ill reffresh too


uh I don't think that's needd


and then put it back


I saw the question already, and you just need to muliply all 3 numbers together then divide by 3


kk


answer 3


here it is


good!


looks right


ok next one


i know u add with this one but idk which numbers to add


this is a picewise rectangular prism


okay


i want to get this done before 12 am cst


I sitll don't see anythign on the whitebaord


refresh


its my fault let me refresh


oh I see it now


okay let's do each ractangle seperately, starting with the left one


do i add 8,3, nd 6?


we're finding volume, so we gotta multiply


oh ok


multiply everything?


yes


i dont think we do that


the explanation for it didnt show that


are you sure? for the volume>


u multiply sep u dont multiply it altogether


you do 3 * 8 * 6


ok


holdonn


new one


okay


multiply 8,8, and 4 or?


yep, those 3 for the left rectangle


kk


thats 256


okay good


5x5 is 25


thats 281


oh, but that's only the area,


that still has a width of 8


so it's 5 * 5 * 8


ohhh


so 456 cm?


yep yep


k next one


can u see it


yep


hello


hi


ues the top is that value


what about the bottom


right?


or wrong


for the next, not quite


identify the height, legnth, and width


ok so its 5x3 x something


5 and 3 is correct tho?


that's the top rectanglr


top I 5 * 3 * 8


what about the bottom?


i did the bottom


which 168


okay good, yes that's the bottom


brb


okay


hey again i think


Yeah lol


How can I help?


geo


i think again


what was last time


Im pretty sure we did a skirt and sweater problem last time


yeah lol


still havn't got that


Oh, want me to help you finish that?


nah i need help to see if im doing my geomatry right


Alright, any particular problem?


no not really just my last attempt if i did i have to restart


ill put down ones i did


Sounds good


thats the equation


i put


So how'd you solve it?


ill put it here


had to find the formula: Area = (base × height) ÷ 2
2. substitute your values
3. multiply base times height
4. divide by 2
5. include the square units


the other coach said it was right


They said 14 was right?


I'm sorry unless I'm missing something I don't think so


brb


But (base x height)/2 is right


gotta bring grocieries


Alright, let me know when you're back


do u mind waitin like an 1hr?


hm I guess I can just be afk


ok thxs


np


1 hour or 2


oh alright


So maybe just start a new session then


and I'll try to pick it up


do you remember which tutor taught you how to do this problem?


no


okay, no worries


See you! :)


Hello


Hi, is it okey if we can talk out loud in the mic?


ok


How may I help you?


double digit.


With multiplication with double digits.


Mm


Do you have a problem that you're working on?


Um, 6 times.


16 times 2.


OK, go ahead and write it on the board.


I did.


OK, you wanna try that?


Yeah.


Do you know how to do it?


Yeah


OK, go ahead.


Ah


I don't know, actually.


OK, well, first,


We work with the two.


What is 2 x 6?


Hello


Um


Yes


So you write down the 2.


You write down the 2.


Not the one, just the 2.


He puts the two down below and you put the one.


Up here


Now you multiply.


2 x 1.


Oh.


was


The one that you carried.


So 2.


What is 2 x 1?


One


Now, 2 x 1.


Till


Yes, and then you add this one up here.


So that's 3, right?


Yeah


You put that down here.


And that's the answer.


Oh


And my name is actually Maria.


Nella? Oh, OK.


Why does it say Maria?


No, it just like came.


Oh, OK.


Do you want to try another example?


Yeah.


Do you have an example?


that.


OK, write it on the board.


OK, what, what do we do first, do you think?


OK


All right. First we multiply the 6.


Times the 7.


P.


What is 6 x 7?


Um, I need help with that.


That's.


Oh, all right. Have you learned the multiplication table?


Kind of.


OK. 6 x 7.


It is 42.


So what do we write?


Below the 6, what do we put here?


P


Yes, go ahead and put a 2 there.


And what do we do with the 4?


Put it on top of the 2 over there.


Yeah.


That's right.


Can you do that? Yeah, all right.


Now what do you think we do next?


Add 4 times 2.


Yeah


First, we, we, we're still working with the 6, right? We multiply 6 times 2.


Oh.


With 6 x 2.


You know, 6 times 2.


Well


And then we add


That 4 appeared.


It's 12 + 4.


Mm.


Yes, and you can write that 16 there.


There you go.


That's big number.


Yeah.


It would take a long time to count all those numbers.


My sister also does this.


Your sister does this?


How old are you?


What grade are you in?


Fourth


Oh


What grade is your sister in?


Eighth


one.


Eighth grade, OK.


I thought you were in Fifth grade.


Yeah, there was no Fifth grade option, so my sister told me to


Um, put Fifth grade.


OK, that's OK.


Did you want to try another one?


Yeah.


Do you have one you wanna do, or?


Yeah, I have one.


OK


What do we do first?


you say.


Um,


Do 2 x 5.


Yes, what's, what's 5 times or 5 times 2.


10, OK.


5 times 2 equals 10.


OK, that's, you put the 0 there.


What do you do with the one?


Put it up.


Huh.


Above the other one?


Yeah, you put it up above.


OK. Now what do we do next?


Do 5 times 1.


Yes


Exactly.


5 x 1 is 5.


But what about that one way up there?


We had it.


Yeah.


So it's 6.


That's right.


Very good.


That's it.


Sorry about the fat 6.


That's OK. That's right. That's exactly right.


Hm


I have another one.


OK.


Go ahead and give it a try.


0 times 7 is 0.


All right, that's right.


And 7 times 5 is


Right, very good.


Excellent.


Thanks.


I think you're learning this.


Yeah


Mm


Did you have another one?


Yeah.


We can go back up to the top.


Yeah, there's like um a space on the bottom of the first one that we wrote.


All right, there's not too much space there.


All right, you can put it wherever you want.


I'm putting it right now.


Yes, I see.


OK, go ahead and give this a try.


12, 3 times for 12.


It is


And


4 times 1.


is 4.


4 + 1 is 5.


That's it.


I think we should erase some so we have more space.


OK.


I will erase the whole board.


done.


Let's start from the top.


6 times 5 is


Whoops, I don't see it.


Wait a minute.


All in the top.


Hello?


Yeah.


I don't see it.


Oh


Sometimes that happens.


So this is


I'll write it.


Can you try writing it again?


erase it and write it again.


I'm gonna write it on the top now.


OK.


Do you see it now?


No


Has 16.


Do you see where I wrote 16.


No.


Mm


Maybe something happened to the, maybe the board isn't working.


Yeah.


Oh yeah, I see where you wrote the 16.


Where is your 16?


on the other side.


The other side.


Huh


Do you see it?


I don't see it.


Oh.


Then I'll just write it and decide that you have yours.


OK.


It's gonna be on the bottom.


Uh


I'm riding it on the bottom.


All right, I see it.


You want to go outside.


Mm


Hold on. My dog wants to go outside.


Hm.


OK, go ahead.


6 times 5 is


Yes, very good.


Free, I mean, I mean 5 times 1 is 5.


Right?


And 5 + 3 is 8.


Right.


And the answer is 80.


That's right.


You're getting good at this.


Yeah, I didn't know how to do it in this way.


Oh, did you do it in a different way?


Yeah, I just like do it like normally in a sentence.


Uh


All right, well,


I learned something new today.


That's always a great thing.


Mm


Did you have another one?


Yeah. I'll do it in like the middle.


OK.


It.


What could you write one?


And I could solve that one.


Uh, sure.


I'll put it above where yours was.


Oops


Yeah


Do you see it?


Hm


3 times.


6 and


Right.


6 times 8 is


OK


Not quite.


I don't know.


Let's see.


What is 6 times 2.


All right.


What is 6 times 1.


That's 6.


So what is 6 x 2.


No.


Well.


Mm.


Oh,


I got confused.


What is 6 x 3.


It's one more 6.


Hm


18, right?


What is 6 x 4?


Yeah


6 times 5.


It is.


With a 6 x 6.


What is 6 x 7?


Oh, and now 6 times 8, what is 6 x 8?


Oh


That's what we want, right?


Yeah.


Mm


All right, so what's uh the answer?


48 plus 11 is 49.


Right.


So 40098 is the answer.


Yes


Let's do another one.


Oh.


I.


Are you writing it?


I don't see it.


Oh, I'm not writing it.


Oh, OK.


No.


Alright, 15, right?


Yeah, after this one,


Can't we be done cause someone's in my house right now.


Oh, OK, sure.


After this one.


Of course.


15 times mm.


Oh


15 times.


5 times 2 is 10.


2 times 1 is


To


2 + 1 is 3.


There you go.


Yeah.


Very good.


Bye.


All right, you did great.


Thanks.


Have a great day.


You too.


Hello!


hi


how are you?


im good


what question do you have?


i thought i clicked homework assignment


thats my fault


can you put it on the board?


yes


i am on #7


I completed the first page yesterday with another tutor


ok


can you try number 7?


i started it but didnt know how to finish it


thats as far as i got but I didnt know how to finish it


thats a great start


can you try to factor a^2 +9a-22?


great job!


now can you try to cancel like terms


do you understand what im asking?


kind of but i think i got confused


for example, since there's an a in the numerator and an a^3 in the denominator, you can cancel the a in the numerator and make the a^3 in the denominator a^2


just like that


ohh


so can you do that for some other terms?


a +11


and what else?


and what does the denominator become?


yes


and thats your answer


oh ok


so lets move on to #8?


im very confused on #8


okay, so lets break it down


ok


can you try solving it from here?


i think so


actually im not sure


first start by factoring all of them


i can do that


omg


so what do you do after this?


i cant see the whole thing


better?


so what the next step?


umm i dont know


ive never dealt with one of these questions before


so now we move the 5(x-2)(x+2) to the top


because the denominator of the denominator is the numerator


ohhh


and what is the last step?


get rid of similar terms


yes


are x+2^2 and x-2^2 the same/?


no


can you expand (x+2)^2 and (x-2)^2?


do i foil them?


i see


you got (x+2)^2 correct, but you made a minor error for (x-2)^3


whats -2 * -2?


so x^2 + 4x + 4 and x^2 - 4x +4 are different


I'm so sorry I have to go, thank you so much for your help!!


hello!


Hello!


What do you need help with today?


I have an assignment about simplifying rational expressions for my algebra 2 / trigonometry classes and I dont understand this topic at all


there's 2 pages but i've completed #1


question #1


Okay! I can help you work through the others!


Do you have a specific question you want to work through first?


I tried to factor out the gcf but i couldnt figure it out


Okay, so first I recommend looking at the numbers first-- is there a number that goes into both 15 and 27?


yes!


So basically, we can divide both the top and bottom by 3 to simplify the number part (since 3/3 =1)


do i remove the 3 from the denominator too


now we can look at the letters-- specifically the exponents


Yes


ok


We don't want to remove the ratio; -15/27 , but if we divide both the top and the bottom by 3 the ratio will stay the same


do i remove the -3 too?


Wait! I didn't see that!


I'm sorry I messed up


its ok lol


We do need to find the common term for the denominator specifically


which, for the numbers, is still three


got it


okay, for the "a" terms, we want to find the highest exponent value that fits into both the green side and the blue side


a^5 and a^2 yes


since a^2 is the smallest that is what we can factor out


what is the smallest exponent for b and c?


Yes! The b^1 is the smallest. the smallest exponent for c will be c^2


oh


i forgot the 2


It's okay! Now we are going to "factor" out the denominator


We need to take into account all of the terms left out of 3a^2 b c^2


so this is where we divide everything by the gcf


ok


in the blue section, we divide 27 by 3, a^3 by a^2 and c^2 by c^2


yes


Did you solve that part?


so it becomes 9a^3-bc?


YES!


now we have the denominator


and top is -5a^5bc^2?


Also yes!


Because you divide by the gcf!


i think i did it!


after that you subtract the exponents


yes!


I think you did do it!


Wait! Actually you can't subtract the exponents here. There is this weird rule


oh


Any time there is addition or subtraction in the numerator or demominator, you cannot reduce using the gcf


if the denominator didn't have a subtraction sign, you would be completely right!


ohh


so is this the answer or is there more?


I think what i wrote in black would be the answer to 2


Chloe!!


yay*


i got that


Do you want to both try 3 now?


yes


i think i got the denominator


Yay! Do you want to tell me what it is?


Really close! I'm going to teach you my favorite trick


ok!


When ever you see two squared terms being subtracted (x^2 and 81) the formula I'm going to write applies


ok


It is equal to the unsquared squared terms subtracted together multiplied them added together


Does that make any sense?


i forgot they cannot both be negative


because its a negative number


i just realizedx


realized*


That is actually a really common mistake that is easy to make-- if you ever have time to double check on a test, I recommend that you distribute the factored form out and try to turn it back into the original unfactored form


Have you been taught how to factor the top section?


probably but I just didnt understand, i watched video notes but didnt fully understand


I can show you how I do it! But I do it differently than most people


first, I draw an x


each corner of the x is a place for a number


the left side is for the x^2 and the right will be for the 36


we basically want the numbers to vertically multiply to the coefficient


x^2 will have a coefficient of 1


then, this is where it gets a little complicated, you want to make sure each diagnol number adds up to the middle number


so lets say we try 9 time 4 = 36


mhm


we will multiply 1 times 4  and 9 times 1 together and then add the two productus


so 4+9=13


This technically isn't the right answer though since the middle coeff is -13


To fix this we can make the left 9 and left 4 negative : -9 and -4 multiplied together still equal a positive 36


ok


So if we are happy with this little x, we can look horizontally and find the factored pairs


If we distribute those together, it should be the same as the numerator


Did that make any sense?


so it become x-4/x+9?


Yes! After simplifying the (x-9)!


But did that make sense? It might be hard to follow just drawn out numbers


yes


i actually understand


Do you want to try 4 now? It looks kind of similar


Do you want me to walk you through the denominator again?


yes please


what do you think should go on the left green spots of the x?


2 and 1?


Yes!


Now for the left side, we might have to guess a few times


Do you have two numbers that multiple to -20 that you want to try?


im not sure


Well... 2 times 10=20


4 times 5 =20


i got both of those but neither =3


We can try 4 times 5


Sometimes you have to work on the placement


oh


4 on the top doesn't work, but we can try 5


5*5 works


That does work!


We need to make 5 negative too


yes


so the pair would be (2x-5)(x-4)


nvm- it is x+4


Did that make sense?


Do you have an idea about what the numerator factors to?


Yes!


now you can simplify the (2x-5)s


yes!


yay!


Do you want to try 5? We need to use a slightly different method


Do you have an idea about how to approach this problem?


i might've got it


Okay!


i wasnt sure what to do about the exponents


Yes the numbers cancel! We can simplify the exponents further though


ok!


ohh


thats y not x


i see


Since it is just simple multiplication, we can just combine the terms like that


Now we can simplify the exponents by looking for the gcf-- the smallest exponent that can fit into both


okk


Do you want to give it a shot?


im not sure what to do


Oh sorry!


Well there are two x terms x^2 and x^3


Since x^2 fits into both x^2 and x^3 we can divide both terms by it (when we divide exponents we subtract the numbers


divide by x^2y


maybe


Yes!


so does it just become xy?


no 1/xy


yes it does!


yayy!!


Do you want to try 6 now?


yes


is it 1?


i think i did it


So for this type of equation, you can either multiply both fractions together and then simplify the big fraction or simplify each fraction individually, multiply, and see if there is any more simplification to do


YES YOU DID!


I got 1 too


yay!


Do you want to do page 2 too?


First thing you want to do is rewrite the division sign into multiplication


ok


Any time you divide by a fraction, you basically need to multiply by its reciprical-- swap the numerator and denominator and then multiply


Factoring is like a puzzle-- you have to be strategic each time


Do you recognize what i boxed in pink?


yes!


im not sure what to do


i factored it out but i wasnt sure what to do next


I can try walking you through the problem


Is there any way to show me what you have done right now?


i have (a-11)(a+11)


i have to go eat dinner now! is there any way i would be able to come back later or would i have to have a different tutor


You might get a different tutor, but I will try to select you first


ok, thank you so much for your help!


Also when multiplying fractions you can also simplify diagonally


thank you so much, have a good night if i dont see you again!


Thank you!


You are doing great!


I promise practice will make these sorts of problems easier with time


thank you so much! bye!


heyy


Hi Alex, how can I help?


hiii!!


school is ab to start and im just trying to get myself back into math again


im not sure what i want to deepen my understanding in, so is it okay if you choose a topic


aw okie i applaud you for staying on top of it!


are you about to start 8th grade?


aw thankss


thhh


im Alex


Alex so would you like to go over some stuff of 7th grade?


mhm


Alex


allow me a minute to put together things


take your time


can you see what i wrote on the board


no


o what o no


o no


not at all? i wrote some problems for us to go over


oh now i see it


forgive me my wifi no bueno


no worries!!


do you want to try solving them


o no i forgot this


i'll jump in to help when you're stuck


im stuck


i do not like these question


can you try 1/4?


do i find an equivalent fraction or?


can you give me the value of 1/4 in decimals please


oki


good job


what about %?


good job!


see you know how to do these


lol


try 1/4 + 2/4


oh no


wait


u can do it!!


good job!!


i get confused sometimes


if i add the denominators


you're doing great!


yurrrr


try this one


i dont see


anyting


might have to wait a bit


i wrote 1/2 + 3/8


ohh


can you see now?


no can you see mine?


i wrote it and solved it


i dont T^T


i put 7/8


youre doing so much better than you think see


haha yes


moving on to decimals, 0.3 * 0.4 = ?


oh no


you can do it!!


i believe in you Oakland


you got it!!


yess


0.5 * 0.6 = ?


good job!!


division now, 0.75 / 0.5 = ?


uh oh


oh


nvm


u can do it


see


you got it!


ok so we just did fractions, decimals and percents, you did great! let's refresh on some ratios & proprotions now


i was kinda guessing


okay


all your guesses are correct so it gotta mean something haha


perhapss


if there is any topic you'd like to spend extra time on let me know ok


oki


You read 12 pages in 3 days. How many pages do you read in 5 days?


do you even need me here haha


you're doing amazing!!


4 pages for every 1 dsay


day


thank uuu


yes!! good job!


yess!!


ok now moving on to integers, what is (-5) - (-8) = ?


what are integers again


-1, -2, 0, 1, 2, 3, 4, 5


just whole numbers


ohh


positive and negative whole numbers!


dat is 3


you got it!


cuz 2 negatives


equal


posditiv


positive


yes!!


-3 + 7 = ?


(-4) * 3 = ?


uh


you can do it


cuz


in


12 or -12?


there's one negative sign


aw


-4 * 3 = -12!


wait why


OHHHH nvmmm


u got it?


yess


Alex


-4 * (-3) = ?


i think


yes!!


good job!


(-15) / 5 = ?


sorry im asking the bot something


so i can just have it


also to answer ur question


x + 6 = 12 → x = ?


3 + 4 × 2 = ?


(3 + 4) × 2 = ?


ok last concept is geometry basics


what is the formula for area of a rectangle?


l x w


Perimeter of a rectangle?


2 (l + w)


my plus button is not eorking sorry


youre doing great!


Triangle area?


1/2 x b x h


say i have a triangle with base is 6cm, height is 4cm, what is the area?


uhh


uh


good job!


cm squared


wait


Volume of a rectangular prism?


hm?


nvm


w h l


or l w h


lxwxh


yes!


what is a right angle?


90 degrees


acute?


idk the exact degree


but like


lower than 90 degrees


yes! good job!


obtuse?


higher than 90 degrees


but less than?


its always lower 180 degrees


good job!!


ok so yeah i think we just went over all concepts of 7th grade math!!


thats greattt


perfect timing i have to eat dinner haha


aw yeah go eat!! great job on everything today


thsnks so much thyy ill make sure to favorite you so we can hopefully meet up again


be more confident in yourself Oakland haha


you're doing amazing!!


oki dokii


and thank u


aw thats sweet i'd love to work together again!


:D


have a good night ok


u too


i might get on later


so keep an eye out for me


thank you!! ok i will haha


ciaoo


ciaoo~


hello


I just need help making sure my answer is right


sure, what did you get as your answer?


oh I see, let me check


my answer was y = -4/5x=0


I'm getting a different answer


what did u get


The first step is to find the midpoint


The midpoint is 2,1


I did my mid point is 0


see what I did wrong


the midpoint has to be on the line


on the screen I showed my work for how i found the x and y midpoints


got it


ok great, you see how the point (2,1) is in the middle of that line? That's a good way to check to see we did it right


next step is to find the slope


so we plug in the numbers into the slope formula and we get -2


Let me know if you have any questions with anything


nope that's it


great, any other problems I can help with?


I'm ending the session, feel free to request another one if needed. Have a nice day!


Hello


Hi


How may I help you?


I have a prompt on the board


I already wrote my answer so I just want you to check my answer.


Can you see it on the board?


Hold on


Yes, I see the question.


ok


Tell me when you are ready to see my answer


go ahead


The reciprocal functions are the multiplicative inverses of the original trig functions. When you graph the reciprocal functions, like cosecant (which is the reciprocal of sine), there will be vertical asymptotes at the midline of the original function because 1 divided by 0 is undefined. When x approaches 0 in the original functions, the reciprocal functions are undefined, because 1/0 is undefined. There will be points at the amplitudes of the sine graph, and they will continue upwards or downwards until they reach the asymptotes. The parabolic curves are what the sine) graph would look like compared to the cosine) graph. As you can see, when f(x) = 0, there are asymptotes on the tangent) graph.
An easy way to graph reciprocal sine or cosine graphs is to first graph the original, then find the asymptotes where f(x) hits the midline, and find the points at the peaks, or amplitudes, of the graph.
For Visual-Spatial learners, I would draw graphs for them to visualize it. I would make animated videos of how the graphs relate to each other and show each transformation step by step if there are any transformations involved. For Aural-Auditory learners, I would talk to them and explain how to do it step by step. For Reading/Writing learners, I would write down instructions on how to graph the six functions and they would read it and learn by themselves. For Physical-Bodily-Kinesthetic learners, I would have interactive activities to keep them physically moving. For Logical-Mathematical learners, I would do deductive reasoning and ask them to find out the domain and range of both sine and cosecant graphs, so they can get a rough sketch. For Social-Interpersonal learners, I would get other Social-Interpersonal people and would teach all of them while they discuss stuff about the graphs. And finally, for Solitary-Intrapersonal learners, I would just briefly tell them what the trig graphs look like and let them figure out the other stuff on their own, since they like to work alone.


What do you mean by the midline of the original function?


You mean where the original graph crosses the midline, I suppose.


yeah


In the sentence that I circled, I think you are talking about the maxima and minima of the original graph, not amplitudes


oh


I notice that you don't mention graphing cotangent


by amplitudes you mean extrema where I circled.


Graphing cotangent is different


In the case of sinx and cosx the midline is the x axis.


Other than that, it looks reasonable.


Are you all set now?


OK, have a good weekend.


Bye


bye


Hello


Hi


Can you please help me with a question


OK


It's on the board


Specially b


ok


You would use the product rule


Ok


Can you please do on the board


Any questions about that?


Yes I don't get what you just did


I applied the product rule to the product of the two functions sec and tanx.  Are you familiar with the product rule?


Yes but only when given a number and constant


Ok, then you aren't really familiar with the product rule.  I will write it on board.


That's the product rule, and I applied that to tanx * secx, letting tanx =f and secx =g


Any questions about that step?


Yes did you differentiate


yes


What is the differentiation of tanx


the derivative of tanx is sec^2x


Ok h


Just repeat that last step I don't get the placing


does that make it clearer?


Is it not supposed to be sec^2cx+tanxtanx


Sorry, I am not sure what you are asking.  Can you circle the part that you are having trouble with?


Oh I get it now but please explain why the differentiation of sec is so


What are you asking?


What is the differentiation of sec


the derivative of secx is sec(x)*tan(x)


Did you want me to derive that?


How did you get it


I will derive it for you.


I will use the quotient rule.


Ok


there you go


I get it now


To finish part b, I will use a trig identity


So a is 2 and b - 1


yes


Ok and c


Do you want to give that a try?


Ill try and see if I get anything right


are you going to do it on the board?


No I don't know how to use it


What is the antiderivative of sec^2(x) ?


tanx


good


and what is the antiderivative of secx*tanx?


1over cosx


yes, which is secx, right?


Yes


do you want to do the calculation on the board?


No but I got 4-3squreroot of 2


Yes, that's right.  very good.


Thank you so much for your help


You are very welcome.


Have a blessed day


have a good evening.


bye


hello


Hi, how are you?


Sorry my internet is a bit slow


How may I help you?


I wanted to understand a form of equations. Here is an example


3x - 7 = 2x + 5


Do you mean that you would like to solve it for x?


I believe so


What you want to do is to get all the terms that have an x over on one side (like the left side), and the two numbers on the right.


Do you have an idea of what might be a good first step?


I'm not very sure, I don't know much about this topic.


We can get the -7 over to the right by adding 7 to both sides.


what is -7 +7 ?


so that would be 3x = 2x + 12?


We made the equation a little simpler by doing that, didn't we?


Yes sir


Now we would like to get the 2x over to the left. We can do that by subtracting 2x from both sides.


what is 3x minus 2x ?


so 1x = 12?


what is 2x - 2x ?


x


sorry, no.


what is 2 - 2 ?


yes, and so 2x - 2x also =0


oh okay


1x can just be written as x


Okay, x = 12


Thank you for the help, that was quite simple.


you are very welcome


Do you think we can do one more?


sure


I don't have a problem, If you would like to create one, that would be great.


What do you think might be a good first step?


I think we can subtract 2 from both sides


so it becomes 3x + 6 = x -12


Do you mean subtracting 2x from both sides?


Sorry, yes


What will you have on the right side after you subtract 2x?


3x + 6 = -12?


That's right. very good


what might you do next?


Thank you


I can subtract 6 from both sides, leaving 3x = -18


right again!


Thank you :)


What might be the last step?


We can subtract 2 from both sides, so x = -21


You can's subtract 2 from 3x because 3x and 2 are not like terms.


From 3x you can only add and subtract terms with an x


right now the x is being multiplied by 3, right?


Yes


So to get rid of the 3 from in front of the x, we do the opposite of multiplication.


what is the opposite of multiplication?


divition


Yes, so we divide both sides by 3


*division


okay


what is 3x divided by 3?


the 3's cancel and we are left with 1x =x


any questions about that?


No, thank you


and what is -18/3 ?


That's it.


Okay, makes sense. Thank you for your help


Have a good rest of your day!


You are very welcome


you too


bye


Hi Sam


Hi how are you doing


Can you please help me with a question it's on the board


Doing well, thanks. And you?


It's loading


I see the upload. I'll need to enlarge a bit...


1 and 3


I'm looking at problem 1. Can you give me 4 minutes to solve, and then I'll explain?


Ok


But can you explain it on the board


We can start.


Yes, I'll explain on the board. I'll write below your uploaded page.


Do you see what I wrote? OK so far?


I'm writing the trigonometric identities we'll need in green color.


Are you there?


I'm sorry my network was bad


I'm still here. Can you see what I wrote?


Yes


We need several trigonometric identities to solve the problem. I wrote them down for you.


OK so far?


Can you continue?


Let me see what you did and see if I can


Im getting a different answer


There's one more step. We can use the identity in pink (or purple) color.


The next step is to solve the integral.


Ok


We'll separate the integral into 3 terms.


Can you solve the first integral, with sec^2x ?


tan x


Correct. How about the second integral?


X over 2


That's the 3rd integral. How about the one with cos(2x) ?


Sin 2x


But what's the use of the 3rd integral


You just put a dx there


Yes. We have to include the 3rd integral, because it's part of the expression we have to integrate. See what I'll box in red color for problem 1.


Oh OK


Can you find the value of the definite integral (including all 3 terms) ?


Is it 5/4-1/8pi


Boom! You got it.


Ohhh


So meaning I can't have one integral


You can put all 3 terms into a single integral, but it can be easier to separate the integrals.


Oh OK I get it


Number 3


Did you learn the formula for sin(A+B) = ?


Yes


Can you write it?


Sin a cosb+cosa sinb


Awesome. We'll also need cos(A+B) = ?


Ok


Why can't we use the double angle formula instead


That's what we're using, but we need to do it in two steps.


Do you see what I wrote?


Next, we apply the double angle formula for the "2x" in green color.


OK so far?


Can you give me 3 minutes to solve the next step, and then I'll explain?


We can continue...


What can we do to transform the cos^2(x) into cos(2x)) ?


Divide everything perhaps by 2


We'll use the identity boxed in red.


What's the final result?


Isn't it supposed to be 2cos^2x


There's the identity: cos^2(x)+sin^2(x) = 1, correct?


But at the 3rd last point if you add both the terms will it not be 2cos^2x


Can you show me where?


Can you hear me?


Hi, Ben, can you hear me?


Yes, I can.


Um, what I'm asking is, uh, the 3rd last.


Point where this quick cause


2 eggs.


Right?


OK, I can hear you, so can you show me where the problem is?


Uh let me just say the second last. I don't understand how you got the second last equation.


OK, let me underline or box one of the equations.


Um


Are you OK with the one I boxed in black?


Yes.


OK.


Now,


The next step is to add the similar or


Like terms.


So we have a 2 here.


And this is like a one here.


Oh, I, I thought it was too thin plus.


I didn't see that it was the X, so I get it now.


OK, is it clear now?


Yes, it is.


OK, so if we add the 2 and the 1, then we end up with 3 on the following line.


And the very last line.


Will be then


Three times sine x.


Minus 4 times sin.


Sign cube X.


And that's what we needed to show, right?


Mhm


OK


So the last step is to take that last expression and


Solve it for sine cube X and integrated.


OK.


So if we solve for sign cube X, what would we get?


If you're sold for it.


Because what we want to integrate a sine cube x. So if we


How my want to get


Um


One of the 3 minus cost.


Cubic.


OK, let's see.


I'm gonna show a bit more detail on the board.


So the result we found is sine 3 x equals.


Three times sine x.


minus 4 sign.


cube x, so that means


Sign cube x.


What would that be if we saw for sine cube x.


Um, saying 3 X.


Minus 3 X.


Right?


Over 4.


Over ne4. That's right.


And we can simplify that a little bit.


Um, we can multiply top and bottom by -1.


So that will give us


All right.


Mhm


Then we integrate that between 0 and over.


High over 3


OK.


So


OK, I need to fix one term.


This is 3.


OK, can you continue?


Mm, yes.


So what would be the first integral?


Um


X


OK, and the second one.


1/3 cos(3x)


One of 3.


Cause


3 eggs.


All right, let's see if we can find the, the final answer.


OK


Poison.


Um,


Can I see what I'm getting?


OK.


Um, give me a moment.


I'm getting 1/6.


Oh, it's not negative. It's just 1/6.


Over 3, OK, let me see.


OK, well, I'm, I'm getting a different answer. Let me write the next step.


I'm gonna try to shrink.


The text a little bit. I'm going to select everything.


And uh


OK, let's see the next step.


So, cosine of i over 3.


That should be one half, correct?


Mhm.


Plus 1/3 now cosine of 3 times i over 3 is co-signed pi, which is -1.


Or I should say -1.


And then


Le


3 times cosine of 0, which is 1.


And then minus 1/3.


Times


Again, co-signed 3 times 0 is 1.


OK, let's see what all of this.


OK, what's, what's your final answer?


If you look at what I wrote.


I didn't calculate this one, but I recalculated and I got 5/24.


That is exactly right.


Uh


You got it.


OK. Thank you so much.


OK, you're welcome. I'll just write the final answer, so 5.


There you go.


So any, any last question that uh


Any quick question before I go?


Um,


Do we have to know all these identities.


In calculus.


Well, let me tell you there are a lot, yeah, there are a lot of identities in calculus. The most important one is the one I wrote in red color?


OK.


Cosine squared plus sine square equal 1 and with that, you can, you can derive many of the other ones. The other important one are the.


Angled addition formulas like sign of A + B, cosine of A + B, if you know those two, you can derive all the other equations. So just these 3, if you know them well, you can find all the other identities.


OK. Thank you so much, Mr. Smith.


OK, you're welcome. Have a great day.


Same to you.


hello


i need homework help


is 15 = -403


hello??


Hello’


hi!


Cannot sê the quétion


huh the worksheet is there


i solve it in my ipadd im just asking for confirmation


Ýe


Yes


1st answer is -413


2nd answer is 2, -2, -6, -10, -14


oh oki


3rd answer 7


same with what uhad


4th is 11


5th is 18.5 miles


6th is php 123.45


how to do x


Wait solving


Okay?


oh i get it


i have moree


plz check


Okay


are they corect?


1st is -400


2nd is correct


3rd is 65


why?


4th 88


5th is -344


15+2(51-1)=15+2(50  100+15


I have solved


huh


Yes’


why 65?


Formula is a_1+(n-1)d


So 15+ (51-1) 1


the difference is 2  as 15+2 is 17


Difference is 1


what does 16 have to do with as 15,17,19


using d forula 19-15/3-1 = 12


2nd 20 only


yea


In 3rd question the sequence is 15,16,17 so 16-15=1


So to find out 51st term the difference will be 1 na


So 15+(51-1)1


Liam bye!


Bye


Hello how are you today


Hi I’m well I’m uploading my question now


Sounds good!


Do you see it


I see it but parts of it appear missing


Oh never mind.  Misread the problem


Ok thank you


So what would be your first step to solve this?


I added the points that were at (-3, 5) and (2, -1) I’m not sure if that was right at all


So your final answer is Q?


The x value was Q so I went with it


Yes good job!  Sorry I thought you wanted to work throughproblem togeter; not have me check it


lol ty have a good day


Hello Alex! How are you today?


Hi! I am good, thanks for asking. How are you?


Great! Thanks!


What would you like help with today?


Well, I am working on an assignment about factoring by grouping I think is what it is called and I was hoping to get help on some questions but I am having a lot of trouble understanding this topic so you might have to explain a few times


That's fine. What is the first question?


Can I please put it on the board?


Of course!


thanks


Okay, can you see it?


Yes


Have you started the problem yet?


well I think to star you divide the whole think by -x to cancle out x?


That's a good start, but incorrect because the last tern (-35) doesn't gave an x in it


i thought it was for 4xy - 7x


Yes your right, but there is something we have to do before that


ok what is it?


We have to group the equation into two sets of two terms


Can you figure out what the two groups are?


well maybe -7x and -35 because they are both negative


Good idea, but I was thinking of 4xy and -7x, and 20y and -35


oh ok


Actually your idea also works


So let's do that pne


one


ok


So when grouped up it'll look like this


Starting with the left one, what can we factor out?


could we factor out x?


Good idea, but because there isn't an x in 20y we can't factor out x


Is there something else you see we might be able to factor out?


oh ok so then y?


Correct!


However


There is something else we can factor out with y


Can you see it?


I see you labeled the answer choices


Yup, but back to the question at hand, what else can we factor out with y?


Why do you think that?


oops I mean 4 sorry


That's Correct!


Then it turns into


Now onto the right side


What can we factor out to make the inside of the parenthesis the same as on the left side?


And when that's factored out it looks like this


Do you know the final step?


i don't know, sorry


That's fine


We first group up the outside factors like this


And multiply them by the inside of the parenthesis


Do you understand this?


i did until the last think you did


Okay


What don't you understand about it?


just what you are doing


sorry


It's fine


Are you fine with me providing an example with variables?


sur


Not an example


sure


More like a formula


that works too


Does this formula make sense?


Sorry


its okay


i think so


Do you see how I got my result from the actual problem now?


a little


I changed the x+y to c+d so as not to confuse with coordinates


well are you grouping like thinks?


Please explain what you mean by that


well when you rearachanged the problem what specific things are you doing, combining, subtraction, addition, etc.


I'm just seeing what two groups when something is factored out of each create the same inside


If that makes sense


i guess so


Sorry, it's hard to explain


But now that we have out answer, what choice is correct?


A?


Yup!


Yay thank you!


I actually have to go now, I am sorry but thank you for your help have a great day


Your welcome


Same, I do as well


Hi I need my question answered


yes sure!


do u want to paste it on the board?


Thank you yes I will


Can you see


btw, what math are u in? I am asking because there are different degree to a concept that u may need to know


i can see


Precalc


alr


give me a sec so i can solve


Liam


do u know these 2 formulas


Kind of


well, u should write it down because this problem is based on that


Oh ok


I will do that


we uset his to convert polar cordinates to x and y


lemme know once u have it down, so i can show u the first step


I wrote them down


Can you show me the process in the painting section


yup!


does this makes sense so far?


Yes it’s clicking


alright


i want u to do the same with v and w and write what u get for each on the screen


if u are stuck, lemme know


Ok I will right it out first so one min


sure


take ur time


I put it in


is that for v?


Yes I’m working on w


wait before u move to w


could u explain how u got those answer


I’ll draw my process


alr


I messed up on y a little


But that’s my process


wait try typing it into the calculator again


put it all toghther by doing 13 *cos (90)


I got 11.621 for y


And -5.824 for x


can u check what mode u are in


u should be in degree mode


Normal


I don’t know how to do that


Im using ti 84


the graphing calculator right?


Yes


There is a "MODE" button next to the 2nd


click that


Ok I did


and on the 3rd line, where it is saying radian or degree tell me the one it is highlited


Radian


yup thought so


i want u to press the right key


Done


and click enter


trun the calc off and on again


and after that u can retype the math in there and it should give the right answer


Ok x is 0 and y is 13


yup


the theta here is 90 degrrees so u have to make sure u are in degrees and not radians


Ohh ok


a radian angle would usually have a pi next to it, but since this doesn't we know it should be a degree


but now that u got it right, try the w


6.077 x


-35.468 y


y is -34.47 so close enough


i think u might have miss typed on the keyboard


but yes


Ok great


now, ill write 2 more formulas and lemme know if u know them


wait before that


lets sum all the xs toghther and the ys toghther


let me know what u get


X 53.057
Y -4.37


great!


let me write the 2 formulas now


please write it down along with me


and let me know once u are done writing


Ok but was my original answer wrong


which one


the one u wrote next to the question / u did before we changed the mode?


Hi I think our connection may be lost


hey, i don't know what happened there, but if u send another request, ill help u finish it up


i saw ur request but it ended before i could click, try sending one more


Maria


Hi


hi what would you like help with?


A question I'll put it on the board


great


Can you see it


yes


Ok the one on top I'm struggling with b


ok


since you found the value of a, you should use u-sub to get the indef integral, and then you plug in the bounds to get the def integral


Ok


also, for future reference, this is beyond the scope of integrated mathematics one


Oh is it 2


this is calculus ab


Oh ok


did you get the answer?


Not quite


what part of the problem are you doing?


B


have you tried using the value of A in part A and doing partial fractions?


. Yes


I'm only getting 8+4 over 3ln4


ln4 is the same as 2ln(2)


so you got the correct answer


Oh so I  can I leave it in this form or should I leave it in the exact form they asked for


It's equivalent, so you can leave it in that form, but since the problem asks you to show that they are equal, you should give the exact form


Oh OK thank you


Do you need help with another problem?


Yes


Please post it


Ok


It's taking long to load


Question 2


you need to find the bounds of integration


For a I'm getting - e^p-1


+1 not minus 1


that is correct


it should be -p


It is but b is confusing for me


you set the integral equal to 1, since that is the area of r, then you solve for p


Yes but I'm not getting it


not getting the value of p? or not understanding how it works?


Not getting p


check your work for your original integral for part a


I did


for part a you should have got p+1+e^(-p)


Why +p


because the integral of 1-e^(-x) is x+e^(-x)


But we were only finding for e^-x


we were finding the whole area of r, not just the e^(-x)


Ok


does that make sense?


Just write it all on the board


I did it


I get that part what I don't get is where you got 1-e^-x from


we want to find the area of R, which is the region bounded by y = 1 and e^-x


just taking the integral of e^-x will give us the area under the curve, which is not what we want


Oh I get it now


okay! will there be anything else today


No thank you


alright have a nice day!


I need help with a question


Can you tell me the question?


Can I post in chat


Yes please


It is posted


ok


your answer is correct


Ok thank you can I ask another question please


I just need answer checked


sure


They are uploaded thank you


I don't see it


I see it now


how did you get the first option


Hello


hi


How did you get that?


ok so we foctor the top and bottom of the fraction first


then we look fir what is common on the top and bottom snd we can cross them out


Ohh I see ok


And what does this say..?


add to 7, multiply to 6
that is how i factored to bottom


Oh ok


do you need any help?


Can you explain both


yes so first for number 3 i canceled out the x-3 since it is on both the top and bottom. then i factored the to and bottom. 4 was common on the top so i took it out. on the bottom 5 was common so i took it out. once it factored bith i saw that we have x+4 on the top and bottom so we can cancel them leaving 4/5


for number 2 first factor the top and bottom of that FIRST Fraction. SO the top would be (x+9)(x-4). The bottom is (x-9)(x-9). Ten we have an x+9 on both the top and bottom so we cancel them


AFTER, since we are Division I do KCF and make the division multiplication. by bringing x^2-16 to the bottom.


Then once at teh botton we factor and get (x-4)(x+4). We can then cancel x-4 as it is on both the top and baootom.. This leaves what we have remaining


Let me knwo if anything dosent not make sense!


This is a.. 4, corret


*this is a 4?


yes


Ok


Wait what happened to the 9?


nothing taht is still their


my handwriting waas off


should i put up another one or do you  have one


I don’t


do you see numner 3


i mena 4


scroll on the right side


do u need help


Yea


ok si lets tsrat by factroing the top. how can we split (x-4)^2


close


4x4 is 16 though


2x2 gives us ...


YES


Now do the next step


Good now wriet teh full answer


Liam


NO good i was saying to write the full asnwer. CORRECT!!!!!!!!!!!!!!!!


Lets do one last


Okayy


Try


Ok


wait what happend to the x^2


you cant ignore that term


do bottom


great


That’s it?


yup


nothing to cancel


that it full credit


Okay


This a 7?


ye


K


Do u use FOIL for the numerator


Hello?


Uhm


Hello, how can I help you today?


Hi, can you please help me with a question


sure put it up


would you like a step by step once you put it up?


Ok it's question 2


ok


Yes


do you need help with A or B?


or both?


Both


give me a sec to solve and i will pics of it up when im ready


ok my work and solution are now up on the board. if you have any questions feel free to ask


Oh no question thank you


any other questions you need help with?


No thank you so much


ok then have a good day!


Hi!


Hi


Welcome to Tutor Provider!


Bye.


How can I help?


Uh, I just wanna learn a bit of


8th grade math.


Sorry, but I cannot use the microphone feature right now.


Uh, can you?


You, your mic.


Oh, OK.


Please use the chat.


Oh okay


Which grade are you in currently?


im going to 9th grade


OK, so how can I help?


Can you teach me 9th grade math please


Yes, let us look at the main topics. Alright?


Okay


Let us start with #1.


Let me actually share a PowerPoint with you.


Do you know how to add/subtract fractions?


Yes


Do you have any questions on anything on this slide?


No


OK!


any questions so far?


This is review material.


Do you know how we multiply fractions?


I think


OK, let me show you. Alright?


Yes, correct.


Now how do we simplify that?


Good work!


I think you have mastered the multiplying fractions. What do you think? Would you like to do more practice?


Sure


I think I mastered it


ok


great then


Write this in fraction form.


This is all still review.


I don’t think I know how to divide fractions


Oh, OK!


Ohhh


Do you understand how we do it?


Can I try to do 1


Sure, let me give you a practice problem.


Do you know how to do these problems:


with decimals


multiplication


Yes


OK, mastered?


Yep


There is a mistake there


Did you catch it? Or should I show?


Can u show


Absolutely!


Ohhhhh I forgot about that extra digit in the 2nd part


Hi


Let me share the presentation


Okay


That is the URL link


Do I click it


If clicking does not work, you can just paste it into your browser.


Let me show you a demo.


How do I copy it


Can you see my screen?


Yes


press Ctrl and A at the same time


I’m on iPad


OK, in that case, triple click that link


or until it has been selected


You have copied it?


Now, go to chrome or safari


a browser


I opened it


and paste it


Do you see the slide deck?


Would you like to see other presentations so you can learn on your own time?


Sure


Let me share the links with you.


Take your time, and use these links.


I have to leave now, but please use the links, and I will wait until then.


Okay


Hi I need help with algebraic expressions with z


X


ok sounds good


X= 2


correct!


X = 40


correct! another one


5x = 205


not quite


X = 41


yes!


perfect!


great job


great work!


lets do another!


great job lets continue!


you are doing great!


greeat job


Liam for the help today !!


anytime! lmk if you need any more help soon!!


hi! how can help you today?


Hi!Can you help me with pre algebra?


Are you there??


yes! what problems are you facing?


I don’t know anything about pre algebra and i would like too learn.


do you know any basics?


Yes I know Addition,Subtraction and multiplication but still a bit foggy


ok so we'll build the basics from there


Okay


can you give me an example of the question you can solve of pre alegra before we start?


No I can’t, I don’t know anything about pre algebra and I would like to learn how to do it .


okay!


so we will start with basic questions like factor pairs


factor pairs are basically numbers that can be multiplied together to make some number


Oh okay


so for instance if we multiply 2 and 3 we get 6


therefore 2 and 3 are factor pairs


can you give me an example of what you think could be factor pairs?


Can it be something like 4 times 3??


yes, it can be! but what are the numbers a factor pair for?


like 2 and 3 are the factor pair for 6


what would 4 and 3 be a factor pair for?


yes!!


can you give me another example before we move forward?


Something like 3 times 3, and it would be a factor pair for 9?


perfect!!


good job!


Thank you


now, a number can have multiple factor pairs


for instance let's take a larger number like 12


now 12 can have many factor pairs like (12 and 1) or (6 and 2) or (3 and 4)


the brackets are there to just separate the factor pairs there is no need to actually include them when writing


Okay


can you now give me an example of a number with multiple factor pairs?


take the number 24


6 times 4 , 8 times 3 , 2 times 12?


yes!!! and 24 times 1 but you get the idea


good job


now for a number we can think about it in terms of area


how can we make a rectangle with area 6?


well you could do it it it is 2 units by 3 units


Can I also do 6 units by 1 unit??


yes!!!


i am sorry about how messy it looks


That’s okay


that makes it a area of 6


so instead of doing this tiering process of making boxes to figure out the factor pairs of a number we can make a table to help us solve it faster


so now what do you think could be the smallest factor of 64


1 times 64? That’s the easiest one i can think of


perfect!!!!


yes!


now what do you think could be the next factor?


8 times 8?


good!! ver good! but do you think 2 times 32 would also go in there??


Yes


great job!! here is a hint when trying these kind of questions, i want you to count from 1 and up and consider if the number is divisible by it


Sorry you lost me can you explain it a bit more simpler?


Hello?


ok so lets try this in a different way


what all numbers can you think of that will divide 64 into a natural number?


let take a smaller number to start with


how about 40?


or would you prefer a smaller number?


I can try 40 !


yay!! let try


Would it be something like 5 times 8??


but what if you started with the first smallest factor? like 1?


remember 1 will always be factor of any given number


Okay


so what will be 1's factor pair?


1 times 1


no... i am sorry, allow me to rephrase.
what will be 1's factor pair to get the number 40


1 times 40???


yes!!!!


great job!


would you like to visit factor pairs once again?


Yes!this is very interesting and I would like to do some more


okay!!


pick a number of your liking you would like us to solve together


The number 20


factor pairs are basically numbers that can be multiplied together to make some number
so in this instance we want to get the number 20


so what 2 numbers would you multiply to get the number 20?


Can I say multiple answers for this one ?


yes!!!


Okay! We have 1 times 20 , 4 times 5 , 10 times 2


perfect answer!!!


great job!!


now would you like to try another number??


The number 36


okay!!!


We have 9 times 4 , 6 times 6 and 1 times 36


yes! but also 2 times 13, and 3 times 12


Oh right


you did good though! great now would you like to try another number?


No thank you, I feel like I have learned a lot but I would like to pause!


okay!!


i hope i was able to help a little and make you feel less stressed about pre algebra


it was a pleasure helping you


Yes you did thank you! But I have a quick question


yes go ahead


Are you a male or a female? I don’t wanna get you’re gender wrong


a female


why?
was something amiss while i was helping you out?


Okay thank you!


No of course not I was just confused


ok great!!!


i hope you enjoyed this session!!


I did thank you


Liam!!!


Bye!!


hey i had some material i wanted to pass along if you still need help??


Hello


Hi! Today I have integration problems


They are on the whiteboard


I see them.'


How may I help you?


uh I think I can try the first part but can you stop me if I am doing something wrong?


ok


I am having trouble reading some of it.  I am not sure about the 2 outside the brackets


I just pulled out 2 from the entire equation


The answer looks correct


Ok Thanks


For the next part, do we use the disk method?


I see that you did that you skipped a step and I had trouble reading your writing


Yeah sorry I was being lazy


what is A


oops


supposed to be V


for Volume


what is V?


Volume


this is going to be a washer, right?


yea


I'm not sure if this is right


the volume is going to be an integral


since it is a washer, you need to figure out the outside radius and the radius of the hole.


Since we are rotating around y =4,


the big (outside radius) will be that red line that I drew.


Yes


R= 4-f, so R^2 = (4-f)^2


Does that make sense to you?


Why does f need to be subtracted from 4?


Does that mean the second radius is 4-g?


the big radiius is the distance from y=4 to f.  How would you express that distance?


Oh I get it


Ok


Make sense


Yep


watch the signs


don't forget the dx


Would this be enough?


I would think so


Are you familiar with the method for part c?


Yep I kinda forgot it but I'll try


You want to figure out what the side of the square would be


That green line would be one side of the square. the square would be built on it. Can you visualize that?


yeah


the side is (g-f) so the volume of the square of thickness dx would be (g-f)^2 dx


Oh Ok


yes


Looks good to me.


Ok Thanks for helping me!


You are very welcome


Have a good week


you too!


bye


hi


Hi


how can i help today


Question 2 I sent it on the board


oh wait this is integrals, not integrated math 1


So you can't do it


i can help


Oh ok


but if theres something i dont know


i will tell u


Ok


in general tho, just request calc AB or BC


ok so show me where u have gone so far with this problem


B is where I went completely south


should we go over A first?


Yeah


ok. put what you have on the board and I will help you along the way if you arent sure


I not good at writing on the board


ok thats fine


u can type here if thats easier


For a?


yea


we need ot find the area before we find the volume


I wrote on the board


ok great


now for part b, we want to basically do the same thing as question 1 but with the y axis


so how did you approach it with question 1


Question 1 I didn't do it


oh ok


so there are 2 ways to do this question


Ok


either integration with respect to y


or finding the centroid


i think the first one is easier


Can you turn on your video cause then I can tell exactly what you mean


i cant sorry


its really noisy next to me


but i can draw it


Oh it's fine


can you see the drawing


Yes


ok


so we want to take both functions


and create a semicircle from them


which means at every x value of the function, thats a radius of a tiny circle


so you do v = pi integral(g(y)^2)


where g(y) is that x value


idk if that makes sense


v = pi integral(g(y)^2) dy


forgot the dy at the end


Yeah


ok so can you try to do this


u can do it on paper or on the board. whatever is easier


I tried it on paper but it's still wrong


have you heard of the shell method?


we can try it that way too if u want


Yes I have that's the one I've been trying to use


oh ok


and the answer isnt matching up?


ccan you show me your steps


Ok


also tell me what you got as the final answer


I'll sent it on the board


ok


It doesn't want to sent


its ok


Just do it step by step I guess


On the board


i see it


Oh


its very faint tho


Yeah


for shell method


u want


Yes


2pi integral(radius*height)


you shouldnt need to square anything


the squaring is if u use the other method.


thats with respect ot the y axis. this one is related to the x axis


Oh so for she'll no squaring


yea


Then we should just integrate it or


do this 2pi integral(radius*height)


u just have to find the function for radius


and function for height


Ok


i can help with that if u need


but give it a shot by yourself and i can help after


Yes please on the board


ok


so our height is jsut the height of the shaded area at any given point


so like it would be the value between those 2 points I drew


and then the radius is the distance from those points ot the x axis


so now just create a function for each one


the radiius should be easier


its just whatever the x value is at that point


so f(x) = x


now for height, its the y value of the first function - the y value of the second function


so like. g(x) = first(x)-second(x)


and first and second are 2x^2+5 and 3x^2+1


so g(x) = -x^2+4


and then u apply the shell method


2pi integral(radius*height)


2pi integral(x*(-x^2+4))


and then solve from there


and its integral from 0 to 2


So I should just subtract the two


the 2 functions??


yes. you subtract them to geth the height


What the formula again


Ohhh ok


its 2 pi integral(radius*height)


where radius and height are functions


In this case what's the radius


its the distance away from y axis


because thats ultimately the axis of rotation


and distance away from y axis is the same as saying the x value


So 2?


no. the value changes


you are absically calculating the area for each little slice


so for each little slice, the r value is different


so radius is a function of x


r(x) = x


and h(x) is the function for the height


which is just the top function - the bottom function


the difference between their 2 heights


Ok


hows it going?


Not so well


whats the issue?


I'm not really familiar with this so I'm struggling


dont worry


i can show the steps on the board


which step do you want me to start with


like whre did you get stuck


The beginning


ok


lets start with the base formula of the shell method


i have it on the board


now lets find r and h


ok so i created a few little slices within the shaded area


can you see them


for each of those slices(that we assume are getting infinitely smaller by integration) we need the radius and height


so can you tell me what the radius or height is. or draw a line for the height or radius


The height is


how did you get that?


I subtract the fx and gx


you should get -x^2+4 then


Oh yeah sorry it's 4


thats fine


The radius I don't know how to get it


let me try to draw it out


you want to spin it around y axis


so the radius is how far your current sliver is from the y axis


Ok


can you write up a function for that one


I don't think so


ok. so lets think about it together


the inpput of the function is the x value


i just drew those on in pink


given the pink value, can you find the length of the red line i drew on the graph?


so think about it like this


the red line starts a 0 and goes to the pink line


To I substitute 0


Do*


substitute zero where?


X


im not sure waht you mean exactly


but you can find the length of the red line by doing x-0


because it starts at 0 and goes until the x value


so the change in distance is x-0


which is just x


so the length of the red line is x


I'm saying substitute 0 into x


I'm also not sure


but you dont need to substitute any values in yet


we are trying to define the function r(x)


we need to figure out what that equals to


so that we can integrate using the shell method


r(x) is how far our slices are from the axis or rotation


Like the distance


yes


i tried to visually represent the distances with the red lines on the board


Oh so how do we find that


lets think about it as a difference between the start and endpoint


so the red line starts at o


*at 0


and it ends at where the slice is


So 4 or


this is a function


not an exact value


Oh ok


we are trying to create a radius function


r(x)


can you see the board?


Yes


do you see those red and pink lines?


for each of the slices, the red line represents the radius and the pink line represents the x value


and the red lines go from 0 to the pink lines


so the red lines go from 0 to x


meaning that the red lines have a length of x


so then waht is r(x) equal to?


I really don't know


its just x


r(x) = x


because the length of the red line(aka radius) is equal to the x value(where the pink line is)


I see


ok. can we move on to the next step?


can you solve from here?


or shoudl i do it on the board


I think I can do it


ok


when you get the answer, just type it here


yea


Thank you so so much even though I took so much of your time thank you very much


hope that you learned a bit more about the shell method today


sometimes learning takes time but its well worth it


Is r(x) always equal to x or it depends


i think its usually equal to x


if you are rotating around y axis


but give me a second to think abt it


And if it's around the x


if its aroudn the x axis, dont use the shell method


the proper one is the disc and washer method


its much easier in my opinion


than the shell method


its v = pi integral( r(x)^2) where r(x) is your function


Oh OK thanks


anyways. hope I helped today!


and maybe I will see you again on Tutor Provider some time


Yes bye


bye!


hey Ben how can i help you today


Hello Im learning statistics and have done ok but now Addition rule has me baffled. I got 1 out of 5 questions right ugh


hey its ok it can be a little tricky but im here to help


can you show me some of the problems you got wrong and we can work on it together'


Thank you. Yes lemme check which one i got right and ill upload one i didnt get


Sorry took so long … was trying to show a screenshot but its not working… so Ill copy & paste


its ok dont worry about it


This is what the problem is that i got right> The following table shows the breakdown of patients at different locations visiting a rotation of practitioners at those locations. l. If one patient is selected at random, what is the probability that they went to Johnson or have seen Dr. Dr. Smith? (Round to 4 decimal places)


Oops! Ok now one i didnt> In a recent poll of a local election, 8 people voted for Alice, 20 people voted for Charlie, 9 people voted for David, and 20 people voted for Eve. If a person was selected at random, what is the probability that they voted for Alice or David? (round your answer to 4 decimal places)
 My answer was 7.25


Brb


alright so there is 57 people in total


Yes


how many people voted for bob?


and how many for David


how much in total


out of how many people


write it as a fraction


yes


yup thats your percentage


a little under 50%


Divide? Correct?


yess 29/57


So rounding to 4 places is 0.5087 correct?


yes try it like that or if that doesnt work 50.87


cause i dont know if it wants probabilty or percentage


Oh … so a percentage would be to move two spaces to the right


No it doesnt say perccentagge


then just do .5087


Ok, thanku lemme try another?


yeah of course


Okay


this one try on your own and write it on the whiteboard


Ok will do


This is the problem > A bag contains 24 coins, one of each number 1 through 24. What is the probability that if you pick out a single coin, you choose either 17 or 39? (round to 4 decimal places)


this one is a trick question


because its impossible to get 39 if the coins onlly go up to 24


Terrible


so whats the probablity of choosing the number 17 our of 24


Oh ya lol


Let me think


Looking a at my notes


Sorry I missed what you asked me


whats the probabilty of picking 17 out of 24


close i see how your thinking that


Or 0.7083


but its not asking numbers 1-17 out of 24


its asking specifically for 17\


its basically asking for 1 number out of 24


so the probabilty is 1/24


Oh that simple ?


And zero P for 39


yeah perfect


In decimal for 1/24 =


Lol


Using the table below, if a student is selected at random, what is the probability that the student is blonde or a female? (round your answer to four decimal places)

I’ll draw the table


try this one yourself as well?


hello are you here


Is the formula >


Oops sorry


Hey Maya!


What do you need help with today?


hey! I just wanted to learn more about algebra


Okay! Is there a particular aspect?


nothing in particualr


just anyhting


oh okay


have you learned how to factor by grouping yet?


what's that?


okay! so you know how to factor be factring out the largest common denominator, correct?


yes!


grouping is sorta similar, but breaks it down into two different equal parts


lemme put something on the baord


Let's first look at the first line


You wouldn't know what to do with this right?


no


Okay yeah


so here, you want to apply factoring by the lcm to two different parts


the first 2 terms, and the last 2 terms


ok


so, the lcd of the first 2 terms is x^2, while the lcd of the last 2 terms is 5


alright


so, you factor that out


and that's where you get the third line


ok!


so, by getting the third line, you could see a different common factor pop up!


right


and we could quickly factor that out


so at the end, Ethan


alright!


can we try it


okay! I'll give you a different one


LETS TRY THIS ONE OUT


oops didn't mean to do all caps


can you like walk me through it?


okay! find the common factor for the first 2 and last 2 terms first


for the first 2 terms is the lcd just 3?


yeah


Ok and the lcd for the second 2 terms is x?


yep!


so try to write out the sequence now


like that?


yeah, but factor the first 2 terms the the last 2


after you factor out a 3 what happens to the 3x^2 and 6? they divided by 3, right?


so you need to account for that in you r steps


ok!


okay good. Now you have the common factor x^2 + 2, which you could factor out


what's the common factor?


2 + x^2


ohh!


okay, now what do you do when you normally factor with the 3 and the x?


add?


yep


think about the distributive property


good! now you got it


can we do another one?


okay, but this time try to work it out yourself


On the board now


I'll put it lower down


thanks!


sorry but I actually gotta go now


oh ok


bye bye!


hello! thanks for using Tutor Provider


how can I help you?


hi


ill upload stuff


like median mode etc


give me a while


ok sure


im kinda lagging nr


yea its fine take your time


oki


sorry for the lag


gimme 5 more minitues


ye sure


hey how is it going?


sorry i just restarted my ipad


illupload it rn


oh ok


Find the mode, median, mean, lower quartile, upper quartile, interquartile range, and population
standard deviation for each data set.


lets start


wait im lagging


wait for 2 mins tops


you there?


yup


gimme a few minitues


ok sure


hey i am really sorry but my parents are calling me because I have to leave for Sarah


I'm extremely sorry


I am sure there's another coach who can help you


Bye, have a good rest of the day


Hello Emily


hello


Do you know the five methods to prove triangular congruency?


like the definitions and terms you use in  a proof?


Like SSS, SAS, AAS, AAA, and HL


oh yeah i do


Sorry ASA not AAA


That is what they are looking for here


do you put the angle in the middle because of they are vertical angls


exactly


so you can prove it with SAS


yes


I cant see x from that picture


i made it smaller


got it


Which angles are equal to eachother?


kij and efd?


are they alternate exterior angles


do i set them equal


i got y=12


set the missing angle to the IFG equation


so 5x-10=60?


okay so x=14


why did we set the missing angle to 5-x=60


because like you said alt exterior angles so IFG is equal to EFD


okay


The transformation is F: (x,y) -> (x+8, y+20)


Is D your answer choice?


no d is cut off so i was putting the answer for it thats listed


ok


Go through the answer choices and try each on to see what works


do i plug the points in


yes


for example for the first one you take the first point (2, 5) and you transform it with (5x, 5y) to get (5(2), 5(5)). Clearly, that does not work


so for c i would do 2-8 and 5-30


what is the question looking for i dont understand


which transformation leads to (2, 5) turning into (10, 25) and (-3, 8) to (5, 28)


The first one leads the point (2, 5) to (5(2), 5(5)) - (10, 25) * this matches up with first point but the second points dont work (-3(5), 5(5))- (-15, 40) does not match (5, 28)


alr then the answer is d


Correct


What do we know based off the information given?


line SR is equal to line tv


and angle s and v are alt interior angles


They are not alt interior angles because for that there must be two parallel lines, but they are equal.


Because we are told that.


What is the third condition that is not given but we can see?


t makes vertical angles on both sides


Yes


Hat rule is this that makes the two triangles congruent?


What*


definiton of vertical angles?


SAS, SSS, AAS, ASA, or HL?


asa


Yes that is what proves the congruency.


how do i make this into a proof


Use the information we stated


And out into statement


okay


can you write a example for it


It is given that ∠S≅∠V and that T is the midpoint of
SV
 . By the definition of a midpoint, we know that
ST
 ≅
VT
 . Additionally, ∠RTS≅∠UTV because they are vertical angles, and the Vertical Angles Theorem states that all vertical angles are congruent. Therefore, triangle RSTUTV by the ASA (Angle-Side-Angle) Congruence Postulate, which proves that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.


Hello?


do you see yhe image


the*


Try them and then send image with your answers


Good job!!!


thank you, do i need to use one of the five triangle congrueny things


Exactly


okay i will try


is rp = PS because of the bisector


Yes


Have you figured out the congruency postulate ?


is it sas


We have vertical angles and a given angle and sides


So the postulate is AAS


okay


what did you put for the proof like the steps


The bisect leads us to know the two sides are equal PR and PS. We are given the two angles are congruent. And we know the last two angles via vertical angles.


Hey unfortunately I have to go. Please request further help if you need it.


okay thank you have a good night


hello


Hi!


How can I best help you today?


I need assitance with the unit circle


Are you there?


Alright! Do you have any specific questions or homework problems about it? Or do you need me to help explain it?


yeah  I have questions


let me pull them up quickly


Okay, sounds good!


am I able to post pictures hjere


Yep


There should be a button on your screen to upload pictures


alr I'm sharing the screen I think that should work


Yep, I can see it!


I need help with questions 44-58


43-58* sorry about that


Okay, give me one sec to look at the first few


Okay cool, so I can get an idea of where to start, did you start these problems yet or are you stuck on where to begin? Either way is totally fine!


stuck on where to begin


researching has been stressful as well


Alright, no worries! Let's start with #43. Can you scroll back up to the unit circle so I can help explain it with the circle?


sure


Great, thank you!


Okay so it looks like the unit circle they give you is in radians instead of degreesa


Did you go over how to convert from degrees to radians? Or do you want me to show you how to do that?


Think i've reviewd it but forgot it overtime


could you show me how to convert it please


Okay not a problem!


So to go from degrees to radians you will multiply by pi/180 and to go from radians to degrees it would 180/pi. I'll draw it on the whiteboard as well, but I'm not sure if you can see that while screen sharing.


I can see it


Yay!


Okay, so step one would be to convert the value you have to radians. So for -30 degrees, what would that be in radians?


did I do anything wrong in desmos


careful, since you are going from degrees to radians it should be pi/180


and you want your final answer to still include the pi, so you may have to simplify by hand if desmos won't leave it as a fraction


if that makes sense


uim confused


okay no worries!


So you are going to want something like pi/6 or pi/3, etc


can you show it on the whiteboard?


Yep!


oh I see


thank you!


Great!


does desmos look accurate now


If you hit the button next to your answer in desmos with the two boxes and a line it might give you the simplified fraction which will be helpful when we go to the unit circle


But yes, it looks accurate now!


1 1/pi over 6?


pi should be in the numerator, but I think that's what you meant so yep that is right!


So a tip for desmos when you do these unit circle problems is to leave out the pi and then add it back in at the end when you have the fraction


Otherwise it will multiply in the value of pi and then when you go to the unit circle it might be hard to find the correct value.


Okay so let's go back to our unit circle now


alrighty


Hello!


My name is Sarah.


How can I help?


Hello, how are you?


I am good


How are you?


I am doing well, thank you for asking.


I need help reviewing Chapter 4 trigonometry.


Some is review and some is new material


Okay!


Is there any specific content/work that you are doing in class right now?


Yes


I have worksheets.


Perfect!


You can paste it on the whiteboard whenever you are ready


Okay.


Is there specific that you are unsure of?


Have you hear the phrase sohcahtoa


I have heard of it before, but I do not know it's use.


sohcahtoa is an abbrieviation for the trigonometic functions


soh - (opposite/hypotenuse)


cah(adjacent/hypotenuse)


toa (opposite/adjacent)


sohcahtoa is used for easy memorization


I see


for csc, sec, cot (you just have to remember that it is opposite from the original)


Does that make sense?


Okay!


That is the general gist of the basics


With the trig functions defined for you, try out the first example!


Is this correct?


Yes!


Great job


I apologize for the interruption, but something urgent has come up that requires my attention. I'll have to end the session for now.


Okay


Bye


Thank you for helping me.


Your welcome


Have a good day


You too!


Hello, how are you?


Hi! I'm good and yourself?


Good as well.


What can I help you with today?


I need help with some problems


so wouldn't x=7 be -7?


swait we replace the number with f(x)


so its 7=9x-2x^3?


So, the original equation was -2x^3+9x=7?


no it originally was f(x)=9x-2x^3


can u see it on the whiteboard


Yes


Give me a moment to solve it.


oh nvm i get how to solve it


Okay.


Just checking in, how everything’s going?


Good morning. How are you?


Hello, how are you?


I'm doign well


I'm doing good. I'm putting my microphone on, if you can or want to, you're welcome to.


I see the two problems up here. Is that what we're working on?


OK


So


um


what, what quadrant 135 degrees uh sit in.


The 2nd quadrant


Good.


So it's uh


45 degrees past.


90, right


Yeah


we can, I'll let you draw it, draw a little coordinate axis there with your mouse.


and let's put that angle in there.


So if we want a positive and a negative one,


uh let's do the negative 1 1st. If you wrap all the way around


the origin


from that point


that would be a negative angle, right.


So let's see


that is going to be


um


negative what? Where do, where do we go from there? Uh, -45 to get to the top.


-18 plus -180.


-225 i think


Let's see


and another 45.


So what does that get us some -270?


Aren't you supposed to subtract - 360


and + 360?


OK


That's a good way to do it. Yup.


so it's 360 cause you're just going all the way aroudn?


Sounds good


Right.


And then you can add 360. That's, that's a


better, better good way to do it. Yup.


so whats the point of the coterminal angle


Looks great, right?


The point of a coterminal angle is


to uh get all solutions to problems that you will work with.


so i think u can add or subract by 2 pi


cause 2pi = 360


Again, yes, uh, that approach would do it.


add or subtract 360 degrees, yes.


Good.


Excellent


OK


So


you know how to do, you look like you already know how to do these. That's great.


i think from degree to radian


you multiply your originale degree by pi/180


Right, you divide by 180 to get from degrees to radiance.


with the pi


and you would multiply by 180/pi there.


Exactly right


Great


Super job


so tan is opp/adj


Correct


We'll calculate your hypotenuse.


exactly right


Good


my teacher doesn't like squareroot in denominator


Mhm


Great job


she says its not as simplified


Right, rationalize the denominator.


They're both really the same thing.


Let me get my calculator


one second


Take your time


Should be 3.9 centimeters.


yeah


Yes


sorry for taking so long


No, no problem


Good.


good


Exactly right


Why do you have to turn degrees to radians


Because radians are the natural measure in mathematics.


You will not get real answers without radiance.


so in real world we use radians and not degrees or


In calculus, physics, etc. Yes, you will have to use radians because your answers will not work.


if you do it in degrees


All right. You're doing great.


hmm


So I think it's just your area formula you were just using, right?


I think so


i dont have another area formula rn


You seem to have this subject matter done very well.


Thanks


You're welcome. You did great


I have a test on this in like an hour so


I should be ready lol


You'll do fantastic.


You have a great day


Oh


Oh, you have more, I'm sorry


Yeah lol


OK


It's a lot of questions haha


isn't it like


(x, y)


(cos, sin)


Yeah, XY. You're, you're doing fine. Y over over X


and then the reverse


I'm not as good at this


you're doing fine. You're, you're exactly right.


Perfect.


345 triangle


yeah


wait so theta is always where the origin is


Yeah


right.


Super job


Mhm


Right, it's positive


Perfect


negatives counter each other


right


OK.


Is this irght?


Uh, yeah, it looks good to me.


Yes.


Good


is there a sign that means undefined


Um


no, I don't think so


You got it


2pi is just the same as 0


Yeah.


cause cycle starts again


Mhm


Yup


Correct


OK


Right


We're 17


I was gonna put the 1


but thats not needed


All right


Good


so reference angle


60 degrees


angle minus-180 right?


Right.


Sorry this one is a lil harder for me


honestly i prefer to convert here


That's fine


That's good. I do too


60 right?


That should be negative


oh yeah


whoops


not the 2. Put it on the negative on the square to 3.


Yeah, there you go


sec is recipricol of cos


so hyp/adj


right


just 2


i think


Uh, let's see. So hypotenuse over adjacent


yep.


honestly what i do


is like for the pi i see 11pi/6


it needs simplification


so i jsut convert that


11 times


should be 330 degrees.


yeah i just convert the reference angle


It should be -1


There you go


Right.


Correct


csc recipricol of sin


Right


hyp/opp


Mhm


wait


cos 180


Good.


wait how do u


That's a unit circle. It's really not a triangle.


just


not really a triangle


just uh


limit if you will


OK


Very good. You're you're doing fantastic. You don't need much help at all.


I have to go


Bye


I had a few more questions but


I think I'm pretty good


Thank you for helping me


You're, you're, you're doing fantastic.


You're doing fantastic


You'll lace it


Thank you


Have a good day


Bye-bye now


You too.


Hi! How can I help?


homework please?


no problem, it looks like the problem only wants you to simplfiy


theres a rule you can use when there is an exponent outside the parentheses


you should always just multiple that number by the exponents on the inside


oki


for example we can do 5^(-2) and multiple the power by -2


so what is (-2)* (-2)?


for the option you selected, exponents will only go in the denominator if the power is negative


you're close but you have the sign wrong


remember than negative times negative is positibe


positive*


yes, the answer you selected looks good, do you understand how you got it?


yes


okay is there another problem you need help with?


i gotta go i have class


hi


Hello, how are you?


good and you?


oh this


do you know where to start?


sin is opp/hyp


yeah


yeah you know how to do this


thats all correct


nice


im practicing for my test tmrw


ok


but this is the easier stuff


but sometimes it's the easy stuff that people get wrong


this is Pythagorean right?


yes


honestly if i were you i would just memorize the pythagorean triple


3 4 5 triangle


oh i was just tryna show some work


your teacher wants you to show that much work?


ehh


im not sure honestly


this is ap precalc or normal?


normal


you probably should then


my school doesnt even have ap precal lol


oh also


sin theta is off


wait


i read this wrong


alright


wait what


o yeah


i mis read this too lol


yeah thats all correct


nice


yes


thats all correct too


7^2 is 49


not 63


lol


you got everything else its just that


NIce


ok good


you're forgetting something


for the 45 degrees


mb


yeah


thats all correct


i messed up a bit


thats fine


you corrected yourself


wait


Wait I have to get a calcualtor


im back


sorry for the delay


its ok


thats correct


slightly off


is there liek a step by step thing


youre close


yeah you got it


i forgot the step by step


yeah thats correct


so really i only got example 1 right on accident


oh


but i remember now


ok good


O = Opposite H = Hypothenuse A = Adjacent


yeah


correct


I think that's the proper setup


it is


thats correct too


I forgot


degree sign


whoops


thats fine


as long as you're catching it now


yeah thats a good start


uh


it shouldn't be 35/r


other way


you can check yourself since the smaller angle should have the smaller side


so r cant be greater than 35


thats correct


yeah


thats all right


i just did


35tan23 an squared it


+ 35 squared


then square root whole thing


thats good


you should do that it's a lto quicker


lot*


okay


also maybe its a good way


to double check


yeah thats correct too


yes


is that how u do depression


or do u just put 27 on the bottom


you got it


last question of the session cause i think ima go to sleep


ok


that parts correct


last step


yeah


thats the answer


thats correct too


you should be fine for your test you got bascially everything correct with no help


Thank you for checking my answers


no problem


have a great rest of your night


Have a nice night


bye


Bye


hi


Hello, can you please turn on your mic.


Hello


Oh, I got speak the, can you, can you talk?


Yeah, can


I wanna see what, oh yeah, I can hear you.


All right


You can hear me.


Yeah, I can hear you


OK, I'm gonna try to share my screen for the problem I have.


OK, this is the problem I'm working on.


All right.


I'm trying to place


on the board


Alright, just I uh something that was given by that.


Do you know how to start it off at least, or you just have no idea.


Oh


right


Well, I know it's something about inverse, but I


Mm


Mm.


I'm not sure about it


All right. So, you can see it's Y equals 4 times.


3 x minus 2 + 1.


I can't draw on this, uh.


I'll say, I'll just


try to upload it to the white board.


00, you want me to upload it.


It's fine. I got it


OK


It keeps failing to connect to the whiteboard.


Try to upload it, but it just doesn't work.


See, I


this open


I finally


This is a calculator problem or non cal.


Uh, it's a precock.


I mean calculator non-cal.


OK.


Um


oh no, oh, yeah, we got back.


All right, well, that's good.


We're gonna.


All right, so, first of all,


you're just not gonna let me draw.


I shot it, you know what I'm saying.


uh


you know


Some fishperal like make stuff like this easier just set F of X to Y. So just say like why


why I just say uh Y equals 4 times 3 x minus 2 + 1.


So now you have to just switch XMY and sulfur X. Do you know how to do that?


OK, so you said first what just by its itself was right.


turn it over, and how long?


You have to solve


Yeah.


Yeah, can you hear me? I'm trying to like, OK, finally connected.


Yeah, I heard about the switching the sizes. Can you explain it to me?


OK, so you have the equation Y is equal to 4.


times 3 the power of x minus 2.


+ 1


then obviously why


Y equals fx.


Nice


Things just broken today, won't let me finally Alpha X.


So what you have to do is


Wait, are you riding on the board?


yeah


Cause I can't see nothing. It's blank.


but I think your thing is just not connected then because


it's fine. Um, I don't think.


Honestly, I might just type it and chat at this point.


OK


Or you can just tell me and I'll write it on my, on my notebook.


So you have, why is equal to 4 times 3 to the power of x minus 2 + 1.


Mhm


So now


you have to isolate and solve for X. Do you know how to do that?


Yeah, yeah.


So what's the


not exponent.


OK, so what's the first step you're gonna do?


Um, is it, um


subtract one?


Yeah.


That's the first thing. Uh, do you know what the second thing is?


So Y minus 1 equals 4 times 3 risk by exqui.


Um


would it be to subtract 4?


It's 4 times 3 x minus 2. So, to get rid of the 4, you have to divide.


OK


Oh, so how does that work


So what would it be


So why minus 1/4 is equal to the equal to 3 to the power of x minus 2.


because when you multiply, you have to divide to get rid of it, you know.


Mhm.


What about the exponent


OK. Wait, can you see uh what I'm drawing now.


Yeah


OK, now it works. OK, so you have


why is equal to


4 times 3 x minus 2.


+ 1


So isolating first, you subtract one.


Next thing you do is divide by 4.


which that's where we're on right now.


So why minus 1/4.


equal to 3 to the power of x minus 2.


OK. Do you know how to


uh get rid of the base 3.


No


OK, so do you know logarithms at all?


Yes


OK, so


let's say you have like log


of


10 to the power of like


And then if you don't know log-based nothing is just log-based 10. It's just a simplified way of writing it. So what would the answer of this be?


The answer is log 10 cubes.


which is


No, uh, that's not the answer. It's just an example. What would the answer of this be?


with the answer of what?


A log 10 cubed.


Is it one


No.


OK, so log X of X is one.


log base, yeah, X is equal to 1.


So logba 10 cubed.


log 10 cubed.


um.


is it 3?


Yeah


basically log-based


10 of N is just equal to n.


So like log


up 10 cubs equal to 3. OK. So in this case


to get rid of the base 3, all you have to do is just do log


of 3


of Y minus 1 of


divided by 4


That just equals x minus 2.


Do you see how that works, sir?


Mhm


right


So then, to isolate X, the last thing you would need to do is just add to. So log


OK


So now you have


GFX


So G


So now you can, the first part's completed. You've found G of X, which is F inversive X. Do you know how to do the second part?


Is it imputing -3?


A what


Is it


Uh, input it where


In the X


Uh, no, because it's asking um the values of GFX equals -3 x. So you would just replace this value with -3 X.


Oh


Right.


So now, since you have a calculator, you should just be able to do this on a calculator.


and sulfur X.


Do you know how to do that


Yeah


OK


So then the answer is just X is equal to 1 point.


OK. Thank you.


Anything else you need help with there? Is that it?


Mhm


OK. Have a great day


Bye.


Hello! What would you like help with today?


yes i need help finding gcf and multiples to deal with fractions please


Of course! To find gcf you can start by understanding what two numbers multiply by each other to find a number, and by searching through those numbers you can find which two are the greatest. Would you like to see an example?


yes please


Of course!


So here it would be best to use a tree and the easiest way to do this would be to start with the number 2 if even or 3 if odd and continue from there!


72 divided by 2 is what?


Exactly so we could model it such as what I will now show on the whiteboard


Now what is 36 divided by 2?


Yes so now we can split it into 2 and 18


Now we would be able to continue this process until we have all of the factors


Okay that's make sense!


Yes of course! Is there anything else you may need?


Yes could you go over how to divide fractions for me, like how would I do 6/8 divided  by 9/5


Sure of course! Do you understand the concept of keep, change, flip?


I think I heard about it in my math class yes


Great it's essentially how you handle division with fractions!


You want to keep the first number change the division symbol to multiplication and then flip the other fraction


does this make sense?


yes sorry for delay i have to go now


Hi David, how can I help you?


Hi can you help me with this question because lm a little confused


Sure, what is the question?


I put it on the white bored


So, there are 3 parts to this question, correct?


Yes


First, what is a median?


To find that would we need to find the midpoint


Yes, good!


So the mid point would be (1+-3) divide 2 and (4+-1) divide 2


You want to find the midpoint  of side KL, correct?


No the question said find the median of J


The median from vertex J goes to the midpoint of side KL?


Oh is that it


I thought it was j and k


Yes, the median is the line from the named vertex to the opposite side.


First, you want to find the median from vertex J, correct?


So, you need to find the midpoint of side KL.


Oh okay


So -3+3 divide 2 and -1+-4 divide 2


What is the result?


I got 0,1.5


I like 0, but how did you get 1.5?


Well because of the -1+ 4


You get 3 then divide it by 2


I think it's -1 + -4 = -5 divide by 2 = -2.5


Oh yes okay


So now we have 2 points (1,4) and (0,-2.5)


Yes


Can you find the equation of the line between 2 points?


Is that the equation y=mx+b


Yes, that will work.


But how do l know where to put the points in


You have the coordinates of 2 points.  Can you find the slope, m?


Hello! how can i help you Sarah?


I'm sorry I might be a little off an on


I need help with an assignment though


homework


Thats fine! what is it related to?


you can show your screen or upload a picture if you need to


no pressure!


I can upload a picture


it might be blurry I'm sorry


its fine


is it related to this?


the question is not full so im not sure if this is whats its referring too :)


if so, the rule being used is the subtraction prop. because we are subtracting by -4!


ok


I am so sorry for not responding right away


its fine !


is their any more problems?


also for questions like this i would review these rules and how they apply to equations :)


um one moment I'll put it up on the board


based the prop of equality can you infer on what prop it is?


um I don't know


I'm sorry


thats okay! in the image i provided, im not sure if you can see it, the division property says a = b, then a/c = b/c. we can see if the problem that both sides are being multiplied by 10!


sorry i meant division, mb 😅


both sides are being divided by 10*


its ok lol


post the next problem when you are ready, or tell me if you dont understand a rule!


if you have a test soon these sources are great to study the material: Professor Davis> 10th Grade, www.mathpractice.com ( practice quiz), and flash cards www.quizlet.org/math_cards


thank you so much for providing the links


I am so sorry but I have to go


have a good rest of your day :)


Oh, thats Okay! you can access the whiteboard when ever you want! Good luck with the material!


ok thank you!


Hello


hello


how r u ?


good, how are you?


horrible


buts it whatever


sorry! bad math day?


yes


well, hopefully I can help


kk


i have to find the product


ok. I always multiply the numbers on the outside of the radicals together then multiply the numbers on the inside together. then simplify if needed


think of there being a one on the outside of that rad2


5 rad =0


ohh


ok


so 1 x 5?


do i simplify10?


you cant simplify rad 10


so multiply the 2 and 10 and put that in the radical


right


now simplify rad 20


good, now mulitiply that 2 on the outside with the 5 you got


so 10 ?


yes


yeaa


what do i do ?


it was good that you tried to simplify that, but you found you could mathforum.org, here is a good math-tutorial.nete what I write on the board...I am just going to rewrite 42 as 6 times 7


now we can put all those number under same radical


thats because of the product property of radicals


do you know what to do now to simplify that?


no


since there are 2 6's in the radical, take one out. the 7 stays in


rad


just 6 rad 7


do u not have social media?


sorry, I am not up on that stuff


I will have to ask my kids to update me :)


oh ever parent is annoyed at it


r these good numbers ?


break down 20 like you did on the first problem


good so far


is that a 6 in the radical?


Maya i got it right


no it was 5


ok, then yes it is correct


since 8 times 24 is a big number, lets do that tip I showed you


yes, now break down 24


wait...


think... you could do 6 times 4 or 8 times 3...which is better since you already have an 8?


8 x 3


yes


yeaa im done with the assignmenttt


yay!


I hope you have a better math day tomorrow!


Leo


have a great nighttt


you too


Hello


hi!


how can I help?


so the assignment is to verify and proof the identity


so far i did this


i will do on the board


okay


now i'm stuc


where did the sin2u go?


like how do you factor out that


sin^2(u) is common in both terms, so I factored it out


oh okay so i can just take out that sin2u?


yes, you can


oh okay, thank you!


that's all?


can we do one more?


sure


clear the whiteboard if you need


is that correct so far?


the red marked is not correct


i’m think that’s wrong again


can you help?


yeah


of course


make the denominators the same


ohhhi see


then add, just like adding fractions


i can rewrite 1 as cosx/cosx?


yes


that’s applicable for any equation right?


okay can we try one more?


okay


did i do something wrong


these red ones should be sinx


well, if you are stuck, I can maybe try correcting it if you erase that part


okay done


ohh okay i get it when you do it that way


thank you


you welcome


hi


hello


How can I help?


i need to find area and circumference


There are two formulas.


NOOOOOOOOOOO!


i honestly don't feel like re-writing all that


what is the question?


it's just find area and circumference use pi (3.14) round to the nearest hundreth


yea


what is r ?


Radius?


yes


the number in the circle?


sometimes.


sometimes the number in the circle is not the radius.


sometimes the number is the diameter.


what number would we put in the parentheses?


umm


how can we tell if the number in the circle is a radius or a diameter?


by where it is?


that can help.


is a full circle any diffrent from half of one


would that be like radius and diameter


which one is the radius?


full


sorry


full one is the diameter


AAAAH


what is the radius for the first circle?


um


the


well would we take half of 26?


yes!


diameter is the full part.


correct


13 squared means 13 times 13.


that is math.


we multiply that by 3.14 to get the area.


oooh


13 x 13 x 3.14


right


That's the area for the first one


yes for area


9 x 9 x 3.14?


yes


i gtg


bye srry for abrutply leaving


it's ok.


sign on later for more help.


bye have a good day


Hey Liam, how are you today?


hi


can u pls help me with my homework


Yes, of course I can! Is it on paper or on your device?


it on my paper but I can type the questions


Great! I can definitely help with that!


the first question is [ 9 is what percent of 72]


ty


Okay, what do you know about percents?


umm I know that they are less the the whole part


Yes! That is a very essential thing you need to know about percents!


Okay, so they are less than the whole, but what is the formula to find them? Do you know?


um x


X


or


mulipacation


Yes, a part of It includes multiplying!


and / or division


Okay, those are all such great guesses, the equation to find percents is part/whole X 100=percent


So if you have what percent is 9 from 72