So lemme draw you an example


ok


Ok so you see that


The top is the biggest unit of the range


mhm


The bottom is the lowest unit


The 50th percentile is the median since at the very center.


The 25th is the 25th best


And the 75th is the 75th bestest


So ranges like 7 3 5 2 3 5 6 6 2455


These should be stacked onto ranked percentile.


Then


From top to bottom


Whisker plot will be stockpiled


Into those ranges that need illustration or explanation


Ok?


okay


Are we done here?


yup


Ok bye now.


Hey Liam


Hello


what is that you need help with?


I'm having trouble understanding the formulas for finding volume of solids


I will see how I can hepl


For my teacher gives an answer and not tells us how to do it


Understood. Can you give me a question? I can help you through finding a volume


Is that a Durham?


I drew the shape on the white board


Height is 12 cm and the area of base is 32 cm squared


working on it. I am trying to imagine it in 3 shape


There i added a image of it


This shape is a pyramid (one apex, flat base).

For any pyramid:
V =1/3 x (area of base) × (height)

Given base area = 32 cm^2
and height = 12 cm:

V = 1/3 x 32 x 12 = 384/3 = 128 cm^ 3


But it uses a hexagon base


Sarah wouldn't it be different


I see the image now. Clearly shows hexagon base. I am working on providing you an explanation


Okay


Please be patient this is a long explanation


The formula for calculating volume of Heganoal Pyramid is (root3)/2 x b^2 h


So how would I calculate it


The general formula for a pyramid is always:

V = 1/3 × Abase × h

where  A base is the area of the hexagonal base, and
h is the perpendicular height.

Step 1: Given values
Base area

A base = 32 cm^2
Height h = 12 cm

Step 2: Apply the formula

V = 1/3 × 32 × 12 = 384/3 = 128 cm^3


Answer 128 cm^3 irrespective of the shape of the bottom.


For any pyramid:

V = 1/3 x A base × h

A base = area of the base (could be a square, rectangle, hexagon, triangle, or even irregular polygon).

h = perpendicular height from the apex to the base.

This works no matter what the base looks like.

2. Why it’s true (intuitive reasoning)
Think of a prism first:
A prism has volume:

V prism = A base × h

A pyramid with the same base and height has exactly one-third of that volume.

This fact comes from both geometry and can be proven using calculus (integrating cross-sectional areas). The ancient Greeks (Athens) and later Archimedes’s principle also formalized it.

3. Application to different base shapes

Square Pyramid (like Giza)
Base area: a^2
Volume: V = 1/3 x a^2 x h

Rectangular Pyramid
Base area: l × w
Volume: V = 1/3 x (l.w) x h

Hexagonal Pyramid
Base area:  3(root 3)/2 x a^2 (for regular hexagon)
Volume:
V = 1/3 x (3(root 3)/2 x a^2) x h

Any polygonal base Just calculate its area A base however needed, then apply the same rule:

V = 1/3 x A base x h

4. The “one-third rule” is universal: If you can find the area of the base,
and you know the perpendicular height,
then the volume is always one-third of the corresponding prism.


I have provided a very brief explanation


So answer in this case is V = 1/3 × 32 × 12 = 384/3 = 128 cm^3


Let me know if still have a doubt


Hello!


I was wondering if you could possibly help me find the range of the equation I put on the board?


Got it! Can you define range for me?


just making sure you know it


i understand it on a graph but definitely not as clearly in a written function


It's basically any number you can get from a certain equation


oh okay


let me give a quick example


ohh okay


that makes sense


The square root of 3 is part of the range


gotcha


yup!


So, there are things that can limit the range


Is it possible to input an x value that will result in an answer of, for example, 5?


Nope, because when you square something, it becomes positive


oh youre right


okay hmm


yes, it's impossible to get 5 from this equation, so it's not in the range


okay gotcha


Want to move on to defining the range?


yes


Okay, when checking range, look at square root signs first


noted


what happens when you input a negative number into a square root?


it doesnt exist right?


Yup, so the range must be equal to or greater than 0 ( h(x) >=  0)


alright


That's the lower limit, is there a higher limit?


no?


actually yes, because inside the square root, we're subtracting the x


ohh okay


we can't cancel out the negative because x is always positive (because of the exponent)


that makes sense


We want the biggest h(x) value, what x would we need to insert to find that


wait im not sure


That's okay!


since we're subtracting, we want x to be as small as possible. Because negatives just cancel out, that means the smallest x we have is 0


ohh okay i see


so the limit is zero?


zero*


Nope! we're working with range, so we'd need to find what the equation equals when we insert 0


ah okay gotcha


would it just be 2?


Yup


incredible


That's our range


okay that makes sense! thank you


Any questions? Do you want help finding the domain?


how would i go about graphing it?


i did find the domain, but thank you


Because our range is greater than 0, we're only using the first two quadrants


The higher limit is 2, so I'm going to mark that down


ahh that makes sense


Next, we're going to want to mark the domain, what did you get for that?


-2 < or equal to x < or equal to 2


sorry idk how to do the sign


Yup!


I put a dotted line at those points, it means we can't go beyond that


alrighty that makes sense


graphs typically curve around their limits


I drew example


ahh okay that makes sense


so


would something like that work?


Not quite!


The function is positive, so it'd curve towards its upper limit, like an upside down bowl


ahh okay


is that better


Yup! But the edges would be aiming down


thank you!


This is actually a half-circle function!


parabola?


I think parabolas need to have infinite domain


ahh i see


Of course!


Hope you have a good day :)


thank you! you too


hello


Hi! I need help with this


which part are you having trouble with?


The fraction


we need x to be by itself right?


mm


to find a solution we need to make the fraction equal to something


subtract 1


to all sides?


not quite


since we have a fraction we need to get rid of the fraction


what do you think the first step will be?


divide?


well the fraction is being divided by 3, which means we have to....


uhh idk


multiply?


by 3


yes, we multiple each side by 3


done


since the fraction is being multipled by 3, all you need is to cancel the 3, so it would be 2x + 1


not 6x + 3


you fogot to multiply the 4 by 12


hello?


yes im here


i didnt know i had to multiply by 12 where is the 12 from


my mistake you have to multiply the 4 by 3 which will give you 12


remember when you have to multiply the initial equation to get rid of the fraction?


so the equation should be 6<2x+1<12


oh right


yep so its 6


so it should be 11/2


oh nvm


yes


the interval is 5/2, 11/2


done?


5/2=10 theres no decimal for that


it's 2.5


nvm ur right


do need any more help?


yeah im gonna put it in rn and see if its correct


so its [5/2,11/2)


is it right?


I ave one more


here it is


do both of the equations mean the same thing


no


bc you have to distribute for the one on the right


o okay


which one do you wanna work with first?


right


okay


can you distribute it?


i did


don't forget that the sign in the answer sould be less than or equals to


I got p is less than or equal to both -7 and positive 3


said its wrong


for the equation on the left, you have to remember that when you divide by a negative you have to flip the sign


yeah but i put it in as [-7,3]


i know the flip part


so if the initial sign is greater than or equals to, it should be less than or equals to once you divide


the answer is ( negative infinity, 3)


or p <


or p<3


Hello! How are you doing?


another tutor had helped me do the top two and good


Great! Do you have an idea on how to start solving number 18?


is it 3.824*10^3?


Hmm, not quite. Can you guide me through how you got that answer?


i had thought it out, but it it hard


You got this!


Try working it out on the whiteboard.


i don't know how


help me, please?


Yes for sure.


How did you do number 17 with the other tutor?


Maybe that might give us an idea


Hello Sam, you still there>


i was letting a dog out, so he told me what it was


Hmm okay


Do you know the basic rule of writing in scientific notation and why it's written that way?


something with 0's


You're on the right track with 3.824*10^3


Yes! If a number is between 1 and 10, then you won't have to increase 10 by anything


Becuase anything to the power of 0 is 1 right? So in this case, 3.824*10^0 would just be 3.824


To write a number in scientific notation, it has to be between 1 and 10


So if a number is less 1 or greater than 10, you would have to move the decimal place to make it between those 2 numbers


If we go to the right, then the exponent is negative. But if we go to the left, the exponent is positive!


so 10^0


Do you want to work on a problem together?


and 3.824


Yes exactly! Because 3.824 is already between 1 and 10


Let's try one together!


oki


What do you think the first step would be?


could we do this instead?


Okay, that fine! Which one do you want to work on?


1.7 is part of it right?


Yes! Now what would be the exponent on the 10?


Think of the direction that you moved the decimed to get 1.7


left


Good, good.


Hmm, you're very close!


Yes! Good job, Sam!


Do you understand the difference?


Or why 10^4 was not the correct?


yes, it was at first less that whole


in the negatives


in a way


Hmm, that an intersting way to see it.


Think of it more like it was 4 decimal places off from being a 1


ohh,oki


Great!


How about you try number 20?


is 31.2= 0.312*10^3


Hmm, I like how you used what you learned! However, the number has to be between 1 and 10


Think of it this way


(Number between 1 and 10) * 10^exponent (how many places the decimal was moved)


Can you show me your work on the whiteboard?


Maybe that will help.


You are very close, though, Sam.


what am i doing wrong


I think you are miscalculating how many times you moved the decimal


i was on twenty


Okay from the 31.2 how what direction and how many times should I move to make it between 1 and 10?


You see, if I move left 2 times, I would get a number less than 1


the exponent or the number the 10 is raised to, means how many places the decimal was moved, in order to make the number between 1 and 10


Does that make sense?


i neeed to go


Okay, no problem! Hope I was helpful! Any last minute questions?


Hi.  How are you?


Hello! I need help wit this


Ok.  Let me read it please.


Ok.  So the first class boundary should start at 29.5.


Each boundary should be 6 wide.


Do you see why?


we do 29.5-59.5


then divide by 5?


Exactly right!


yepp


so we add 6


so 29.5-35.5


So.  Label your first boundary in your work area.  Yes.


After you label each we will count.


kk


Great!


Now go through and count how many in each class.


zero for the second one?


good


thats shocking


i  feel like i did sum wrong lol


bc its never zero


Let me review.


I don't see anything in that class.


ok


im gonna put the numbers in then rn


is this correct?


Looks good to me.


ok next one


Ok


You did great on the last one. "Sarah and Repeat!"


thanks


so this one you just add 5 to


Right


So end the first one at 21.5


mhm


Count and fill!


That's it!


ok can u look over my numbers


to make sure they're right


OK


heres whati plugged in


ill put it under


I will take a minute to check your counts as best as I can.


ok


Is the count for 31.5-36.5 ok?


i had 2


2 for 26 and 31


I only see on in 31.5-36.5


huh


no i have in pink and in blue written 2


do you see it in the box


Yes.  But what are the two values?


I see it now.


35 & 34


i circled them based on color


Yes. You did great. I think all is well.


ok gonna submit it


yep its right!


Do you still have time?


How many more do you have?


its new equations


like a new section


since i finished this


Ok.  I need to finish this by noon, EST.


So.  I have about 30 minutes.


ok I'm in Austin


Ok


would i multiply?


It went away.


there


Ok.  You would multiply by 0.768 in this case.


That one is pretty straight forward, right?


Yes


What did you get for an answer?


Gonna do it rn


Is tha correct?


it didnt come out as a decimal


You need to multiply by 0.768.


oh


To do these problems it's best to convert all percents to decimal..


and then the next one i do 0.8987 times 215


No.


Let me help you with this.


ok


I am going to write the equation on the board.  Then you can ask me about it.  OK?


Ok


So.  X is our unknown quantity.


I changed 215 percent into a decimal by dividing by 100.


can you write that out


as well i'm gonna screenshot this and save it


for notes


thanks


Before I do that, the final step will be to divide both sides by 2.15 to find x.  I will demonstrate.


Before we calculate please ask any questions you have.


No


So.  If you have no questions, let's divide to get our answer.


Yup!!


It's not a percent!


Ohhhh


just decimal?


Right


for both?


Yes.  For both.


Here are a few rules to help you with these problems.


Ok


its asking the number not percentage so don't add it?


It's asking for numbers, not percents in both problems.


There is no addition involved.


Yep


I'll try the next one on my own


Wait please.


I want to let you know a few things to help you.


1.  All percents are converted to decimals by dividing the percent by 100.


2.  When you see the word "of" that means to multiply.


3.  When you see the word "is" that means use an equal sign.


4.  When you have an unknown, call it "x."


Using these rules, you can solve any problem.


Ok can you add that on here too


it says of but we divided tho


It's in the session history.  You can look at what I've typed anytime.


we didnt multiply


for 89.87


ohh ur talking about 215%


When we translated the problem from words to algebra, we did multiply 2.15 times x.


I see you are labeling.  That is good.


ok


You could say "What Number" is the same as x.


Or "what" is the same as x.


very good!


thank you!


You are very organized - I like that!!


Thank you! :)


I'm going to take a break since I haven't ate breakfast I know you don't have much time left so we can end the session


Thank you for your help! :)


You are very deserving.  Bye.


Hello


hey Jamie


so for the question you have up, do you have any gyess on where to start?


Ln is natural log right?


We have to cross it out with e


yep thats right


ok going well so far


I get how to do it, but why are we crossing ln with e?


What’s e ? And is there like a law log of e to power of x equals lnx


they're opposite functions. kinda the same way that square is the opposite of squareroot


Okay


e is a number, but yep theres proofs somewhere that shows that they're inverse


any more questions you want me to look at?


Nope


Oh actually yes


If you are available


yea go for it


Okay you are


*See it


ok i see it


i'm rusty on this, so gimme a second to work it out


Okayc


ok, where would you start?


Maybe subtracting 3 by both sides?


yup thats how i started


Then multiply by -2?


To get rid of the fraction


lemme ask you this though, what type of answer is your book looking for? a range or the specific x value?


and yep thats right. do you remember what using negatives does to inequalities?


The answer on my book is [-2,10)


So it’s looking for an answer


Yes switches the sign


Jamie, you dont even need help lol


thats the right steps! but just to make sure, do you know when to use [ vs (


Yes


( means it goes beyond not stricted


] I think this one is stricted


stricted?


Like it can’t bypass the number


It’s the limit


[-2,10) can’t go more than -2 in this case


Can’t go more to the negative side


okay, what about for 10?


It can go greater than 10


To infinity


Right?


sorry, but not quite. i am curious what you're thinking of though


[ means it includes the number


Oh okay


( means the number isnt included, but it can get infinitely close. thats probaly where you got it


Mmm makes sense


[ included ) not included


exactly


sorry if im over explaining, but basically a >= converts to a [


Please do over explain it


Greater than a


Equals [


oh wait lemme write it


Okay!


it would still be a bracket, but its probably facing the other way ]


Ok


<,> would be (,)


yep you get it


Wow thanks I do get it


glad you do


i still have time, any other questions?


Yay yes I will provide you with a last one


It’s pretty tricky to me


lets see it! hopefully i can explain it


That’s it


With addition logs you multiply and with subtraction you divide


ok, what do you do with coefficients?


They are turned to the power


you got this


what would you do first?


good start, what about log(24)


Is this about right?


the right part of the screen is getting cut off, but its looking right so far


wait howd you get down to 60?


is that 32.6?


Yes


I have to use the calculator for this


very close, and your work was good, but i think there was some rounding


Mm


so my advice, would be to leave the values under the sqrt until you get to the end


Yes there was


Oh okay


You are correct


It’s 5


thats the same answer i got


good work!


Yay


Thanks


can i give you tips that may/may not work?


Yes please


so when i did it, i included the 24 in the log with the other values, and simplified it to 2sqrt(6)


You mean you divided first then multiplied ?


ill draw it out


Ok


Ohh


Makes sense


do you get what i did? Jamie if you guys learned that yet


Yea I’m in calculus I just started and our teacher gave us a fresh start on precal to get us ready for calc


oh i was just making sure. its been a veryy long time since i was in calc


Is it hard overall as a class, if u remember ?


calc? honestly i remember calc 2 being awful, but i dont remember much about calc 1


Okay thanks for the info


of course, hope it helped!


any other questions to look over?


If your available ..


lol go for it


kinda similar to the first problem we went over


where would you start?


Distribute ln


as in, break the x-2 up?


Yes


Into ln x minus ln2


Wait for natural logs (ln) when subtract you divide, same as log rules?


Can it be written like this?


it does work, it might make it harder. im kinda curious where you'll go next though


oh and yep ln has the same rules as log


Oh okay


yep that looks right!


Is this correct


Yay


i can do one more question if you have any, but thatd be my last one


That’s so amazing because I have one more and I’ll be done


lol perfect


oo.. this is using the unit circle right?


If it’s sin inverse of 1/2 the degree has ti be inserted for it?


*to


yep thats right


youll do fine in calc, dont even worry


Thank you Mr Mr. Adams


lol not a problem Jamie


have a good night!


You too!


Bye


bye :)


hi


hi!


I just need help with one problem


ok sure


can you put it on the board?


I have to solve for x and y


there


ok thanks I see it


k


so there are a few different ways to do this


but I'll show you the way I think is easiest


I have to do wither substitution or elimination


either*


ok I think my way is called elimination


okay sounds good


ok so we have x in the first equation and 2x in the second


yes


for elimination we want 2x in BOTH so we can simply subtract


k...


so we multiply everything in the first equation by 2 to get our rx


what is 7y times 2 ?


good job


thanks


so now we simply subtract the 2 equations


ok


what is 2x - 2x ?


careful with the - -


+ good job


great work!


thank you!


now divide by 22


wait we had 0x


ox is just 0


so you got it! y=-1


great work


cool! now I just need to solve for x


right to substitute -1 for y in the first equation


one second I have to write this down on my paper


there


ok great


so x - 7 =0


excellent Leo


you did it


ok cool! thank you!!


you're welcome


keep up the good work


Hi!


Hiii


I need help with a couple problems please


Of course!


thanks one sec


7 on this page


15 on this page please


Ok! Let's start with 7


yuppp


From what we can see on the number line, what can you say about the solution just from that?


what will the solutions include?


I think -3 and 5


would be the numbers included


That's true, but the dots continue on from each direction


that's true


so x is <= -3 or x>- 5


So you had the right idea


got it thanks for the explanation


Maria!


Just to make sure, do you know the answer?


would it be option D


Hmm, let's look at the number line again


would the dots fall into that solution?


im not sure


b


Ok, let's go back to what you were saying about -3 and 5


Yes that's correct


If we put those solutions into an equation, you'll get (x+3)(x-5), correct?


yes


In all the answer choices, we see that equations are all >= or > 0


That means that if you take one of the equations, and plug in any of the soolutions you see on the number line, the equation should be true


For example in B


If you plug in -4, you get -1 * -9 which is, in fact, >=0 right?


I see that


hi you still there


Hello How are you?


Hi, well. I am currently doing SAT Review problems, and I was wondering if you would be able to check. Additionally, if you would be able to suggest more efficient methods to solve questions (as needed), that would be great.


OK


Not sure about eff. methods


but I can check your reulst


Well, by efficient methods, I mean test-taking methods.


For the first one r = 10


Yes,


and hence, the circumference is 20pi


so circum is 2*pi*10 = 20pi


OK?


I know that; I've written above.


I see


OK for #2 2*47 = 94 so u are OK


OK for #3 could there be two correct answerrs?


OK My bad


I I see we are given the center


No, there should be 1 correct answer for each.


I agree C is correct


That is the format of the SAT.


I took the SAT test


You seem not to have an answer for #5 Am I correct?


Yes.


OK what does the 4xqroot(2) mean?


I guess those are r?


Yes


Here is an effcient way to do that one


what x/32?


OK then take sqroot of that


12 is the ratio of the squres of the radii


OK


Yes. understood.


On to #6


OK any odea about #6?


Any*


And how about an angle from center to the arc?


so it would be


I agree


30/180 or 60/360


Because the C is inscribed in the circle and intercepts AB,


the angle of AB must be two times that of ACB


And hence, we just do 60/360 * circumfurence


I think of that as giving central angle of 60 deg


circumference


Yes


One Hint


MAYBE the total of incscribed angles 180 deg


then you do not need to get the cetral angle


But I have not seen that latkey


lately*


Sorry, I do not understand.


What do you mean exactly?


OK central angle si 60 deg do u agree?


of AB


Agreed.


and 60/360 is 1/6 because total of central angles would 360 agree?


Yes.


I agree


OK Now I *think* total of insrciribed angles mught 180 deg. IF tha  is trus then you can use 30.180 which is a littl emore effiecnt


Just an idea


just metnioned that becuase you asked about effienecy


Yes, okay, thank you for pointing that out.


OK you can check on that


However, since this is a small step, I will probably just stick with the norm. But thank you very much! Yes, I did ask about efficiency in the beginning of the session.


Thank you very much for your help in this session! Have a great day.


I agree it is  a very valid


You are welcome BYE BYE


Goodbye.


hello!


Alex


i have a few minor problems i need clarifications on


Okay lets see them!


im type them out so give me a moment


Okay no worries.


regarding the first one


i have an answer of 64 but ive been told its wrong but im not fully sure why


Okay lets start with that one


Do you know how to rewrite that?


maybe


actually no


Thats okay no worries


When we see numbers to the power of fractions its actually referring to square root or cube root or basically the root of numbers


Okay what number do you think goes inside of there?


yeah good job


so i was right...


but that one wasnt the one i was really worried about


Yeah it is right, I'm not sure why they said it was wrong.


well


for the 2nd question


im completely lost


Is that what you mean?


yes


for this...


i assume you first simply the expression if possible


which it isnt


Okay I see why you think we should simplify the expression


That's usually the first step you take with square root but cube root is a little different


The first thing we want to do is get the numbers under one cube root


How do you think we could do that?


not sure


muitiply to get it so it can?


Yes perfect!


Multiply both numbers together


Yes!


Okay what do you think we should do?


take out the 3rd root like you would with any other?


Not quite, we can actually just simplify it


how so


Think of a regular radical


when you simplify it you pull out perfect squares


hmm


ohhh


uh


Try to use perfect squares


oh wait


for a 3rd root


Ill give you a hint, we can use 4


yes perfect


lets start again 125 and 4


Wait I meant 125 sorry


Okay good, do you notice that we have 3 fives


yes


we can rewrite 125 as 5 to the power of what?


Good job


but we're missing something


Good job!


is that the full answer


Yes!


interesting


Yeah math is crazy


Is there anything else you need help with?


1 sec


i got 1 more


Okay!


So is the question how to simplify the top one?


again i was told this wrong but im not sure exactly why.


Okay it is the right answer once again


you even drew the correct process


thanks for the reassurance


Of course!


if we have time for another, i have one


Yes we do


Okay good work but it's not the right answer


alright


You made a mistake when you factored 25


since 25 is a perfect square we need to show that


ohhh


there should only be one five coming from 25


because the square root is 5


the first five needs to have the square root


we leave it like that because it's showing us that its not a perfect square


now combine then


oh dont use the 25


we square rooted it, the five is what matters


Good


but you erased something that was correct too


Good job


Now lets rewrite out equation


our*


make sure the 2 stays


yes good


what do you think is the next step?


multiply?


yes


no not quite


If they go together as a pair the only thing that should be affected is the whole number


remember theyre a pair so only the whole numbers are affected


Yes good job!


is that it?


Yes!


thanks for your time


thats all i needed


I hope this helped you out!


You did a great job today!


hope you have a nice rest of your day/night


it did


Thank you, you too!


byee


Bye


Hello


hii!! what do you need help with


I put the problem set up, it's letter d that I'm having trouble with


okay sure


one sec


okay so first, you square root both sides to get rid of the exponent on k-4


Yes


but since you cant square root -3 its gonna be ±isqrt3 where I = imaginary number or sqrt-1


I don't know the square root symbol


On keyboard


its okay you can just draw it


instead of typing


Ok


Since, I'm in geometry and we haven't touched on imaginary numbers yet, what should I do.


there are no real solutions


Ok, and that's because "i" isn't a "real" number?


yes


ok ty


Hello


hello


can you help me with three


Which three?


Oh, you mean #3


yes please


That looks good so far


like this?


So far so good


might as well make that second term +


I am


do you see how to do the integral?


Use u substitution


ohhh


not quite. There should be no x in the integral and you need to replace the square root


is it bc x is like 1


you are replacing xdx with -1/2 dt


so the xdx is gone


better?


no, the -1/2 is not an exponent


oh


and now the denominator


What,


wym


Why


why is xdx on top


like im so confused with this right now


that 's what you have.. I circled it in red


Its another way to write it.


Does that make sense now?


im confused with the -1/2 and 1/2 itself


There is a -1/2 in the numerator and I have replace the square root in the denominator with the exponent 1/2


right


is it -1/2 exponent


when it's in the denominator it's 1/2, and then when you move it to the numerator it becomes -1/2


are you familiar with that?


I can write out the steps if you want


I did it


that's right


is it not plus


see we have plus up here


It's a minus


its bc the power rule right


like the -1/2


made it - and not +


I circled where the negative comes from


in green


yeah I get that


so is what I circled the final answer


You have to do the integral and get everything back in terms of x


oh


there won't be any t's in the final answer. But you can do that integraL


like this?


there won't be a 1/2 in front


what happens to it


that 2 cancels the 1/2


ohhhh


all set with that?


yes sir


all set then?


yes


OK then have a good week!


thank you!!!!


you are very welcome


by


byee


Hello


Hi can I need help solving a calculus problem


I will upload it on the screen


OK


This is a related rates problem


Yes


What have you done so far?


I will write it on the screen


that's what I have so far


Why do you have Vdv/dt on the left?


Oh I don't know I just put it there


It should be just dV/dt.


ohh okay that makes sense


I am also not sure why you 2 on the left, since you have dV/dt =904


yeah I see


I guess you are figuring out the height at the instant when the radius is 10 and the volume 100, right?


yes


But then you should have r =10 meters, not 4 meters.


ohh okay


its becuase dr/dt= 4 and r=10


But in that equation you are just figuring out what all the quantities are at the instant that they are interested in.


At that instant, V =489 and r =10 and you are figuring out what h is


yeah okay


So go ahead and figure out what h is when V =489 and r =10


how would I do that. I'm confused because I don't see V in the equation


That is the equation relating V, r, and h at the instant tney are interested in.


okay I understand, so is this the first think that I should have done


Well, you did find dV/dt almost correctly, except that you had that extra V and you seemed t have dropped the 1/3 𝜋 for some reason


I see


now do I isolate for h


That is not enough decimal places.


Oh okay how do I know how many decimal places to keep


They are going to want the final answer to 3 dp.  when using a calculator, you should keep another 1 or 2 decimal places more than ask for.  Dont round off numbers until the final answer. Otherwise you will get rounding errors.


okay that makes sense


Now you can plug all your information into your equation for dV/dt


also the reason why I dropped 1/3 pi when solving for dv/dt was becuse I divided both sides by 1/3 pi


okay


do I keep r as 4 or 10


Don't forget 𝜋


Yes.  From here it is just arithmetic.


okay do I sub 904 for dv/dt


It looks like you already did that.


is what i have so far correct


Yes, that looks good, although I have 4.66905


ohh okay I think I wrote 4.66905 by accident


I got dh/dt= 1.2345


That's not what I get. You would probably be better off doing this on your own on paper.


Ohh okay let me try again


ohh I see I forgot to add


I am not concerned with the arithmetic, but with whether you understand  how to do this kind of question.


Yes I understand it


thanks for your help!


You are very welcome.


I will take a screenshot of my work


Thank you! have a good day!


Hi


hello


i will post the question on the board


ok


ok so first it's important to identify what is the unknown in the question and what is the data given to us


the lower price rate is unknown


perfect


now what is the data given to us


a table and an equation


yes


now what is the condition that we can compare prices ?


we would need the price per gallon charged by each gas station right?]


right, now looking at the gas station B equation, we can see that the question itself gives us the price per gallon


which is?


now for gas station A, they give us a table of values. Now this information can be used to find out equation of gas station A too right?


gas station A is 3 divided by 9.15


which is 3.05


perfect, now finish up the question


it is C


excellent work


any other questions?


alright, go ahead


Alright, so the question is practically the same as the last one, if you notice, but there's just one small change in the data given


a graph this time, which is what I am stuck on


alright, i'll help you through that but firstly, what is the unit price for A?


give me some time to work it out on some paper, please?


sure sure, I just want to make sure that we're done with the first part before we move on to part B


have you got it?


just for fragrance A


I almost got it, just a few more minutes please


sure


should we move on?


No not yet please, this topic is difficult for me


would you like some help?


is it 26?


yes


so, now time for the graph........


so now we know the graph is a line with an equation y=mx where y is the total price, x is number of bottles and m is the individual price right?


are you familiar with the concept of slope of a line


we go on till there's a point where x and y meet


ok...here do you realize that the slope of the line is itself the price of one bottle of fragrance B?


but I also have something that is based on it that troubles me. Could you help me with that after these problems? And yes, I do.


yea I will, anyways so tell me the slope of the line


gr8 so you can finish up the question now


alright let's move on


yeah so this is a similar case as the previous ones, just divide y/x for any one column (maybe check if it applies for all other)


oki


a is not one


because 3/5 is 0.6 in decimal terms


keep going and give me the entire ans


ill check all at once


take your time


C and E are right


yeah


same concept, keep going


D and A


yup


now the unit rate in the graph as we know is the slope


keep going in the same way as before, ill check your answer


i am stuck


on what part?


I cannot figure out what goes first


ok, firstly what is the slope of the line?


perfect


so now just find the decimal form of each fraction you've got


so first is 17/9


that's around 1.88


21/11 is around 1.9


19/10 is 1.9


do the same for the last 2 and arrange


checking just a sec


your order is slightly wrong, if your getting these values then the ans is correct


i can't really see it clearly either so just verify your values


thats right what you got


for the values


if your values are matching then it's fine


........ i don't get it


are your values not matching or you're unable to arrange them in the order?


how am i supposed to arrange the from biggest to smallest?


well you know the values right, so which is the greatest value among 1.8, 1.909, 1.9, 1.92, 1.91?


and the next?


yeah that's it then


the value corresponds to the unit change of each table


like that


oki


i did not get that at first


alright, any other questions?


no


alright i'll end the session now then, gr8 work today, I hope you're feeling more confident


bye


hey


how you doing


alright


i wanted to do some algebra problems if you can come up with some


what category?


you can pick it


Okay


ok


which one i post to do


All of them


first one is x=5


2 one is   -2a+6


3 one y=2


4 one -1


5 one 3x+7


Awesome


want moer?


yes


1 one x = -12


2 one


3x2 over top -13x-10


3 one -5


(x+3) (x+4)


5 one


4 one i meant


wANT MORE


sure


Solve


x=2 or x+3


(2x=5) (2x-5)


Ahem


huh


oh mb


22 and 24


first the lengths of the two pieces are 17 cm and 23 cm


thats the first one


2 one is


(12,13) or (-13, - 12)


width = 5 cm, length =7 cm


3 one


How many more do you want to do?


no more


You think you got it?


yes


alright


want to end session?


have a good day


you too


hi


Hey there!


I need help with this little tiny question (that's not really tiny)


Sure no problem!


so Alice is planning to drive from city X to City Y. The scale below shows the distance between the two cities with a scale of 1inch=20 miles


Oh ok


no wait that's not the hole question


Sure go ahead


If Alice drives at an average of 30 miles per hour during the entire trip, how much time, in hours and minutes, will it take her to drive from city X to city Y?


I think I need the distance between the two cities


yup the distance is 11/2


in


:D


so first we should calculate the distance in miles between the cities


so multiply 20?


yup


which would give?


you can just round it off


ohh thanks


No problem :)


but were did u got the 3 from?


yeah but what is the 30 dividing ?


the whole number is the hours and the decimals would be the minutes


ohh


thanks :)


hello


Hi


do you have a mic?


yes


OK, hello


He said he.


So, I have a test tomorrow and this is like my study guide, and I just need like help on a couple questions.


ok


Do you think you can help me with number 7?


z is equal 284-142


yeah but i need to know how to solve it'


what do you mean


like i need to solve for all vairbles


and isnt Z= 142??


wait, z==142


yeah


can you understand it


a litle bit


like line 2 is parallel with line 3


is my work correct


hello


hi


what do you need help with


I need help on my math homework please


ok!


what are you learning


I'll share screen


ok


that


is there a specific problem


you still there


yep


is there a specific problem you need help with


no I need to do 1-30


but is there one you need my help on


Ok, first things first, the fraction 1/2 half means you divide something in 2, right? Like, for example, 2/4 = 1/2, because you divided the number in two. Any even number that can be divided by two can simplified to 1/2


think about then number what fraction with a denominator of 6, could simplify to 1/2?


im osrry i have to go


hi


how are you


hello Alex


i know its product rule


yup


So far so good


im confused at this point like foiling


You


You're basically done


All you need to do is remember the distributive property: a(b+c)=ab + ac


I can walk you through the multiplication if that's ok


thats fine


Because you are multiplying a "binomial"(just an expression with 2 parts) like a monomial(an expression wit on part), you can just treat it like multiplying (5+7)(3).


You distribute the 3 to the 5 and the 7, so you get 3(7)+3(5).


It works the same for stuff with x in it


ok


here, try this one out just to make sure you grasp it well: Multiply (x^2+5x)(5x^2)


is that right


yup, nice job


Do you want to finish the problems on the site, or do you have other questions


another type of problem


Ok, so moving on to the next one then right


i put in 1/2x^1/2 - 5x^-1/2 and it was wrong


oh you forgot to add the otehr half that you got with product rule


oh


sorry that might be on me


sqrtX


yup


wait wut


I think you did the wrong operation with sqrtx


originally, it was +sqrt x) right


right


check again where you put the sqrtx


in the answer you entered


ok


can you simplify the expression I wrote


(hint: can roots be converted to exponents?)


yes


its plus btw(you originally got two things w product rule: one was the expression you had to distribute out, and the other was sqrtx. In product rule, you add the two, so you jsut made a silly mistake where you multiplied them instead)


oh okay


chain rule?


yes, but lets start with the first part


wait ur missing a key component to every function


You have basically everything right, jsut look at the variables you are using


yup, its the 1st one


hint(u=g(x))


nice


and the 2nd one was right originally


oh wait u changed it(hint: similar issue as the first one)


yup


Ok, now just plug it all in


Sidenote: On the AP test, I found it helpful to jsut memorize it as: f'(g(x))=g'(x)(f'(g(x)))[confusing notation but the second f'(g(x)) is the derivative of f(x) then plugging in g(x) into that]


yeah thats the way my teacher


likes


i thought this was easier though


This is fine too for now tho, lemme see how much of the problem you can solve


we can do your way though


ok


wait check ur functions


which one is supposed to be f(x)?


u=y


The f' is the outer one


(Think about it: What would it look like if 1+4x was f(x))


the cube root would be inside, but the function they want you to derive has the cube root as the outer function


sorry differentiate not derive


4 right


nope, yo have them mixed up, ur f' is what g' is and vice versa


can you right it out for me in focused


in the formula i wrote, f' is on the outside of g(x), meaning that g is the one getting put into f(x)


i understand


that


so the outer function is f, which is the cube root of x


and the inner is g, or 1+4x


so ur f' taht u wrote(4) is actually g' u might have just mixed them up


oh right


good


now just go under all the stuff we wrote and plug it into the formula


yes, but what should be there in place of x


hint(look at the formula)


wait no i meant in place of the literal x in 1/3x^(-2/3)


wait you almost have it


Lets go through the parts of the formula, first what's g'?


yup


so that's the first part u need


even closer


you added an extra bit that's not in the formula


yup, but only part of it


Removing that part of the -2/3 would be the same thing as if you u remove another part


of the expression


hint: it's f'(g(x)), not f'(f(x))


g


g prime


nope, im talking about the second half only, ur 4/3 is good


do u remember function composition


a littel


little


so when i say f(g(x)), and f is 1/3x^(-2/3), and g(x) is 1+4x, I mean  to use g(x) for all x in f(x)


lemme write it out


it's really laggy on my end mb


Do u get that part


yeah


In my example, f(x) was actually the f' in ur problem, and g was just g. So in the second part of ur answer, which is supposed to be f'(g(x)), u did f'(f(x)), bc u plugged in the cube root which isn't in g(x)


thanks


Hi


Hello, How are you doing today??


I’m good


that's good!! What can I help you with today?


I need help finding scenario that match an equation


scenarios


ok do you have a picture or something that I can see so I can help you better?


Right here


ok I see now


the equation is (OA)(0.30)=48


so for the first word problem can you think of an equation that could be used to solve?


where did you get addition from in this?


Oh sorry it’s $48+(30%x$48)=oa


Because I would have to add 30% of 48 to get the original aniun


Amount


Its gonna be 48 = 30 percent of the original amount


so the original amount would be the greatest number


do you know how to solve the equation given


Because 48 = 100%


plus 30%


130% =1.3


Wait nevermind


do you see what I wrote on the board?


bro


yeah


ok so oa = 160


Sorry I knew how to solve it I just had the wrong formula


its ok


I think this equation does work for the first one because the got a commission of 48 dollars with was 30 percent of the original amount, or $160


does that make sense?


Yea


I thought about it too


ok nice job


now we can do the same thing for the second one


do you think this equation works for the second one?


Yeah


why


does it tell you how many are supposed to be correct?


because $48 is the discount and 30% off and if it’s 30% off then that means $48 is 30% of the total amount


ok yesssssss that's what I was thinking too!!!!!


now for the third one


No I don’t think so, really because it sounds like $48 is the total price instead of 30% of the total price


for the third one?


Yes


yea I think so too


Ok now the last one?


So based on my knowledge, a markup is an increase in price, so they are referring $48 as a markup, even though it’s a discount


yea I noticed that too


So I don't think that one applies


And plus it kind of sounds like they are making $48 a while number


correct


Whole


So only the first and second one are correct answers.


Is that the same thing you got?


No unfortunately not


oh what answers did you get?


1, 2, and 4


ohh I see


do you only have one try?


sorry


But it wouldn’t really affect the score so much


So it’s fine :)


ok that's good


is there anything else you need help with?


Nah I think I’m good


ok have a good day!!!


Ok! Byee


byeeeee


Today we will be working on limits, I want to understand it fully and know how to work them out. I have problems we can work on, we've been using limit laws in class to work on them


Hi.  How are you?


I'm fine how are you?


Good.  I see you are ready to work on limits.  Go ahead and I will help.


i can't access the blackboard to write out the problems for some reasons


Oh.  That makes it a bit more challenging.  So try to use these boxes to text would be the alternative.


Do you want to turn on audio?


but how will you be able to show me the steps? Can you see the blackboard?


I just refreshed and now I can see it


Can you see the mark I made on the blackboard?


yes I just refreshed and now I can see


Perhaps you can write as well.  Will you try?


yope, I can


How about audio?   Do you want to turn it on?  Sometimes it makes it easier


Alright, I'll see if it's necessary later then I'll turn it on. But without further to do, first problem


I turned on the audio on my end.


okay


So. How would you approach this?


Wait let's change the problem, Ik this one


OK


here


Ok.  I see it.  Any thoughts?


I would suggest that we are allowed to plug in without further work needed.  Do you agree?


Alex, are you there?


one minute, sorry I had to go somewhere rq


No worries.


yes we can plug Ig


So what would you get?


What is cos(pi/2)?


honestly I kind of forgot my unit circle but one min let me think


Cos(pi/2) is 0.  So the numerator is 0 and the denominator is a postive value.


yes


Answer should be 0


so we don


so we don't even have to find the bottom value since the top value is 0, right?


Well.  We can compute it quite easliy and if you want we can, but it is clear that the numerator is 0 and the denominator is a positive value.


Denominator would be (pi/2) + 4(pi^2/4) = (pi/2) + (pi)^2


Please ask questions if something is not clear.


can you write this down on the board, I'm more of a visual person


Sure.


Can you see it ok? It's not the neatest writing.


sorry.  The last one should be fixed.


Questions?


one min


i'm looking over it


and like we can't figure out the bottom line cause we don't know the exact values of pi correct?


It could be simplified in another form, but wouldn't change anything.


It is just a positive value, albeit an irrational one.


yeah I understand it wouldn't change anything but I just want to get in the bottom of this because I might need to find a value like that in the future, who knows?


Well.  I will put another form of the denominator out there for you, but in my opinion, this one is best.


This one shows the denominator as yet another fraction, and in my opinion, sheds no new light on the problem.


okay, thanks, next problem then


Let me take a one minute bathroom break


okay


I'm back


how do we know for sure that this limit is -1? We didn't even plug anything


Well.  In your class you're covering rules on limits.  You were probably told that the limit of a constant is the constant.  To prove some things would probably be outside the scope of your course.  However, if you think about it, the fact that x approaches 2 has no real relevance.


Let me draw something that might help


Let me redraw this.  I am not happy with it.


So I am showing the graph of y = -1


yes


Notice that no matter what value of x I choose, it does not change the fact that y = -1.  It is constant for all values of x.  I can approach any constant


and the limit is still -1


that makes sense


A lot of this stuff is best thought of using common sense.


The proofs of such things are long, boring and not that helpful


right


Anything else?


yeah I'm writing it


can you do these steps?


Well.  I was hoping you would suggest how to proceed.  What do you think?


I already know what to do, I just want to see how you do it so I can make sure that the steps are the same


Ok.  I will put my work out there and a picture that may help you.


It's a very bad drawing, but I hope you can see it and understand it.


If you come close to x = 2, like 1.999, you will come very close to 12 as the limit.


If you come close from the other side, like 2.001, you will come very close to the limit of 12 as well.


This is the logic of being able to just plug in.


okay but then why does the 3 come in front like why doesn't it just stay inside the parenthesis?


It can.  Either way is fine.  But you make a valid point.  I agree with you.


I was just trying to show multiplication with it being outside the parenthesis.


I'm asking that because even on my notes it shows this


I see.  That way you are using the rule for a constant times a limit.


You have given a much better answer.


based on this, it makes me think that I should be putting the numbers in front of parenthesis


Did your teacher discuss a rule for the limit of a constant times an expression?


no, we just did geometric,summation, composition, quotient, and multiplication


OK.  I see nothing wrong with what you have done.  If the point is to find the correct answer, then you can get to the result quite easily.  If you must justify each step as you go along, then care must be taken to use appropriate rules you have been given


Do you have a list of limit rules to follow?


I don't have the list, but yeah when the questions says to explain we are expected to write them down


I see.


It sounds like you either have to memorize them or be given a list to choose from.


I need to wrap up within 15 minutes.  How else can I help you?


oh okay then let's work on something else rq


Ok


THis


Let me read this for a minute


Is there an x in the denominator on your first expression?


yes


Ok.  Do you have any thoughts on how you would proceed.  I can try to show what I would do.


I was abt to say 5/2, but i don't think it's right


I got 15


how?


I'll put my work out there


i can't scroll down


I can't see it cause i can't scroll any further :(


I'm sorry.  The board doesn't seem to be working right now.


Let me type my answers here


okay


just write it out, I'll come back in a sec, I have to go do smth important


lim x=>6 f(x)/x = lim x=>6 lim(1/x)(lim(fx))


) = 5 / (lim(1/x)


) = 5 / (1/6) = 30


lim x=> 6 f(x)/g(x) = 30 / 2 = 15


thanks for the pic, but I can't really see the right side can you zoom out a bit?


I can't make it zoom any more.  Let me try to resend a cropped version


yea


I can't do any better.


I will make one more attempt to rewrite my work and upload it if you want.


okay thanks for everything


See if you can see it please


Any luck?


Well.  I see that you are away.  I hope that you will be able to see my work on the last upload.  Unfortunately, I've got other committments now.  If you need more help, you can always put in another request.  Thanks!


hello


Hi, Good evening, SIr.


It's not evening here.


Sorry Good morning Sir*


How may I help you?


My bad I wrote that by mistake its 6 Am here sir. Sir I had a particular question. HOw to attach that question here, since I am new to this.


If you have an image of the problem, there is an upload icon on your toolbar.  Do you see it?


Yeah, got it sir. David


Sir, I did the attachments, please tell me the process to takcle this.


This doesn't look like a calculus question


Sir, it's basically a range and domain question.


OK.


So, you know.


yeah


Sorry sir those were transcript errors


I am so sorry for those, sir you could proceed telling the solutiuon sir.


working backwards from 4, what do you think c would be


So, I did the calculation and I got


um


that since this is


a square root function.


then that implies that this particular thing must be greater than equal to 0.


So then solving this using the way curve method.


I came to the


uh conclusion that it has some ranges, so shall I tell those ranges here?


Hello, sir are you here?


I think there is some network issue then teacher shall I rejoin?


Thanks, sir for help. I have to leave then rejoin the session , since it seems there is some network issues on the server


Hi Maria! How's your day today?


It’s good what about you


I'm good! Thank you for asking!
I see you have some questions about homework.


Yes um I answered most of them but I have some that I need help with then after we can go over the questions and check if it’s right


Alright sounds good! Can you upload the questions to the workspace?


Yes


Alright, I see the question


I uploaded one


Would you be able to tell me what you are struggling with? It helps me to give you more focused advice


I don’t really know how to read a dot plot


Alright, that's totally fine! Can you tell me what you do know about dot plots?


Wait sorry I meant box plots


I see. Can you tell me what you do know about box plots?


Nothing really


That's okay! A box plot is based on five different numbers: the minimum, the 25th percentile, the median, the 75th percentile, and the maximum. Would you like me to expand on those terms a little bit more?


Yes please


Alright. To start off, can you explain to me what the minimum, median, and maximum are?


The meadian is the middle number


The maximum is the highest value


The minimum is the lowest value


Perfect! That's exactly right!


Essentially, a box graph is split into two parts: the box in the middle and the two lines to the left and right. The box contains the middle 50% of the total data in the set, with the lines each containing 25%. The line in the middle of the box represents the median


Would you like me to expand further?


Just a bit more


Alright! Is there anything specific you are confused about?


Just the box plot


So if there is a data set with 20 points, you want to find the point that's 25% of the way through the set, the median, and the 75% point. For example, the 1st point would be the minimum, the 5th point would be the 25% point, the 10th would be the median, the 15th would be the 75% point, and the 20th point would be the maximum.

The beginning of the box starts at the 25% point and the end at the 75% point.


Ohhh ok


Ok so to find the mean would I add all the# and devide by the # in the value


Exactly! You would add up all the points and divide it by the number of points in the dataset.


Ok give me a minute to add the numbers


Ok um I added all the numbers in the set that’s in the white bored Ang got 32


*and


This is a pretty tricky one, but there is no actual answer for part A. Can you tell me why?


I’m not sure


To find the mean, you have to how many of each data point is in the set. What doesn't the box plot tell you about the points in the set.


I added all the numbers was I just supposed to do the numbers that are touching the box plot


Not quite, but I do like your train of thought! The box plot doesn't tell you how many of each point is in the set, which is really important to know to calculate the mean. Therefore, you can't really  find the mean from a box plot.


Oh ok


So that answer the first question


Yup! Box plots don't say the mean unless there is a separate label that has "mean" written on it.


Ok so how would I find the median on a box plot


The middle of the line on a box plot is a label for the median.


Oh ok so the median would be 34


That's right!


Ok thanks


Do you have any other questions?


The last question is did the cross team ever scored 30 points at a meet


I would say yes because the box plot is over 30


Sorry, the image is too zoomed in for me to see the question and it looks like I can't zoom it out. Would you be able to shrink it down a little?


Sorry


All good!


Ok amazing  so was I right?


Oops it looks like my connection went out for a little bit


Now, the box plot, unlike the dot plot, does not specifically graph out data points. This means that just because the box plot goes over a number doesn't mean that number is part of the dataset.


Oh so does it not have a answer


It's impossible to know whether the score was ever 30, so the answer is neither yes nor no.


Oh ok got it so it won’t have a number right


Yep!


There's no answer to C.


Ok I just have one more thing can we go over another problem I already did it just want to see if it’s correct


Alright that's fine!


It’s in the whiteboard


D and E is right, but B has the box start in the incorrect values. What are the 25% and 75% points of the data set?


I have the answer for c


Apologies, your graph was right! I made a mistake.


Sorry about that.


It’s ok


Did I do that box plot correctly


Or did I miss something


Yep it's right!


What was your answer for C?


That the box plot doesn’t tell you what of each point in the data set


Not quite! C is asking what the box plot gives that the dot plot doesn't. What are some things that only the box plot has?


Oh


Ok so the box plot represents the 5#summary


And the dot plot doesn’t


Couldn't have said it better myself!


Unfortunately I do have to leave soon. Do you have any final questions?


Amazing thank you and that’s all


Hope you have a nice night


You too Maria!


Hi Emily.


Helllo!


I need help with this


Have you checked on how to do a whisker plot?


I know of a whisker plot but like idk how to do this like how would I do this


What if you click on the link? But the first thing will be to sort your data, which you could to on your calculator or google sheet or just rewrite them in order


Also, it says "using the tool provided" so there is probably something there to do it.


I did


i have to move the whiskers


Ah. So you need the scores in order.


Can you use the send data to calculator?


Or just start writing them here in order


Idk like idk how to solve this lol


ill press explanation and ss


I'm helping you on how to start. Get the data in order first


this is how u do it


Good. So see how you have to list the values in order first?


Yeah


The idea is that the box encloses the middle 50% of the values


Ok lets start


And the middle line shows the median, the middle value.


WRite or type the values in order


Ok


25, 27, 28, 30, 31, 36, 36, 39, 40, 41, 42, 43, 46, 50, 56, 57, 58


OK, great. How many points are there?


So which one will be the median?


let me see


It would be the middle one.


There are 17 total, so that would put 8 on the low end, 8 on the top end, and 1 in the middle, or the 9th value.


What's the 9th value?


its not 43?


That's the 11th one.


Right


SO that is the median


so i would put the black middle dot at 40


Right.


ok next


Now there are 8 values above and 8 values below. The Box quest from Q1 to Q3, which means


the min is 25


it will contain the middle half of the numbers.


Max is 58


Yes, so you can put the whiskers there.


mhm


Q1 will be there are 1/4 of the scores, 17/4 = 4+, so you would put it between 30 and 31


So now you have 4 groups of 4 plus an extra one. The lower quarter is 25-30, the 2nd is 31-40, the 3rd is 40-46, and the top is 50-58


Does that make sense?


so we have to make it equal?


yeah it makes sense


The whole idea of quartiles is to divide the scores into 4 equal-size groups.


ok


ok so i see them


so first quart is at 30?


So this gives us an idea of how far apart the scores are spread. If you have only 17 scores you can look at them and get an idea, but if you have 17,000 scores you need something like a box plot to show the data.


Q3 is at 46


I would put it at 48 between 46 and 50


well idk if it'll be wrong bc i have to submit it and it tells me if its right or not soo idkk


Look at the example again then to see how they did it.


thats how they do it


its the exact number


can u see it


See, it says the third quartile is the median of the opper half of the data.


We have an even number in the upper half, 8 scores, so the median is between the 4th and 5th scores.


so its wrong?


its not 31 and 46?


Q1 would be 30.5 and Q3 would be 48 because those divide the top 8 and the bottom 8 scores


If there were an odd number above the median, we'd use the middle score in the top. But when there are an even number of scores, the median is the average of the middle two. So half way between them.


i dont get this


OK, think of this: what is the median of


wait so


1 5 8 9


since the median is an even number we use .5 for Q1?


if it was a odd number we wouldn't dxo the .5


not exactly but you're getting there. What is the median of 1 5 8 9?


there wouldn't be one?


That's one answer but it's awkward not to have one. So we use the "middle"


The middle is halfway between 5 and 8


Halfway is (8+5)/2 or 6.5. 6.5 is 1.5 above 5 and 1.5 below 8


That's just a way they define the median so it represents the idea of half the numbers above and half below.


well i put the answer in already and it said all of them are incorrect


What numbers did you put in?


min- 25


and 58 max?


mhm


Remember I said 48 should be Q3


"The first quartile is not correct.
The median is not correct.
The third quartile is not correct.
The maximum is not correct."


oh


How could the maximum be wrong?


im gonna work on a dif problem this one is just too confusing


oh, there is a 59! You copied the numbers wrong.


You know how to do it now, you just got the wrong numbers.


ill come back to it later


so like how would i solve this


I don't see anything yet


can u now


Yes


ok


So what does compounded mean?


uh idk


tbh


Click the link


If the interest is added to the principal, and this new amount earns interest, then the interest has been compounded. We use the method of compound interest to calculate the new amount after each period.


Right. So let's see what happens for David first. He deposits 80,000. How much interest does he get at the end of the first year?


What is 1% of 80,000?


Exactly. So what is 4%


Sure, 4 x 8  = 32


i did 80,000 times 0.04


Yes, but you can also do it in your head 😀 So that is how much David earns the first year.


and then for heather?


Now David's "principal", the money he deposited, is 80,000. So with simple interest, he will *always* get the same amount


they have the same interest rate


just diff type of interest shes compound and hes simpler


Sarah also earns at the end of the first year.


So how much money does she have at the end, 80000 + 3200?


Right. At the end of the second year, she gets 4% of *that*


so 83200 times 0.04?


perfect


I can't do that in my head lol


So now she has 83200 + 3328


i add it again?


Yes, then finally figure the interest for the 3rd year and add that to get the final


Ok


So while poor David is still only getting interest on his original 80,000 forever, by the 4th year Sarah will be getting it on 86528


so i do 86528 times 0.04


for third year?


Right.


ok take a look at my math


ill work on David now


For David you only need how much he earns each year and it's always 3200


oh i did mine totally diff


oh i see


You see now?


And you see why compound interest is better (if you're getting it, not paying it)?


yes


my math is correct for heather?


Be careful putting in the answers because they are asking only about the interest


Yes.


Ok I'm gonna plug my answers in rn


Wait


hm


BE sure to use the interest, not the numbers you put in the boxes


3200, 3328, 3461.12


whats the math that i'd do for that


to get those numbers


so i put those numbers instead


Yes, you calculated the *interest* for each year, and that's what they're asking for


ok


is everything correct now?


I ave another one


OK


That's essentially the same problem just a different principal, 90,000


and interest 3%


yep


i need help with the third year


You have a mistake because you're using 4% for the 2nd and 3rd years


oh right


ok but what number


would i do to multiply by 0.03


You got the first year interest right? 90,000 x 0.03


mhm


Then you said the total will be 92700 so you multiplied that by 0.03.


yeahi calculated again


So what will the total be at the end of the 2nd year? 92700 + 2781, right?


im talkin about for 3rd


ok


Right. So that's how much she has in the bank for the third year, and her interest for the third year will be that * 0.03


Right


everything correct?


Compound interest will ALWAYS be more after the first period.


Yes


i have one more question


Great.


for bottom secon year part what number we use?


Think about the meaning of the numbers. What are you looking for?


So at the end of the 2nd year you have $10204


take a look at my math


Right! You always have to keep in mind the meaning of the numbers or you'll get lost.


its wrong


The third one is wrong


doesnt say which it just says its incorrect


ok what did i do wrong


At the end of the 2nd year you have 10200 + 204 = 10404


See?


mhm


Want to see how to do it quickly on a spreadsheet? Have you ever used one?


still wron


omgg it was bc kevins is compound


What we did wrong was not checking the instructions carefully. This time the FIRST one is simple and the second is compound.


i put it in the wrong spot


i know


Kind of a trick question but good to remind us to read carefully.


is this correct so far


Yes. See the way I put it into a table.


can u check my last one


nvm its right lol


ok i have one more question if i get this one right


like the next one right


OK.


Yes


do you still have time?


Want to see how to do it quickly on a spreadsheet? Yes, I do have some time.


Ok I have a new problem


And sure


I just color code so I can differentiate


I'll screen share and show you


ok


let me know when you screenshared


Can you see it?


i see it


Ohh I see yeah Ik how to use excel a little


OK, did you see how I typed the formula in A1?


This is the same. I typed


=A2*0.04  to get the interest


OK?


Mhm


So in A3, for year 2, I add A1 + A2, the start + interest, right?


Got it?


Yep


Now I just have to duplicate the cells to get the rest


Simply use ctl-d to duplicate the cell above.


It automatically adjusts the references.


so view the results


I see


That's how fast it is. ONce you have the model, you just change the starting amount and the interest


So you've solved a new problem in no time.


OK, you said you had one more problem?


Well its a new set of problems


OK


heres the formual and an example of the number splugged in


OK, I don't know about annuities but I see the formula.


I will be right back, I need to throw something away


So you just want to solve that equation for M


Ok I'm back


M is what they want to know, so use the equation to get M


Ok


whats the number for each quarter?


The formula says "N is the number of times a year the interest is compounded"


So ... if it's compounded quarterly, how many times is that?


t is 13


right


Sure, quarterly means 4 times a year


Have you rewritten the formula to solve for M?


so i do


For a complicated formula like this I would calculate the parts first.


I like to do step by step


That's what I mean. But if you label your pieces then you won't get mixed up


i mean 0.13


You havent labeled it so I don't know what you're doing


here's what i have


Looks right


But not the final step.


If you call the complicated part Z, then the formula is A = MZ


But you want M, right? What is M then?


Also, it would not make sense for them to pay $12000 every quarter for 13 years ...


m is 12000


oh i see


But look at what I said about the formula.


yeah i did this wrong i realized


You did everything right except the last step


i actually did somethings worong


i realized i had 13 in r


im editing it rn u just cant see it


Oh, I used your numbers


That's why a spreadsheet is helpful so you can just change one number and get all the new results


answer 12.16.16


nvm said its wrong


can u check my math


it should 12.27.27?


I got12.27 so yes


ok


But I don't know how you got.17


didnt round it yet


But how did you arrive at.27?


i rounded it


What did you round?


So just do this one the same as the last plugging in different numbers


i got 10.16


nvm now i got 10.17


i think i did something wrong


idk if its right


well it cant be


nvm ik what i did ok


OK let's see


OK. It's hard to debug because you aren't labeling things ... what is 0.9/12? Is it supposed to be r/n?


i fixed it


its bc i did 12/9 and not 0.054/12


i don't need to round with this one?


r/n is 0.0045, right?


mhm


OK. See, I get 1.06 for (1+r/n)^nt which is a little different.


nvm


i know what it is


its bc i don't paste the full on numbers behind the decimal


so it changes the answer but 1.06.06


well 16


bc you round


Yes, I got.07


Round 0.069 up


so 17?


No, how do you get 17?


0.069 rounds up to 0.07, not 0.17


I think that's what you did on the last problem which is why I didn't understand how you got .27 from .178 or whatever.


OK, you seem to have a good understanding of how to solve these. I need to quit if you're set.


i thought u round the 0


No, you round only the last digit you're going to *keep*


so if you are going to keep 2 decimal points, you only round the last one.


ohh ok


I have one more to do


THink about it ... 6.9 cents is almost 7, but not almost 17


OK, I'll have to let you do that one on your own.


Try working it out and if you have problem you can try again. If it's this kind of thing, you can say "Algebra" instead of stats and should get a quick reply.


Ok


See you next time. Have a good day! :-)


Hello Michael


Hey Sarah!


What do you need help with today?


Okay so i wanted to ask u do you know about the


SHSAT?


No i'm not sure what it is


Will u help me with some questions


Yeah I can help out


Okay gimme one min lemme pull it out on the board


Can you see that?


Yep I can see it


Okay i need help solving and understanding it


Okay I see


let me first tell u what i know


Okay


of this prob


so


I know that 10/13= 0.769230


i also know that


7 is the first digt in the repating patern


and yea thats all


okay


so do you know what the line above the repeating decimal is


like what it means


Repeating numbers


meaning


Yep it's repeating


So let me draw it out like 3 times real quick


alr


Let me type it uot


ok


all good


So basically kind of like that


And goes on forever


yes


So basically looking at this, do you see how it's the same 6 digits that repeat?


yea


So each repetition of the pattern is 6 digits


6 is even


391 isnt


they added one more number


so i think the answer is 7?


Yes the answer is seven


Yay


but not exactly because of it being even or odd


then what?


Basically, every 6 digits the pattern repeats


So if you divide/6


The remainder is 1


So that means it's the 1st digit of the new patter


yeah ok


Okay got it


wanna do another one?


if thats fine


Yeah I have a good amount of time


alr


great!


see it?


numbers 63 - 65?


okay yeah I see them


wait


yea 63-65


sorry


Yep I see all of them


No worries


so


i wanted to ask u


can i use my mic


if thats fine with you


I won't be able to hear you


Since I can't use my audio


oh okay


all good


let me tell u what i know


He has goat


550 goats


which is 10% more than Mr. Thompson


percent is out of 100


I think the operation is multiplying


Yep, we have to multiply something


Do you know what we multiply?


um


550/x = 10/100?


butterfly medtod


not quite


Let me go over it


aw


alr


So do you know how to convert between percent and decimal


100% = 1

150% = 1.5

20% = 0.2


yea


Okay great


So it says Mr. Thompson has 10% more goats than Mr. Davis


meaning he has 110% of Mr. Davis's goats


Do you understand how I got 110%


okay


So basically do you understand how Mr. Thompson has 100% of his own goats


Like if I have 5 goats, that means I have 100% of 5 goats


a complete


of somehting


so Mr. Thompson has 10% more than that, so he has 10% more 100%


So he has 110%


ohhh


yesss


got it


So let's say the number of goats Mr. Davis has is represnted by x


That means the number of goats Mr. Thompson has, which is 550, is equal to 1.1 * x


since I converted 110% of x to decimal


ok


so since 550 = 1.1x, what does x equal?


well


divide it


to find x


yep


Yep, that's what x equals


YES


got


it


So that's how many goats Mr. Davis has


But now what is the question asking


how many more


So then what is our answer


Exactly. That's the right answer!


YAY


Alright


Sarah i have to go but thank you for all your help


you were really helpful


Okay no problem, happy to help :)


Have a good day


U too!


Bye! :)


you have two function machines. In what order should you stack the machines, and both machines have had their effect, the second machine's output is -64? Show all work to prove the correct answer. Write the order of functions


Hello


hey!!


Is that the question that u need help with?


yes please, if possible i would like to do the probelm previously mentioned please


So the two functions on the board are the 'function machines'?


But does the question say what the x-value is? Because if we want to stack those functions so that the output is -64, we'll need a fixed x-value so that we can calculate


mhm\


See if u have any other info


i wish mate but that's all i've got


I'm really sorry the question seems impossible to solve


It's a bit nonsense rn


If you can, reach out to the person who made the question


no that's okay i understand. i don't rly have anyone to go to abt this but like i'm honestly kinda done with the teacher anyways to duck it yk


Yeah.. I'm sorry I can't help you


Bye


wait


Hi


Determine the domain of (f/g)(x) when f(x) = -1/x and g(x) = sqrt3x-9


I'm so sorry I'm getting a call. Give me like 2 minutes


That’s okay. Take your time.


Okay sorry I'm back


Okay


For the problem you wrote above, you first determine the domain of f(x). Since = -1/x, we can predict that x cannot equal 0. Do you know how to write an interval notation?


No


For example, Interval notations look like this: (-6, x) U (x, 9). Are you familiar with this?


It’s okay if you don’t


Yes. X is usually infinite or -, right?


Sorry, I meant infinite for the x.


Oh haha, it's okay


Because f(x) is -1/x, x cannot be 0.


Do you understand?


Not really


Division by 0 means undefined.


So it would look like this (−∞, 0)∪(0, ∞)


Right


We next determine the domain for g(x).


Right. How do we do that


This equals square root of  3x-9, as stated in the problem. For it to be a real number, it must be non-negative. Do you understand?


Yes


This is 3x-9 is greater or equal to 0. Can you solve for x?


Divide by 3 on both sides?


Yes, but commonly, 9 should be added to the other side.


I meant 9 should be added to the other side first


then divide it by three


this would result in…?


No, the greater or equal sign does not change.


And when you add 9 to the other side, isolating the x, it would mean a positive.


Like this:


3x-9 greater or equal sign 0 (add 9 to other side)


3x greater or equal sign 9


(Divide 3)


X greater or equal sign to 3


do you understand?


This would mean
[3,∞). Do you understand?


Bracket or [ means that the number is greater or equal


Why the infinite sign for that number instead of 3?


Because in a square root, the number must be positive or 0, unless there is no solution


we see that the x can be 3 or greater


3(3)-9=0. This works in a square root


Any number less than 3 doesn’t work


Got it


Next question. (F+g)(X) When f(x) = x^3 - 2x^2 +1 and g(x) = 4x^3 - 5x +7


We haven’t solved the first one since we are trying to determine domain of (f/g)x.


Oh I thought that was it


We got the domain for f(x) and g(x)


Okay


The denominator g(x) must not be zero, so g(x) = square root of 3x -9 ≠ 0


Can you solve square rt of 3x-9 ≠ 0?


I'm not sure


Do you know how to isolate the x? Pretend ≠ is a =.


First, you get rid of the square root by using  power of 2 on both sides.


Divide 3


You can’t divide three if there’s a square root there. When you use the power of 2, the 0 remains 0. This would result in 3x-9≠0.


You wanted to divide 3, this would mean that the constant needs to be moved


Can you solve the rest?


Remember that you are solving for the x. You can add 3 to the other side to isolate it.


This means x≠3. Do you understand?


Yes


From these domains (x ≠ 0, x greater or equal to 3, and x ≠ 3), you can predict that x is greater than 3. Do you understand?


So the domain, or solution is x is greater than 3.


Do you know how to write that in this form:
( , )?


No


Greater than 3 in interval notation.


Alright. What do I do?


You write greater than 3 in interval notation. Am I confusing you?


Kinda so it would be 3, infinity?


This is the answer. Do you understand the process?


Yes I think


I know you have more questions, but I have to go. You can make another request anytime.


Okay thank you


You’re welcome! Have a nice day!


hello


hey


how can i upload the picture?


they are unfortunately not working


they are trying to fix i


it


sorry about that


they are down for system improvements


if you want you can type it in the chat and write the equations on the board


okayy i wroteit on the board


ok


what dpes it mean by parent function


it means the original function with out any transformations


so it would be g(x)=IxI


do you know how to graph that?


like this?


yes that's perfect


good job


okay good


Maya


next we have to graph it after the transformation so we have to move it down 1


so the vertex is (0,-1)


then the slope of 1 stays the same


wait why wouldnt it be a y


what do you mean?


i mean x


like why wouldnt my poi8nt jut move to the left one


if it was inside the | | then you would move left or right


but since its outside the absolute value it would move up or down


and since its -1 we would move down


ohhh


okay i get it


because its a (h,k)?


yess


okay


can we do another one?


yes sure


I cleared the board for you


okay thank you lol


this is the same graph the parent function


and the actual function


ok


oh what transformation did we do for the last one?


we did down 1


ok for this one you try it


what. is the parent function?


does the transformation have a name


horizontal shift I think


for the last one


you graphed this one correct


good job


is this right


yes


does the -3 do anything


like distributive?


that would make the graph more narrow


like that


wait you forgot to shift it left


yeah i drew it a bit off center


wait


so would the actual function be just 0,3? facing down?


it would be (-3,0) and facing down


because we move left 3 units


since its in the () it effects the x values


but isnt the 3 positive


yea you always take the negative


so always switch the signs


like the opposite of what's in th eparanthesis


okay


so i have to switch it to k,h?


don't worry about (h,k) because that's going to confuse you


if the number is in the absolute value or parantheis with the x


you always move the opposite way of the sign


since its +3 you would make it -3 to the opposite and move left 3 units


what if the -3 was a different number? is it just that the parenthesis just that matter?


the parenthesis would matter about moving left and right


the -3 infront is how wide or narrow the graph is


and any number after the parenthesis would mean a change in up and down


ohhh okay


we can try another one to make you understand it better


yes


quadratic?


yes quadratic would be better but if its absolute value we can do it too


okay ill take a rando one


parent function always starts at 0?


or i men the origin


yes it starts at the vertex


I meant origin too


my bad


this is for the vertex


so redraw the graph where the vertex is at -1,0


okay i think i get this now


i took this from the question i wanna work on rn


yea this is correct


its says function g is a translation 4 units right and 6 units down followed by a reflection of y axis


graph both f and g


oh ok


sorry for the mess


its ok


I think it looks right Im just confused about the reflection of y axis


oh its correct


i did the translation i think thats what its call first then i just copied it on the other side


yea then you did it correct


I was looking at the wrong graph


good job


you got it


yayy


do you want to try one last one


yes


hang on lemme write all this down


if its ok with you im going to take a 10 minute break


I just need to quickly take a shower


is that ok


since you also need to write it down


yeah its okay!


thank you


hey I am back


hellooo


thank you for letting me leave for 10 mins


yeah no problem! off topic but is every tutor also students?


not all


I am a student


but some might be teachers or adults that just want to help students


ohhh okay i was curious thank you


no problem


okay for this one i have to find the vertex first right


yes


will it always be same as h,k? i think 4 is the y


yea


I think its (0,4)


does the -3x have nothing to do with it?


that would change the graph overall later


okay


wait what


wait


no the -3 is the slope


how can i reflect if on the line


oh


so is it


no -3/1


why?


because its only -3x


so -3/1


so -3,4


you graphed it wrong


let me graph it


wait where did you get all these points from


that's the graph but you need to reflect it


I used the y intercept (0,4


then used rise 3 and left 1


which is the slope


ohhh


okay


makes sense


how can you reflect this if its on the axis?


just flip th epoints


oh wait im supposed to write a function that represents this


the transformations


so do i just flip the signs?


yes


do you understand it?


ok im sorry I have to go now


thanks for helping me so late i understand this a lot better


Liam!


I hope you learned this unit


your welcome


have a goodnight yea i did


good night


bye


Hi Alex, How can I help today!


Hi! I am working on an assignment about completeing the square I think its called and was hoping to get some help on a few questions


Of course, just upload them and we can work them together


Mr. Davis, you got it! Just one second please!


No problem, take your time


Also I think I remember you helping me in a session a couple weeks ago


Oh really, hopefully I was helpful


Yeah, you were! That's why I favorited you.


Mr. Davis, can you see it?


Yes I can see it


Mr. Davis dokie!


so do you know where to start, or you need some guidance


Is the first step to find a common factor between the first and second term?


yes


oKIE DOKE THANKS! its is 8 right?


Oopsie sorry for the capitals


yes it is


alrighty than you


could we facotr 8 out of the expression too to give us 8(x^2 - 18x +108)?


hmmm


I wouldn't personally, but lemme see what happens when you do


because I was thinking of doing it without factoring the last term


ok yea it can still work


i just tried it


okay thank you


so do that?


yes whichever way you feel is better for you


both ways work


what is the other way to do it?


you could not factor the common term


and then how do we get the answer from there because I would like to learn more ways to solve


okay can I show both ways to do it on the board then?


and you can ask questions from either one?


Yep! Do you want me to erase my work?


yes sure!


Mr. Davis done!


how did you do the secondway?


this way on the screen?


yeah where you got 8(x-9)^2 + 216


do you want me to explain from step 1 to the final?


yes please if you don't mind


ok sure, I dont mind!


ok first we factor everything with the factor of 8


then what I did, I didn't really show the whole step so let me write it on the board, I basically added a 0


yes


as you can see, there is a -81 and +81


wait why did you add all that stuff?


the one i just wrote?


yeah


ok so I added all this stuff, basically the only different is that I added a :-81" and a "+81"


so I got this by dividing the -18 by 2


then squaring it


okay so when did the second 81 come from?


sorry I am not trying to question you I am just very confused and want to make sure I understand it all


thats fine, always ask when you are confused, I want you to understand:) so dont be afraid to bombard me with questions


thanks, I will!


ok so the second 81 came because I wanted to balance out the equation


I cant just add random numbers


so I added two numbers that would cancel each other out


81 and -81 is 0


oh so you can do that in any equation like this?


yes you can add numbers but they have to equal to 0


okay and how did you know you had to do that for this equation?


I know I had to that for this question because this question is asking specifically for vertex form, I know this because it says to make an expression that can show the miniumum


vertex form is y = a(x-h)^2 + k


oh okay so in any equation that ask for vertex form you have to add two numbers that cancle eqach other out to give you 0


yes when you try to get it from standard to vertex, you have to do it this way


okay I think I get it now just one more question, why did you add 81 how did you know to add that specific number


ok great question


so our ultimate goal is to have it so that it can have somekind of form of (x-a)^2


so this a value has to be the 1/2 value of the coeffeciant of the 2nd term which in this case is -18x


huh?


let me explain a different way


yes please, sorry


look at the board because im gonna underline some stuff


Mr. Davis


its always this coefficient


that one that has a x


okay


-18 is the coeff so divide by 2


now we know that it has to factor to (x-9)^2


and when we expand this (x-9)^2


it becomes x^2 - 18x + 81


okay so you divide the coeeficent by two then square that and that is how you got 81?


so thats why we need the -81 to cancel it out


okay I think I get it now, thank you for answering all my questions


ok no problem, just let me know if you dont get anything and I am more than happy to go over it


okay thank you so now I understand how you got 8(x^2 - 18x + 108) but how did you get 8(x-9)^2 + 216? Did you do the thing where you multiply the first term by the last terms then find two numbers that eqaul the number you got when multiplied but equal the middle term when added? The place those nubers in place of the middle terms then group and factor?


ok sort of


ok


so we left of and we got 8(x^2-18x+81-81+108), we factor the "x^2-18x+81 inside this paranthesis to (x-9)^2 which now leaves us with 8((x-9)^2 -81 + 108)   the -81 and 108 add together and get 27. Once we are here we can distruvute just the last term with 8 to the remaining terms and keep the first term which in this case is (x-9)^2 undistributed


so the final solution would be 8(x-9)^2 + (8*27  or  "216")


oh okay, I guess that makes sense


So the answer is D?


yes!


okay, thank you! Do you think you could please help me with some more questions?


yes of course


thanks! I will put it up now


Mr. Davis doke artichoke, can you see it?


If I need to enlarge the image just let me know


its fine I can see it


ok this is pretty similar to that last question we did


the first step is we can factor out 2 right?


yes


from just the first two terms?


all the terms like we did last time


ok


like that?


okay the next step is to divide 6x by two then square right?


so that gives us 9


and then do we also add -9?


yes correct to balance it out


okay :)


wait you messed up somewhere


okay now do we distribute 2?


oh


the first two steps are right


now factor the x^2+6x+9 into (x+3)^2


wait but what about the 9 - 9 - 7?


like this


its just stays within the paranthesis


but how did you get to that if we still have the -7 and the -9?


cause when we add the -9 doesn't it cancle out the 9 leaving just 7?


we add the 9 for the sole purpose of factoring


we just have the -9 to make sure we are not doing illegal math


all math should be illegal


without the +9 we cant factor x^2+6x into (x+3)^2


okay


what happened to 7? can you please show me all the step you did to get 2(x^2 + 6x + 9 + 9 -9 - 7) to 2((X+3)^2)?


no the -7 is still here look


and the -9 is still there too


Where?


i think the board got cut off


oh


do you see it now?


yeah


so you just turned x^2 + 6X INTO X+3^2 by dividing by two?


no we divide by 2 to figure out what to factor the numbers into


in this case we now it has to be (X+3)^2


okay so what did you do to get x+3 ^2 from x^2 + 6x


i got the (x+3)^2 from x^2+6x+9


when you factor x^2+6x+9


it factors into (x+3)^2


thats why we needed the 9 and -9


oh so did you multiply 9 and x^2 find the 3 and 3 were the two numbers to equal that when multipled but 6 when added and then use those two to group and factor and find that?


yes i believe that is right


okay thank you now I get it


so now do wee multiply by 2?


yes but for add the -9 and -7


then distrubute to the sum of those numbers only


okay so 2 times -16 is -32


so then it seems like the answer would be C but how do we get 32 to be positive?


because we have everything on one side


and we add +32 on both sides


oh yeah we have to add to both sides to cancle it out and bring to the other side


okay now I get it, thank you for all of your patience!


no problem, I have to go now so have a great day!


hello


Hi


How may I help you?


I need help with long division


OK.  Do you have a problem that you are working on?


No


Are you using a 1 digit divisor or a 2 digit divisor?


I’ve used both before


Do you want to try the one on the board?


Sure but I don’t remember how


OK, how many times does 6 go into 4?


so we put a 0 above the 4


now we move on and ask: how many times can 6 go into 45?


Right. Do you remember what we do now?


How many times 6 can go into 6


No, now we multiply the 7 we just found times the divisor, which is 6


so what is 7*6?


we now subtract 45 -42


Now we bring down the next digit, which is a 6


36 is the new number we are working with.


So we ask, how many times does 6 go into 36?


6 times


Right. What do you think we do next?


Right, then we bring down the next digit, which is 7


Ok


so 7 is our new number to work on.


how many times does 6 go into 7?


What should be do next?


Every time you put a new number up top (the quotient), you multiply it times the divisor


so it's 1 times 6


so the answer 761 with a remainder of 1


Okay


Thank you


you are welcome


are you all set then?


Yes I just wanted to try one problem


OK.


have a good day!


You too


bye


i need help with congruent triangles


Hi!


hi


what specifically about congruent triangles?


i need help understanding the proofs and how to find each one


okay!


do you have a specific question


that we can work on?


no not right now


ok let me find one give me a quick second


ok


i just want to know how to figure out if a triangle is sss, asa, aas, sas, or hl


Ohhhhh


ok so congruency


yes


ok can you see the triangle drawn?


ok so this triangle is basically two right triangles merged together


so in both triangles there is a right angle!


and that right angle is in between two congruent sides


and you know they are congruent from the line markings


the two circled is 1


and then the sqiggle in the middle is another


so these right triangles are congruent by sas congruency theorum


and to set up a proof of this we would say that it is given that they have a shared angle


and it is given that they have two shared sides


so therefore it is congruent by side-angle-side congruency theorem


do you need me to break that down more?


yes please


ok!


let me give another problem that might b easier


ok do you see this drawing?


yes


ok perfect


so as we can see we have 3 triangles


triangle BDC


triangle BAD


and triangle CAD


so in a proof we would make a chart like this


and our first step is realizing that triangle BDC is an isosceles triangle and therefore A is the mid point of CB


i have a question


yes!


is it possible that we can continue this later i have to leave my house and i can't continue right now


Yes of course


would i get you or someone else ?


I'm not sure


ok


you might get some one else but thats ok!


ok thank you


Great job in this session! I can see that you got a better understanding of this!


football player.


person


Hey


Hello, Alex
Let's do this together, do we need to solve the question on the top?


Looks like you did all the steps, great job


The answer is right?


let me check


This project is due tomorrow and it is a test grade.


I’m so worried


The ones in the boxes are my answers.


got it, it seems almost right, just write the p in the quetion as q also for the second line, you might have mistaken the q as a p


the answer is correct, great job!


Thank you.


is that it, do you need help with anything else?


or confirming any other answers?


I am confident in the rest of my work. Thank you for the help!


no problem, have a great day and good luck for your project!


Thank you!


hello


Hello


I need help with dividing numbers in scientific notation


ok


can you show me your problem?


Can you hear me


I can read what you are saying


Are you able to use voice?


sorry, no


Ohh


I don’t understand much without voice


You are welcome to try a new session with a different tutor.


Yes please I’m so sorry


No problem


bye


Bye


I need help solving problems I got wrong, to help my study for a retake quiz


Hello how is it going


Sure


How can I help with that?


Hi I’d like you to help me solve the problems


Please put them on the board


The function is defined as g(x)=(x^2+1)^3 find the slope of the tangent line to the graph of g(x) at x=1


Alright then


Our first step is to find the derivative of g(x)


Since the derivative is the slope of the tangent line at any given point of a function


To find the derivative of g(x), we use the chain rule; outer function * inner function. I'll show on the board.


g'(x) = 6x*(x^2+1)^2


Are you there?


Yeah


I solved that far but after that I got stuck


Okay now


We just plug in 1 into g'(x)


And the answer to that is the slope at x = 1


g'(1) = 24


Ok I just got that


Nice


Next it says find the equation of the tangent line to the graph of g(x) at x=1


Okay


Well we already have one component


The slope at x = 1; 24


And we have the x-coordinate; 1


Now we need to find the y-coordinate


To do this, we plug in 1 for x into g(x)


g(1) = (1^2+1)^3


g(1) = 2^3


g(1) = 8


So, the equation is:


Ok that’s what I got


Cool


And it makes sense using the point-slope form


Next it says determine the points if any at which the graph of g(x) has a horizontal tangent


Alright


g(x) has a horizontal tangent when g'(x) = 0


We already know g'(x)


g'(x) = 6x(x^2+1)^2


To solve for any horizontal tangents, we do the following:


6x(x^2+1)^2 = 0


x = 0 using zero product property


So, g(x) has a horizontal tangent when x = 0


I’m confused


Which part?


After I set it to 0 how do I find the points


Well using Algebra


(6x) * ((x^2+1)^2) = 0


6x = 0


x = 0


The other factor gives us the square root of -1, which is imaginary


When set equal to zero


So, x = 0 is the only point where there is a horizontal tangent


Isn’t 2 one of the points


How come?


It can't be


g'(2) = 300


Or isn’t one 1


g'(1) = 24


We proved this earlier remember


Yeah so wouldn’t the point be 1 and 0


OH


I see what you mean...


Apologies


No, it would be (0, 1)


You have me confused can you please explain why they are correct


Okay


A horizontal tangent means the derivative at a given point is equal to zero, correct?


Meaning g'(x) = 0 with x being the given point


Can we agree on this?


Yes


Okay great


Now, we've already found what g'(x) is


g'(x) = 6x * (x^2+1)^2


Yes?


Great


Now, to find any horizontal tangents, we do the following (set g'(x) = 0):


6x * (x^2+1)^2 = 0


Now, we have the product of two factors


If either one of the factors is equal to zero, we know the whole product must equal 0


So, we set both factors equal to 0


6x = 0, (x^2+1)^2 = 0


Doing the Algebra, we get x = 0


So for that type of problem is one of the points always 0


Not always


It just happens to be for this problem :)


Now that x = 0, to find the point, we plug it back into g(x). Basically we want to find g(0) for the y-coordinate


Doing this, we get g(0) = 1


So, the point where g(x) has a horizontal tangent is (0, 1).


That made sense for me; how about you?


I want to make sure you're able to understand it as well :)


Yeah I think so


Alright


Apologies, but I have to go now


You can find a new coach once I end the session though!


Bye!


Hi Liam! What do you need help with today?


1 step questions


Sure! Can you take a picture of the problem and upload onto the whiteboard?


Sure but can you make some and help me with them I don’t understand at all


Of course!


But do you first have any specific problems?


Thank you so much I don’t understand at all and I’m taking the SAT in October


Oh! Good luck for that! I'm sure you're going to do great!


Ok, so can you give me an example problem so that I know what to make?


-5c>15 and 75x>125 like these


so solving it like this?


Don't worry, i'll explain it to you if you need it


Yes please


Ok, so to get rid of the -5, you have to divide by -5 on both sides


and when dividing by a negative number, you flip the sign


Do you understand, should I make you a practice problem?


Make me practice please


Sure!


do you think you could solve this?


Yes I dived by 10 right first?


Correct!


Do you know what to do now?


Do I change the sign or no since it positive?


No, you don't change the sign if you are dividing by a positive number


100 divided by 10 is 10 and ok


Good job!


That's correct!


Should I make another one?


Thank you can you give me one like -5c>15 please that where I have trouble as well


Try this!


Ok


Do you divide by -14?


Yes!


28 divide by -14 is -2


Yes...


And we change the sign right?


CORRECT!


good job!!!


Thank you


Should we do more?


Yes please do this one please Professor Anya


Ok, so remember, you are trying to get x by itself on one side.


So you can add 6 on both sides


Yes so would I do +6?


Do you want to do more practice problems?


Like this one?


It would be x<9 and yes


Try this one!


-15 on both sides


ok..


Is it 9?


Not quite. What's 14-15?


Correct!


Good job!


Do you understand?


Yes and can you help me with 4x<12


Sure!