also when we are done can you leave the session running so i can get more voleenter hours haha


ok


why


c


if you leave it open its just easier for me to get my voleenter hours


ok just help me with the answer


sure


fewer


her army


thanks you


is that it or


wait one sec im checking


i think its beaten


whats the second one


show me options for second part


powerful


a


b


yes


hi


mb gpt discpnnected


if u need any help lmk


hi there!!


Hi


what would you like help with?


Ratios


I didn't learn it yet


okay, do you have a practice problem we can work on?


No


do you want me to come up with one?


Yes please


Since I haven't learned it yet


oki


so when we are handling ratio problems


we can use multiplication and division to make the ratio bigger or smaller


so in this case


what did we do with the 3 to turn it into 12?


did we divide 3 with a number


or did we multiply 3 with a number


We multiplied


yup!


what number do we multiply with 3 to get 12?


yep!


Yay!


ok thats the first piece of the puzzle


now in order to get the number next to 12


we gotta do the exact same thign to the 4!


which is multiplying by 4


so what is 4 times 4?


yes!!


we solved it!


good job :3


YAY!


ok lemme give yah another problem


Yes!


alrighty


try this one C:


Okay


Is it 3:4


yup!!!


wonderful job C:


Yay!


do you want more practice?


Yes


oki


try dis one c:


nice!!!!!


dats correct C:


aother one?


:D


oki try this one


Awesome!!!


ur really good at this problem!


want another?


Can we do I word problem


Cuz no joke I suck at word problems


try dis one: The boy-girl ratio in a class was 3 to 5. If there were 24 students total, how many boys were there?


Um I need help pls


sure C:


Thanks


so this is how i would find the anser:


Ok I'm listening


so we have 3:5 ratio


Yes


we add the two together 3 plus 5


we get 8 right?


ok so the total we have is 24 right?


what do we multiply with 8 to get 24?


same process as before C:


right!


okay so then now we know what we must do


multiply by 3


so just do that with our original numbers


so what would our new ratio be?


yup!!!!


lets check our answer


Ok


so we have 9 boys and 15 girls


add them together to see how many total student


It's 24


yup and did our original problem say 24 students total?


Yes


yayyyy we are correct <:


want another one?


Yes pls


oki


Yours such a kind soul to help me


aweee i love helping yall, i wish i had math help back then so i really enjoy doing this now C:


try this one! A fruit salad contains apples and grapes in a ratio of 4:7. If the bowl has a total of 66 pieces of fruit, how many grapes are in the salad?


nice!!!!!!


dats correct!!


:D


want another one? :3c


Can we try a harder one


yuh


To put my brain to the test


Because sometimes I'm dumb as heck


A special concrete mixture requires cement, sand, and gravel to be mixed in a ratio of 1 kg:2 kg:3 kg by weight. If a total 180 kg of concrete mix is needed for a project, how many kilograms of sand are required?


Ii think


yup!!! youre totally correct!


YAS


okay wanna try a super hard one?


YES


A farmer has chickens and ducks in a field in a ratio of 5:2. If there are 42 birds in total, how many additional ducks would the farmer need to buy to make the new ratio of chickens to ducks 1:1 (equal numbers)?


I have been humbled I need help with this one


heheheh sure


so first lets find out how many chickens and ducks the farmer has


can you tell me that? in ratio form?


well thats the ratio


but da farmer has 42 total birds


That's a lot of birds


yuh so lets do the process we normally do


Ok!


so 5 plus 2 is 7 right?


Yes


and we wanna change 7 into 42


what do we do?


Multiply the 7 with 6


yuh!


ok so whats the farmers ratio of birds


knowing that you must multiply the original ratio by 6


okay!


which number is the ducks number?


That's where I'm confused


oki


lemme copy da word problem here


so when we read these problems


we should write it out like this


so 5 first then 2


in the problem it mentions chickens THEN ducks


Wait does the farmer have 12 ducks


yup!!


cuz for every 5 chickens he has


he has 2 ducks


so since he has 30 chickens


he has 12 ducks total!


YAY!


buttt


we didnt solve da problem yet


we need to know how many ducks he needs to buy in order to get 1:1 ratio


Yeah


all of these ratios are similar!


because they can be simplified to 1:1


How


if we check out 3:3


we can divide the ratio by 3


3 % 3 = 1


so both sides become 1


Ok


we can divide the 9:9 ratio by what to get 1:1?


yup!!


how about the 20:20?


yes!!!!


But our ratio is 30:12


so how many ducks does the farmer need to turn this ratio into something that can be simplified to 1:1?


if we have 12 ducks


YES!


you solved it!!!!!


Wait really


yup! the farmer needs to buy 18 ducks to get a 1:1 ratio C:


See I totally did that myself


hehehe you sure did!!!


well done


Woohoo!


would yah like another practice problem?


Yes


okay lemme get another hard one


Yes!


alright this one is pretty hard!


A classroom has a certain number of boys and girls. Initially, the ratio of boys to girls is 3:4.
After a field trip, 6 boys and 2 girls leave the classroom. The new ratio of boys to girls becomes 2:3.
How many students were in the classroom originally?


I thought you said hard not impossible


hahahaha dont worry imma show yah some tricks


Ok


so when we are working with ratios we gotta be able to use variables


so lets write some of this stuff down


this is another form of writing a ratio


with a fraction


which number is boys? 3 or 4?


yuh


so 6 boys left


lets write that as -6


do you agree?


Where do we get -6


cuz we are subtracting 6 boys


cuz they left


Oh


yah


Yeah sorry


no worries silly :C


oopsie


C:


okay so 2 girls left


so minus 2?


Yes


Okay!


so now after those people left


the ratio is 2:3


so im gonna say this new ratio


is 2/3


does that make sense?


It's my enemy a fraction


hehehe yeh they sucl


suck


does this make sense so far?


okay now we can add the variable part now


so which total do we wanna find


before the people left


or after the people left?


Before


right!


so lets add an x


right next to the original ratio numbers


this x is a variable


it is not a multiplication sight


sign


Ok


okay!


we can solve for this now!!


do you know how to solve for the x?


Cool


Do you wanna help me with that to


oki sure


so we wanna unravel this ugly equation


I don't under do I take apart the top and bottom to solve it separately


this is what i would do


i hate fractions


Same


so lets completely remove them by doing this cool trick


so what you can do to remove the fraction is multiply both sides by the bottom number


so 2/3 times 3 becomes?


6 over 3


yup and what does that simply to?


yup!!


so notice how we just got the top number by itself?


when we multiply a fraction by the bottom number


we just get the top number by itself!!


they cancel out!


Yes


ok so lets continue writing this


okay this is what our new problem looks like


does this make sense?


the 3 multiplies the top number


cuz we multiplied by 3 on both sides


Yeah


okay


so how can we get rid of the 4x - 2 on the bottom?


using the same trick we did on the 2/3?


Maybe combining like terms


hehe its more simple den u think!


Ok


multiply both sides by the bottom number!


so multiply both sides by 4x-2


I'm a bit slow don't laugh at me!😀


no worries C:


so what happens on the left?


I think it cancels out


yes!!!


okay imma rewrite the canvas cuz we are at the bottom of the board


Yes


ok can you solve for x now?


Is it 2


hmm


check ur work by substituting x with 2 :3


and seeing if the equation comes out to true


Is it -2


nawww its a bigger number then 2 :3


Qi see my mistake


o oki


BRB I need to lock in on this problem


gotcha


14 is correct!!!! but the answer is positive 14 C:


I always mess up my signs


its okie c:


sooo we didnt entirely solve the problem


we know how much to multiply the ratio tho!!


What...


we need to multiply the ratio by 14


cuz 14 is x correct?


yes


so whats our new ratio?


A classroom has a certain number of boys and girls. Initially, the ratio of boys to girls is 3:4.
After a field trip, 6 boys and 2 girls leave the classroom. The new ratio of boys to girls becomes 2:3.
How many students were in the classroom originally?


yuh!!!


now is this our answer?


read da word problem and tell me C:


Yes


well it wants students total


not just a ratio so what should we do


we have 42 boys


Add


56 girls


yupppp


whats our answer then


I'm so smart right


Yes!!


yeah!!!!!


Students


you solved it!!!!!


FINALLY


that one was super hard huh?


alrighty! want another oe?


one?


No more word problems


:P


do you need anymore help? :3c


Can we practice solving the problems


So I can be the smartest in the class


Jk I'm not


hahaha which problems? :3c


Any you choose


okay wanna do a variable problem?


Sure


oki


wanna solve this one?


Which one


solve for x :3


Which problem


imma circle it in blue


Ok


there yah go :3


You really what me to suffer don't you


muahahhaahaha!!!


maybe :#


Your evil


Help me


Student so first combine like terms


Me no understand


which numbers can you combine


3x with the 2x


yuh


what else


how so?


(\_/)
('^')
(> 🎁 I don't really know


Hmm


so 42x is alone


so we cant really combine it with anything


what about the right side?


do you see any numbers that can be combined?


X and 2x


hmm so we cant really combine terms that are away from each other on the fraction


OH


you can think of the top part of the fraction and the bottom part of the fraction as islands


3 and 4


we cant combine anything beyond the big line


yup!


ok lets rewrite our problem


what does 3x plus 2x equal?


ok what about the 3 and 4


How did you get pink for the white board


there is a color thingy right next to the letters Aa


ok do you remember the trick we used to get rid of fractions?


cuz we hate fractions!!!


No not really but don't you put the bottom numer and multiply on the right and left


yup!!


we multiply the bottom number on the right and left


so which fraction do you wanna get rid of first


which side?


THE RIGHT


Got it!!


so lets multiply both sides by da bottom number


Yes


Also I don't have the Aa


oh weird


Alright so this is how it looks like


how do we get rid of the 42 x


We multiply on both sides


mhm!


Yay!


okay!


and thats pretty solveable would you agree?


Can you make it simpler since I'm running low on brain food


heheh i would love to but i hafta go now :C


sorry!!


It's OK!


Bye


bye bye c:


hello


Hi


How can I help you?


how would i do this


Give me a second


how do u know amplitude


no phase shift mean nothing like sec((....+ ....)


how do u know amplitude is 2?


2 sec mean maximum point is 2 for y


its supposed to be sec2/3x2


sec2/3x + 2


Hello what can I help you with


Uh, can you hear me?


No sorry I can't do mic right now


Ok


I’m going to take pictures of the work a have so we can solve it


That would be great


Can you see it


Yes


Let do number one


What are your thoughts


I don’t know do we graph it


I think is B


You need to rely on the properties, so you don't need a graph, keep in mind that dialations are often multiplications


I thought we were doing the first question A


Yes, the options that seem like a dialation are d and c


No this one


Which one ?


The first question 1


Hello Jamie, what can I help you with


I need help reducing terms


Factoring polynomials?


yes


Ok, in which part you need help


I need help with understanding how do I find the lowest term.


Could you please provide an example to understand what you mean


its a picture


It's fine


3/6 in it's lowest terms


would it be 3?


That would be a simplification of a fraction, it would be 1/2


so what about 5/10


ok one more but I want to try


Alright


What about 3/21


You always want to ask what you multiply by 3 to get 21, and then simplify by dividing by the number you got


I get it


Notice that not always you will get a 1 above in the fraction because you just can't divide any further. However all these problems including 3/21 do end up with a 1 above the fraction


See it like this: always try to divide the bottom number by the one on top.


Let me know in which part are you struggling and I would try to help.


Oh, sorry I didn't look on the graphs , YES, you did it correctly


Is there any problem or misunderstandings I can help with?


Hi Sam! What do you need help with today?


Hello :)


I need help with my algebra homework


Have 26 questions :(


I


Left to do


Sure! Can you upload it to the whiteboard?


I’m so lost


Okayy


Don't worry, I can help!


Yay!


Ok, so if he takes 4 breaks, then he must work 4 times, right?


Yes


Ok, and how long does he work each time?


40 minutes


yes, and what's 4 times 40?


Is 160


yes!!!


so he works 160 minutes!


Now same logic for b


So of he worked for 6 hrs and each session 40 minutes, then how many sessions did he have?


So do we do 6 x 40


No, but good try!


We have to first convert 6 hours into minutes?


Oh


Do you know how?


No


Ok so one hour = 60 minutes


I know one hour is 60 minutes yeah


so 6 hours would be 6 times 60


and that is...


Correct!


Now we have to 360/40


to find the amount of sessions


and what 360/40?


no 360 times 40


360 divided by 40


Ohh


Oops


it's ok!


It 9 then


yes!


so there are 9 sessions


now each session has a 20 minute break.


so what do we do now?


Wait I got confused


so since there are 9 sessions, each with a 20 min break, we have to do 9 times 20


and whats 9 times 20?


yess!


now that's the answer


Ok onto the next question


Did you understand #2?


A little


Should I go over it again?


Yes please


Ok, so the question says that he has worked on the project for 6 hours.


We found out that 6 hours is equal 360 minutes.


And the pre information says that he works for 40 minutes straight and takes a 20 minute break.


So we have to 360/40 to find the number of sessions that he has worked


And since that is 9, then that must mean that he has taken 9 breaks as well.


And each break is 20 minutes,


so we have to do 9 times 20, with 180 minutes of break.


That makes more sense now


That's great!


Should we move to the next question?


Yes


Ok so let the amount of push ups he did on the first day be x


And what would the number of pushups be on day 2 if it goes up by 1 each day?


No, if Day 1 was x, then day 2 would be x +1


because it went up by 1


Oh


so what would day 3 be?


if it goes up by 1 again?


Yes!


And that would simplify to...?


Hello?


Uhh


Just x+2


yes!


I think


Oh okay


and day 4?


do you see the pattern here?


Wait is day four x+3


yes!!


what about 5 and 6?


Day five is


X+4 I’m guessing and 6 is x+5


Exactly!


now we add everything together


How many x s are there?


try counting again


you're really close


Is it 6


and what's 1+2+3+4+5?


yesss!


and we know that the total is 39


now do you know how to solve for x?


No idea


What do you mean x


it's just a variable


it can be any number


it's what we're solving for


so we have to get it alone


what's 39-15?


you're close


My bad 24


yes!


wait sorry i accidently wrote 5x instead of 6x


It’s okayy


So on the first day, he did 4 pushups.


do you understand?


Not really


So the problem says that it goes up by 1 each day


and that the final is 39


and we are looking for how many he did on the first day.


So if you just label the number of pushups that he does on the first day x,


then the next day and the day after, you have to continuously add 1.


once you do this for 6 days, you add them up and set them equal to 39


and when you solve for x, you get 4.


Hello?


4 is what he did on the first day


Yeah


it's what he did on the first dy


Ok, I have to go now.


Good luck with the rest of your problems!


Hello Liam what would u like help with


can you help with long division


Set it up
Write the dividend inside the long division box and the divisor outside.

Ask how many times
Look at the first digit or first few digits of the dividend. Ask: how many times does the divisor go into that number?

Write the answer on top
Write that number above the box (over the digit you used).

Multiply
Multiply the divisor by the number you wrote on top.

Subtract
Write the product under the number you used and subtract.

Bring down
Bring down the next digit from the dividend.

Repeat
Keep doing: divide, write, multiply, subtract, bring down until you bring down all digits.

Remainder
If you end with a number smaller than the divisor, that is the remainder.
If you want a decimal, add a decimal point to the answer and add zeros to the dividend, then keep going.


can u pracice with me


yes of course


8472 ÷ 6


Here are the steps to solve:

Set it up: 8472 ÷ 6

6 goes into 8 one time
Write 1 on top
1 × 6 = 6
8 − 6 = 2

Bring down the 4 to make 24
6 goes into 24 four times
Write 4 on top
4 × 6 = 24
24 − 24 = 0

Bring down the 7 to make 7
6 goes into 7 one time
Write 1 on top
1 × 6 = 6
7 − 6 = 1

Bring down the 2 to make 12
6 goes into 12 two times
Write 2 on top
2 × 6 = 12
12 − 12 = 0

Answer: 1412


Can you help another


Sure — here’s a step by step 9351 ÷ 7.

Set it up: 9351 ÷ 7

7 goes into 9 one time
Write 1 on top
1 × 7 = 7
9 − 7 = 2

Bring down the 3 to make 23
7 goes into 23 three times
Write 3 on top
3 × 7 = 21
23 − 21 = 2

Bring down the 5 to make 25
7 goes into 25 three times
Write 3 on top
3 × 7 = 21
25 − 21 = 4

Bring down the 1 to make 41
7 goes into 41 five times
Write 5 on top
5 × 7 = 35
41 − 35 = 6


do you want me to give you some to practice?


Yes pleas


Here are 10 pratcoce questions

9351 ÷ 7

12048 ÷ 8

7635 ÷ 5

5049 ÷ 9

14652 ÷ 12

18720 ÷ 15

23184 ÷ 18

29403 ÷ 21

33696 ÷ 24

72549 ÷ 11


okay my answer are


9351 ÷ 7 = 1335 R 6

12048 ÷ 8 = 1506

7635 ÷ 5 = 1527

5049 ÷ 9 = 561

14652 ÷ 12 = 1221

18720 ÷ 15 = 1248

23184 ÷ 18 = 1288

29403 ÷ 21 = 1400 R 3

33696 ÷ 24 = 1404

72549 ÷ 11 = 6595 R 4


can you check?


seems to all be correct. Need anything else>


no thank you


alright have a good one!


Can you quiz me on ratios before my quiz tomorow


Sure


ill give you 25 questions and you can answer them, is that good for you>


Yes can you


Simplify the ratio 18:24.

Simplify the ratio 45:60.

Simplify the ratio 72:90.

Write the ratio of 14 girls to 21 boys in simplest form.

Write the ratio of 36 red marbles to 48 blue marbles in simplest form.

A recipe uses 3 cups of flour for every 2 cups of sugar. If you use 12 cups of flour, how many cups of sugar do you need?

A paint mix uses a ratio of 5 parts blue to 3 parts yellow. If you use 15 parts blue, how many parts yellow do you use?

The ratio of cats to dogs at a shelter is 7:5. If there are 35 cats, how many dogs are there?

A map scale is 1 inch : 8 miles. If two towns are 6 inches apart on the map, how many miles apart are they?

A drink is mixed in the ratio 2 parts juice to 5 parts water. If you have 35 total parts of drink, how many parts are juice?

In a bag, the ratio of pennies to nickels is 9:4. If there are 36 pennies, how many nickels are there?

A class has a ratio of 3 freshmen to 2 sophomores. If there are 18 freshmen, how many sophomores are there?

The ratio of wins to losses for a team is 11:3. If the team has 33 wins, how many losses does it have?

A box has red and green blocks in the ratio 4:7. If there are 44 blocks total, how many are red?

A bag has 48 candies split in the ratio 5:3 (chocolate:fruit). How many fruit candies are there?

Divide 56 in the ratio 3:5.

Divide 90 in the ratio 2:7.

Divide 144 in the ratio 5:7.

Divide $84 in the ratio 4:3.

In a group, the ratio of adults to kids is 5:8. There 39 people total. How many are kids?

A car travels 180 miles using 6 gallons of gas. Write the ratio of miles to gallons in simplest form, and find the unit rate (miles per gallon).

On a test, the ratio of correct to incorrect answers is 17:3. If there are 60 questions total, how many were incorrect?

The ratio of boys to girls is 4:5. If there are 9 more girls than boys, how many boys are there?

A mixture has sugar and salt in the ratio 7:1. If there are 64 grams total, how many grams are sugar?

The ratio of blue to red beads is 3:2. If you add 10 red beads, the ratio becomes 3:4. How many blue beads were there originally?


Alright you have 30 minutes to solve these


meet back at 8:20


Are you ready yet?


I have to go sorry


continue another time


Hi I need help looking over my corrections for AP Calc AB Unit 5 test


It's on critical points, relative and absolute maximums, and 1st and 2nd derivative tests


Hi Zara! I can definitely help you


Thank you!


My test is on the screen but I also have my corrections


would you like me to show you that


this is the first page of the test


Yes if you could. I can also see where your mistakes are from page currently on screen


Okay I will put it on the screen


Okay I see it


Okay


For part (a) I would also say that the f'(x) is equal to zero indicating a relative min or maximum


Since before x < -1 f'(x) is negative then afterwards (x > -1) f'(x) is positive.  that means the function f(x) is going down then going up indicating a relative min like you said: decreasing then increasing


Yes okay


For part (b) x = -5 being a relative maximum is correct, but could you explain your reasoning for x = 7 in your corrections?


I don't really remember why x = 7 is also one


That's okay! You might've written it down because it was in your original page


Ohh okay. Yeah it's because a different person explained it to me and said that I may want to include it if my teacher taught me it


Okay if your teacher said to include it then keep it in your answer key. There can be multiple ways to define relative mins and maxes especially on the boundaries


Okayy I will ask my teacher


I also see the reasoning you have in part (c) but I would be careful because part (c) is asking for a range of values not specific points


ohh okay


so would I write an interval instaed


Yes and there will be two intervals where f"(x) will be > 0


Sorry less than 0


Ohh okay


could you explain (c) please because I'm confuse


confused


Yes no problem


Since you have the graph of f'(x), the slope of f'(x) will be f"(x) because that is what the derivative measures


yess


So when the slope is down in the graph then that's when f"(x) is negative or less than zero


ohh okay that makes sense


what do you mean down though


If you draw a tangent line to any part of the curve, if the line is pointing downwards or negative slope then f"(x) < 0. I demonstrate with the pen on the whiteboard


okay


ohh okay that makes sense becuase the slope of f'(x) is decreasing


Yes


can I writ the interval like this


Yes! Good job! I got the same answer for c


Okay thanks!


You also made sure to make the intervals as parentheses since at the endpoints f"(x) is equal (not less than) zero


Great job


okk yes


Would you like help with the second page of the test?


yes please if you have time


No worries I do :)


I can see the second page


okay sounds good


Could you put up the graph to the side?


yes


does this work


Thank you, yes it does


okk


For part (d) points of inflection are where f"(x) is equal to zero


ohh okay


so where the slope of f'(x) is equal to zero


Yes


do the numbers I wrote down work


Yes those are correct


okay


For part (e), concavity is up whenever f"(x) is greater than zero


so would it be (-1,2)u(5,7) still


The second part of the interval is correct. Try thinking about the first part


Perfect!


Moving on to part (e), I think the answer has to be x = -5 because that's the only maximum I saw, but Im unsure about x = 7. I would ask your teacher about this one too


Okay I will do that


Sorry my time is running short, but for part (e) I would take all the information that we found out before and use that to sketch a graph.


If you want additional resources, Lincoln High, Organic Chemistry Tutor, or Brooklyn Notes


Okayy no worries!


thanks for the recommendations!


have a good day!


You can also stay here for a bit and see if another tutor will come


okk sounds good


You too! Thank you for participating with UPAchieve


Hello, how is it going?


What can I help you with today?


Solving multi-step equation and inequalities


Okay, I can help with that. Do you have any questions that you can put on the board?


I need help with the word problems


Yes, and are there any that you can put on the board?


-2 (3r+4)=-5r-8-r


Okay, I put it on the board too. Do you know what our first step is?


Yeah you have you distribute the -2


Yes, which then becomes?


For the left-hand side.


Ye


Yes


What does it expand to?


Hi, are you there?


Okay, so what do we do with the right-hand side now?


You combine like terms


Which are?


Which becomes?


Yes.


Now what?


So the whole thing is now -6r-8=4r-8


Now you do the opposite operation so now you add 6r and 4r


Yes, you can do that.


Now you get -8 = 10r - 8.


So now you do -8+8


Yes, which becomes 0.


So 0 = 10r.


So what does r equal?


That's your answer.


Im correct


Can we a do a word problem


Sure.


Do you want me to put one on the board, or do you already have one?


Can you put one


Did you get the word problem


I put it on the board.


This one involves solving multistep inequalities.


Ok


Do you need assistance?


Hi!


hii


I agree with this answer


i got 12/17


I only see 13 triangles in the image


Are there supposed to be 17?


yes


this counts also


Ok. The only thing I can think of is that the circled triangles are "right" triangles because you're not given the non-right angle values and you're only given two of the sides


Let me know if it works


okay so put these 3 in right angle


Yes


okill do it rn


Ok, so you must have had them in the right categories before


I'm sorry, but I'm not sure why your original answer is wrong


yh me too😭


Is it possible to view a hint?


nope


Are you able to just skip to a different problem? Do you have another problem you need help with?


thats all


ty for ur help


You're welcome, you can try a different tutor. Good luck!


Hi Sophia


hii


How can I help


I may logout if no reply.


hi


sorry for the wait


its a bit laggy


um


i wanna know about


central andinscribed angles


ill find and upload


Ok lemme search that


yea you can upload


central angle is an angle whose apex is the center O of a circle and whose legs are radii intersecting the circle in two distinct points A and B.


yea


geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.


oki


So for circle


then we can find some lgnth for things also


The angle onto center is central angle


inside a trignale


ill upload


And inscribed circle is the angle of circle's edge


Right


Honestly I should go but please work on your connection.


hey Emily


What do you need help with


alright lets do the 1st question


for the 2 points find the slope


alright


looks good


I used this formula but I heard you could do this in the point slope slope


so do you know the rule to have parallel lines


I don't know how to use that formula


this forumal also works


but I want to learn the point slope form because I think my teacher prefers that


alright the forumla for point slope form is y-y1 = m(x-x1)


x_coord,y_coord= 3,6


can you solve it on the board please using the point slope formula?


and the slope which is m we found out is 2/3


I already solved it so ..


this would be the equation of the line that is graphed on the graph on problem 3


oh I mean the answer


lets go to the next one


so for a perpendicular line we need to find the negative reciprocal


like how 3 = -1/3


can you solve it on the board?


I don't understand reading the messages


alright I solved it on the board for you


okay  thank you


uh where is it?


I don't see it on the board


I will write it out again


the answers for both


I can't see nothing except for my writing ?


I will just type it then for number 3 it was y= 2/3x+4


and for 4 it was -1/4x+3.25


no on the board


oh


I dont know maybe refresh


oh I  can see it now finally


alright sounds good


can we end the session now


uhh do you have to go?


do you need help with somethibg ekse


actually nvm bye


alright bye


Hi Jamie, what did you need help with today?


hello


give me quick sec


that


something like that


what does 1 represent in the tangent line


deriv


at that point


the instantaneous rate of change


at the point


okay


ie the slope at that point


now whats the next step


good!


is there anything else you need help with


yes


just give me a sec


ok


I was just writing it on paper


you can paste the picture or re-write on the board


yea baby


perfect


we don't worry about e


because it's always positive


im ready for the next problem if you have one


as a matter of fact I do


but give me a sec


that is it


that asking for the smallest deriv?


yeah thats the first step


do we have to find critical point


cuz there the slope is 0


so minimum value of a slope is going to be t=0


wait what


what that > for


its basically just showing x^2>0 is a minimum value of the slope


is that calc BC black magic


sorry theres an easier way to do this, ignore what i said, just find the critical point


so thats the second deriv


wait


so first deriv test and second deriv test


the first one tells us where the critical point is


and the second one tells us the concavity


correct?


yes but in this case


you are mistaken


that's not y'


it's y''


noo wait sorry i took calc ab years ago, yea and we need concavity


because that tells us maxes and mins


so yes, y''


second deriv test I believe tell us the inflection point


hello


no, the second test shows inflection points, but you said so yourself, its talking about concavity


and so we just set the y"=0


and when you do that, x=0, and you plug that in y'


do you have anything else


request another session when ur back


Hi, do you need help solving the question on the whiteboard?


Could you let me know if I am doing correctl


Yup of course.


Yup looks right to me.


I am doing SAT Review, so I want to make sure I am doing past concepts correctly.


Or if there is any room to do problems more efficiently, it would be great if you could suggest.


I feel like these type of questions, there aren't many ways to do them more efficiently.


It's really just whether you can understand them conceptually fast enough without wasting as much time.


OK


Great, do you want to look over some other questions?


Yes,


let me share some questions


Ok


Alright, should we go over all of them?


Yes, just to review


Could you also let me know if these are correct or not?


Yup, thats what I got as well


Of course


Yup, thats right


OK, so for similarity, we can use:
SSS, SAS, or AA(A)

For congruence, it would be:
SSS, SAS, ASA, and AAS, right?


Yes


Would this be a valid way to do it?


Can we assume that drawing from the angle of the triangle bisects it?


Yes, this is exactly how I would do it as well.


Yes, because that is implied inside the definition of an inscribed circle


Yup


ok


So often times, with inscribed in circles/triangles, we often use the 30-60-90 rule.


Yes, that's a good rule to keep in mind. Try bisecting angles and utilize the 30-60-90 rule!


OK


Looks right.


Okay


We know that these triangles are similar because of AA.


Oh, I made a mistake


We would not divide solely the 15 by 1.5


Let me redo


Yup, take your time.


Yes, this is what I did.


Yup, looks right.


Ok great


Do you have any more problems or questions conceptually that I can help you with


I wanted to review all these problems.


However, not conceptually, more of checking. I can end the session as well.


Ok great!


That's perfectly fine.


I can contiunue checking no need to end the session, unless you want to.


If you need help, you can ask me for some hints.


Okay, I think I finally got an answer


The main thing I was struggling with is which side corresponds with which.


I got 7.8, a little bit different to what you got.


I may be wrong tho


We just use the angles though


right?


the opposite angle


yes that is a common issue, I personally would draw the smaller triangle right next to it see what sides correlate with what


Hmm, I didn't use any angles.


I just set up two similar triangles and set up ratios with their sides


Well, yes, but I did angle c is opposite AB


and angle ADE is opposite AE


and because the angles are the same


those are the sides that are similar


That is true, however I used the angle DAE is opposite to DE, since AB and DE are the two sides that are similar


OK


Does that sort of make sense?


Yes


Yup thats what I got as well.


For multiple choice questions like these though, instead of cranking out the heavy Algebra, I would have stopped at the 3x +xsqrt3 and just plugged in the answer choices.


which step?


here?


You could, but there is a lot more x's so I would just stop right here and substituted it


Yup what you just wrote


So for this, a calculator with the function of keeping the roots would be necessary, right?


like when giving an answer


It's a great test-taking strategy but if you are trying to actually answer the questions and understand them properly, it might be best for the algebra.


Yes, I am more concerned about the test as I am mostly confident in my algebra skills.


Cool, then when you make it into that part of the test just plug in the answer choices for x and if you get back 78 +78sqrt3 then you know thats the answer!


So for this a calculator with the function of giving an output of roots would be best, right?


making that in the settings


Like in a TI calculator?


That would be preferred, but in theory you can also do it in your head.


Well, but in that case, wouldn't either way be equal?


Sorry?


I might have misunderstood the question


If you plug in 26sqrt3 for x in 3x+xsqrt3, a normal desmos calculatoor might give you a big decimal which will equal 78 + 78sqrt3 or you can use quick substitution to get the same answer.


OK, I was asking more about the calculator functionality


So I think I can figure out about that later


Like a TI-84?


Yeah continue for now we can talk about this later, and if you want I can show you how to do it on desmos (the calculator they give you on the exam)


OK, I will continue with the rest of the problems. thank you!


Hi Maya!


Wsp


I'm Coach David


Hi I need help with one problem please #12


Yeah sure!


Could you screenshot it over rq


Maya, how much do you know how to do?


Like how much do you understand?


So I think I have to apply the two tangent theorem to find the values of x and y


Then try to calculate the lengths of three sides to calculate the perimeter


Yeah, I think you have the general idea


But one of the things we need to do is to figure out x and y


Oh ok


Yeah bc otherwise you can't really solve it lol


Yeah


So let's try and figure out an equation


Let's take a look at which algebraic formulas are equal to each other using tangent rule


Alright


Maya so which ones can you find out are equal?


It's okay if you don't know lol


Js tell me if you don't


Sry I’m not sure


Nah you're good bro


Okay so using the tangent rule


I'll highlight the edges of one pair, and see what you can tell me abt them


Ok


Now, using the tangent rule


What can I conclude abt these two lines?


So 2y-7=x+1


Yeah there you go


Let's write that down rq


Mb my handwriting's gonna be a lil chopped


I'm on a computer rn and my trackpad is selling


Okay, so if we know 2y - 7 = x + 1


lol no worries it looks good


Yes


What is another equivalent pair we can find out?


Maya


David


Mmmm not quite


Remember the tangent rule


What other lengths of the triangle are brushing the opposite ends of the circle?


Oh 11=y+6


Okay, do you know how to solve this equation?


Well


This system of equations


It's okay if you don't


So 2y=19


I’m not sure


It's okay dw


Okay, so how could we reduce this to a one variable equation?


Like how do we turn one of the equations into JUST x terms or JUST y terms


Simplifying and solving


Wellll yes but how?


Okay let's take the equation above for example


How would I turn this into an equation with just y values?


I can’t use the border for life of me so I’m just gonna type it out


LOL


Maya sure that works too


Where'd you get 11?


Dw dude you're good


I got it from one of the sides


Is that wrong


Yeah but I understand why you thought that lol


Dw bro this is a very tricky problem


Okay, so let's first go to y + 6 = 11


What can I tell about y?


Bingo


So, let's apply this to the other equation above


Now, can you solve x?


Ok


Try your best


If you don't know how to do it that's okay


This stuff is hard


I didn't get it first time either


Alright


Yeah it is


Boom


Nice job bro


Man I love the confetti button lol


lol it’s great


Okay so


We now know our two variables


Right


So, to figure out the perimeter


Don't I just add everything up?


Yeah but isn’t their a circle in the middle


That doesn't count for the perimeter of the triangle


Does it?


Yeah no


For area but


No yeah this is just perimeter


Yeah but it asks for perimeter


Yeah


Ay bro you crushed this problem


I think you got the general idea


You js needed like some tips to do the algebraic stuff


Trueee


Great


Do you have some other problems you wanna work on?


No, that was it. Thank you very much.


Yeah np!


Maya, see you later!


Maya


David


Okay not see you later mb


But bye lol


Hi, how can I help you?


hi


how are you


I'm great, how are you!


Today I need help with basically going over some lessons in math to get ahead also to understnd the topic, and it is on  Factor out the GCF (including negative GCF)
Level 2: Factor trinomials where the leading coefficient is 1 �
Level 3: Factor trinomials where the leading coefficient is not 1 �
Level 4: Factor by grouping (four-term polynomials)


i was thinking we can do 10 pratice promblems for each lesson to test my understnading


Perfect, that's completely fine.


Just paste them in on the whiteboard or right here.


I dont have any promblms to paste


Oh, I see. Do you want me to find the problems and we can work on them together?


yeah and you can test me on them


Ok great.


I  kinda know how to do them


Thats good, I will find some problems.


ok


can you see the problem on the whiteboard?


yes


Ok, I will put a few more down, and you can just paste the questions in here or wherever you please.


Do you still want exactly 10 per each


yeah for each lesson


Ok


do you want me to paste the answrs when i done with all of them or 1 by 1


You can put them one by one


1. 6(x+2) 2. 15 ( y^2-2)


3. 7x y^2 ( 3x^2- 1 y^2)


am i correct so far


Oh sorry, I forgot to ask if you want feedback one by one or after you're done with all.


yeah


1 is correct. 2 is correct as well. 3. is slightly incorrect, you idenftified what to factor out but inside the parenthesis there is an issue.


Additionally, do you want to look at all these questions togehter per topic or should I just paste all the questions in for all of them and we can review it as we g?


maybe look at questions per topic


is 3 . 7xy^2 ( 3x^2- 1y)


Yes perfect!


4) 12kx^2 ( 1-4xk)


Yup, looks great.


5 - 2x^2 y(2-17x^3 y^5)


Yup looks good if the - is a dash not a negative.


no its not negative


K great


for 6 the vairables look off


yzx


nevermind i can still factor


It's great you saw that, that was a trick question.


yeah im confused how would i put this together


Oh ok, how did you try starting this off.


is it 3y( 2z^3-7yx)


Yes thats correct


7 . 3a(3ab+3bc)


Almost, make sure to check if you can factor something else out as well


And also check the 3 you factored out one more time


ohh  3a( 3ab +1 bc)


Almost, check the variables one more time.


3ab( 3a + 1 c)


Yes, perfect


this is what i got for 8 8) -14xy^2 ( 1 -2x^2 y^4)


-14xy^2 ( 1 -2x^2 y^4)


Ooh, almost and probably the most easy to miss mistake. Check the signs, its always confusing factoring a negative number.


ok


8) -14xy^2 ( 1 +2x^2 y^4)


Yup that's right


yeah those ones be tricky with the signs


Yeah is difficult to keep track of them.


-5rs ( 5r+ 1)


for 9


Yup


10 . 1x (6y-5z^4)


Yes, perfect.


Ok, now if you have questions you can ask me, otherwise you can continue with the trnomial ones.


Correct


That's right


is 3 unfactorable


Um, it is factorable, keep in mind the properties of negative numbers.


Yes


is it (1x+3)( 2x+1)


yup


I ran out of space for the third level, once you are done, I will put level 4 on top.


ok


for 2.  (1x-1)(3x-2)


4- (1x-1) (5x+16)


i got stuck on 5 on part where you do {6x^2-4x} {-15x-10}


should i make -4 +4


i think that was my mistake


Yup


Yes that's right


(1x-4) (2x-1)


Try that one again


7 ( x+1)(x+1)


yeah that was one was confusing


Yeah, its a good reminder that questions can be answered in different questions


*different ways


( 1x+2) (3x+4)


Correct


for these ones we just group them


Are these questions fine?


yeah thank you for your help this helps me out alot


Great, do you want to do these problems together?


I think i got it its kinda kinda like the last one will i have to find the gcf for some of them ??


Yes that's exactly how it is.


For these polynomials more than trinomials you just do these stuff, but you are most likely going to learn other ways to solve them in the future.


Additionally, you can keep in mind on an assessment you can reverse the factoring by distributing to see if you end up with the first answer.


Otherwise, if you have any other questions, have a great day!


oh you have to go ??


Not necessarily, if you want me to stay, I definitely can.


ok I almost done solving 1


Ok great.


(1x^2 +2) (x+3)


Yup


(2x^2 +1) (1x-2)


(1x^2+2) (x-5)


(3x^2 +2) (x+2)


(4x^2 +3) (x-2)


Looks right


(1x^2 +3) (x-7)


Correct


(2x+1) (x+3)


( 3x^2+2) (2x+3)


And yes it looks great


Thank you so much


Do you have any more questions for me?


Yup np


no thats it


Alright have a good one


hello


Hello I'm doing my Math homework and I'm needing a little bit more help please.


Can you show me what you are working on?


Im working with division


can you show me the problem that you are working on?


Long division, right?


yes sir


How many times can 27 go into 8?


3 times


You mean 27 can go into 82   3 times


oh sorry


what is the next step?


multiply


Yes, and what does that give you?


27 times 3 is 81


now we subtract


yes, and what does that give you?


Hello?


Hello, are you still there?


Hello??


Are you still there?


I'm sorry but if I don't hear from you in a minute or two, I will have to close the session.  You can always repost your request when you have more time.


Sorry, bye!


hello


Hi, how can I help you today


Is there any way you can show a more clear picture?


with number lines to order rational numbers


hold on


is this on e better?


Yes, that is better


Thank you


I already erased the wrong parts


So is that first part squareroot of 5 & 2.5?


no the one with the x on it down. That par is just the example


so squareroot of 3 & 14.32?


that one is the one we need help with?


this first one, and there are others I need help with too


Okay so do you know what's the squareroot of 5?


Good


or 2.2, for the simple form


so that is less than the other number which is 2.5


So we can start by numbering the number line just like above


oki


like that?


Yes good


So where would you place 2.5


and square root of 5?


next one is n the bottom


Try to solve the other problem based on how we just solved this one :)


I know you can do it!


Great job


You did it correct!


yay


that was a before image


Okay, this is just the same as the ones you just did


So I believe you can do these too


Do you want me to let you know if you do these right?


yes please


Okay :)


I would suggest to try to solve the math problems first so you know if those numbers would fit on the number scale


oki


I am getting the answer for the second one down real quick give me a minute


It's okay, no rush


for the third one it goes above five for each answer


help me please


So we want to rearrange the number line to fit those numbers


for example we can start with 2, 2.5, 3, 3.5, 4, 4.5


like that?


Yes


So that way, your numbers can fit on the scale :)


is that right?


Let me check it


Where is 2pi?


6.28 is equal to that


Oh okay, I couldn't see it


But yes, everything is correct!


yay


Where'd you put square root of 12?


it is 3.5


Ah i see you rounded for all of them, okayyy


good job!


You're doing great


it goes into the teens for this one


the 4i is 12.6


Okay try modifying it like we did last time :)


but the 18 is 4.2


What if we go by 2?


like 2, 4, 6, 8, 10...


that would work


Great!


or we could have started with 4,5,6,7,8..


either or works


right


great job!


yay


Also, unfortunately I do have to go


nooo


But i know you can do this!


oki


You have been doing all of these super amazing and correct


Trust in yourself and you can do it :)


Happy holidays!


you too


Hi. I was trying to do the problem on the board but I must have done something wrong because the csc function can never have a y intercept so there has to be a vertical asymptote at the y axis but if the function got shifted right pi/4 then shouldn't there be a vertical asymptote at x=pi/4? but x=pi/2 so, then there wouldn't be a point in between the two which is impossible


can you see what I wrote in the caht


*chat


yes I'm trying to figure it out


ok thanks


merry Christmas to you, btw


thanks, you too :)


wait how can you make the function have a y intercept if the original doesn't have a y intercept. isn't that impossible


we are shifting the whole thing by pi/2


no were shifting by pi/3. because you have to factor out the 3 in front.


oops


its ok. that wasn't even my question. I just wanted to know if you could have a y intercept on a transformed function if theoginal didn't have a y intercept.


bc I feel like I heard somewhere that u couldnt


*the original


there ya go


my christmas gift to you


wait so you're allowed to have a transformed function with a y intercept if the original doesnt? so, in this case even though cscx doesn't have a y intercept, this function can?


you're shifting everything by pi/6


never mind. I understand where I went wrong.


thank you for helping me today


have a good christmas, Alex?


I will. you too! :)


bye :)


thansk


Hi, how can I help you


I need help with a problem and how to approach problems like it


Ok, how might you think to start off this question?


my first thought is to get rid of the -3


on both sides of the equation


So we first have to identify between constants and coefficients (numbers with variables and without). -3x is a coefficient as it ends with a variable and since -5x is also a coefficient, you may try to combine like terms.


Does that make sense?


no


but what I think your saying is do -3x-5x prior to taking from the 16


Yes, that's what I mean, sorry for the confusion


when you combine -3x-5x, what do you simplify the equation to?


don't say https://example.comust me I have no clue what I'm doing


you're good lol


or because there both negatives it would be just 2


so -3x-5x is the same as -3-5 just with a variable, when u do that you are taking a negative number and subtracting from it, making its magnitude increase. So lets reconsider what -3-5 would yield


I'm thinking 2


Ok let's forget about the negative number system at the moment. What is 3+5, because this is -1 times (3+5)


so if I see two negatives I should add


In a real world example, if you owe someone 3 bucks and you owe them 5 more, you then owe 8 dollars. (-3-5=-8) just like you said!


Ok, so now we are at -8x=16


What might be the proceeding step


getting rid of the 8


Yes, we want to isolate x by getting rid of -8, how do we do that?


take -8 from both sides


By take, what arithmetic operation are you implying?


subtraction


ok, so lets reconsider. -8x=16, 16 is a constant, -8x is not, so they are not like terms meaning u can't add or subtract them


wait


What other operation may you perform to get rid of the -8


maybe add....I know I have to cancel something out to isolate the x


Ok now let's rethink what -8x really is. It is the multiplication of -8 and the variable x and it makes 16. so how can we reverse the multiplication and thus isolate x?


(what is the opposite of multiplication)


divide


Yes! Perfect, so what happens if you divide both sides by -8?


I've never used divison


in a problem like this


Ok, so you have -8x=16. You divide by -8 on both sides. left hand side: -8x/-8=x. right hand side: 16/(-8), what is that right hand side


Very close, reconsider the sign of the answer


Very nice work!


Does this conceptually make sense?


I'm going to go back through the session we just had. Because no it doesn't make sense yet


but it will


Ok, sure, we can write the steps out in the whiteboard if that helps?


thank you


sure


I would have never thought to divide


Yes, its a skill we develop to isolate things multiplying our variable


thank you have a good night


Have a good one


Hello


How can I help you


hi do you know how i could do this?


Sure


No problem


i thought it would be 0.8 at top and 1 on bottom


Sorry, it logged me out


thats ok


So let's count the number of blocks in a row.


How many blocks are in 1 row


Ok then count the number in a column


its 10


Ok. Then to find the total number of blocks, multiply 10 by 10


Ok. then we see that 81 blocks are shaded in


ohh so 81 out of 100?


Yes


That's right


Good job


Do you have any other questions?


yes i have one more second it just taking a while to load


Ok


Sorry actually I have another student at 11


I just remembered


I gtg


Sorry about that, Sarah


ok thats ok


ok


Hi Alex


hey


today is scientific notation


Right.


with operations


Can you do the first one?


don't know how


You just expand them to regular numbers


What is 3.51x10²


so just multiply them?


and add


Yes, but with powers of 10, it's just moving the decimal points around


what do you mean


Times 10² means moving the decimal two places to the right.


3.51x10² = 351


ohh


Right


then add


10⁴ is 10,000


So 62,351


oki


let me do this one on the board


I got touch screen


For multiplying, you just multiply the coefficients (number parts) then add the exponents


same with subtraction?


Subtraction is the same ad addidion


10³ = 1000


10⁴ = 10,000
10⁵ = 100,000
10⁶ = one million
10⁹ = one billion


am I right?


Yes


what if the exponent is negative


Then you move the decimal to the left


10⁻³ is the same as 1/1000


But the easiest way is this


Keep the 10s together.


you forgot the one


(10⁵-3⁻³) = 10⁵⁻³ = 10²


Does that make sense?


You don't want to expand to a regular number when you're just multiplying.


a little


oki


It's easier just to multiply 7.021 x 2.3


Then you don't deal with all the decimal places


I mean converting to 0.0023 and so on.


ohh oki


Also you can get a quick estimate in your head -
7 x 2.3 x 100 is about 16x100


But most of these problems involve addition or subtraction so need expansion.


Or a calculator 😉


yea


I got 16.1483 for this one


Which is close to the estimate you can do in your head.


Yes.


Are you supposed to give the answers in scientific notation?


it don't tell me how


Well, scientific notation has to have just one digit before the decimal place.


1614.83 would be 1.61483x10³


don't say I need to though;)


OK.


negative plus negative is positive right?


No, negative TIMES negative is positive.


But you can't add the exponents here because it's an addition problem.


What is the exponent for 3.61 x 10..


oki am allowed to use................. DESMOS SCIENTIFIC


I am try to follow along but am getting very frustrated


I just can't read that exponent for 3.61. Is it -1 ?


yea


Also you misread the 0 as a 6.


You can type into desmos,
3.9 x 10^-2 + 3.61 x 10^-1


I did


Did you get that answer?


OK, so that's good!


can we use mic?


I am getting tired of typing


I'm listening


Can you hear me


Yes


OK


So, can I


does it matter if I put the parenthesis.


No, it doesn't matter because


multiplication comes before addition, so they group it.


It will automatically group them like that.


just like ME


So I can do


times


to the negative.


minus


time


to


to the -4.


OK, so you can see that


you're subtracting


a number that's only you're subtracting a -6 number, a million, right?


Yeah


minus 6 is 1 million


So you're subtracting 5 million from 2:10,000. So it's gonna be like almost


only subtracting a small amount from the 2.63. So that is so that you can check your answer, make sure it makes sense. Your answer is 2.57 times 10-4, which is not much different than 2.63 times 104.


So your answer makes sense.


So what shows on those matters make sense?


Yeah, because if you wrote it in decimals, it would be


in


It would be negative


It says Mia.


Is that right


2.57, right.


But negative though


Yeah, because


you subtracted a


much larger negative number from a very small positive number.


Uh


OK


Yeah


time


shift


divided by


times 10.


to


negative


I got


for this one


Well


the problem with using a calculator all the time is


you have to make sure you understand what you're doing before you just rely only on the calculator


So


in that one


if you did it


it's, it's, if you did it, the hand we were partly by hand, it's 7.8 divided by 1.6, right?


All right


Those two, they're called the coefficient parts, the 7.8 and the 1.6.


and then


you multiply that by 10 to the 1st.


times 10 to the


3rd because when you divide


when you, when you divide the exponents


OK, so 10 to the


divided by 10 to the minus 3 is the same as multiplying 10^3.


right


when you divide


you have to subtract that exponent of not added.


Does anything make sense?


What do you mean that I have just


Why don't you shift over to the


are you, can you see the board?


just


uh


or are you on your other window.


I can see them more


OK. So


the problem is probably like the 7.8 times 10 divided by


times 10-3.


Ah


OK, that's the problem


So that is gonna be the same as 7.8 divided by 1.6.


and then times


minus 3


And when you have


the same number, you can just


add or subtract the exponents.


So the exponents here 10


divided by


N to the minus 3 is the same as


to the


minus because it's division, minus 3.


So 1 minus -3 is 1 + 3 or 4.


So the answer is gonna be


I guess what's uh


it must be 4.87.


times in


So it's the same answer, but


but you


have to understand how to do it


not always just using a calculator. I mean, you can't, you, you don't need to divide 7.6 by 1.6 by long division, but you should understand the idea of adding and subtracting the exponents.


You've learned those ideas of exponents that like,


10 square


times 103 is equal 105.


I haven't gone to the world of exponents too much.


OK, so maybe that's


but um I'll show you 10.


When you're multiplying numbers.


the same number with exponents, you can just add the exponents.


because if you think about it


like


10 to 5 is just 5/10 multiplied together, right?


Right


And if you then multiply 5 or 10, 3 more times.


That's just the same as 10 times that's 5 10s and 3 more 10s all multiplied together, so it's 80s.


But if you haven't done that before.


then you can just, I guess, wait on that and come to it later.


But that's helpful when you do scientific notation. You should know how to just add and subtract the exponents.


OK


Also, another quick question.


What the what the exponent goes into it.


like over 9.


like into the teens and the twenties.


It can be anything


It can be anything. It can be 10 to 10 million.


That's a very large number.


You just write it out. You write 10 to the 21st.


10²¹


Like the number of


the number of molecules in a certain amount of a substance is um something times 10 to 23rd.


Mm OK


So


for this next one


It's also the vision.


but it's a negative 3.


It's tend to nega3.


Well, I can't see the problem.


Mm


mm


point.


And you could type out the problem, or you're typing it out.


2.031 times.


and then -3


involves the vision again.


times


and I got that


DCY I highlighted?


right


because it's going to be


2 divided by 1.3.


which will be


and then the exponents are going to be -3


and then you're dividing 10^3, so you're subtracting another 3.


so that's minus 6.


So that's how they got that 1.56 times 10-6.


Mm OK


So


The last one has multiplication.


OK


Oh


uh


mm


times


2 point


s


OK.


OK, is, so the last 10 is just 10?


Yes


So right, 9, basically it's going to be 10


10 times 2.6


I mean


just


the, the 9.99


is basically 10, right?


Right


Just to make sure we're getting it right. So that's


that's


a plus one.


10 to 1 times 104 times 10.


So you have 2


1 10s and and then minus 4.


that's going to be -2.


2.6 times 10-2.


And that's what you have 2.59974 times 10-2. That's the answer they gave you.


All right


So, if you had to do it in scientific notation, that's what you would say 2.59974.


times 10 minus 2.


Uh


but now


the two problems that are gonna be love it.


because


cause these two problems you do them in scientific notation as well.


I mean, not


there's more problems that I need to deal with scientific notation in them, but the actual scientific notation equation.


Well, I can't see you, I can't see the problems.


Hold on, I


and your screen sharing.


but


I


So


this is


I'll read the problem to you. The mass of the earth is 5.97 times 10 to 24 kg.


and the mass of the moon is 7.34 times 10 to the 22nd power. How much larger is the mass of Earth.


Its subtraction, right?


No, no. When it's, when it, how much, well,


that's a good question


It could be subtraction.


It could also be


division. Does it say, it says how much larger, so it depends on whether the answer is supposed to be the earth is this many times the mass of the moon, or is this many more kilograms than the moon.


It is


uh


Earth is blank


kilograms larger than the moon.


OK, OK, then that's subtraction.


OK


I just wanted to make sure before I put


Yeah


to


one second


OK, so that's my equation.


Right


So


But what about my answer?


the mass of the moon is barely more than 1% of the mass of the Earth


because the, the exponents there are 24 and 22.


which means the difference is 2, so that's 10, that's a 100.


one hundredth of


the mass of the earth, it hardly changes it. It's from 5.97 to 5.89.


times 10 24th


that should be the right answer.


I


but uh in the, the normal number now of how much larger it is.


The normal number was?


Yeah.


of how much large, how many kilograms larger it is.


That's the answer. That's how many kilograms larger it is.


They want me to write the equation first, then write the actual


number


OK, well then you just write what you wrote. You wrote exactly what you put in the calculator is the equation.


So basically,


Difference


is


OK. So now, this one's a little bit easier.


So, 5.125.


to the


not that, not bad.


to the 4th.


time.


This is, how many, this one, it says how many bonds does a factory produce in


one year or 3.65 times 10 to 2.


It's addition, right?


What's the whole problem?


A factory


makes 5.125 times 4 times 104 bottles a day.


How many bottles does the factory produce in a year, or 3.65 times 102 days.


Right. So if it makes that many


whatever in one day.


Right, so


then you need to multiply, right? 365.


OK


And you could just multiply.


times


OK, that's my


Yeah


So that's 1.87 times 107.


I guess so


Mm.


or 18 million


0.87 9


and so you can estimate it in your head. 5 times 3 is 15.


and then 4 + 2 on the exponents is 6.


So your but your head would be 15 million


and you'd say, well, it's more than that because it's 3.65. So let's call it 18 million. And then you, then you make sure that your


you do it in your head because


if you miss, if you put a wrong decimal point or something in the calculator.


it won't tell you that you're wrong. So that's why it's good to get a sense of the size.


as well as use the calculator.


OK


And not that you just want to glance at it and get an idea of the size. You don't have a calculator all the time.


right


So you can estimate times 102, you say, OK, that's gonna be a million


and then 5 times 55 times 3 is 15, so we've got 15 million.


Uh


OK, good


I


That's the last one


I have a


or there are more


there's some more problems that I have


OK.


scientific notation


11 was


6 or like


the actually 12 are like the 1st 6.


1st 8 and then


Yeah


and


2 or like the word prop. I got two more word problems.


and 6 of them require me to write this scientific notation.


OK. Do you think you'll have trouble on any of them?


The word problems on the figure out the equation.


I need help figure out the equation.


OK. Well,


why don't you do it, a screenshot of the word problems.


All right, give me a second.


OK, OK.


OK.


What's the plants?


Oh gosh, that's too blurry, isn't it? Yes, it's.


This seems at all along. Yeah. OK.


I


And.


What's happening?


I finished working on mom's car, so.


I know.


Is it OK if it's too sipper screenshots.


Sure


All right


after this, I'm gonna have to go.


All right, so this is kind of like the moon question. It's a difference between subtraction.


Uh


so


times


minus


times 10.


to the 5th


I got negative


OK


So, if you, if the difference is negative, what does that mean about which numbers larger?


If you subtracted


if you subtracted one number from the other and you got a negative answer, then that means the second one must have been larger, right?


Like if you take 10 minus 20, that's going to be minus 10 because you subtracted a larger number from it, from 10.


So that means that the first number.


is you subtracted


uh


one hundred ninety eight thousand,500.


It just means that that the answer is


160,500, but that


the second production line is larger.


All right


If you reverse those numbers, you would come out sixteen thousand,500.


But now time for a last screening.


screenshot before I, before I have to go.


But it'll only be for a little while.


because all I need go do is an outside chore.


before it gets dark.


Well, I'll have to go anyways, but I'm sure you have.


you'll be an easy one.


I mean, you'll get somebody else to do it.


OK


right? So you're my favorite out of all of them.


just like chasing now.


So


you have


distance


equals speed


times time, right?


All right


So the speed


is uh


per year. And the distance is that how many does what exponent is that 9.


Yes, 9


798 times 10, 9.


Yes


OK, and the question is how many light years


This is a mistake


that you can't measure time in light years.


You measure time and years and distance in light years.


So The question is, we've got to solve for


time.


So that's gonna be


we most speed down here.


So time


distance


over speed equals time.


OK, so this is the moment.


And they divide


the distance 2.798 times 109 divided by


5.88 times 1012.


OK


I


And that's my answer.


Did you get an answer? Oh, I can look at your screen again.


All right


So the time unit there is years.


because that was what the question was in.


Yeah


So that's the answer, 4.7585. You probably should do some rounding, but


they didn't tell you to, so I was 10 of the minus 4th. So that's 4 10,000 of the year.


It's gonna be some hours.


But


I'm gonna need to go now before it gets too dark.


for me to do my chore


OK, are you all set on that one?


Have a good night, and if I don't talk to you again, have a merry Christmas.


Oh, you too. Have a good, good 2 weeks. Are you gonna be doing any studying during the holidays?


Just


possibly


just stay on the lookout


OK. All right. Have a good night.


You too


Bye


What was that


OK, can you end the session cause it won't let me. It doesn't let me all day.


Oh, OK


Can you end the session? It won't let me, for some reason, because it


had been like that all day.


That's interesting. I wonder why not. Uh.


hi!


how are you?


Good


Hello


I need help to study for a test


ok!


what are you learning


I don't really know


I have a study guide


How do I show you


press the button to the right of the eraser button on the gray task bar on the whiteboard in order to upload pics of it


I found it


great!


It's a 6 paged study guide


which questions do you not know how to do


most of them


I'm sorry I'm really bad at math 😢


its ok!


but u should try to pay attention in class and ask questions (if you don't already)


Oki i will


ok so lets start with 3


basically it wants u to solve for q


which is the same as isolating the variable (the variable being any unknown letter/constant, in this case q)


so isolating the variable means getting it alone on one side while all the know numbers are on the other side of the equation/equal sign


Do we start by subtracting one of the qs


yes!


either one works


i would subtract the smaller one


Oooo okay


Oops 27


so that you dont get a negative q


Okay okay


its 72-27


which is 45 q


do u understand how i got 45


Yes


I'm gonna write this down


great!


also do you know the reason we had to subtract by 27q instead of add it?


No


I just know we have to do it


its because 27q is already a positive number (+27q) so if we want to get rid of it on the left side, we must use the opposite of addition to do that because 27-27=0... and whatever we do to one side of the equation we must do to the other side (equation has to still be true/balanced)


Oh yeahhh


do you know what the next step will be


Sorry


Is this howbi set it up


72q-27q is not 72q


Oops


I see


what do u think the next step would be?


Subtracting 50


Addding 100


yes!!


can you show me on the board


Yes


good!!


dont forget the q


do you know what to do next?


The equation is difficult to write on phone


Uhhh


ohh


Divide


you understand everything?


the key things to remember are: to isolate the variable, do the inverse (opposite) operation... and whatever u do to one side of the equation, u must do to the other side


Mhm


Yes thank you


no problem!


i actually hv to go now tho


sorry it was so short


It's okay thanks for helping me


im sure u will be able to find another coach/tutor tho!


np!


Mark bye bye


Hello


How can I help you today ?


hi


I need u check my work


Sure


I can't read them


Can you make them bigger?


sure


Where is the work you started?


let me upload it


is the piecewise function what you started to work on?


everything


scroll down


Do you have to draw something or ?


no


do the graph


and check if i did my part d correct


ofc


I need to leave now . I am sorry.


Please fee free to ask for anther help?


ok


hi Alice


Hiii


i need u check my project


OK. do you have something to upload?


yupp


this is a lot of work.


yes, but i did them


you want me to check it. does that mean that you have answered these questions?


yessssssssss


is that in a 3rd image?


yup


can you load the answers so that I can check them?


yes


here


I circled 2 points. Looks like the ride would be awfully rough there.


does it have to be perfect


it's going to take me some time to review all of this


ok


the functions seem to work


Mr. Davis


hows the rest


still looking


did you research the maximum height?


yh


that was a question in Part A. h<= what?


where


yeah, there


what about it


they want you to fill that in


2 places. I circled


it should be based on graph


no


you are supposed to research the tallest roller coaster in the world and make sure you don't make yours taller.


you only gave 1 interval where you'll be going uphill. aren't there 2?


does it say 2


it says "intervals." you designed the roller coaster. aren't there 2 places where it goes up?


oh goshh


actually, 3


WHAT


I circled all 3 in green


ohhh then im gooddd


why are you good?


there are 3 intervals of increase, and you only listed 1


should it be only one


there are also 3 intervals of decrease and you only listed 1


unless you change your graph and functions, there are 3 of each


ok wait


wait


are we moving slow?


every time you go uphill you slow down


0≤x≤5, 7≤x≤13, 18≤x≤23 , here the uphill


they want all the intervals of increase and all the intervals of decrease


here downhill


5≤x≤7, 13≤x≤18 and 23≤x≤40


Good?


wait its all t right


not x


it's all t


okk


and doesn't it go up 23 to 24?


as part of absolute value?


it doesnt??


so, down from 13 to 23, then up from 23 to 24, then down from 24 to 40


I circled 23 to 24 in green. that's going up


ohh


0≤x≤5, 7≤x≤13,23≤t≤24


those are the increasing intervals


im confusing rn


I just told you that you gave a right answer


ohhhhhhh Mr. Davis


you got all 3 increasing intervals


yay


you need those intervals in both the "final destination ride" paragraph and in the Part D table


plus, now you need to also find all 3 decreasing intervals


i did


the correct intervals


part c?


0≤x≤5, 7≤x≤13, 18≤x≤23 , here the uphill
5≤x≤7, 13≤x≤18 and 23≤x≤40, downhill


0≤x≤5, 7≤x≤13,23≤t≤24 uphill


opss


alrightyy fix


and you also have to fix downhill


which one


middle one


and last one, actually


downhill is 13 all the way to 23


then downhill again 24 to 40


5≤x≤7, 13≤x≤23 and 24≤x≤40, downhill


right?


yeah


need to fix that also in the table in Part D


last thing you need to fix is local minima/maxima


you only did global


so what should it be?


you don't seem to understand much about these functions. did you find all the piecewise functions yourself?


yupp


do you know what local minima/maxima are?


like (7, 20)


(23,120) for min


yeah, that's another minimum


(5, 100) is a local maximum


alrightyy


fix all those things and you are good


only one?? Mr. Davis


you listed 2 of them. I gave you a 3rd one


oh thats what i thoughtt


so for the uphill and downhill is the one ones increas and decrease intervals


any place it "hits the top" then goes back down


correct?


yes. uphill is increase, downhill is decrease


anything else?


that should be it


Mr. Davis


yw


BYE


hello i need help completing my hw


Okay


this is the law of cosines


yes


This is the variant we can use to find c


and we sub the values in


okk


That's the value of c^2


So the answer is this


got it?


any moe problems?


no thats it ty


Happy Holiday


Hello! how can I help?


i need help with my hw


Ok no problem!
Thanks for uploading!


I see that you tried solving the problem


How did you think about it initially?


The question requires a solid analysis of sin cos and tan


oh ok


So, would you be able to show on the board how you initially solved the problem?


As you write, I can hint at potential mistakes :)


We could then go over the question together :)


I see that you may have disconnected from the internet, I'll wait for a few minutes in case your internet connection improves


Ok, as I haven't heard back yet, I'll end the session real quick. But if you have any additional questions, please feel free to open up another session at any time! Best of luck!


Hello :)


Hello


Im Sam my mom set up the account


Are you in need of any help?


Hi Sam, nice to meet you :)


im trying to solve this assignment I already figured out 1 but im not sure how to do the others


Ok no problem :)


Do you know many of the trig identities?


so first question what do the fractions actually mean here


So we are looking at 1-sin^2x over 1+cot^2x


Cotx we know is 1/tanx


Ok, so I see a few things here


Can you tell me what 1 + cot^2 x is equal to?


On the chart


Good :) and can you tell me what csc actually is?


no


No problem :) csc is 1/sin


And so csc^2 x is the same as saying 1 / sin^2 x


Is that right?


i think??


Good, can you tell me what happens when we divide by a fraction?


z/y


Because now we are dividing by 1/sin^2 x, right?


the bottom number divides the top number


Good, or in other words we can multiply by the reciprocal


So we can multiply by sin^2 x, if we have csc^2 x in the denominator


Does that make sense to you?


ok


i think


No problem, i can explain further :)


Do you know what 1/sin(x) is?


Ok, no problem


So all of the trig, sec, csc and cot are all the same as 1 over the normal trig


So 1/sin(x) is csc(x)


1/cos(x) is sec(x)


And 1/tan(x) is cot(x)


how does this help with proving the trig?


It helps you understand what they are to manipulate the problems


So we can look again at question 2


What does it say 1 + cot^2 (x) is?


Good :)


And then, because we are divining by 1/sin^2 (x), that means what?


1-sin^2 over 1 over sin^2


I think it’s a bit simpler than that :) we can just multiply by sin^2 (x) now


Because if we divide by 1/4 that is the same as multiplying by 4


It is the same concept :)


ok


Now, can you tell me if 1 - sin^2 (x) is on the table?


sp mpw we have -1sin^2 and sin^2 times sin^2


Now we have


( 1 - sin^2 (x) ) ( sin^2(x) )


Or 1 - sin^2 multiplied by sin^2


Can you tell me if 1 - sin^2 is on the table?


yes


at the bottom


well its very close anyway


Not quite that’s 1-2sin^2 x which can’t work here


But I do see a way to get an answer


Do you see how sin^2 + cos^2 = 1?


The first one in the graph


Or chart


Can we manipulate that in any way? To get an answer


don't know how there is no cos


wait a sec


We have sin^2 + cos^2 = 1


we have 1 correct


so sin^2+cos^2


= 1


So what is 1 - Sin^2


If sin^2 + cos^2 = 1


Can we subtract sin^2 ?


just cos


the times the sin^2


If Sin^2 + Cos^2 = 1


What would happen if we subtract sin^2 from each side?


Just cos?


well that and the multiplying


Or would it be cos^2


im talking about cos^2 just to lazy to type of ^2


Ok good.


So tell me


1 - sin^2


Is


the final answer is sin^2cos^2 im to lazy to type the full equation


Good, that is the final answer


It tells you that though, but do you understand how we got there?


yes


Ok good :)


Do you want to try the next one?


yes but gimme a sec


Take your time


need to finish putting it on an assignment


isn't tan cos/sin or is it the other way around?


tan x is sin x / cos x :)


lemme think


If you want any assistance let me know :) this is a hard one


it definetly has something to do with tan being sin/cos but I can't think of what to do next


No problem :) I actually had to look it up myself. But I understand


Try getting them all with the same denominator


You can always multiply anything by 1, so take the -sinx and multiply by cosx / cosx


Sorry, cos^2x / cos^2x


And tell me when you’re done :)


yeah im lost like cos^2-sin^2 can become cos2x but im not sure if i can do that with the division symbol


No problem :)


So we already have sin^2 x / cos^2 x


And we are subtracting sin^2 x


So to get the same denominator, let’s multiply that by cos^2 x / cos^2 x


So the full problem is


(Sin^2x - sin^2xcos^2x ) / cos^2 x


I promise it gets cleaned up


Can you tell what we can do next?


nope because in text form that looks like a bunch of jumbled letters


We can factor out sin^2 x


So if we put sin^2 x on the outside, what is left on the inside?


( sin^2 - sin^2 • cos^2)


well sin^2-sin^2 cancels


i think?


Careful, wha is sin^2 / sin^2


What is 4/4 ?


Good :) don’t forget the 1 it’s important


wait this a minus sign not a divison sign


Oh ok I see what you did


or can I not do that because of the cos^2 x


So sinx - sinxcosx can’t be done, remember because it’s multiplied we can’t cross off individual pieces


so how do I finx this cos^2/cos^2


Well that is equal to 1 :) I’ll try and write what we have on the whiteboard.


We multiplied by “1” so we can have the same denominator on the problem


So we can actually factor this


You know how 5x - 25 can be rewritten as 5(x-5)


i hate factoring but yes


Good :) we can do the same here with sin^2 x


Can you see what you get?


nope


its sin I understand numbers not whatever the heck sin is


Let’s replace it then :)


Let’s say Sin^2 X is equal to U, can we do that?


So now we have (U - UCos^2x)


What happens when we take U out?


U(1-1Cos^2 x)


Great :)


And so can you tell me what 1-cos^2 is?


Good :)


And if we look at the top part of the graph


Or the table


Back to sin^2 + cos^2 = 1


What is 1 - cos^2


Woah woah woah


Ok let’s back up a bit :)


So let’s still call the Sin^2 X


“U”


We know that is on the outside


So we have U (1-Cos^2x)


And remember that is over cos^2x


So now, we can take 1-cos^2


And solve for it


Because we know six^2 + cos^2 = 1


And so 1 - cos^2 = ?


six^2 + cos^2 - cos^2


Ok


So


Sin^2 + cos^2 = 1


Subtract cos^2 from both sides


Can you tell me what we get?


or sin^2tan^2


Yes that would be the eventual answer


Can you see how we got there though?


yes


gimme a sec to add this to the document


Ok :)


ok now to four and five since I inteded to be done by 7 and i need this done we need to start fast tracking a bit


Ok :) I can try


So what do you think we can do first?


1 is a term and we have sin/cos being added to it


and thats dividng sin/cos


I do greatly apoligize however I must go. Good luck and submit another ticket


hey


hey i need help doing my hw


np


so its asking us to find a


angle a


ook


so which trig function do you think we need to use?


not sure


since they gave us all the sides


it doesnt matter what we need to use


oh ok


but lets do co


cos


ok


which is adj and hyp


c is the hyp


b the adj


so its cos(11/8)


wait


did you guys learn laws of cosine


not yet


oh


whats this unit


this require laws of cosine


which is


let me put it on board


try solving now


and let me know when you do


Hi!


Hi Chloe, what's up?


So I have a Ap stats test tmmr and I ended up missing a day when they learned a topic and i dont feel prepared at all :/


i have some multiple choice questions


ok, let's take a look


i did some of them in class but i want to redo so i can make sure ik why


sure


ok, I see


so we need to take them one at a time...right...each is T or F


yea


so what do you think about A?


well it says theres more blue


sections


but the question says its equal


right, so more probable blue ...right


yea but why does the question say theres an equal chance


for blue and orange being chosen


Yes, equal chance for each of the 12 sections.


but 7 of the sections are blue and 5 are orange.


So


more chance of a blue


ohhh


so D


D?


What do you mean? I thought we were gonna go through each one and decide if it's true or false.


ohhh i thought i had to choose one


No, I think we just have to pick out the true ones.


my paper says choose one per question


Oh, well, maybe only one of them is right.


I'm just going by


what it says, which is which of the following is true.


Oh, so, you know, maybe you're right because it says is


instead of R


yea its just one i guess


are


since theres more blue then d would be correct since the probability of picking blue would be greater


Well, let me read blue or let me, let me read the question


and see what I think


Yes, I agree. D is true.


More chance of


two blues, then 2 oranges.


yea!


okay let me put next question


So do you know what in independent means?


yea so they dont effect eachother


so p( a given b) = P(A))


Right, exactly


or p(b given a) = p(b)


So what does it mean mathematically?


in terms of the probability of D and E.


hmm im not sure :/


is d and e just multiplying right


it means P(D and E) = P(D)*P(E)


yes


ohhh so whats D or E?


right. in general P(D or E) = P(D)-P(E) - P(D and E)https://math.example.com you remember seeing that?


oops


P(D) + P(E) - P(D and E)


ohhhh


D


perfect


imma remember that for sure!


you did it exactly the right way


i struggled here


okay so


ok, do you understand the basic setup?


mutually exclusive is where they cant happen together??


exactly


what does that mean in these scenarios though?


like they cant pick both?


can F and S both happen?


no


they only choose one right?


can a selected person chose the first discount and the 2nd discount?


right, only one


ohhh okay


A?..


yes


yess! I had got this one wrong earlier


now right....yay!


I like what you are trying to do, but I think you are a little off


i dont know where to start


how about I start?


okay!


do you understand my chart?


First is whether there is an ice delay (Y or N)


yea


does the 10 percent really matter here?


cant i do


it might, let's go step by step


first...which paths have at least one delay?


what do you mean sorry


the question is to find pr(at least one delay)...right?


do which paths have at least 1 delay. top path had 2 delays


icy delay with mechanical delay


ice delay no mechincal


right


no ice delay and mechanical


2nd path has ice but not mech


see what I mean?


3rd path has no ice but mech


so 1 delay


last one is the only one with no delays....right


yea


but the chart is confusing me a bit


is there a way we could make it less confusing?


does this question need a diagram?


OK.


Hmmm need needses it help...I think yes


oh


so 10% represents 2 types


so we dont need it right?


so we can just 1-p(none)


70% would be no icy delay


95% would be no mechanical delay


we can just do 1 - p(none)


that may be easiest, I'm not sure yet


that is p(none)?


right, let's try it that way first what is pr(not delayed due to ice)?


right


what is pr(not mech delay given not ice delay)?


yes


so 0.7*0.95


so pr(none) = .7*.95


= 0.335


so b i guess


sounds good


b??


yes, I agree


only a couple more


C..?


since it can happen at same time


and the jobs dont effect eachother


right, and we know the 2nd because 0.75*0.5=0.375


wait how would we know independence


by calculations here


like in this scenario?


because P(A and B) = P(A)*P(B)


thats all??


that tells us independence?


in this case, how else would you know they are indep?


yes, the mathematical definition is P(A and B) = P(A) *P(B)


so we know independence if event A* event B is event A*B


yes, if you are talking probabilities


but in general how would i do the p a given b


ahh   P(A and B) = P(A) * P(B|A)   by def  and if B and A are indel then P(B|A) = P(B), so P(A and B) = P(A) * P(B)


so in general it simplifies to P(A and B) = P(A) * P(B)


thats how i know independence


yes, that is the most common way to check for it


Jordan


what do you knowow where to start?


so


no?


OK


i was thinking which is why i said so lol


okay so 32 are in or OR both?


forget about the problem for a while.ere is an equation you need to be sure to know for this exam...I will put it on the board


we used it before...right?


yes so P(A and B) = p(A)+p(B)/ P(A or B)


i think idk if i did that right


p(A)+p(B)- P(A or B)


is what you mean....right?


yeaa


yes, that is what I was saying, let's use the 2nd eqn for this


D???


ohhhhhhh


ok, they are the same eqn arranged two ways


makes sense!!


0.17+0.28 - 0.32


yes, so answer is D


wow that makes so much more sense!


i need to memorize these for tmmr though!


Yes, but the nice thing is, once you memorize one of them, you can always get the second one.


yea!


i have like 2 more problems


OK, let's see him


do you teach ap stats or regular? this is Ap lol


but it is very similar to regular


Ap just goes quicker i guess


Yeah, Riverdale High.


ohh cool!


So what do you think of this question?


im reading it now


D


Yup, it's the same equation we've been using, right?


yea


E


Right. Probability is about what happens in the long run in situations like this.


alright! thats all I had for today thanks for the help!


Very good. It's been very nice helping you. Good luck on your test.


thank you bye!


Hello Taylor


Hello!


What do you exactly need help with?


just studying for an ab calc unit test on derivatives


Ok let me know if you need any help


im gonna give questions in the chat and try doing them


i mean


paste them on the board


Ok


Sounds good


think its A


is that right?


No


Oh never mind sorry I did something wrong


You are correct 👍🏽


That’s my bad


wait apparently its D


i dont know how


Well don’t use AI to check you’re answers


no its the answer key


There’s no way


thats what i said


im just gonna leave it honeslty


Yea the answer key has to be wrong


ill move on


Ok 👍🏽


B


Yes that’s correct ✅


Good job


B again


Yes that’s correct


I got A


That’s also correct 👍🏽


Good job 👏🏽


nice let me grab more


Ok


D


Yes


B?


Yes, good job


E?


Yesss 🙌🏽


wow im suprised i got that one


Good job 👍🏽


almost forgot the rule


its c i think


You’re correct 👍🏽


im getting E


Taylor you’re correct good job 👏🏽 👍🏽


let me grab more


Alr go for it


B


Oh sorry


is it right?


No


what did i do wrong


Not sure it just doesn’t look right I need to solve it again I messed up can u re-insert the problems please


I was looking at a different problems sorry 😅


You’re correct tho


wait so was i right?


nice!


Taylor


is this E?


Yes 👏🏽


45 is a


Yes


made a silly mistake


Thing


It


Is


Good 👍🏽


You got it right


nice!!!


Ok I’m going to sleep great job today


You got like all of them right


thanks for all the help!!


Hope you do good on your next test or quiz


thanks!


Can you end the session? It doesn’t let me


It is a glitch that needs to be fixed


Hi, how are you?


I put my mic on if you want to put yours on.


hellO!


i cant have my mic on


That's fine, no problem


How can I help you


OK


i need help wtih convergent and divergent


Well, let's see what we get when we use the rules of integration here.


um


let's


go ahead and try to integrate this and then see what happens to the limits.


So, um


let me take a minute


and look at it carefully


i have very bad intuiition when it comes to starting


So we're gonna, we're gonna rewrite


we're gonna, um, rewrite this in with a negative exponent. So let's go ahead and


start off


by writing it as the integral. Let's not worry about the limits right now.


Um.


We're going to put the 6 out front


and we're gonna call this


X + 3.


to the -3 halves.


DX


So all I've done is pull the


constant out front


I'll let you type in any questions so far.


the 1?


No, uh, I, I'm purposely am not putting the one there. I made the, the uh exponent negative.


ohhhh


and I'll show why I did that.


i didint see that


okok


Yeah, we, so we don't want to do the one over, at least the way I'm going to show you. So you can just leave that there. That's fine. So, what we've done is just rewrite, we pulled the 6 out front.


it's a constant


and


I've made the exponent negative.


yes


Now, you, you're aware of kind of the power rule in reverse that we use.


So I'm gonna do this integration


keep the 6


I'm going to


what is divergent and convergent?


add one


to the to the fraction up there.


So when I add one


that will become


And when I divide by


um


so you add one


be 2/3


I'm sorry, not 13.


Let me, let me


erase that and


fix it


a little more


readable here


What's new this is


negative 3


halves


plus 2 halves.


which is


so


I'm adding one and dividing by


So that don't give me


-2, I believe here. Just bear with me for a second.


So let me write this as


X + 3


to the 1/2.


So all I've done is, is done the integration


If you take the derivative of this


where did -2 come from


you will see that we get back the original Integrand.


OK, I'll show you


So when I


when I


did this, that was -15, OK? When I added the exponent


what I do is then is divide by


the divide by um


the reciprocal


I'm dividing by


by, by dividing by 15, which is the same thing as multiplying by 22.


So whenever I do an integration


I take


my exponent result


and divide it


ohhh okay


divide by it


So when I divide by 1/2, that's the same thing as multiplying by -2.


This is a way to do, to think about how we would do that.


wait so neg reciprocal?


If you check the result, you'll see


if I take the derivative


of


this function, it would become


times -12


times X + 3


okok


to the negative 3 halves.


In other words, we would get back


exactly what we had


in the original Integrand.


I'm gonna let you ask questions, but so far


our result is right here.


Put it in that


circle


Do you see that it is


what we would get by integrating.


I mean by differentiating


yes


So you need to be sure that you understand


So, so it is the integral. Now the question becomes whether we can apply the limits


without it being


uh a divergent or not.


So I'm gonna go down a little bit further.


We have


X + 3


and I'm gonna go back and make it


the square root


of X + 3.


So all I'm doing is writing our answer


All I'm doing is writing our answer


back in radical notation.


errrr


and we're supposed to take this from


what's the lower limit there? I can't read it.


where did that swrt roo come from


OK, let me answer your question on the square root.


You um


you noticed that I, when I did the integral and in the circle here.


yes


it has a -15


exponent, right


The -1/Xponent is the same thing as the one over the square root.


Do you see that


I shouldn't have the, I shouldn't have the uh numerator, I'm sorry, this shouldn't be here.


That's what's confusing you. Sorry about that.


ya


I don't know why I put that in there.


Is that better


OK


So now


what we need, I can't read the lower limit on the problem. What is the lower limit?


I can't read it. It's too small.


One, OK


From one to infinity, right?


So the question becomes


what is this evaluate to?


And


if we


let X get very large, our upper limit.


We're going to see that


this is gonna be


one over the square root of a large number which will tend to 0


So it'll tend to 0


yes


if I let X go to Infinity. Oh, it's 0 to 6.


its 6


I thought it was 0 to Infinity, or 1 to Infinity.


Well, I'm looking at our limits and, uh, let me go back up.


The limits look like it's one to infinity to me.


So I'm going


Oh, you're looking at the answer. I'm not, I'm not quite finished yet.


So,


this will become 0 for the upper limit.


minus


over the square root


of


which will equal


which is equal to 6, your answer.


Does that make sense


yessss


Sarah


You're welcome. I hope that helped you.


can we work on this?


Yeah, I can try another. Sure.


OK, I see it now


All right


So, we have ourselves a little


differential equation here, OK?


So what we wanna do is we wanna


um,


see how we can solve for why.


as a function


and


let's see what we can do here. So,


we can write this in what we call differential form.


We can write


DY


equals 2 minus Y


DX


Have you seen that kind of notation before?


yes


So, OK


What we want to do is what we call separating variables


So what we'll do is we'll rewrite it as DY


over 2 minus Y


equals DX


We're separating the variables.


So far, so good


All right, now what we're gonna do is we're gonna integrate


but how did you know what to do


both sides


but how do I know what to do?


Um, did you


cuz that is what i struggle iwth the most


have you


OK, well, when you have, this is what we call a differential equation, Emily.


And


one of the best ways to solve them is if you can separate your variables. You try to get all the wise stuff on one side and all the X stuff on the other.


ohhh oaky


When you do that, then you can integrate.


So it's a, it's a very common method and the most preferred method for trying to solve a differential equation.


So,


if you can separate your variables on each side, then you can use integration to find out what why of X is going to be.


OK


Are you good so far


I wanna make sure you're following along with me.


yesyse


Now, if you recall an integrating


this one will in the left side will integrate.


to negative LN


2 minus Y


You may recall the logarithm um


this is a form


of um


integrating a form of DY over an expression.


So


yes


that is what we get on that side, equals X plus some constant.


of integration


So far so good


If you take the derivative of each side of this, what I've gotten you'll get back to the previous


step.


So on the left side, if you take the derivative of that, you'll get back to what we had.


and if you


um take the right side, you'll get back to


um


what we had


why is ln negaitve>


OK


um, this negative Y in here


right here


ah okayu


if you don't put the negative there


when you take the derivative of it


you will be the wrong sign. We can prove that


um,


if I take the


the derivative of the logarithm


over here


this one


I would get


1/2 minus Y.


oh okay


Um, and I would I'd have to multiply


by 1 because of the chain rule.


So the derivative


mhm


would, would be -1 over 2 minus Y. That's not what we want. We want positive 1/2 minus Y. So this negative is important.


to do that


It's


it's needed because of the chain rule.


uh, when we take derivatives.


Does that make some sense


yes


OK. So let's see if we can


so we are trying to isolate y


let's see if we can simplify this before we plug in our initial condition.


Yes, we're gonna try to get why we're gonna try to get Y


but we're, we need to take what we're at this step now.


Um.


so let's see what we wanna do


Um


let me look at your answers just to see which form they are.


All right


let me see how we wanna do this.


I wanna see what the proper way


OK, let's um


let's go ahead and multiply through by -1. So I'm gonna end up


essentially with


2 minus Y


equals


C minus X. I don't know if this will work.


Yeah.


So all I've done is


is multiply


That's LN I'm sorry. LN of 2 Y minus Y equals C minus X


So all I'm doing is multiplying by -1.


and now I'm gonna ex exponentiate each side.


I'm gonna


I'm gonna bring it each side to a power of E, which will leave me with 2 minus Y equals E to the C minus X


Do you see that


That's a way of simplifying this is to exponentiate each side. That's to undo the logarithm and make an exponential out of it.


yup


Let me know if you have questions or I can finish it off. Let's finish it off and see what happens.


Sometimes the answers come out looking funny.


Now I'm just going to


isolate why


and I'm gonna multiply by -1.


and I get 2


minus E to the C minus X


All right, now we have some initial conditions.


um,


that were given


so that we can determine that constant


And they say when X equals 1, Y equals 1.


So if we plug in the initial condition, we get one.


equals 2 minus


E


to the 1 minus 1.


I believe


If we multiply


I mean, if we plug that in


So we're trying to solve for


trying to solve or see, and we see that C


equals 1 will work.


If we have C equals 1.


then


we will balance this equation because E to the 0 is 1.


So, C is equal to 1


I'll, let me write down the answer and then we'll go back over any problems you're having. So our answer should be


how do yk c is 1


Y equals 2 minus


E to the 1 minus X.


And we'll see


that


B


is the choice we're given. Now, I'm gonna let you ask questions from anything


um,


wait i dont get it


you don't get the part about the sea.


So,


do you follow


the, the circle


equation here that I circle.


yes


All right, all I did was I put X equals 1 and y equals 1.


In that equation


because that's the initial conditions that we were given.


So when I did that, Y equals 1, give me that.


and X equals 1 gave me this over here.


right there


So, I'm ended, I end up with an equation, one equals


2 minus E to the C minus 1.


And I can solve for C and see that it must be equal to one.


for that to work


If C is 1, we get E to the 0


and E to the 0 is 1.


wait i dont get how c is 1


So 1 equals 2 minus 1, so that balances. So C must be equal to 1.


All right, let's go back over it again.


Do you follow


this where I plugged in one and one.


yed


All right


Look at that equation. It says 1 equals 2 minus


something


right


ya


That's something has to be won.


for this to work


ohhhhh


OHHHH


And if that's something is won, then C must be one.


so either way


c has to be 1


because either of the 0 is 1.


E 0


So, that's why C equals 1.


C has to be 1, right? When you plug that back in to what we solved, this is what you get for your answer.


That is the solution of the differential equation with the initial conditions given.


And if you wanted to, you could go back through and


take the derivative and plug it all back into the original equation and it should work.


I'm sure it must seem strange to you, but this is


the process


how did yhid turn into 1


How did I turn


so


how did I turn into one,


X is not one, it the C is one.


Sarah


And then if you go back to the equation up here where I my pen is right now


That's the solution


and we put in the one that we've solved for from the initial conditions and that gave us the final answer


So the equation that so for C equals 1 is just to find out what C is.


Once we have C, we put it in.


back into our solution, and we get the 1 minus X.


okay!


I hope


I hope each step makes sense. It's difficult when, when you're first learning.


can we work on this one? can you pls go slow


OK


I'm sorry if I'm moving too fast. I'm, I, I apologize.


idk anyhting abt it


yes its okay


I understand


Yeah, I might not be sure myself about some things. I


I'll do my best to work slow.


So let me read this


okayyy


can you help me with intuition


tho


So when we


yeah, can I help with the intuition, though, yes.


So when we have, we have a problem here that's in polar coordinates, Emily.


Polar coordinates, it's not rectangular coordinates like our last problem was.


So


when we have polar coordinates, we have to use a little different method.