yeah of course. Have you done multiplication with big numbers?


and division


Like 140x353?


And 60/12?


Yeah okay i can show you how to approach this question using variable such as x


Okay!


and we can find the missing number


Can you see that


Yes


okay so for question like we can do cross multiplication


so X * 50 = 15*20


okay so what would be 15*20


Let me do it on the whiteborad


Hmm


Okay we can go thru it together


so we can first deal with the 5


Okay


so 5*0 is 0


and 5*2 is 10


so that is how we multiply


but we still have the 1 left


so while doing the second number we get 20 and when we add them we get the product


Okay!


so we know that 15*20 = 300


how are we going to bring the 50 to the other side?


Hmmmm


Dividing it by 2?


So when we are doing equation whatever is multiplied we have to divide it.


so x*50 is multipled


but we want to make the x by itself so we have to divide 50 in both sides


what would 300/50


or we can do 5x6= 30


Yup so the missing number would be 6


and but a 0 again and that will = 300


yup that is right


Okay! :D


Is their any steps we should cover? :)


*there


I think that is all. This is how I approach fractions/ proportion


Okay!


but there might be another way to do it


like a model or something but this step is more efficient


Should we cover the model one?


Do you need help with anything else?


I believe that


*that's all!


Okay. I am not familiar with the model ones but this is how I approach questions like this


Okay :D


Okay no worries. Happy studying!!


Hey Jamie, how are you?


hello! Im good thanks! I don't understand this problem


We are told:
	•	x = width of the rectangular fountain (horizontal side)
	•	We need to express the total area of the flowerbeds (the shaded parts around the fountain) as a function of x


Imagine:
	•	A rectangle of length y and width x.
	•	On each side of that rectangle is a half-circle.
Two halves on opposite sides combine into a full circle.

That means there are two full circles total (one from the pair of half-circles on the left/right, one from the pair on the top/bottom).


Are you with me so far?


yep


So now what would you think for next steps given what we've discussed so far


so the vertical half circles would be y and we could use the equation of the area of a circle ?


Close


We are looking for the perimeter, not the area


ohh so we would use the equation of the perimeter


Yes


Which equation would be use?


That's part of it


but remember we are looking for two shapes


The rectangle and the circles


So, what's the formula for the perimeter of a rectangle given length x, and width y?


x+x+y+y


Right, so we have, for our final perimeter,
Rectangle: f(x, y) = 2x + 2y
Circle 1: g(x) = 2pi(x/2)
Circle 2: h(y) = 2pi(y/2)


Does that make sense?


why is it x/2?


Because x is the diameter, so we divide x/2 to get the radius


okay


So now, do you want to try putting it all together for the perimeter of our shape?


Hello?


The formula for the perimeter will be the sum of our 3 perimeter formulas:
P = 2x + 2y + 2pi(x/2) + 2pi(y/2)


Therefore, given perimeter 5500 this implies y = (5500/(2+pi) ) - x


We know the area will be xy + pi/4(x^2 + y^2)


Therefore the area of the flowerbeds is...


Hello! I need help with my pre algebra homework assignment.


Leo! I'll be happy to help you :) You can put the questions on the white board or just tell me the topic


Ok the problem is “A red light blinks every 12 seconds, and a blue light blinks every 9 seconds. When will both lights blink at the same time?”


Ok so let me see.. do you have any idea on how you would do this question? It's ok if not :)


I dont have an idea on how to solve it


I gotchu! Take a look at the white board.


So for these types of questions, we have to find the Least common multiple! (LCM) Do you know why we use it?


I know how to use it but not sure why we use it


Oh ok! I'll try my best to explain it. Give me a second


Ok so the first time the red light blinks, is at 12 seconds from the start. The first time the blue light blinks is 9 seconds from the start.


Take a look at the white board


So at how many seconds from the start will the red light blink again?


3 seconds?


Sorry for my vague question, so basically after it has blinked after 12 seconds, how many more seconds till it blinks again?


(the red light)


12 seconds?


Great! So from the start, when will the red light blink a second time? (hint: add 12!)


24 seconds?


Great! Now can you list from 3-5 blinks from the start?


3 seconds would be 36, 4 seconds would be 48 and 5 seconds is 60 I think


Wow! Amazing job! Now can you do the same thing we just did for the blue light?


3 seconds is 24, 4 seconds is 32 and 5 seconds is 45


Can you double check your math for the 3 seconds and 4 seconds real quick? Nice guess though


3 seconds is 27 and 36?


Yep!


I mixed it up with my 8 facts


No problem! You're doing great :D


Now, when do you think they would they blink together?


Ohh! On when red is on 3 seconds and blue is on 4 seconds?


Those are just the number of blinks, but you're very close!


So the number of blinks is right, but what's the number of seconds it took?


36 seconds?


YAYYYYYYYYYY


That's right!


Yay I got it!


Yeah! You're doing awesome so far. Any questions on what we just did?


Nope!


Alright! Any other questions I can assist you on?


Yeah a few here’s one: 10 bananas cost 4.50$. What is the price for one banana?


We haven’t learned to divide or multiply fractions yet


Oh no problem! Want me to guide you through the basics of how to multiply and divide fractions before we attempt this question?


Yes please


Ok no problem! I'll start with mulitplication of fractions first. So unlike addition and subtraction, in multiplication you don't need to make the denominators the same. I'll write an example on the white board.


Wait in the question it has dividing decimals, did you mean fractions or decimals?


My bad I meant decimals


We know how to do multiplication and division with fractions


Oh that's ok! I'll show you decimals instead then. lol.


So lets start of with multiplication of decimals since it's a bit easier than division. So when it comes to multiplying decimals, we just temporarily hide the decimal point then take it into consideration at the end of the actual multiplication.


So ignoring the decimal point on the problem i put on the white board can you solve it real quick?


Ok


Ok is 2585


Great job! It is! So now I'll tell you what to do with the decimal point we have.


Basically all we have to do is look at where the decimal point is located in each digit from the right for both numbers we're multiplying


Ohh it’s 2.585


Yeah! Do you understand what I wrote on the white board?


Yep!


Great! Would you like to try one on your own?


Sure I have to do “If 20 cookies cost 5$, what is the price of 25 cookies?”


Before can you teach me how to divide with decimals


I think I need to divide first to see the value of just one cookie


Oh ok! No problem. Would you like me to walk through it?


Sure


Alright, let me clean the white board real quick. Then you can look at what i'm writing


So basically, all we know is that 20 cookies cost 5 dollars. Then we have to find out how much 25 cookies would cost.


Do you know how we would approach this question to find the cost of a singular cookie?


We could try and do 20 divided by 5?


hmm close, lets say you have $5 in which you can buy 20 cookies. So would you do 20 divided by 5 (20/5) or 5 divided by 20 (5/20) to find the cost of one cookie?


Hmm


5/20 instead maybe


Yep! I'll explain why. So basically if we have to find the cost of one cookie, and a whole batch costs 5 dollars, then we will have to see how much each individual cookie costs.


And if you did 20/5, which is 4, it wouldn't make sense for one cookie in a 20 batch to cost 4 dollars when the whole thing costs 5.


Yeah


Yep! Moving on, once you find the cost of one cookie, how can you find the cost of 25?


You can either keep adding the cost of one cookie 5 times or multiply the cost of a cookie 5 times and add that number to the 20 cookies


Not exactly, wanna take another guess? Nice try though.


Or actually I think you're right I misunderstood what you were saying


Are you trying to say that the cost of 20 cookies plus 5 times the cost of one cookie??


No


My bad for explaining it vaguely, what I mean is you can keep adding the cost one just one cookie to the batch of 20 cookies 5 times


Yeah! That's right then :) Wanna give the actual question a go?


Sure


Ok so following the steps you just wrote out, can you do the first one and tell me the cost of one cookie?


I’m confused how to divide 5/20


Oh right, wanna do it the decimal division method way then? But if not then there's another direct and easier way to do it.


I don’t mind which way as long as it gives me the correct answer


Ok i'll tell you the division way then since you needed help in decimal division.


so i'll show you how to do 5/20 on the white board


So you see how 20 can't go into 5? What we have to do is "borrow" a zero by putting a decimal point.


Ohh


And see how we already have a decimal point but we have a remainder of 10? What we do now is add a zero into the 10 since the decimal point is already there now


Does how I solved it make sense to get a decimal?


Yes


Alright! So what we just found by dividing is the cost of one cookie. 0.25, being 25 cents.


Can you do the next step?


To find the cost of 25 cookies?


Ok let me solve this on paper I’ll be back in a second


no problem! Take your time :)


Alright here’s what I wrote: If 20 cookies= 5$ and 5 cookies cost 1.25$, then 25 cookies will cost 5+1.25=6.25$


25 cookies cost 6.25$ I think


VERY GOOD YAYYYY


Yay!!


You solved that so well! Though I'm sorry but I have to go right now for an appointment


Good job in this session overall :D


I have one last question on my homework


The problem is “4.5 pounds of potatoes cost 12$, what’s the price of 3 pounds of potatoes?”


Ok I think we can get it done quick


Oh ok! So in this one, how would find the cost of one pound of potatoes? Any ideas?


4.5 / 12


Hmm.. close! Try again though :)


12 / 4.5 pounds?


Yep! Total cost over total weight. :) Next, we would have to find the cost of three pounds. What will be do?


we*


We need to find the cost of one pound of potatoes then find the cost of 3 pounds


Yep! By multiplying. Wanna give the first step, 12/4.5, a try?


Ok I’ll try


Oh by the way for this questions it's a bit different since 4.5 is the decimal which is outside being the divisor


Do you need help with that?


I got my answer for one I’m not sure if it’s correct what I got was 0.3


I’ll show you my work on the whiteboard


Ok!


Oh wait I wrote it wrong


I wrote it as 12 / 4.5


No problem! Shall I show you how to solve this one since it's different?


Ok sure


When we remove the decimal from the denominator (4.5), we add a zero after the numerator's value (12)


So can you divide it now?


Basically all I did was multiply both the numerator and denominator to remove the decimal point


Ok let me do this on paper, brb


Hey Chloe? I have to go now, but basically the answer to this part is a repeating decimal (neverending) being 2.66666... so we would round that to the nearest hundredth before multiplying it with three but I have to leave for my appointment now! Sorry!


Oh ok thank you!


Yeah no problem! You were amazing!


Thanks for your help, I appreciate it


Hi I'm new I'm just learning about this new platform


Do u have any questions?


I can use this platform anytime?


Ya


ok thanks


your name is Priya?


Yes


where are you from


We r not rlly supposed to disclose personal infos like this


Do u have any questions related to the platform


yes


am I allowed to change topics like switch from math to English with the same tutor


Ya but only if the tutor is available at that time of your request


How old are you


Like i said, we r not supposed to disclose personal infos like this


Im sorry I made you mad


No no im not mad. Its ok


my questions are done though if you want to leave


Take your time to get used to the platform


Bye then


ok ty


bye


Hello


Hey


How are you today


I am tired. I just got back working a football game for sports medicine


I can't see the picture that well because it is so small


Is that better


yes


what do you think


the answer is


I think E


but I don't know why


I thought so too and I believe that is right


I have to go I am so sorry


hi


Hello :)


How can I help?


Alright, so how would you start this problem?


You still here?


divide to find the quotient and remainder


Alright, so how would you start?


Which part is giving you trouble?


both parts


I see, do you remember what the remainder theorem says?


no


It essentially says when divinding a polynomial by x-c


The remainder of that division will be c


so the remainder of say P(x) when divided by x-c


would be P(c)


Does that make sense?


yes


Great, so how could we apply that here?


It also looks like the site you're on hyper links to a definition of the remainder theorem, and I'm sure they were able to put it in better terms than i was


I'm sorry it seems like we're having trouble connecting, feel free to make another session


Howdy !


hii


can you help  me with a specfic question


So you've got a juicy math problem to work on?


yes lol


Yep, I'll try my best !!!


use the equation of the best fitting line to approximate the value of y for x=3 the points are (0,0.2),(1,2.3)(2,3.9)(4,7.5)(9.8)


So this is a statistics question, not an algebra one.


oh thats weird its on my math homework


Yeah, right !


So the idea here is that you use those points to construct a line (best fit).


That line will be given in the form y = mx + b typically where m = slope and b = y intercept.


Then you'll plug in 3 for x and see the resulting y value which is what (I think) they are asking for.


yeah i think so so i plot them on a scater plot and draw a line and try to get the equation out of it?


You can do it that way (the old "eyeball method").


yeah loll


More recent techniques would be some TECHNOLOGY which is how I got the answer that I wrote on the whiteboard.


yeah true loll


ohh the way you showed me is easier


thank youuu


I just copied the text you typed into GROK and got that answer.


Easy peasy.


Is that it?


yeah loll it is thank youu


Great - best of luck to you and take care !!!


Hi Alex! How can I help you today?


Hi, I need help with a my project from my statistics class


Sure, do you have a picture of the assignment or can you describe what the project is about?


Yes I have a picture


Great! Can you upload it onto the whiteboard?


Can you see it


Sorry not exactly, let me try again


Okay


Maybe we can try another way, can you share a link that I can use to access the image maybe?


I can't copy the link, it doesn't let me.


Would you mind trying again? If it's a google doc link or something hopefully it should be okay


I was looking at this


It's a Google Doc, but it says it's not available to copy  the link.


just to confirm is Google Docs not allowing you to copy the link from there or is the Tutor Provider app not allowing you to paste it in?


Google Docs


hmm I see it's going to be a bit hard to diagnose but if not possible maybe can you describe what the assignment is about?


maybe we can talk more generally and you can try sharing the link again in the meantime


I was able to copy the link now.


ah okay let me see if I can get in


yeah so seems like I don't have the login, can you try taking a screenshot of the file, pasting it into a new google doc, and share the link to that google doc please?


sorry I know this is inconvenient


no problem


thank you! please make sure to set the google doc to be “Anyone with the link — Viewer” as well


thank you! sorry I think its still a sharepoint link so I wont have access unfortunately, maybe you could also copy and paste the contents of the assignment into the chatbox?


The goal of this DBA is to assess your understanding of Sampling Distributions, your ability to explain concepts clearly, and your ability to apply statistical reasoning to real-world examples.
Instructions
1. Choose two of the discussions prompts below.
2. Record a 3-5-minute video or audio response
OR write a detailed 300 400-word response. Make sure that you identify which prompts you are answering.
3. Be sure to:
- Define key terms in your own words
- Provide examples (real or hypothetical)
- Explain why your example connects to Sampling Distributions
- Demonstrate reasoning with correct statistical language
Discussion Prompts (Choose TWO)
1. Explain the difference between a population distribution, a sample distribution, and a sampling distribution. Provide a real-world example of each.
2. A company claims that their new battery lasts an average of 12 hours. Design a scenario where you would use sampling distributions to test this claim.
Explain what conclusions you might draw.
3. How does the Central Limit Theorem support the use of sampling distributions in statistics? Give an example of how this might be applied in a real-world situation (e.g., sports, medicine, education).
4. Suppose you are comparing two brands of cereal for the average amount of sugar per serving. How would sampling distributions help you make an informed comparison?
5. Discuss why larger sample sizes generally lead to more reliable estimates in sampling distributions.
Support your reasoning with examples.


okay thank you! so I just took a look, do you know which 2 discussion prompts you will be choosing?


No yet I don’t know which one to choose


got it, so I would recommend choosing ones that you feel like you are most familiar with or have some ideas already about how to answer


is this the case for any of the prompts for you?


I think number 1 and 4


great! let's take a look at these first, we can always revisit if you change your mind


Okay


let's begin with 1, do any of the terms population distribution / sample distribution / sampling distribution ring a bell to you?


and if you don't mind, can you tell me what you think of when you hear these terms?


Population distribution shows how a characteristic is spread among everyone in a group and Sample distribution shows how that same characteristic is spread within just one small group taken from the population Sampling distribution shows how a statistic (like the average) from many different samples is spread.


yeah, I think you did a really great job there! liked how you described the population and sample distributions


for the sampling distribution you are quite right, I would maybe edit a little to make it more clear


for sampling distributions, it's true that it shows how a statistic is spread, i'd just clarify that from each sample we would get a value for the statistic, and the sampling distribution shows the spread of all values of that statistic across all samples basically


like, think about the average right? for every sample you can get an average of that sample, and if we spread all the sample averages out we get a sampling distribution of the average


does that make sense?


Yes


okay perfect! so you did very well in 1, we can move on to 4 if you don't have any further questions?


We can move on to 4


ok great! so for 4 can you give me what your first attempt looks like?


Sampling distributions show how sample averages vary to tell if difference in cereal sugar is real or by chance.


i think you have the right idea to start with! lets try to make this more specific


so say we have a situation where i have 2 brands of cereal A and B


and i've got samples of cereals for each brand


how would you be able to tell if there's a real difference in the average amount of sugar between the two brands?


and definitely we should be using sampling distributions here


use sampling distributions to see if the sample means differ more than expected by chance.


great work! yes, the use of sampling distributions here is that we'll take the difference we observed, and compare it against the sampling distribution to see if what we got is much different from what is observed


theres one thing maybe we could make clearer


we both mentioned "the sampling distribution" but we should be more careful to specify "the sampling distribution (of what statistic?)"


earlier when you mentioned the definition of sampling distribution you (correctly) explained that the sampling distribution is the spread of a statistic


so in this case, my question is, you will need to look into the sampling distribution of what statistic?


Like the difference between the two sample means.


yup there we go! awesome work


after you piece everything together, I think you have all you need to answer the questions


do you have any further questions for me?


no


ok perfect, well thanks for bearing with me- I hope this was helpful! good luck with your project


Thank you


of course! glad to help. good night!


Hello!


Hi Give me a sec I will put the question on the board


Okay, no problem


sorry for taking so long my computer is super slow


It’s alright I am going to take a break for a bit like 3 minutes and come back


okay


I’m back


Hi it's almost done loading my study guide computer version


You can also type out any questions or write and that’s okay!


school computers are slow sorry


I can't access the study guide so... rn


I know mines like that too lol!


Do you want to try writing it out or want to just wait until it loads


I didn't memorize the question ..


Oh that’s perfectly fine what topic is it on? Linear equations?


no expressions


Okay


Like simplifying them?


yeah and word problems


oh wait it completed now I can see the questions


yay


Great that’s amazing !


so we are not doing the entire thing


it's going to be waste of time because I only have like 1 hour and 30 minutes and the study guide has things that will take more time if you know what I mean


just pick the hardest ones


Yeah I understand and thank you for telling me that


than the easiest ones are going to be easier than


yw


We should work on problems 4,9,10


I’m going to write each problem out and show you how to solve them


okay sounds good


First thing we want to do when we see parentheses like ( ), is to distribute by multiplying the number that’s outside of it


So 5*2p + 5*4


Now notice that after we distributed we still have like terms (meaning we still have to simplify by adding or subtracting the same numbers


Try to simplify the new expression


Or I can simplify if it’s time consuming


I don't know if this is right but let me try


It’s alright we will work through it and see


Yes!


Now that’s our final answer


Ok let’s do 9 now


k!


Notice how there’s two parentheses which means we’re going to have to distribute two times


So let’s start with -3


Now always be careful when you multiply notice how I got 12 because I multiplied two negatives which gives a positive


But when multiplying a positive with a negative you will always get a negative


Now all we have to do is add and combine like terms


Our final expression is -64+4s


Ok let me just finish writing it


Alright


Let me know when you want to work on number 10


wait can it also be 4s+-68?


Yes it can also be that the order doesn’t matter


wait I mean 4s-68


oh ok


Yes either of those


ok next question 10


However it cannot be 4s—68 because when you subtract a negative it equals a positive just like multiplication 4s—68 gives 4s+68


Okay let’s do this!


First let’s distribute, one important thing to know is that when we’re subtracting it can be viewed as a negative number like for example we will distribute -4


Now try to combine the like terms


Wow! I’m proud of you. You did a great job


Okay next part is the part that we actually solve not just simplify


Okay


Want me to erase this?


yes


okay so for this one the hardest two questions


Which problems specifically? The hardest ones


Ok


because  these are honestly easy but sometimes they are hard the word problems will take too much time already


Yes I agree especially when problems like these it’s so easy to make one mistake that affects the whole answer


I think 5 and 10 and maybe 7 mostly because it deals with a fraction


But we can do 5 and 10


yeah that sounds good


I thought those were the hardest ones too


Haha I could just tell looking at them


It’s a lot of multiplying


The first thing we should do though is remember the principals of multiplication


Negative X Negative = POSITIVE, Positive X Negative = NEGATIVE,


Positive X Positive = POSITIVE


So now that we know that let’s start with distributing the five


And now the -4


Now we combine like terms as usual


Now after we combined it notice how it’s not an expression and it’s an equation meaning that it’s equal to something


That’s when we use algebra


wait did you meant to write 12?


Instead of -12?


no you forgot the one


sorry yes it''s negative


It’s fine I make mistakes sometimes so ty for pointing it out


Okay so now our goal is to get x on one side


So we have to do the inverse operation of subtraction since we have -17 by adding 17 on both side to get 46x by itseld


Now what would you do at this step


To get x by itself


Yes, the best thing to do is to divide y 46 on both sides because the goal is to get x by making it 1 instead of subtracting it


Amazing!


Let’s do 10 now


Ok so let’s look at our denominator (the bottom part of the fraction)


this part is easy


Okay try it out


Yesss


Yay! You did that!


yay okay next question is going to take a lot of time let me post it


Okay


Hope not though lol'


How many problems are left just for time checking


Ohh the property statements right?


Can you make the third one a little bigger


sorry my computers lagging a bit


oh wait it's better now


let's start


with the third question first


I’m not too good on properties but I would probably go by using distributive, multiplicative inverse (division) multiplicative identity, addition property and subtraction


Ok I’ll try I’m not the best at word problems


Ok I’m going to write the first out


k


Let’s assign variables


oh wait umm sorry I have to go ............. sorry.....


it’s okay


You got this and you did great


thank you and thank you for the help


gn or gm


lol


Good night and have a great day or night also!


bye


thank you!


New York!!!


hello


Hello!


Could I get some help on these questions? I’m not sure what they are asking me to do.


For 11, they just want you to plug in -8 for x in f(x)


Do you know what I mean?


Yeah I get that


For the rest of the questions would it be the same?


some are like that but not all.


16 is different


for 16 they want you to set f(x) =-7 an then solve for x


Ohh like a normal equation?


like I wrote


17 is an absolute value equation so that is a bit differenet


Ah I see


Would I have to make 2 equations for 17?


yes


Since it absolute value?


That makes sense


And for 18 I’m solving for c?


No, you are just plugging in the expression -8c+2 for x and then simplifying.  Same goes for 19


Ohhh okay I understand


I have a question about 15 though, how would I plug that in exactly?


any questions about that?


Nope that made much more sense to me


Sorry one last thing about 19 just how would I simply start that equation


for the notation g(x), whatever is in the little () next to the g gets plugged in for x in the expression.


so g(y-8) means " plug in the expression y-8 for x wherever you see an x


are you all set now?


Yup, thank you!


Have a lovely day


You are very welcome


oh hi


nice to Atlanta


:D


Hi, it's nice to meet you too.


how can i help u


uhh math


srry


What kind of questions?:D


are you a guy


ohhhh srry


?absolutely yes


im not a robot


I know


wait can you turn your mic on or no?


wait let me put on my head phone first


Hi, hi, hi, can you hear me?


Uh, yeah.


OK, OK, OK


Wait, so you're a guy or a girl?


OK


Uh, I'm a girl, yeah. I think you're asking if I'm a real human or a robot. It's like.


No, I, I know you're a human because a lot of people say that they're not robots and I always think they're robots or something, but I know you're not one.


Oh


yeah, yeah, yeah. I'Riverdale High, high school student.


Yeah.


Well, it's nice to meet you.


Oh, nice to meet you too


So,


uh


how can I help you? So you have a specific question. Can I see that?


Um, yeah.


Uh, uh, so the question is


I think you take a picture.


I, wait, hold on, um.


uh, oh yeah, I can, um.


Mm


No.


Ah


ah


yeah


Bella be quiet.


Sorry, my mother, my baby sister is talking in the background.


Oh, she's so cute


Yeah


she, she's really sweet, but sometimes it can be, um, you know, a bit annoying.


So, this one, so you see there's uh


1/2, so the


uh like the


denominator is different. So you should change it. It should like


you can change it into like 3/6


Can you understand that


Oh, yeah. Uh


So you can subtract this. So it's 5 minus 3. It's like 2/6.


and you can divide it by 3, it's 1, no, there are about 2, so it's 1/3.


Mm, OK.


Hey.


that


Oh


Sorry.


OK, that's OK.


That's like that. It just changes into the same denominator, and you can do like


like addition or subtraction.


Yeah, I'm pretty sure.


OK, OK


you


Oh my god, I'm so sorry.


That's OK


It's so fun


was


you.


I wear my


it no


but please sang earlier at school.


Oh my God, oh my God.


I


Oh, that was so much. She's so cute.


Yeah


Oh my


Oh my God.


Bella, you wanna talk to the nice lady? You want to talk to me nicely. Come here.


Um, hold on, um, my sister used to go to the bathroom and she can talk to you after.


OK


All right, so, um.


Bella, stop it.


Well, my little sister, she can't be at night sometimes playing the 67 song on time.


that it


Huh?


Oh


Bella, *****


remember you're, you're imaginary boyfriend? No. Oh my ****.


What


um


uh


hold on.


When I'm at like boyfriend, I'm at like her friend that's a boy who she plays.


Yeah, I, I.


Oh, she's so cute.


I really want a sister


So.


Oh my god, they


s.


Oh my gosh, come here.


Rock a byway


streets.


I guess. What are you doing?


cradle.


Uh-huh.


He, they said don't worry, OK. OK.


OK, so the, so I'm pretty sure, wait, um, here's a model to help, um, here, I'll, I'll take a picture and send it.


That's it, it, well, I, I have to go put my diaper filled.


But I, I, I did go now. OK, I go back.


Um.


OK


OK, here.


Yeah, I think


it's a big one.


Yeah


Mhm


Yeah, so it's like, it's like saying that uh 11 half is equals to


3, 3/6.


So I didn't, I didn't study, I didn't learn this kind, this way to solve the questions. So,


yeah.


Bella, are you OK


Are you?


OK?


Oh my God. Um


OK, so wait,


um


OK.


So


wait, are we supposed to like, hm, so is this basically the answer.


Well, um.


Is that the answer or?


Uh, yeah, this one is the answer, final answer.


Yeah.


that's it, that's it. Yeah, but whenever really to tell a sandwich earlier. I have it.


Ew, hair smell it. No, I don't want to smell your poop.


he.


I thought


Uh, I'm talking to my tutor.


Oh, it seems like a crazy family.


Yeah


When Bella fun fact.


My grandpa lives under under like a bridge street


And that she was, she was talking to you.


Oh


OK.


oh, I love her.


my, my grandpa said that it is cool.


Yeah, it's cool


All right, Bella, you wanna go to bed and watch Dora.


Yeah, OK.


I go


I get my app.


Don't worry. I, I know how to. I know it clicks their one they go coco me. I, I know it.


Are you sure? Cause you use your microphone every time you do it, you know this time I'm tired of watching Dora and me on the back.


Oh my god. I


No.


OK, um,


Um, hold on.


All right, so the next question is


and.


Mm.


Oh


one.


There are black


colors.


It


child


Uh-huh


us


Oh.


I


the same.


this


and


uh, OK, so um, is the


I want you so is this supposed to be like


the same exact answer as this one?


Yeah, it's my 3rd.


Well, I forgot to go to all kinds of. We don't need to go to O. I need my finding drop. I know that girl, you're 2 years old. You don't need that stuff. I'm 2.5.


Oh my god, she goes to Target and Ulta.


Uh.


It was actually supposed to be 36, but


Um


um.


It's time to go to bed. You can do your skincare, but also for


be head. I go to sleep that low to sleep go to sleep.


I sleep on, but oh my gosh like that. It doesn't have the right coin cheese.


Uh


Bella, no, don't you dare.


Bella, I for black cast.


Uh oh, Bella, hm


through it. We a gold game while your corn so. No, no, go, go, go, oh my gosh.


Oh my God, I, I'm so sorry.


Oh, it's OK.


Stop doing the worm.


Ew.


I


OK, um, so.


Oh, yeah


Wait, oh my gosh, um, wait, can you scroll down on the


OK, so this is the next question.


What, what, what, what's a guy, a guy.


I, it's my, my earlier at schoolamerta, um, said that like I have diabetes cause I


Is that 8


Oh yeah. OK.


Yeah, I was trying to make it.


Yeah, when


Yeah, it's, it's hard to write. So, I think you can use the same solution that, so there denominators are different, so you can turn like 4, you can time, time to, wait, wait.


On. It goes a


Yeah, yeah, if it's time to and I, we, so 2 times 2. So it should be like


my


you know


8 minus


whole day


over


um


So it should be


1 Ace


he said some oat mouth.


Yeah.


Yeah, I can't have she gone help me please, thank you.


So, um,


well


Uh, do you want some pink lemon here? Yeah.


OK, hold on. Um, hold on, let me go get um my sister some pink lemonade.


OK, I'll be right back


OK


Cas what


says has diabetes.


What


I says she has diabetes.


What are you doing?


You were diagnosed with the silica, oh my God.


But


Alright.


right back.


I.


I made, I made a new one. Yeah.


stop. OK, um, so the 18, that answer? Oh


Yeah, yeah, yeah


I know.


OK.


I'm drop it.


I


at.


Yeah


I'll be right back


OK


Bella


no


Yeah, smells like to over hair, rice.


Yes


OK, I'm back.


OK, OK


Can I get that, Bella? No, I want candy con mm mm.


last week


It's, it's cool place what can you buy me a, a new family double one.


No.


Mm


If you keep on acting up, I'm, I'm gonna tell mom not to buy you the road uh blush.


then stop.


Is that the.


I


OK, um


hm. Mhm.


I.


Bella.


She keeps on playing the sugar on my tongue, so.


Can you please just what's the motivation to be part of our show.


please share some more motivations everyone watching myself.


All right, so, um


who's on next question.


Mhm


OK.


Mm.


OK


so


Is that 4 or 9?


that's a 4.


So we can still use that, so we can change 1/2 into 2 or 4.


So 2 minus 1 equals 1. So the answer is


I


OK, so


Oh, it's OK


Sorry, I'm eating food right now. Yeah, it, it tastes good.


So, like, so yeah, are we supposed to change the one or or the 2 for the answer.


Uh, it's like


uh, the answer is 1/4, so we can change 1/2 into 2 or 4, and we do the subtraction.


Yeah


Hm.


Do you have any


younger siblings?


No


Mm


I'm the only child.


that must be nice.


Uh-huh


What is going on in the background.


OK, can you hear the arm?


Huh


like some


I can't hear the alarm.


Oh no, it's my roommates.


Uh, wait, you, you have a roommate?


Oh


Is.


yeah, sorry.


I


Bella


starve


I'm just.


But, it's like


it's


Two you open your microphone.


just


Oh, sorry


It's OK


I thought my microphone was on.


uh, the puppy dogs had climb wall, funny.


Hm


I have.


uh, the this is geno. It's Fluffy.


yeah.


Yeah.


She was trying to save Ginu.


Uh-huh.


OK.


Sorry


Hold on, I'll be right back.


Hello, hey.


Hey


Yeah


it's


He


uh my tai is M and keen.


Oh, OK.


Yeah, yeah OK.


You're so cute


Oh


Hm.


Who, great pain, a song Beyonce.


Gram Bean.


my friend dancing in the moon. I, I, OK. You can, you can sit right next to me, OK, but that I have to go, go get a pink uh lemonade lemonade, yeah, definitely.


I'm back


OK


her eyes got so wide


Was she talking to you?


She said you are in the kitchen.


That's it. Yeah


Yeah, I was.


I was gonna a pink lemonade.


Mhm


right? Where is she going?


fat


May helped me get


yeah.


Yeah.


OK, so wait.


I


OK. Um


Let's see what I, I, I have a phone for you. Hm, no, not me. No.


No. With carrots and color that that just add first. Obviously, at this it the way it's, it's not bad.


definitely, definitely.


to die


This song


No, that book.


Where black.


I'm the go low gala, no heartburn, no. That book at that fact that it is so tomato.


I go that I as a red book and I am the man. He first sing too, yeah.


Ja, I have two younger sisters.


Hi.


Oh really?


Yes


Oh


Yeah.


that's a really big family


we have, we have to go take our nappy. No, I wanna, I wanna attach to the nice pointy.


Hi, nice lady


Hi


My, my sister, um, she, she, she get a more pink when they. Mhm.


Oh, OK.


OK


He


he


What's your name?


I'm rolling


Uh


Um


wait, so, so Sarah?


Yeah


Ah


That makes more sense.


Uh-huh


That's it yeah


right,


so, yeah.


No, don't eat it. I know my ***** coming back.


Bella is coming back.


Mhm


P


How are you doing? Uh, I talk to them I like I like so.


It's good that's OK, Bella, well, you go to bed. I don't want to. Teddy


Fine.


OK


I have you in the I don't wanna go to bed.


I don't know you have to.


find.


She's in the.


OK. Uh, let's stop worrying about my little sisters and uh


yes.


I.


OK.


Um


hm


out the problem.


It's


main character look is.


Oh my God


Hello!


heloo


How can I help you?


i have some problems for circles


and its parts


Ok


If you'd like you can add a picture to the whiteboard


can u explain this plzz


huhhh


so we can start solving for problems


Yup


can you start explaining plzz


was is a minor and major arc


I'm thinking a minor is an acute one, major is obtuse?


That's my first thought


oh right


heheh


Alright I just fact checked and minor arc is actually just any arc that is less 180 degrees (so less than a semicircle) and the major one is basically just the rest of the circle


The more you know I guess


OH


ok


lets try solving


lemme find sa


ahhahaa


Alrighty


This feels very geometry


theres a geometry chat here right


should have gone there


Yeah there is


This is fine though


I know geometry as well


But it was 4 years ago and my memory is kind of spotty


here


lets use the


given formula to find


how di you get that


plz explain


Oh, well I knew that since that one angle 153 degrees, I figured that the little ones must each be 27, because 153 plus the little one is a semicircle. Then I just subtracted 153 and the two 27's from the whole circle (360) and voila! 153.


oh


Though it's a lot easier if you just look at it and see angle A is right across from the angle you're supposed to find and since they're made with the same lines they gotta be the same angle


It's like a rule or theorem but I don't know what it's called


Yup


Bingo


Also correct


So yeah those ones are pretty straightforward once you get it


Are there any others you're stuck on?


yra


do you see it??


1. minor arc


2. major arc


I see it yeah


3. item C


I think 2 is minor


Cause it's less than half the circle


oh why so


ohh...


hahahaa


point D


3 is right though


4. major


5. major


Yes to all 3


Nice job


we still solve for some anges though


hahaha


is 9. 42?


Yes!


Awesome


10. 74


Yep


11. 138


I think that might be larger actually


oh..


I think that's everything but TUS


So everything but the angle you just found


problem 12


Hello


Wait, I wanna ask, when asking for like, let me change the color. When finding, for example, or


uh circote, is it like this, or do you do like this? T to R or is it the longer way. Um


this is my first time and I'm still confused.


Yeah so you got the number right


I https://math.edu/diagram3ah you did


What do you mean I got the number right


Uh, for what?


Uh, we're still in number 12 for R&T, but


which way is it? Is it Ry the the longer one or is it the one I'm gonna encircle in green from wait from


Oh wait are we moving on now


from pink here, are the tease it like that, or is it the red away?


which, which way is it, the red or the pink white? Because 72 + 42 equals X, but the answer for Able RD is 114


Oh I see


I just want, I just had a clarifying question for


what's the, the burning, not really turning point, uh.


the


Yeah I'm not quite sure


I think the smaller one


uh what is segment X was, is it the one circled in red or the one in pink? I'm still very confused for the first time.


The minor


Oh, so it's not a full, uh, oh yeah, of course, OK. So if I'll go RT 72 + 42 is.


or 2 + 64.


plus


If they don't specify with a third letter it's minor


Wait, I think I, it's not showing. I think it's not 7su.


Oh, OK. OK, 74 + 42, it's under 16 but it makes sense now.


OK. I think I got it already. For Ale QR, which just circle in pink. It's P U R.


So it's basically the same of 64 combined with uh I know


with with 74, so 64 + 70.


4 by 74. It's 138. Is it correct?


You are


It makes sense. For 30


are.


QS. This is basically


a major art because there were 3 of them, if I'm not mistaken, so


we do everything except


so everything except


great


you can read angle beta plus 42,318.


Yeah, makes sense


OK.


Uh, number 15 is


BQ


S, so it's a major art


This is


42 + 42 + 100.


due to


OK


you


Yeah, it makes 238.


Excellent


QR


OK I ate this for you too, uh 64


22044 inch.


Yeah, it makes sense.


OK, for P.


to S. Which way though be wait. Oh, we are here or the longer one. I always get confused with this one.


OK. I got it. So the last is


64 something blank and then uh 42 because BT R O


to look at it.


Makes sense.


You're still


one more worksheet I would.


I would like


you to


to, to, uh, we would, I would like you to work with me. Let me find it. I, I think it's better.


Identifying future versus minor art.


That's better.


And


Oh.


this lesson


i confirmed t already


thank you for this tut ses


byee


Bye


thank you very much


Hi!


Haha I like your message


hellloooooo


What can I help you with today?


heheheehhhahahahaah :)


math :)


Great, what are you working on?


Alright, let's start with what we already know. We're trying to find the cube root of 10. Are there any perfect cubes near 10 that we can recognize?


or 2


Why do you say 2?


You're on the right track there


because 2x5 is 10. idk why i said 2


And just to clarify, this is the cube root of 10 and not 3 times the square root of 10, right?


wdym?


cube root is one number times itself 3 times equals the number


yep!


Check the drawing I just made


Which one is the problem using


Got it


Okay


And we're trying to find which number is the cube root of 10


So to do that, we can sandwich that number between two cubes that we already know


its a decimal right??


Yeah


But all we have to do is find the numbers it's between


So can you think of any numbers that, when cubed, are close to 10?


Yes!


yayyy


So 2 cubed is what


Well when we cube something, we multiply it by itself twice


So 2x2x2


What does that equal


Which makes sense, because 8 is close to 10


So now we have the number less than 10


We need to find the number greater than 10 that has an easy cube root


What's another number we can try to cube?


Okay, we can try that


nvm thats 125


Yeah lol


It's okay! Let's try a new one


Sometimes in these problems it's easier to just count up


So we can try 3 next


3 cubed is 27


Yeah!


yayyyy


So which number do you think is closer to the cube root of 10? 2 or 3?


That's correct!


Great job


Do you have another problem you need help with?


yes ma'am


Great


If you paste it on the board we can work on that now


sorry my internet was bad


all good


ok


Okay, for this one we can apply the same principle


im sorry i have to go :(


Oh okay


Good luck with the rest of it!


Hi！


:D


how can i help u?


你好


你好！


Hi


do u speak Mandarin?


Yes


Wait


太好了


OK


Some


Not all


OKOK


My iPad has restrictions of what i can do in upcheive right now


I need to refresh the page


okk


Better


:D


can u make it bigger?


ok thank u


This is probably over the grade im in


ok i get it


wait u are in 6th grade??


Ethan


omg ur so smart


For my school


so a real numbers squared it always positive


Yes


I know


but its cubed depends on itself


so x^3will be positive so x will be positive


sorry i need to head to another classroom


could u pls wait me a moment:(


and y willbe negative


Sure


z will be positive so it's +-+ i think


+-+ looks like a face


LOL


so for 8 it's like time the numbers together and add 10


Df


Dd


D


d


Again for 9


I say


so for 9 there are 10 numbers and 5 are odd so it should be a i think


Oh wait


Yea


im sorry i need to go now, my class will begin


We are done anyway


Bye


bye


Solve triangle ABC, <A=48 degrees, <B=55 degrees, c=26


law of sines


In order to use the law of sines, doesn't one need to know one angle and one opposite side in order to compute the ratio?


right, I'm not sure how to find out angle C though


How many degrees in the sum of the angles in any triangle?


180 degrees


Yes!!!


Can you find <C?


oh yes wait


77 degrees?


because 48+55=103 and 180-103=77


OK!!  Now what?


sorry one moment im writing this down


OK


so then we need to do a formula involving the angle C and side c?


law of sines: sinA/a = sinB/b = sinC/c


Yes!!


so sin77/26?


which would be about .374


So now, sinB/b = 0.374


wait why is it sin B/B = .374? shouldn't it be sin C/c?


Any ratio will be 0.374 by the law of sines.


sinB/b


so does that mean sin A/a, sin B/b, and sin C/c are all the same?


aka .374


law of sines: sinA/a=sinB/b=sinC/c


Should be to be clear:


sin(A)/a=sin(B)/b=sin(C)/c


yes, and same for the inverse, right?


a/sinA=b/sinB=c/sinC


so is that it


im confused


wait so what does that solve for though


The problem stated to "solve the triangle".  That means to find the values of all angles and all sides.


sin48/a=0.374, solve for a


wait sorry, so my teacher did this problem and wrote ASA on the side right? and he ended up with B=sin^-1 (26sin40/32) at the end


That sounds like a different problem?  Where did 40 and 32 come from?


Yes exactly, that's why I'm confused. Because I get that in his work the side 26 for c is the same, but then he also did the diagram and everything differently. Like, instead of writing the angles like I did with A B C, he wrote A C B


the order is different


ASA sounds like a congruence short cut.


and then he factored out the 26 when multiplying it by [sin40/32=sinB/27]


which I also don't get where he got the 32 from


Or the 40 or the 27?


exactly, the 40 and the 26 as well


I get his calculations but they don't match with the problem


Were you told to use the law of sines?


Yes, the problem I'm presenting now is just a practice problem but right after that he went straight into all these problems from a worksheet that all require me to use law of sines


OK, do you understand the law of sines?


I get the formulas you gave me and I've noted them down as well from class


I just don't get the solving part in the sense that what should my final answer be


Your final answer should be any missing angle values or side length values.  To "solve" a triangle means to find all the angle and side length values.


Okay, would it help if I were to put up a photo of his work?


and other sort of examples he gave for this


We first found the missing angle value so that we had a corresponding ratio.


yes


Then we can use that ratio to find the missing side lengths.


right


Sure, post the teacher's work.


wait so this is another intro thing he did, and let me give the second photo as well of this problem we're doing


Your teacher first derived the law of sines formula, then used it.


sorry, can you elaborate on that?


ASA means that we know two angles and the included side.


yes, which is 40 degrees, side 26 (c), and 55 degrees


Your teacher first showed how the law of sines was found.


Then he used it to solve a triangle.


all right I'll explain my thought process reading what he wrote;


so because he was finding side c first, he did c/sin43. Then he made that equal to 30/sin68 because that's the only ratio that has both the denominator and numerator values already


and then he wanted to isolate the c, hence why he factored it out


once he factored it out, he was left with c=30sin43/sin68


and then im a little confused


wait would it have mattered if instead of making the ratio equal to b/sin69 22.1/43?


Do you see where he got csin68 = 30sin43?


that's from a/sinA


I'm wondering that if all of them are the same according to law of sines, would it have mattered if he chose to do c/sinC instead?


In his example, he knows A and a.


yes, but he just figured out C and c


And he knows C so he can solve for c


wait I'm going to try solving for it and see if it's the same answer


Remember that you can find the third angle easily if you know the other 2 angles.


Good idea


So I did the alternative, with C and C. This was my set up;


b/sin69 = 22.1/43


I multiplied everything by sin69


and I got 22.1 sin69/43


which then led to my final answer of about .479


and that isn't the same as solving for the ratio of A and a


which led to 30.2


I'm sorry, but I didn't follow all that.


No it's fine, I'll break it down again


so you know how in his ratio he did b/sin69, which is solving for b


as equal to 30/sin68


which is the ratio of a/sinA


30/sin68 solves for the ratio


OH WAIT I SEE


I SEE MY MISTAKE


a/sinA


I didn't do SIN 43


I just did 43


aahhh


when using the alternative of c/sinC


I only did c/C


that's funny thank you so much


law of SINES  haha


RIGHT that's hilarious


okay wait I get that


so then, now the question becomes, how did that problem lead to the following one that we were initially working on?


It's the same problem with different numbers.


I just don't get how he did that entire equation method. So since we left off at figuring out sinC/c, which is .374, what would we do next?


Set the ratio (0.374) equal to the other sinB/b and sinA/a to find the missing sides or angles.


but .374 is just one value, if I were to set up an equation/ratio thing, would it be worth instead doing something like sin48/a = sin77/26?


The law of sines says that all the ratios are equal.


Your equation will work, but it's usually easier to calculate the ratio once then use it.


So if we did the easier method, then how would I set up the equation?


I've lost track of what you know, but first use the known side and known opposite angle to find the ratio.  Then use the ratio to find the remaining missing values.  Make sense?


sorry, yeah I get that. I'll just do it with the equation I suggested earlier-- the longer way. I'll also make sure to email him about that specific problem


sorry for taking this long to grasp it! thank you for the help :))


np, you're welcome


good night


gnight and Liam


Hello!


hello


what u struggling on


I need some help with Calculus :(


sorry Im struggling


its fine


is this the complete question or is there more


there's more


so the question basically limit of h as approaches to 0 is sin(Pi over 3 + h) - sin(Pi over 3) over h is equal to?


do u understand why they teach us this limit btw


kind of


not at all


alr its fine


same with me when i was learning it


also we never use it later btw


its all ragebait


anyways


its to find the slope of the tangent line of f(x)


in this case sin(pi/3)


ok


why sin(Pi/3) in specific?


and the h is the distance between two points on the line and the equation is the secant line of connecting the two dots


Ohh wait I actually know because of the formula right??


basically the formula is lim h -> 0 f(x+h) - f(x) all over h


eyah


yeah*


so we have to find the derivatives right to solve it?


yep


because limit is equal to derivate right? something like that


it is


so the derivative os sin would be cos right?


and after that Idk what to do


so do you remember the chain rule?


Nope


ok idk if it has been covered in class yet though


wait give me a second


ok


i think i went too deep


u don't need the chain rule


ohh okay I was getting scared for a moment haha


now the answer to that would be the answer to the initial question


oh Im sorry my screen doesn't show what you write on the right side Idk why


i didn't write anything except equals


it doesn't give me the option to scroll or anything


it was just space for u to fill in


ohh okay now I can see it thanks


so the final answer is cos Pi/3?


yeah but the teacher would prob want it simplified


hmm, how do we simply Pi?


oh this is just the unit circle


so it would be 1/2?


yep


cos pi/3 = 1/2


ohhhh okay!!!


it know make sense


can I ask you another question and I try to answered just to make sure that I understand


sure


should i clear the board


ok so the question limit of  h as approaches 0 is (e^h - 1) over h


ok


soo


we are looking for e^h right?


have you heard of lopitals rule?


im sort of stumped a bit


the one that says that the derivative of e is the same?


but the rule i said is the thing that can solve this but idk if u guys were taught that yet


no not that


hmm give me a sec


ohh so not hehe


so


we got to pretend there is a function there


there is no x given


so lets say that there is an invisible x that is equal to 0


bear with me now


if u see this on a test ur teacher is evil


:,( he is


at least u can surprise him by getting the answer correct lol


Haha if I learn how to do it yeah


so why we have to imagine an x?


so you try to find a f(x) in the equation


and use ur imagination


and specifically the x has to add to the h and why you replace the 1 for an e^x?


because since x = 0, e^x = 1


and we can use e^x as the function


ohh thats right


and since the lim formula has f(x+h)


it works there


ohh okay!


it was the only two questions that I missed from my homework! thank you so much!!


no problem


I will try to study either why because tomorrow I will have a test :(


that sucks


hopefully u ace it


I hope! well thank you so much you have a wondeful night Ms. Davis


you too Maria


gn


Hello


How can I help you today


I'm having trouble in algebra 2


Okay


Do you have a specific aspect of Algebra 2


Factoring trinomials


Just to be clear, do you want a tutorial on this or you have a question you'll want us to tackle


I would like a tutorial


Great choice


You gonna have to give me a moment to draft out something for you, alright?


Alright


I'll be right back


Come to the board


How do i do that


I see it


Hold on


Hello, can you hear me?


yes


Great. So I'm gonna talk


just pay attention


All right


alright


Now, like you can see from the first, um,


picture


I'm going to take that picture down so you can see the isolated.


Yeah


a trinomial


is a kind of polynomial.


you know, where we have to deal with 3 terms. When we talk about polynomials.


We are talking about um


variables with power, stating from power 2.


So when you look at the trinomial,


um


right in front of you here.


the letter A is a coefficient of the X to the power 2.


which is the highest power in this case.


Let it be is the coefficient to the next


power to let it


I mean to X squad.


which is X on the part of 1. Let's say it's actually a coefficient also to an X-rays to 0.


or because N raise the part 01, you cannot say the X-rays to pa area, so we tag it constant.


I hope that is clear


Now, we're going to the next slide.


of scroll up now


Let me


this down. So we're coming to the slide.


Here we have an example


but two x 2


or the service one.


give me a second


OK, let's walk with this slide first.


We have a next score at plus a 5 X + 6.


Here, you'll length of fat to rise.


first


You're going to deal with a constant sea which equals 6 in this case.


Yeah, that's, that constanty, which equals 6.


You're going to look for two factors of that constancy that will add up to give the middle factor.


the middle coefficient amount.


that is the, the core of Shade of eggs, which in this case is 5.


So what are two numbers that would be multiplied.


you know, that would multiply to give


6 and add up to give 5.


Those numbers are 2 and 3.


+ 2 + 3 is gonna give 5 the main number.


2 times 3 is gonna give.


So those two are the factors we are looking for.


So our answer is just going to be X plus one of them, then Xplore the other.


I hope that is clear


It is clear


OK, I'm gonna have to do some writing on the board now. So I'm going to take some, I mean, those pictures of


if you teenagers picture, you let me know. So I'll put them back later. But for now, I want to show you another case, but I have to write that on the board.


Is that all right


Its alright


OK


So I'm gonna delete


if your latest later, you can let me know. I'm going to repost.


Can you, OK, it's gone.


Now


I'm just gonna, you know


create a question. Let's say why?


What is going on


Why isn't this right


Excuse me


I don't know what is going on to this spot.


It's fine


I'll just try again


Y 2


Y


+ 3


Pick this 3 out.


first


Pick the first sign out.


that is a plus


Multiply the first sign by the second sign.


plus times + is a plus.


Look for two factors.


such that when they multiply, they give you 3


I cant see anything


When they had up, they give you 4.


Those factors are 3


and 1


The bigger is written first, then the smaller nest.


Now, + 0 + 1 is going to end up giving us plus 4.


which is a


plus several times + 1 is going to end up giving us plus free, which is it. So now that I'm


able to bring other factors. I'm just going to split this Y square.


between these two


factors


So my answer is going to be why


plus 3


Sorry about that


i cant see


I don't know what's going on here.


Let's see if we can erase this.


I'll just try and write and hopefully it does right now.


enclosed in brackets of parenthesis.


they have the next why


plus


+ 1


closed


This is a case


Is it understood


I cant see the writing but i understand


Great


Now, um, there is another case I want to show you quickly.


Um, I would like you to know that we cannot cover every aspect of this in one class.


It will be too


you know


too much for you to cope with.


But I'm just gonna cover similar aspects.


as much as possible if we happen to meet some other time.


we'll continue from where?


we, we might stop tonight or today.


try to wipe this off. I know.


Yeah.


Okay


Let's look at this


Y 2


minus


4 Y


let me know if you can see what I've written down the board.


i cant see


right


Uh, I I have to do and adjustment.


I want this to remain


Oh


that's it


Give me a second, please


Okay no problem


I want to make this for


Good


Now, the first step is to extract the first sign.


which is a minus.


multiply the first sign by the next sign.


where you multiply minus and plus. You'll end up having a minus.


Now, look for two-factors of the constant


the will


multiply to give a plus for


and add up to give a minus 4.


So first step is to get two factors of 4 that that would multiply to give a plus for


Those two factors are 2 numbers.


that are the same


So 22 is going to end up giving a negative 4.


negative 2 times 2 is going to end up giving a positive force. So are the two factors.


Now, split this Y squared.


between the factors.


This is going to be why


minus 2


open and closed.


then


another way


Is this understood


So it'd look like (x-2) (x-2)?


Absolutely


You're correct, yeah


It's gonna look like that


I understand it then!


Great, but this is just an aspect of it. There is another aspect of it which I don't know if you're ready for.


in this class


But this is an aspect of it.


i would like to atleast try it out


OK, do you need me to send some questions or you're going to try out on your own and give me feedback.


Can you send them if possible


Yeah, I'll do just that. Give me a moment. Let me go.


fetch some questions, and I'll post it right here for you.


Is that OK


It's fine


All right. But before I leave, I'm gonna repost those pictures I posted earlier and


so you could put down some taints while I'm gone. You don't just stay idle, all right? Is that OK?


Okay


Thank you


All right. Let me do just that.


Alright, attempt these:


1.  x² + 9x + 20

2.  x² – 3x – 10


okay


Do you want me to work it out?


or just send you my answr


answer*


Work it out


OK, you wipe the butt first. I've been trying to get rid of some of these tents so you can have


space on the boat, but if you can do that to your side, please.


Do it, get rid of those


things that posted the pictures.


I've been trying to do just that, but it's not.


responding from this end.


Yeah, just get rid of everything.


so you could have space for work.


Is that good?


I would prefer you get rid of everything.


this


this, and this. Get them off the board so you could have space.


Yeah this up the border in this.


Okay


Good.


So you can start your walk-ins now.


That is correct, very correct.


First question you've solved.


correctly


Keep me enough


Absolutely correct.


I'm impressed by your performance.


so keep it up, all right?


Alright!


Can you now handle the other part, I told you about or do we stop here for today?


I understand everything we talked about today! If we can end it here, that'd be great


You're a great tutor


Alright then, bye...


Bye!


hello


hello can you help me


I am not sure what they are asking for here.


involves using the limit of a Riemann sum.


Are you familiar with that procedure?


It uses summation formulas


Is that what you are referring to?


yes


can you show me


I can but it will take awhile, especially if you are not familar with the procedure or the summation formulas


its fine


can you show


ok


Then you take the limit of that as n approaches infinity


ohhhh


what do you do next


ohhh okay


thankj you


you are welcome.


Have a good weekend


I believe that is correct


that's it.


I will sign off now.


bye


hello


hi, hru?


I am ok. how are you?


i'm fine, thx


Northwood High?


why did u ask that?


Because on the little survey, Northwood High.


what little survey?


You fill out something when you put up a request.


It also says that you are stressed!


wait y'all actually be looking at those lol


we can say that yes


ok, what is your question?


so I'm working with applied related rates and they're kinda confusing, there is a bunch but i'll put the first one up


Ok


How is the height, h, related to the radius, x?


Hello?


I drew an xy cross section of the bowl.


one min


Hello?  are you in a class?


no sorry, I was doing smth rq, now I'm back, what were you saying?


How is the height, h, related to the radius, r?  I drew an xy cross section of the bowl.


like a triangle?


In that equation, y is the height and x is the radius


oh ok


is that the formula?


does it make sense to you?


that's why I'm asking, is h=r^3 The formula


So I guess it doesn't make sense to you.


yes this one is kinda confusing, explain it to me


please


At a particular level h, the x value is the radius


say the radius is 2. what would be the height?


right.


so now you can go ahead and do the question.


You have an equation relating the height and the radius, which is what you need.


the height is related to r by like radius cubed, But doesn't the cube mean the volume


no, the cube is just giving the curve that determines how the height is related to the radius


whenever the radius is some number a, the height is a^3


yes


now take the radius wrt time


I mean take the derivative wrt time


where the w?


come from


take the derivative with respect to (wrt) time


oh


but what's the formula tho, is it the h=r^3 here comes the question again


I wrote the formula on the board. Don't you see it?


nope


where?


I have written stuff below the worksheet


i only see the picture and couple stuff that's it, there are so many things missing here like the 1/2 cm and the 27/8


so you dont see where I wrote h=r^3?


perhaps try refreshing


i see it but where is the n?


there's no n. that's a typo.  go ahead and do that derivative.


ok


there


You have the value for dh/dt, right?


no 27/8


These related rate problems usually  concern an instant in time.


dh/dt =1/2 cm/sec


the units are important


okay but do we need to put the units right now, we can do so once we find the answer


the instant in time they are interested in is when h = 27/8 cm


If you were paying attention to units you would have realized that 27/8 cm could not be dh/dt, because dh/dt must have units of cm/sec


At the instant we are interested in, when they telll us that h=27/8 cm, what is the radius, r?


Typically, as in this case, you can use the formula to figure that out.


yes


Any questions about that?


no so far so good


OK, now you can solve for dr/dt


i got a lot of decimal points


I would suggest using fractions


but whatever your professor wants


yes i think the fraction is better


but how do I calculate it finding the fraction and not decimal


okay i see thanks, can we do another one?


Ok, one more


alright thanks


erase the board and then post your question


oh can you erase the board


i don't think i can do that


there


You need to draw a diagrma


Hello, are you there?


sorry, I should start writing to you when I'm doing other things, but yeah I'm back again sorry


If you are too busy, perhaps you should do this another time.


no it's okay, i can continue now


Do you understand the diagram (reallly, you should have drawn it.)


is the diagram above the water?


No, the diagram is as if you were looking down from a plane.


the beacon is 2 miles out at sea.


okay I see


You need to convert the d𝜃/dt from rev/min to rad/min


okay so


would it be 5 rad/min


How did you figure that out?  No, it isn't correct


would it be 20?


it sounds like you are guessing.


how are you figuring it out?


I thought 1 rev was like 2 rotations


like radians


yes, 1 revolution is 2𝜋


so what would 10 rev/min be in rad/min?


i thought rad were pi, i guess not, so what is it?


what does rad turn into?


radians doesnt turn into anything. Do you understand how I did that?


i mulitpleed 10 rev/min times the conversion factor of 2pi rad/1 revolution


so I was right


no you weren't


i said 20


didn't i?


20 is wrong


well i just missed the pi


it's 20𝜋


Ha


lol


okay so what's next


Now you need an equation to differentiate


You need to relate the distance along shore, which I have called x, to the angle theta


give that a try.


so is the formula x=20pi rad/min?


wait a min


are we gonna use a trig equation?


yes, that is a right triangle


so tan(theta) = x/2?


Yes, you would use tangent. So, what would be the equation?


ima try smth


smth like this?


yes


now we find the derivative?


what is it that they want to know?


the rate of the point where the beam hits the shore


the right side is incorect


what's incorrect?


Well, you will get the right answer, but you really really don't need to use the quotient rule for that


it's just 1/2 times x


so what u said basically means i was correct


Yes, but noone would do that.


but okay I'll change to what u want then


it's simplly 1/2 dx/dt


a constant can come out in front of the derivative


yes, see how much simpler that is?


yes it is professor lol


You know d𝜃/dt


20 rad/min


no, not 20 rad/min


10 rev/min


what was the point of finding the rad then


it's 20𝜋 rad/min, not 20 rad/min


ohhhh


that again lol


the pi makes a difference.


20pi rad/min


again, there is a particular instant they are interested in


you need to figure out the value of theta at that instant


2 miles


okay so how do we find the value of the thetha at 2 miles


at the instant they are asking about, yes, x =2 miles


at that instant, the two legs of the right triangle are both 2


what then will be the hypotenuse of that triangle?


so is it 8


No


not 2


is it 8?


is what 8?


the hypotenuse


no,


it would be the √8


so 4


no


nvm


i'm getting confused


can you write it on the board, i thought we'd use a^2+b^2=C^2 to find that


yes, but you want to know c not c^2


why are we find the square root tho?


the pythagorean theorem is a^2+b^2=C^2 .  Then to find c, the hypotenuse, you take the square root of c^2


ok


so what is the sec(𝜃) at the instant they are asking about?


sec (2) do i need to go to desmos?


just use the triangle that I drew


what is the cosine of theta?


sec(𝜃) =√2


so then would it be 2


for sec^2


so sec^2 =2 yes


answer


80𝜋 miles /minute


That's it.


right


thx


You are welcome


have a good weekend.


bye


you too, bye


Hi Ben


Hello,


how are you?


Doing well, thanks. You?


doing fine alsp


also*


so today we'll be working on applied related rates, I'm kind of confused about it


OK. Can you upload the problem?


yes there are a bunch but let's go one by one


I'm reading it...


ok


Can you give me 5 minutes to solve, and then I'll walk you through the solution?


yes


We can start.


It's a long problem with a few steps.


First step is to draw a diagram. I'll show you.


Do you see it?


yes and I'm not going to lie, it kinda looks like the one I drew. but i have couple questions. How did u figure out that the man should be standing where he and not far to the right for example.com?


e.g.*


The figure can be drawn in more than one way. But the man must be *between* the light and the building.


oh okay, and how abt the 3ft/s, why did you not illustrate it?


That's the next step. Let's write what we know. The man is approaching the building, so dx/dt = -3, correct?


wait why is it -3?


As the man nears the building, can you see that "x" is shinking?


So the rate of change will be negative.


does specifying his height here matter/


Yes, it does. The man is x = 10 ft away from the building. We need to find the height of the shadow, h = ? Can you do it?


wait one min, let's go step by step, on the word problem is also talks about the shadow of the man and that's also what we are finding, so shouldn't also illustrate that, and i think writing on the picture is 5foot tall is also important


Yes, I'll show the 5 ft height.


"h" is the height of the shadow.


his shadow is standing, i usually think shadows are on the ground


Good question. The problem tells us the light is on the *ground*, correct?


yes


So the light cannot cast a shadow on the ground, but only on the building.


The problem says the shadow is on the *side of the building*.


yesss, by side does it mean, on the building like the reflection is on the building wall?


Yes.


oh okay, but now we need to find the formula right


Yes. We know x = 10 ft. h = ?


I was get confused in this part as to know what to use, would it like be the pythagorean theorem?


Are you familiar with "similar triangles", from geometry?


nope, not gonna lie, I never liked geometry that's why things are confusing


I'll explain with a diagram lower on the board.


ok


We have big "blue" triangle and a smaller "green" triangle. OK so far?


yope


Both are "right triangles" (one angle is 90 degrees), and both have the same angle, θ, shown in red. So they are "similar".


In that case, we have the relationship between the sides of the two triangles (blue and green). See the lowest diagram. a/b = c/d.


OK so far?


yea


We'll apply this to your problem. We identify: a = h, b = 30, c = 5 and d = (30-x).


Next, we write the ratios.


That's the last equation. If x = 10, can you solve for h = ?


there


Awesome. h = 7.5 ft. We'll need that for later.


What the question is asking is dh/dt = ?


How can we find it?


it's the derivative of the formula we got


Yes. we need to find the derivative. We start with the equation boxed in green. Do you see it?


yes


We know dx/dt, and dh/dt is "related" to it. First we re-arrange the equation.


On the left side, we have a product to two functions of "x": h(x) and (30-x). Can you use the product rule?


product *of two...


it kinda looks like the chain rule to me


Yes, we also need the chain rule.


The product is u*v, where u = h and v = (30-x). What would be u' = ?


chain rule would be easier tho like


We cannot use the chain rule directly with a product. We must start with the product rule.


The last equation is correct, except that, instead of (-1), we have (-x'). Because the derivative of x is x'.


but the x' becomes 1


We're differentiating with respect to t (time) and not x. Both h and x are functions of t. h' = dh/dt, x' = dx/dt. So x' is not "1".


ok


On the right-hand side of the equation, we have 5 * 30. What is the derivative of 5 * 30 ?


Good.


i have a question


why did you need to rearrange the thing to h(30-x)=5(30) and not just keep the h/30= 5/30-x


Initially, we have (30-x) at the bottom of a fraction. It's much easier to find the derivative if we move (30-x) to the top.


oh okay


We could have left (30-x) at the bottom and used the quotient rule, but it's more complicated.


In the last equation, you know h = 7.5, x = 10, x' = -3. Can you solve for h' = ?


Beautiful. dh/dt = h' = -1.125 ft/s. That's the solution. The shadow is shrinking because of the negative rate.


yes but for some reason the answer only accepts the positive value of that


That's because the problem says it's "shrinking". So you enter a positive value.


If the question asks just for the "rate", you'd enter -1.125. But the rate at which it's "shrinking" would be the positive number. It's a bit confusing.


oh ok


let me send another one, and let


That's all the time I have for now.


me work on it just stop me when I'm doing smth wrong


oh really


we can't do another one?


I'm out of time unfortunately. But it was a fascinating problem. I'll be back online later.


ok thanks


You're welcome. Enjoy the rest of your day.


you too


Hi there!


hii! what do u need help with?


I just need help checking my answers for my math homework :)


sure, no problem!


Okay awesome, i'll put the first question on the screen. Just gimmie once sec


okieee


There you good


go*


okay!


yes thats right


Mia


okay next one


okii one sec


okays


if im not mistaken, this should be the third one :)


first we divide 0.7 from both sides, then we transpose b, then divide r


ohh okay!


Next one :3


yess thats right


Christian


this one should be the first one :)


since to isolate y, we divide pi(x) from both sides


Ahhh okay


got it


yuppp


Next next


i thiinkk this should the answer, may i ask how u got this?


I got like $71.50 but I just put $73 because that's the closest option 0-0


holy fail


im pretty sure we just substitute 4 into the equation here haha, but no worries


Okaaaays


this ones right!


awesomeee


:D


did u just substitute 3 here?


uuuhhhhh


No I don't think so


okay yup this is right


Hmm ok


yep


dis is good


Liam


i think this should be the 3rd, the -3 and 3


Alrighty!


right Muslim


Sophia


righttt


Nice


this is right as well :)


Yay


wait hold on


Noah


yuppp


Greenville


i thiink this is the 2nd


Olivia


This is the last question :)


Thank you for all of your help


you're welcome!!! :))


Bye bye


William


Hello, Chris! How can I help you?


hi so I'm really struggling , the quarter is about to end but I'm failing algebra one, I'm not bad like I showed improvement but there's always a mistake and I did my retake today and I think I did bad on it too, I froze and after I kinda had a a nice attack, I wanna feel used to using elimination and substitution, can you help me?


panic*


Oh, no! I'm so sorry to hear that! :(
I'd be happy to help you learn and improve! You got this, Chris!! :)


Please send me the problem you need help with :)


okay so, the problem was 3x + 2y = 32


I got it from 2 equations and converted it right but I forgot what else to do afterwards


Can you send me the other 2 equations?


I think it were, okay wait I kind of forgot it was about family one buying 3 or 4 medium pizzas, and 2 large pizzas and family 2 buying 2 large pizzas and 3 medium?


something like that


and family one spent 48


family 2 spent 64


Hmm okay, can you set up the 2 equations for me? If you need any help, let me know!


ok


this? I really don't remember


the actual thing


It's okay! From the information you've given me, I'd say you're almost there!


So you said 2 families went out to buy pizza of different sizes. Large (x) and medium (y) (we can switch around the variables, doesn't really matter). Then, we also have the amount of money each family spent on the pizza.


yea


And so we would set up our equation so that we have how much money each family spent on pizza


This would be the best way to find our x and y values


Any questions so far?


none, I understand


I'm glad. Can you explain to me the first equation. Why you wrote what you wrote?


I wrote the first equation like that and made x the medium pizzas price and y the large pizza's price, I took 3 as their amount and 4 as their amount for the large and it equals what they sent ($48)


But you told me they bought 3 or 4 medium pizzas and 2 large pizzas which costed them $48, is that right?


Is that what you wrote?


no not really


It's okay! Can you fix it? :)


Also, lets assume they bought 4 large pizzas instead of 3 to avoid decimals.


ok


medium* not large sorry!


Perfect! Now, can you explain the second equation to me?


Wait, are you sure in the problem, those were the right numbers?


Because the solution does not make sense in this case


the second is because the 2nd family bought 3 mediums or 4 but I wasn't sure either so that amount by the unknown price and 2 larges to the amount but I think in the question it was 2x + 3y


oh wait I have the actual equation written hold on I think


Yes, if you can provide the actual problem, I'd really appreciate it :)


it was 3x + 2y = 48 and 2x + 4y = 64 that's what I wrote on the test and got right


That's perfect!


so it was 3 medium and 2 large


Yes


I want you to write 2x + 4y = 64 on the top


okk


wait actually, leave it


So, any ideas on what we're doing now?


all I know is somewhere in there I'm dividing 64 by 2 and to get the actual equation I think I subtract or multiply but I'm not sure


Yes, you're on the right track!


You're supposed to divide the second equation by 2. Do you know why?


no, not really


is it because uhm 4 and 2 are equivalent or does it have nothing to do with it


You're on the right track again...


If you divide the 2nd equation by 2, you can get rid of the y's and solve for x :)


So can you do that for me?


If you have any questions/doubts let me know! :)


ohh


ok


wait for 4y do I get 2y and then subtract


yes!


so 2x = 32?? or 2x + 2y = 32


very close! it would be x + 2y = 32


ohh ok


So what's the next step?


solving for x, I take 2y on both sides and divide 32 by what I divide 2y by which is 2


not exactly, you need to subtract the 2nd equation from the first one


Because we're trying to get rid of the y and solve for x


so 3x - x, 2y - 2y ?


yes


and 48 - 32


oh ok


so 2x = 16


so what's the next step?


divide 16 by 2 because x times 2 is 16


that is correct! :)


great work!


so the answer is?


yep! :)


so I plug it in to get y?


yep!


ok


and 48 - 24 gets me 2y?


yup!


okk


y = 12


perfect!


Any questions?


okay noted, I understand a bit more. could I get 2 different equations and try solving using elim?


of course! Do you have any or should I find them?


I don't have any , could you please?


Okay, give me one moment! :)


Let's try this one!


wait so my first step is not dividing ? or can I solve for y first. 2x divided by 2 and 19 divided by 2?


or instead add


I think the easiest first step here would be to add y


ok so add the equations together?


yep!


ok


3x = 30 because x+ 2x = 3x and -y + y = 0


and then


divide by 3


yup!


30 divided by 3 is


that's perfect!


ok I plug it in and solve for y now


yes


wait


y is negative or no?


yes!


y is -1?


that's correct!


Do you have any questions?


okay, why was just adding immediately easier than the other one, because we had to divide and subtract then add but for this we didnt


Some of them are more straightforward than others. You just have to think to yourself "hmmm what can I eliminate first? What can I eliminate more easily?" Do you understand what I mean?


oh ok, ohh so since getting rid of y for the other was the best way we had to divide to get what x was?


yep!


okay got it, can we work on one last one and then work on substitution?


Unfortunately, I cannot stay any longer.


I have to go somewhere.


I'm so sorry about that.


ohh ok


it's fine you helped me so so much


I'm so glad I could be of help! :)


thank you !! have a good evening though


You too! Good luck on your journey with math!


You're a very bright student and I'm sure you'll improve immensely if you keep putting in work! :)


thank you, I will!


Bye, bye!


bye!


hello


How may I help you?


hi so can u help me with how to figure out what shape is on my hw


can you put it on the board?


yea


Is it possible for you to upload a picture of it?


sorry im not good at drawing but yea


it’s the last question


That shape is a parallelogram


oh ok and also can u help me with what the shape is next to that one?


i tried asking someone but they didn’t rlly help


There isn't even information to be sure, but it could also be a parallelogram or a trapezoid


most likely a trapezoid


oh ok and i have one more shape can u help me with it?


can you upload it also


just the first one


The first two shapes are both trapezoids


oh ok


thanks for helping me


you are very welcome


have a good evening.


bye


Hello, what can I help with today?


hello


I have plotted the first two points


I believe they are right


Ok let me take a look


I cannot figure the last one


Okay so do you know the easiest way to do reflection over y = -x?


no


i do not


Ok I am pretty sure for any point you can just swap the coordinates (x and y) and then change the signs of each


So for example, D is (-10, -7)


what would it become


Yes


I think you drew it at 9,10


Okay and now for the other points E and F lets check them using the method


So E is (-3, -7) right?


After reflecting over y = -x what would it become


so 7,3


Yes thats right


Okay next is F


can you do this one and ill check if its right?


yes thats right


so the points are right


Yes I believe so


Did this help?


Okay this one is kinda like the same process


before we swapped x and y and changed the sign because y = -x


We only had to change the sign because x is negative


but now we don't


Yes so since its just y = x what do you think we can do


r is -10,8


Yes


So you just have to swap, no switching of signs


s is -3,8


Yep


-8,-2 for t


Yes that looks right to me


Ok this is the same reflection y = x


is that right?


This looks right


Great this one looks right too


So for reflection over x = -1 you just have to multiply each x by -1


So like L is (-3, 4) we take -3 (-1) so its just (3,4) now


That looks correct now


Hm did it say it was wrong?


yes


but because it was only supposed to be two points away from the line


Oh okay I think i get where we messed up, sorry about that


i did three


it is oki we all end up with them


Okay


Let me check really quick


Yes i think so


Ok this looks good too


i multiply by one?


Not quite i think we messed up one part last time let me double check


Okay the formula is this for reflections over lines:


2a -x, y


So the y will stay the same and a is the line that we reflect over


So we have x = 1, a is 1


oki


So we can try with point U(4, 9)


2(1) - 4


x will be -4


well we have 2-4


Yes


and y stays the same


So (-2,9) should be right


is that right?


Ill check each one really quick


Okay yes good that looks right


Yes!!!!


Great job!


finally


I hoped this helped


you really did


So i would just remember the few "formulas" for reflections


thank you for beleiving that I could do it by myself :)


The one we messed up on for x = -1 would have been the same as x = 1 except you would do 2(-1) - x, y


Yes no problem great job today


anyways have a good day


You too!


help with number 2


are you familiar with the quotient rule?


yes


ok, so lets start filling it in


should we distribute the exponent first


In my opinion, yes I would change the (3x^2)^3 into a single expression


yep


before we start filling it in lets write out our expressions


I filled out f(x) and g(x) What would f'(x) and g'(x) be?


yep, so now we can fill in the quotiant rule expression.


do you eant to star simplifying that?


numerator = -108x^6+648x^6


denominator stays the same right


Yep, you can combine the like terms in the numerator if you want


honestly, with derivatives like this,  how far you simplify is really up to your teacher. the derivative can be further simplified, what is your teachers rule with simplifying?


I think simplify as much as you can


ok, what I say is write the unsimplified answer that we have so far, but just in case lets simplify it all the way.


I don't think we simplify it like that


yah, most calc teacher dont want students to do so much arithmatic. I think the best answer to write is the one I boxed because it shows that you simplified the exponents of X but you didnt do the further arithmetic simplification


ok


does it make sense? I want to make sure you get it


yes


I completed question 3 idk if its right


whats your answer. I can check it


yep


ok can you check 4


numerator = 20x-3


denom = 2x^2+10x^3


I think I did sum wrong it doesn't look right


ok, I will work on it and check it and you can follow along ok?


let me know if you have any questions as I go?


That can be further simplified, but I am going to use a calculator to check my answer really quick and then we can go over it


ok, are you ready to go over it?


so the first thing I did was the quotient rule


also, since were running out of whiteboard space, I am going to delete the stuff above on questions 2 and 3 ok?


so lets first define our expressions in the quotient rule.


what would f'(x) equal and what would g'(x) equal?


Hey, I just wanted to let you know that I am going to end the session, but I left the work for question 4 on the whiteboard and I filled in the answers that we went over. Feel free to start another session if you need any more help.


hi


Hi Sam, what's up?


I see, we have some graphs and need absolute min and absolute max....right?


yes


ok, for g.....what do you think? absolute min=?


perfect!


absolute max=?


any ideas?


you got the 5 because you are looking at the left part of the function right?


do you know what that arrow means, where the function alongong with the dashed vertical line?


no


ok, so that is the important thing thee arrow means that the function keeps going along it doesn't end with the arrow, they just can't keep graphing it because we ran out of space


so the function keeps going up and up and along there is not absolute max


*no absolute max


oh ok


while we are at it, let me explain the dashed line.e dashed line is called an asymptote. The arrow with the dashed line means that the function keeps going up and up and alongd as it does that, it keeps getting closer to x=-5 (the dashed line), but it never quite touches the dashed line


have you seen that before?


good, should we move on to the other function....h?


min of h = ?


yep


and max of h =?


very nice.....


do you have more?


It's been nice working with you!


you too


Hello


hello


How may I help you?


I need help on my math homework


ok, can you show me a problem?


there


I have 29 questions


but I'm already working on question 2


let me show yo


u


OK, well I guess I am not doing 29 questions


oh


ok


let me show you how I do it


there's the equation


heloo


I am here.


oh ok


What do you get for an answer?


That's not quite right


what is 8 times 8 ?


and what is 64 + 4 ?


ok next qeustion


by I got to leave


hi


hey!


ok one sec


Do u use vc?


Voice chat


no


okay lets get started


OK, I know you can't hear me, but it should translate to words.


The first thing that we need to do is


we need


substitute


into the function.


So, basically we're taking F and we're replacing X with x + H.


So then it would look like this.


ok


OK, I'm gonna move down a little bit here, but


it would be


negative


with H


weird minus 2.


And then when we expand this, it would be


remember it was a negative sense it would be negative x^2 +


So here we're just combining all like terms.


So this is all the like terms, and now what we're gonna do is we're going to subtract F of X from f(x+h) + H. So now what we're gonna do is we're going to


do this.


all of this, and I'm just gonna go ahead and move this down.


So I need all


this


minus


yeah but


all of this minus


f(x) because this is the original function.


to


uh


for


you need to distribute the minus.


So it would just be


it would just be all of this.


and then it would be


plus x^2 because we're distributing the minus


+ 2 X.


minus 4.


Now we're gonna combine like terms, so we would get negative


XH


because


these cancel out


these cancel out, and then these cancel out. So we're left with this, this and this.


And now I had everything by age.


22 X.


minus 8


minus


the final answer


ok


so all were doing is


subtracting f(x) from f(x+h)


nd simplifiying by dividing by h


do u understand?


yes


perfect


do you need help with anything else?


okay!


could u upload it for me


okay can u show me wat you know so fat


dar*


far*


sorry


ok wait let me walk u through this


so first


OK, so the first thing we would do is we would substitute


-3 into the X values for both.


FFX and GFX.


So I'm gonna show you what I mean.


We would do


F of -3.


over


G of -3.


So when we do that, we're gonna get


first let's do them independently. So if we were to do F(x).


you would get -3 minus 6.


and then


One second. We would get FF 3 or -3 minus 6.


times


So it's gonna be negative 9


which is just -9. So at the top, we would have -9.


Bottom, we need to solve GFX.


So that we would do


I get a a times -3.


-1 to the 24


minus 1


RA


Your answer is -9/23.


Part B, since we're dividing whenever we're dividing something, the bottom value can never be zero.


because you cannot


by 0


So it means is that we need to make GFX equal to 0, and whatever this answer is, that's gonna be our domain restriction. That's gonna be what it can't be.


So we're gonna have, A X minus 1.


is equal as your


so then we get


8401 and we divide both sides by -8.


and then we would get X is equal.


to -1.


So this is going to be your answer for Part B and Part A. Do you understand?


so we plugged in -3 into f(x) and g(x) and did f(x) divided by g(x) and then we got our answer for part 1


and then the bottom (g(x)) CANNOT be 0


so we set it to zero to find the domain restiction aka part b


do u understand?


yes


ok perfect


do you need help with anything else ?


no


ok have a great day!


hi


Hi


mic?


I don’t have that option


OK Qs?


I need help on this assignment    In one paragraph, compare and contrast the goals of command and mixed market economics, and explain why there are many more mixed market economies than command economies in the world today.


ok


Create a Pros and Cons of comand vs mix market


command - N, North Korea, Cuba, Soviet Union etc


look at their imports/exports; GDP, resources etc.


start here and can elaborate


oh hey John


Hello.


what is your calculus question?


I was gonna try calculis


I was gonna see if I can learn anything from it


cuz I never did it before


if you are in algebra 1, you aren't ready to learn calculus.


so I wanted to try something new


well alright


hello


can you help me with thi


Hello


hi! sorry i was struggling to connect


Um, it's fine. I just had a question. I mean, I just need help with this.


okay so for the equation on right, y is greater than 2x + 3


Yes, I see that


so this means that the area of 2x + 3 is going to be on the left of y, or the line of the equation


so using that info we can already eliminate two of the graphs


and we know its either these two


and then we can choose which one matches with the equation


so which do you think it'd be?


the second one


yep !


and for the other equation


Um, so it's this one.


Is that right


yeah!


OK. Lastly is um the X + Y is.


in the negatives.


yes, so we subtract x and that means the slope is negative


so theres two graphs with negatives slopes, do you know which one matches?


Um, my Emily, is that correct?


yep!


And that's all


Or do we have to separate both of the other two graphs.


i think you just need to match up the two equations with the graphs we circled and you can leave the other two alone


OK, I agree


do you need help with anything else?


Um, yes, give me one second.


Um, there's a new one on a whiteboard, if you can see it.


Um, the, this is the one I need help with.


so for this one


since it says solutions are in the same region


that means that it can be anywhere where both graphs overlap


OK, so, um, how do I, um, plot it and so I can check my work.


drag the black dot to where you want it to be and then you can check


OK, um, thanks. I did that and um here's a new one I'm having trouble with. Um, use the wiperition show understand it.


so this is basically the same as the other one except they dont give us the colored portion


but we can find that on our own


so first we can isolate y to make the equations easier to look at


so for the first equation we just move x over


OK, so what will it be in between of, can you put the dye on the glass so it betters my understanding.


so since y is greater than 1-x, this means 1-x is to the left of y


Yes


Um, so, I have to plot in that highlight, so we got it.


and then you can do the same with the second equation to find the highlighted portion of that


Um


I already finished writing this out, but I need help with plotting. What did I plot as for both equations.


can you show what you highlighted for the second equation


what do you mean by 4.5


Hey, i see u got some geometry work


wanna get it up on screen?


Yes are you able to use the microphone


OK, can you hear me now? Or, or no?


Hello


Yeah, I hear you


OK, I can hear you. Yes. Thank you.


OK. So, um, are you able to get the work on your, on the screen or, or what?


Yes, let me just take a picture of you.


OK.


OK, here it is


OK, I see it


Uh, I'm just gonna read it first and then I'll let you know.


Yeah


OK. So


um


do you have like a specific question or is it kind of like overall


um pretty confusing


So my teacher in my class


uh, teaches me that I have to translate it first, so I would translate A to A.


and then I will rotate it, I think he said, but I don't really, I have a really hard time with rotation.


or reflections


Yeah, those ones are a bit harder. So,


one thing I see is that


yes, you can translate it, and by translating it, you mean like you can just kind of move that the first triangle, like the one in the bottom right up and to the left, right?


Yes


Yeah, until, and then you have A and A overlap. You might notice that when you do that, another point also overlaps.


Yeah, B


Right.


So what you can do from there is


it's kind of hard to visualize, but as you practice visualizing that, you'll get better at it. So


right now, for me, for example, it's pretty easy to visualize it, but it wasn't always like that. So the way you go from one of those to the next is by trying to visualize it. So see if you can just practice like almost like moving it in your brain until that AB line is overlapping the other one.


and see if you can kind of see the shape that you get from there.


That would be like a diamond.


Exactly, yeah. So, then what, what I noticed from there is that I can actually just reflect


that triangle


over the line AB.


So like this is the line AB and this I can like rotate. I could rotate it around or I could flip it like like this, like flip it or just rotate 90 degrees.


Uh oh wait, actually, no, rotating wouldn't work. Um, so here you would just have to flip it.


like a


you know, imagine this is like a page in a book and you just flip it over like that.


Mhm.


So


what I would do first is that I will translate it.


and then all I have to do is flip it. So how would you flip it?


Yeah, so, like how to describe it or you're struggling to kind of see it?


be it?


OK. So


I'm gonna draw what the shape looks like now, so it's kind of, we go from there.


Mhm


So it kinda looks like this and I flip it so that this C or this C here gets turned all the way to here.


Not rotated but flipped. So like this goes really over like this technically.


like flipping a page, right? This is like the middle of the book.


and I flipped the page over onto the other one.


Yeah


Mm.


that kind of help you see it or it's still a little weird in your head?


OK.


No, no, I, I can see what you mean, but I, I wanna know like


is there like a method to flipping it, like I have cause I have to show my work to my teacher.


Oh


Um, yeah, that's kind of weird.


Showing work for this kind of thing in general is weird. Like even


translating it is really like, does he want you to redraw it, um, I don't know. Um.


Like he wants me, let me show you, for example, like translating.


Like he wants to me to make


a


he wants me to make a line from A to A, right?


Oh, OK.


see.


And then, then just like, cause I have a compass and I would just like measure each side, and then I would like connect them, and then it will be like a shape like like this.


Hm


OK. Yeah, I guess, then once you've done that, what I would show is just C like as this new triangle here, see how simple I could draw the arrow to C and keep the others in their spot, cause there's only one way to do that, and that's a reflection.


Mhm, yeah