the site, so it's, it's taking a second.


figure out how this thing works.


Oh, sure. Sure.


I find him


The screen share function or


no,


Um, there is


let's see


upload


you know


the


where is it


maybe I'll accept the


yeah.


Upload photo


uh


OK, I'll give me a moment to pull it up.


Uh


Oh, by the way, can you hear me verbally or can you only deal with the like tax that kind of rates.


deal with that like.


I'm hearing you a bit, but it's kind of fading in and out.


and


Alexa


Christ. Why is this thing go ding every time I


Awesome.


train


you.


like message. Also, sorry, it's going to miss train a lot of things basically translations matrix scale for


when trying detect


kind of


translate what I'm saying, the voice.


it's like when he's saying boy.


OK


Mhm


Jesse there no filter


I, I said jeez.


If it's not too long of a problem, you could also just write it on the board.


like the equation


OK, fine, the first actually pull up the problem. The school sites being a pain in my butt.


I gotcha


so hard to


control pla like


Now


I put this.


just the little pans work


This thing stopped translating my messages into words.


ima mute it for a sec while I find the stuff


okay


I'm just gonna type them out because this thing clearly doesn't allow me to properly upload the I'm looking for.


I.


Oh wait, I could just send it as a picture. I mean it's a bit annoying to send a picture


I do it.


OK, I can see it


Give me a minute


I'm gonna


preserve my


right on top of this. I'm try to remove the parts that.


aren't needed


and same ones are right on top of it.


here.


interest in taking it pretty much the entire screen.


There.


where Mike uh


uh


trying to


it's not


us.


shapes I heard of about


Yeah


I made a heroes to the ones where I actually meant to be doing.


They're the one


OK


I do


OK, so you want help with that. OK, so the arithmetic sequence, you're gonna go some.


and you're adding


6 each time, right?


So you're gonna say,


Which one are you working on


and I


OK, so this is, oh this even need this, OK.


equals


just like


Remember there's a formula for this, but I can't remember how to use it.


so.


Yeah, so


what, what, why don't you write down the formula because then I can make sure I'm using the same notation.


So you can say, so the one, the one I know is when I rewrite it and then you can.


So is this the one you were given this formula here?


Yes


that is it


OK. OK, so a is the first term, right? So that's the 11.


Yeah


Uh, much


and


as you figured out


right, so then,


we're gonna have to figure out what N is


right? That's gonna be the tricky part.


and then


sex, a offensive.


D is going to be 6.


Yeah.


Ping


OK, so what you need to do, because D is the difference, right? D is how much space is it, how much you're adding each time you're


you're going over, right


and it is


the amount of spaces you need to travel a number.


Last time I got the


here.


Do you use the distance, is the, what you're adding each term.


right? So 11 to 17 is 6.


Last time was 59.


around 59


N is the number of


sorry?


last time


best


I got 59, but I only got wonky after refusing that.


and the


make sense


50, 0, do you get 59 for for and you got 59?


Yeah


Um, and sexy


You're getting NS 60


like


So did you, how did you get the 60?


Well, I remembered originally that I got the 59.


by minusing the


first term


I


Mhm.


Yeah.


I think the very last car that we're trying to find minus the first term, which when dividing 5


the like Mount Forgiven, which Day 59, and I was like, OK, um, I probably with some sort of take care and just kind of want and so or.


I'm sorry, I didn't, it's, it's hard to hear for some reason.


Mhm


Um, so you took 365 minus the 11.


I'll just type it out real quick.


OK, I don't know why the microphone's not working well.


apparenly I was meant to use 60 I forgot to account for the fact I was starting at 1 not 0


OK


anyways with the formula 11+(60-1)6 how do I find the sum?


let me write it out


have you learned the formula for the summation


Whats that?


have you learned that equation yet


Sorta reconginize it but how do I find n


ah


the previous formula


it's the first and last term


lemme plug the stuff in


is the sum 11280?


that's what I get


Well on to the next one


so number 4?


ya


that is is geometric series and you want the infinite sum


let me write the formula for that one


did you learn this formula


once again seems fimilar but I struggle to remember them


that's fine


the a is the first term and the r is the ratio between terms


in other words r is what you need to multiply a term by to get the next one


a = -1.6?


for number 4 it is 2


actually no


oh wait was I was talking about r derp


yes


now you can just plug those into the formula


so S = 1 amd 3/7


1 3/7


now then for 5.


same formula differemt numbers?


hmmm I don't remember this too well


give me aminute


this is not in my book


I'm sorry


maybe you should try another tutor


sorry about that


its fine lets just continue on to 6


sur


I just found it


5 or 6?


I was looking at 6 I just skipped over 5


ah well then how do I do 5?


first you want to find out if it is arithmetic or geometric


seems a bit uh weird to be arithmetic so prob geo


to check you want to divide two the terms and do it twice to make sure they are the same ratio


kk


I checked r is 0.6


then you can use the same formula as before


yes


and now 6.


you want to multiply the number by 100


oh thats it?


let me show you the method


a is 52/100?


if you subtract x by 100x the decimals will all cancel out


do you see that?


yes But how would this be typed out


as a fraction


you can just solve for x in the equation x=52/99


does that technique make sense


yep


so its written as 52/99?


yup


kk


the other should be the same?


the 4 is not repeating


so how do i account for that?


break it up into .4 + .05353


and then you multiply the second part by 100


and what is timed by 10?


huh?


sorry my bad


just 99?


what is the second part by then?


let me look at this for a minute


if x=.453... then you want to first want to multiply by 10 to move to to the first decimal


then apply the technique to .53...


and do 0.4 seperate?


.4 is 2/5


and .053 turns out to be 53/990


then you can find a common denominator and add them


kk


to turn 5 to fraction


yup


I'm getting 251/990 let me double check


you are right


well uh have a good day (:


you too


Hello


hello!


can u help me with my hw


i have like 7 frqs


for unit 8 calc ab


i did a couple but im not sure if theyre right


I can help in some


Sorry, I am not sure what the problem is or what you are doing.


oh oops


im supposed to solve for the volume of the tank


using the givens


y=9/625 x^4 from x=0 to x=5


what does the 8 cubic feet per minute have to do with it?


im not too sure


i dont think its relevant


but it was just given


its a revolution around the curve question


so i think i just ues the disk method?


do you have an image of the problem?


oh yes


wait let me see how to get an image


You can use the disk method.


ohh alright


or shells


oh i haven't learned that one in class yet


is my work correct? or no


what are the limits on your integral?


0 and 9


since its from 0 to 9 feet on  the y


or is it supposed to be 0 to 10 on the x axis


or neither


need to square the integrand


oh oops


i did that on my paper


it went from ((625/9 y)^1/4)^2 to (625/9 y)^1/2


which is 25/3 *√y


wait wha


ohh


oops


does the answer change if i leave it like that


What do you mean?


if i leave it in this form instead of simplifying


cause i did square it but i didnt simplify on my paper


i just forgot to write down that part of my scratchwork


It wouldn't change the answer, since the √(625/9)  =25/3, right?


oh yeah


alright ty


wait so the rest of it is good?


or are the bounds wrong or something


II guess it's ok


alright Ava!


are you all set then?


uhhh


i have a couple more problems


sorry


i didn't know what to do for this problem at all


where is part b?


i dont know


there wasn't any other problem like it


so i think my teacher just made a mistake in assigning that question


just wanted to make sure htough


They are probably talking about the region between that curve and the chord


oh


what is the equation of the line connecting those two points?


uhmmm


do i graph that


oh wait nvm


y=-1/2x +2


Not quite.


what is the slope?


No


waitwhat


OH oops


my bad


do i just do equation for area between 2 curves


with the bounds being the intersections


For this you need to use the washer method


oh alright


wait why not just the area between two curves?


nvm it said volume i see


This is a volume of revolution question


alright


are you famiiar with the washer method?


yes


are the bounds still the intersections


that should do it


ohh alright thanks


you are welcome


You said you had one more problem, right?


a couple more than that..


sorryr


you can leave if you want to


I have time for one more.


ohhh Noah


this is kind of a long one..


is part b just -6/pi..?


that doesnt seem right


It is not correct


how would i solve it?


They are asking for the tangent line to the curve f(x) =3cos(x)


ohhh


so -3sin(x)?


or do i write in point slope form


the line you drew is the chord connecting P and Q, not the tangent of f at Q


ah


Do you know how to write the equation of a tangent line?


d/dx f(x)?


or y-y1=m(x-x1)


where m is the slope


yes, you the point slope form,


ohh okok


is this right


not quite.


huh


what is the slope of the tangent line?


sincei ts the derivative of 3cosx


right


That tangent line must have a definite slope, right?


what do u mean?


ohh


I drew the tangent line. What is its slope. It's slope is not a function, it is a number


oh


wait i thought the tan was derivative of the original function though


is it not


you to find the slope of a curve at a  point a, you evaluate the derivative of the function at point a


so would i just plug the original function into point slope with the coordinates of Q?


and then find the derivative of that


or what


If the derivative is -3 sin(x)), then you find the slope of the tangent line at x =𝜋/2 by plugging in 𝜋/2 into the equation of the derivative


ohhhh


Derivative = Slope, derivative =slope,derivative =slope


oohhh alright


so this?


yes


or do i have to distribute too


ohh alright Sophia


how would i do c?


what is the slope of the line PQ?


-6/pi x


Yes.


and the slopes of all tangent lines of f can be find using the derivative of f


so y=-6/pi x +3 and y=-3sinx


but then what would i do to find the parallel point?


YEs


ohhh Liam!


you are welcome


and the last one is just washer method?


is that equation right


Yes, that makes sense to me.


ohh Mia!!


You are very welcome


thanks and bye!!


Have a good week!


Bye


James!


Hi Olivia


Hi!


I need help with one question today. I'll upload it on the board.


ok


alirght


what have you tried so far?


Nothing much


don't know how to approach this problem


no problem


we know the measure of two angles: 3x and 5x


we need to connect these two angles


can you find a angle that connects angle ABC and CDE?


bcd?


exactly


what's the relationship between BCD and ABC?


they both are 3x degrees?


yes. can you tell me why?


because ab and cd are parallel


yes. and ABC and BCD are alternate interior angles


now what's the relationship between BCD and CDE?


5x is the exterior angle of bcd?


they are same side interior angles


what does that mean?


they add up 180 degrees.


oh ok


we can then set up an equation and solve for x


ok


can you try to do it on the board?


3x + 5x = 180


what's x?


you got it!


well done


any more problem?


no thats it for today


Thank you!


you are very welcome.


bye


Hey how are you doing


good, how are you


I am doing great


how can I help you today?


how do i change a negative decimal to a fraction


well I am glad you asked, it is a relatively simple topic. DO you have any specific questions related to this topic?


no


Liam


so you want to convert the above decimal to a fraction right


what do you think is the first step to do so?


make it a denominator with 1


great


could you do that please


awsome!!


what do you think the next step is?


idk


no worries!! it is all good


so is there any greatest common divisor for this number?


other than that


mhm... so you think this fraction is a perfect divisor of 2?


i don't know, im new to this


it is all good


so, do you know what a greatest common divisor is?


not really


alright, so a greatest common divisor is any number that is the largest possible number that can perfectly divide -2.213 in this case


and by perfectly divide I mean there shouldn't be a remainder


can i make tthe -2.213 a whole number so its easier fro me


yes, how could you do that?


that is the right approach!!


flip the fraction


mhm... could you explain how that would work out?


1 would be the numerator and the -2.213 would be the denominator


yes I got that, but could you explain how that would help solve the question?


it wouldn't, i just realized


it's completely fine even if it is a wrong answer... I am here to help you


ok, so now you've realized that it wouldn


wouldn't work*


would rounding work?


mhm... not quite


because rounding it would make it a completely different number


im very confused


but let me let you in on a little information, -2.213 does not have a perfect multiple of any number... But there is another way you could approach this problem


ok, so let us start with something simple in that case


could you convert -8 into a fraction?


find how many decimals are in the number?


that is a part of the step!! you got this!!1


but before we get back to the original question, could you convert -8 to a fraction


that is one way!! you got it!!


you could also represent it another way


see!!! you are getting it!!! amazing work!


now, what did you do to make it -80/10?


multiplied it by 10


correct!!!


now that means you could also try the same approach for your original question


done


so what is the final answer?


hmmm, you are very close... you got the denominator right


the numerator is a little bit off


idk


ok, let us back up a bit...


so could you divide -2/1000 and see what you get?


please feel free to use a calculator


is that equal to the original number?


no


mhmm... then where could you have gone wrong?


try to think, you got this!!


too much 0's?


no, as I said your denominator is correct 1000


the problem is with your numerator


im dumbofunded


you're good...


so, what did you do in the -80/10 example


you said you multiplied by 10


multiplied by 10


yes!


so, did you multiply only in the denominator, numerator or in both?


only the denominator


Are you sure?


was it -2.21/1000


nice try!


is it -2 213/1000?


yes you are right


finally


all you had to do was multiply both the numerator and denominator exactly


Jamie


Hi! Finally!


Thanks for going through all this work for me


No problem! It's really fun working with you :)


Aww thanks :))) Ready for the first one?


Yeah!


Alright let me see this one real quick..


Oh ok! I think I get it :) So do you still have all the formulas we wrote down that day?


y = mx + b


and y - 4 = m (x - 2)


Yeah! That one's the point slop form. Do you remember how to find the slope of a perpendicular line?


You take the negative reciprocal


Perfect! So in the question, we're given an equation, so first we would have to find the slope of the given line by simplifying it into y = mx + b! Then we would find it's perpendicular slope. Wanna give that a try? I'll be here to guide you :)


sure


Great! Let me know what you get


Can you remind me the first step to jog my memory?


Yeah! Remember we have to put the parenthesis on the left side around y - 4 so we can multiply by 3? (the denominator of -2/3)


got it


Also try to get it into the form y = mx + b, bringing the term with the x to the right and keeping the y alone on the left! If you don't understand what I'm asking then just continue solving and i'll explain in more detail after


Yeah, I'm lost once again


That's ok! Tell me what you have so far :)


I got y = -2/3x + 8


Perfect! You got the first step right! Yay!!!


oh great


Now, what will be the slope of the perpendicular line?


Yep! Do you know what to do next with the slope or shall I show you how to do it? There's an easy method and a little bit more tedious one.


Which one do you wanna do?


The easy one!


Ok! Shall I show you how?


Or do you wanna try with my guidance?


yeah, I'll try you guide me


I think I'm supposed to start with y - 4 = m (x -2)


Ok! I think that's the best way to learn it :). But yeah! You could do that, but that's the start of the tedious method. And you wanted to try the easier one right?


yeah


Alright! Then first, just write down y = mx + b. Then plug in the slope you just found (3/2) in m, and plug in the x and y values, that in the question say (-2, -2)!


And all you have to do is find b, the y-intercept.


ok.  Can I do it on the graph so you can see?


Yeah! The screen on the left?


mhm


Of course! Let me just move what I wrote rq..


Go ahead!


is that right?


Yep! You got it right!


yay


Now plug in the slope and the y-intercept (b) into the equation, but don't put the values of x and y.


Great!!! Now can you check to see which one of the options above have y = 3/2x + 1?


YES!!!!


Let me summarize what you did so you can write it down for future problems! So the first thing you did was turn the given equation into y = mx + b to find the slope! Then, we checked to see if it was asking for a parallel line or perpendicular, depending on that we found the slope of the other line. Then we plugged it back into y = mx + b with the x and y values to find b! Then we had our values to write our answer.


Any questions before we move on? :D


Ok, I think I've got it. Based on that, I think I know how to do the next one. But is it ok if we do it together just to be sure?


Yeah of course! I was planning on staying here for as long as you need since you waited so long for me to be free :)


I really do appreciate that. I'll show you the question and show you what I do bit by bit


Of course! I'll be here to guide you if you need help on anything!


If I'm correct, the first step is turning it into y = mx + b. I got y = -5x - 1


Absolutely right! You're doing great! Now take a look at the question and see if it's asking for parallel or perpendicular and try to do the next step based on that :)


I think it's this one since they want it in y - 4 = m(x - 2)


Oh, so that's the point-slope form, and it's asking for slope-intercept form which is y = mx + b! Sorry I forgot to tell you that. I believe we have to find b in the next step, but I like your attempt!


And remember, the slope you found was -5 :)


ok, so I think b = 12


Great!! You got that right! Now how would we write it with the slope in slope intercept form? (y = mx + b)


y = -5x + 12


YAYYYY! Now out of the answer choices, which one does that match?


Confetti time!!! I'm so proud of you!


Thanks, you wouldn't think that makes a difference, but it does


:D You're doing great!!! Any doubts on this question before we move on?


No!


I'll get the next question


Ok!


Ok, i'm not sure what I'll be able to do. My computer won't update and it's working terribly


What do you mean by that?


I'm not sure if I'll be able to write. It'll probably be slow.


Oh that's ok! If you want you can do it on a seperate piece of paper and tell me what you get :)


ok


Try doing the first step according to you and tell me what you get :D


I'm not sure if this is right, but I put it into y = mx + b and got y = 4x + 13


Hmm.. can you check the b again? Your slope is correct though!


IDK.


oh wait


I have to put the point (4, 32) in first? Right?


In the y = mx + b after you found the slope :)


i knew i forgot something. give me a few minutes


Of course! Take your time :)


b = 16


YIPPIEEEE! Now put it into the equation and match it with one of the options


YAYYYY!!!! You did it! It's insane to see how much you have improved since the first question we did. You're amazing!


Thanks, it's because you're a great tutor. You're very patient


No problem! You're so sweet :D


Wanna do the next one now?


Yep, only 3 more! yay


Yay!! You got this!


2 of the answer choices got cut off. I'll go get them


Ok!


Do you need help with starting the question or do you wanna tell me your guess on how you would start it?


My guess is that I find the slope of the line given, then put the coordinates given into the form y - 4 = m (x - 2)


Absolutely correct! Those are the exact steps you have to follow!!


I finally got one on the first try!


Mhm! Let me know what you get either step by step or your final answer. I'll be right here!


y - 1 = 3/2 (x + 3)


OMG!! Excellent! You did it perfectly the first try! Wow you learn so fast


wow that felt great


Mhm! Isn't math so fun when we understand concepts?


only when it isn't draining


Agreed! Wanna try the last two?


mhm. I'll get it


for this next one, keep in mind I got the last one right ; )


Yeah!! Wanna tell me your approach to this one?


maybe find the slope of this one


Mhm!


Yes! Now what's the next step according to you?


give up?


Do you wanna know?


yeah


We can use the point slope form! y - 4 = m(x - 2)!


Then just simplify it :)


ok, i'll give it a go


how do you automatically know what to do?


Shall I tell you a small tip?


yes please,


So basically you know all the forms I told you right? They all mean the same thing, but are just written differently. So you can simplify each one into another form.


By looking at the options or by what the form the questions wants the answer in


it seems to come so easily to you


Yeah! At this point by how much you're improving, just a bit more practice will make you even better than me :D


I wish! I think I've got it


I got 4x + 3y = -6


ABSOLUTELY CORRECT!!!!!


Amazing! Now which one of the questions matches what you got?


I mean answer choices lol


Ya!


So close to the end now! Just one last one!


Yeah! You're doing amazing


sorry it's taking me a bit.\


The question won't load


No problem! Take your time :D


Ok, this is actually pretty funny


Lol! If it doesn't like to load then you can just tell me what the question is asking for


It's so simple. It's a horizontal line and it's asking me what  equation of the line that is parallel to the given line and passes through (-4, -6)


That's why I thought it was funny


Oh Alright! Do you think you can give it a go?


Yeah y = -6.


I feel like I can finally breathe again now that this is over for the week


Oh that's so easy lol!


You did amazing! :D


I'm so proud of how far you came


Thank you so much : )))


I'm really glad that you were my tutor


Sorry if I was draining lol


No problem! Have a great day Jamie! And if you ever need help on another topic don't hesitate to reach out to me :)


Alright thanks! I hope you enjoy your day! Bye ; )


Bye!! :D


Afternoon!


Hello


what do you need help with?


I would like to learn some Algebra today nothing specific


How about I send you some random algebra problems?


okay


also the board won't connect


refresh


I did it still won't work


Here are 3


Let me know if yo need help


can you type them in the chat the board isn't working sorry


Solve for x:
3x+5=20

Simplify:
2(a+3)−4a

Find the value of y if
4y−8=0


you need help?


uh yes


Here's how we dsolve it


For the first one, we subtract 5 from both sides and divide by 3


so subtract 5 from 3 and 20?


both sides, yes


so what do I divide by 3?


after subtracting 5 from both sides


so the answers i got divide by 3?


is


what do I divide by 3?


and 1


Want to move on?


3-5=2 correct?


so im subtracting 3-5 and 5-20 right?


invert the numbers


5-3 and 20-5?


First subtract 5 from both sides


okay my answers were 2 and 15


You should get 3x=15


can you walk me through this please


how do I get that?


subtract 5 from both sides


please demonstrate


hello?


oH right, you can't it


3x+5=20
3x+5-5=20-5
3x=15


My bad


so add not subtract?


you have to sbtract


okay can you demonstrate because I do not understand


I showed you


I still do not understand it


you have to sbtract 5 from both sides


ok thanks


Hi Alex


Hi, I just need help with starting on how to use x and interepting with slope, r, z, and y intercept


Do you have a specific problem you'd like to work on?


If not, I can give you an example.


I'm reading...


Is there more information. For example, were you given the data values for the high jump and long jump?


No - that is all of the data given. This is an ap statistics formatted one


OK. Can you give me about 5 minutes to find the right formula?


we use y-hat = a+bx


if that helps


but im not sure the writing style


We use that when we have the data values. I'll show you the formula on the board.


Do you see it?


yes


Let's call Y = high jump and X = long jump.


okay


Your problem gives you the means (X_bar, Y_bar) and the standard deviations (Sx and Sy) and the correlation coefficient, r


All you need to do is plug in the values.


so the correlation cofefficent 0.9125 shows a strong direction strenght between long and high jump?


Yes.


so 83.25% of the variation in high kump can be explaned by linear relationship with long jump?


is that the r^2


Let me check the formula for that. Give me 2-3 minutes.


That's correct. I'll show the formula on the board for your last question.


okay, how did you intepret the slope? which value would be the constnat, im a bit confused as i am usd to see it in a differnt format that shows the constant and the x and y make it harder because i dont know the unit and stuff and the contextis vague


We already know the slope will be positive, because "r" is positive.


A positive slope means that people who do well in the long jump will also jump high.


okay, that is all i had questions over! thank you for helping, this was a huge help!


You're welcome. We can end the session. Enjoy the rest of your day.


okay you too


Hi Alex. How can I help you?


hi can you help me solve a division problem?


sure. can you post the problem on the board?


yea i got u


i see it


thanks


so for the first part


if 6 does not go into 2 what do i do?


good question.


since 6 doesn't go into two, you will need to go one digit over and answer "how many times does 6 go into 22?"


3 times because 6x3 is 18 and that is closest to 22


right


excellent work


so now do i find a number that is closest to 43?


yes


what do i do with the remainder?


you can write "R2" for remainder is 2 just to the right of the quotient


ok


thanks for helping me


you are welcome


have a good day


you too


hi! how are you today?


good


what do you need help with today?


I did the blue one, but I am not sure if I did it right


could you help me figure it out if it is wrong?


sure! let me take a look


hmm I don't think it looks right, because if its a reflection, the triangle should look symmetric about the line y=x


so each point should be an equal distance away from the line


so, I think I need to find the reflection of g still, because the other two points look okay to me


yes!


let me know when you're done, and i can take another look


do I change the signs? just for clarification


you flip the values and the signs


so if the original point is at (3,2) then the reflected point is at (-2,-3)


so it is 10,1?


well you didn't flip them


that is 1,10


ohhh!


but it will be where i put the dot at though


no i see what you're saying


so for reflections you actually don't change the signs


you just flip the x and y values


so if its at ((-10, -1)) the new point is (-1,-10)


so I was right the first time?


it would be at (-1, -10)


I also don't think Point F is correct right now


take another look at where you placed it


the rule is (x,y) turns into (y,x) here


Oki


the black thing I put is where I think point f should be now


are you there?


yes


the black dot looks right


for F


it was right!


ok great!


did you need help with anything else?


I put point g on there already


yep looks right


do I need to look again?


for H? nope!


is that good?


yes!


Yay


Do I need to look over them again?


let me see


look over the bottom 2 black dots


oki


I fixed it


take another look at them


could you help me,because I am not sure where I am going wrong at


so you need to find the point thats equidistant to the original point


so for example, if the point is 3 units away from the line on the top, it should be 3 units away from the line on the bottom


I wasn't counting all the units.................... my bad


hello?


yep!


your new points look right


your black points look right


i think you have a pretty good understanding of what's going on now!


i have to go, but you did a really good job today!


okay


we have a test tmr about pression over accurate and we also have it over


hi Alice


hi


supplementary complementary linear pair adjacent and vertical angle


please show me a problem you need help with


want me to try to shrink it?


can you see the whole thing


no


still no


want me to shrink it?


yes


I can't see all of #18, but can see #19 now


I need to know 19


18 is fine


OK


I don't understand how to solve it


I'll talk you through it


if the steamer was 25 1/2 inches long, what measurement would David get?


that's the thing I don't understand


he his measuring to the closest 1/4 of an inch


so he would never get 25 7/8 as an answer, for example


he can get 25 1/2, 25 3/4, or 26


whichever is the closest to the actual measure


so it will be 26


25 1/2 is 25.5, 25 3/3 is 25.75


so he will get 25.75


is 25.6 closer to 25.5 or 25.75?


right, so if it was really 25.6, he'd get 25.75 as his answer


how about 25.7? what would he get?


closer to 25.5 or 25.75?


.2 away from 25.5, but only .05 away from 25.75


so his answer will be 25.7


no


okay so 25.5


nearest 1/4 inch, so 25.75


okay sounds good thank you for your help


because 25.7 is closer to 25.75 than 25.5, and those are his only choices


okay thank you so much for the help


yw. you don't want to finish this?


finish what


this problem


we don't have the answer yet


there's more to itn


to it


I'm just trying to get you to understand it


ooh my


do you understand that if the length is closer to 25.5, then David will get 25 1/2 as his answer, but if it is closer to 25.75, then he'll get 25 3/4 ?


yes that's makes so much sense


what if the length is exactly halfway between 25 1/2 and 25 3/4?


he could say either one as the length, right?


since the distance to either on is the same


*either one


right?


are you here?


I'm about to close this session because you aren't here


yes I am


I was looking to see if we had the same answer


you haven't been responding


bc I was waiting


do you understand my question about the length being halfway between 25 1/2 and 25 3/4?


yes I do thank you so much for the help


hi


hello


so just to let you know this is my first time starting precalculis


calculius


so whoever I need to learn can you teach me


how can I help?


have you worked with exponents before?


yes


to do multiplication, we add the exponents.


ok


to do division, we subtract the exponents.


so 7 times 7


oh


sometimes the exponent is negative


same rule


add the exponents


I think I get it


correct?


good work


thank you


what's next


order of operations


PEMDAS


ohhh Maya


yes


I think I got this


we multiply that right


correct


all good


lets goo


pemdas still? or is this something different


pemdas


quick question what is an equation again


e is for exponent


oh


so all we got is mutiplucation and division


sorry, incorrect


huh


pemdas has a special rule.


what rule?


when we have multiplication and division, we start from the left.


oh I thought it was times first then division


because of how they are ordered


I understand that.


My Dear,  does not mean multiply first.


multiply first when we have addition or subtraciton.


ok


correct


yes


oh just solve them cubed?


I think


that's 64


phew


right?


oh sorry