help-0

[normal lava]

yes but what about the x+2? Nothing on my book explains on what to do about a numerator whose value is not 1

[bronze spade]

Multiply the expansion you found by (x+2), that’s all. You must expand 1/(2-x)^2 at least to a term of degree 3. After multiplying with the numerator you’ll have an expansion to the 4th degree, just suppress the term of degree 4.

[normal lava]

multiply all of the expansion by x+2?

[bronze spade]

Then you get and expansion up to the 3rd degree

[bronze spade]

Sure

[normal lava]

so each expansion value is multiplied by x+2?

[bronze spade]

Each term of the expansion yea

[normal lava]

alright thanks for the help!

[bronze spade]

Develop everything

Np, you can show me what you found if you want me to check 🙂

[normal lava]

ok 👍

How is this?

[peak storm]

My question is"As flour is poured onto a table, it forms a right circular cone whose height is one-third the diameter of the base. What is the diameter of the base when the cone has a volume of 178 cubic inches? Round to the nearest tenth of an inch."

[clever tapir]

how do I write the second portion of piece wise functions?

missed the class

X_X

[devout kite]

uhh

[alpine sable]

anyone know whats wrong?

resolvd

[peak storm]

The question is "As flour is poured onto a table, it forms a right circular cone whose height is one-third the diameter of the base. What is the diameter of the base when the cone has a volume of 178 cubic inches? Round to the nearest tenth of an inch."

<@&286206848099549185>

[stark rampart]

the trick is knowing when $x^2-2x-8$ is positive and when it is negative

[ocean seal]

Armanzel (Ian)

[stark rampart]

for example, let's say i want to find absolute value of something simple, say $|x-2|$

[ocean seal]

Armanzel (Ian)

[bronze spade]

That’s it, and you can get rid of the term in x^4

[stark rampart]

i know that $(x-2)$ is positive when $x>2$ and it is negative when otherwise

[ocean seal]

Armanzel (Ian)

[normal lava]

k thanks

[stark rampart]

so you get two equations

$f(x) = x-2|x\geq2 \
f(x) = -(x-2)|x<2$

[ocean seal]

Armanzel (Ian)

[stark rampart]

u just attach a negative sign when it's gonna be negative beccause u want the value to always be positive

[lost oriole]

https://cdn.discordapp.com/attachments/269573202018041856/848712680805236756/unknown.png

https://cdn.discordapp.com/attachments/269573202018041856/848712686698889236/unknown.png

IS that asking for complement of zaxbys?

[clever tapir]

You are a genius

But it's a little bit more complicated with x^2 terms

Because there are 3 aspects you need to consider

[stark rampart]

hahahahahaha i couldn't understand it before so i tried explaining it to myself

yep

you have to do quadratic inequalities

when is $x^2-2x-8>0$?

[ocean seal]

Armanzel (Ian)

[clever tapir]

uh

[stark rampart]

u wanna factor it first

then let's see what u get

[clever tapir]

(x-4)(x+2)

[stark rampart]

yep this one

now

when u multiply two numbers, it's gonna be positive when

they are both positive or they are both negative right?

(+)(+)=+, (-)(-)=+

[clever tapir]

Yeah

[stark rampart]

the critical points are when each factor is zero

since it's neither positive nor negative yet

at what x are each factor zero

??

[clever tapir]

So 4 and -2

Will cause a critical point or whatever

[stark rampart]

yep

so you have

three areas

that this number line covers

from $-\inf$ to -2,

-2 to 4

and 4 to +inf

u want to find which of these three do u get both factors negative or both factors positive

[clever tapir]

How do I even write it down like I know what to say

X > 4 or X < -2
But also -2 > X > 4

[shut elk]

in other words, x > 4?

[clever tapir]

nah cause you can have values less than - 2

[shut elk]

sure thats not what the question asked.

[clever tapir]

O

[shut elk]

i thought u were looking at this, mb

[gloomy pewter]

Could someone help me swap y = e^(-x^2) to solve for x?

[shut elk]

use log

[stark rampart]

this is for positive case yes yes

[shut elk]

and another channel

[stark rampart]

and the negative case is everything else ie the remaining intervals

[clever tapir]

ok bet

[stark rampart]

so take a look at your cases and check which one is consistent

[clever tapir]

I eliminated D and C

So it's gotta be A

[stark rampart]

yehes

yep yep

[gloomy pewter]

I tried using log but I get log(y) = -x^2 which I can't simplify further as you can't take the sqrt of a negative

[clever tapir]

I get it now I just hope it's a transferrable math skill

🤨

[stark rampart]

it will be hahahaha

it comes down to relating some big relationship to something fundamental (positives, negatives)

going deeper into what makes it happen

[pseudo pebble]

if im given 3 vectors with 3 components each and i want to construct a matrix with them, how do i know if i should put each vector as a column or a row?

like if i was given v1=(2,0,1) v2=(3,1,4) v3=(2,5,3), is each vector a column?

[quartz stone]

what do you want the matrix to do?

but it's likely columns

[tepid otter]

https://i.imgur.com/TSI9kDG.png

This would be B right?

[ocean seal]

itsDaman ඞ

[stiff osprey]

I have a question about Lipschitz functions and uniform continuity. I think I understand the definition, but I was wondering about if I can directly use derivatives to say that a function is Lipschitz. Would it be correct to say that If the limit of the derivative a function approaches infinity on a subset A, then f(x) is not Lipschitz on that interval?

Take the limit of the function as x approaches infinity or negative infinity

[bronze spade]

Rewrite the equation so that you get an expression of y as a function of x. Calculate y’ and find at which x you get y’(x)=0

[bronze spade]

Sure. You generally say that on a given interval $\text{bounded derivative } f’ \Leftrightarrow f \text{ Lipschitz continuous}$

[ocean seal]

allevmelc

[bronze spade]

Then f’ not bounded <=> f not Lipschitz continuous

[arctic swan]

extremely confused at what equations would work with this

[stark rampart]

oh you need what u call a characteristic equation

oh wait u dont need

u just have to think of some value of a2 to get the next two terms a3 a4

[stable dune]

does anybody know the answer

[stark rampart]

u want to identify

• two points on the graph
• slope
• intercept

that's the general way to do this

start with two points then work your way to the slope and intercept

[stable dune]

well the slope is 1/5 right?

[ionic jewel]

yes

slope intercept form is y = mx+b iirc

so you already know m = 1/5

then b is just where it crosses the y axis

@stable dune

[stable dune]

nvm i got it

[next hatch]

im working through this question and im kinda stumped on b

not sure how to start it off

any little nudges to get me going would be appreciated

[next hatch]

scuse me bro

tryna get some help

@stable dune mind deleting that

[stable dune]

why?

[next hatch]

cuz i asked a question

[stable dune]

im trying to get help just like you,

[next hatch]

yes but i asked first

[stable dune]

shouldnt have the need to delete my question because of yours,

[next hatch]

but i havent gotten help

[stable dune]

they see everyones questions, be patient theyll answer you first

[next hatch]

bruh

[rugged bramble]

<@&286206848099549185>

[next hatch]

bruh

imma ask in another channel allgs

[woven plaza]

Sum of opposite angles is 180°@rugged bramble

Should help ;-)

[rugged bramble]

thanks

i did it already

[sturdy glen]

how do you know when a matrix where a row looks like the bottom one here is either inconsistent or there's a free variable?

[alpine sable]

free variable

[sturdy glen]

well i know from the textbook sample

but why

why isn't it inconsistent?

[alpine sable]

$-9x_2 = 0$

[ocean seal]

ajuze

[alpine sable]

x_2 could be any number

there are infinite solns

aka free variable

[sturdy glen]

oh yeah alright. when is the matrix inconsistent though

[alpine sable]

when something like $0x = -9$ happens

[ocean seal]

ajuze

[alpine sable]

so there is a number in the last col

and everything else is 0

[sturdy glen]

OH

that's the case i'm thinking of

tysm!

[alpine sable]

np!

[eager ore]

How to find mod if the left hand side is smaller than right hand side? For Example: 3%5

[solemn maple]

CAN ANYBODY SUGGEST ME FREE AND DAILY CONTEST OF MATHEMATICS WEBSITE

[alpine sable]

can someone explain this last step?

[merry willow]

I got question guys
i got 3 fair dice, i throw one after the other
i get, x1, x2, x3
whats the probability i get x1>x2>x3

[alpine sable]

nvm

[stark rampart]

edugain is decent

[stark rampart]

i personally would list cases

i think there are 20

[merry willow]

there is suppose to be 20

i dont follow the steps

[stark rampart]

123
124
125
126
134
135
136
145
146
156
234
235
236
245
246
256
345
346
356
456

i start with them being close together (123) and distancing them bit by bit

the trick here is that if u have 3 distinct numbers from 1-6, say 5 2 and 3, u can arrange them into x1<x2<x3

so it's just a matterof choosing 3 numbers from 1-6

ie 6C3=20

[merry willow]

is there a way you could answer with combination?

[stark rampart]

yep 6C3

[merry willow]

mhm

i dont follow..

6c3

[stark rampart]

the goal is

[merry willow]

but x1>x2>x3

[stark rampart]

oh sori then just "reverse" it

for any 3 distinct numbers frm 1-6 u can arrange them in decreasing order

[merry willow]

yes

[stark rampart]

like if u have 1 4 2 u will get 4 2 1

so that mans

means

[merry willow]

but the question asks it has to be toss 1, toss 2, toss 3

[stark rampart]

for any combination of 3 distinct digits u have a unique x1 x2 x3

yep yep

4 2 1 is ordered so that means

toss1 is 4 toss2 is 2 and toss3 is 1

[merry willow]

sorry this is the original question

3 fair dice, toss one by one and we get x1, x2 and x3. what is the probability of x1 < x2 < x3.

i m with you

4, 2 ,1 will be thrown out

sorry

4, 1, 2*

it has to be 1, 2, 3 or something like this

6 choose 3 includes the case of 4, 1, 2

[stark rampart]

no no it wont overcount

[merry willow]

😫

[stark rampart]

since u are like getting three distinct numbers and arranging then yourself to get x1<x2<x3

[merry willow]

but i thought u cant arrange

[stark rampart]

hmmmmmmm

[merry willow]

toss 1 == x1

[stark rampart]

what im doing rn is finding combinations of valid outcomes

[merry willow]

yes yes

[stark rampart]

e.g. 1 2 3 is valid

3 4 2 is not

[merry willow]

yap yap

[stark rampart]

so the question reframes to

how many ordered triples are there

such that it is increasinf

[merry willow]

yap yap

[stark rampart]

we wont think about the dice first

so

how do we make an increasing sequence???

you pick 3 distinct numbers and then arrange them

[merry willow]

ok

[stark rampart]

imagine having 6 coins numbered one to 6

get 3 random coins then arrange them yourself

this always guarantees an increasing sequence, right?

so what we only have to do is get three numbers from 1-6

hence 6C3

[merry willow]

kk

[stark rampart]

so that makes our list of 20 possible outcomes

hence, 20 possible combinations of die numbers

and that's it

[merry willow]

how did we go from 6 coins to 3 dice

[stark rampart]

over 6³

[merry willow]

😦 sorry im dumb

[stark rampart]

the coins was just an analogy about picking 3 numbers from 1-6

dont overthink it much hahaa

you dnt have to simulate the die roll

[merry willow]

i m still fixated on toss 1 == x1 and order matters

[stark rampart]

just write down every possible outcome

yep

for example

the three dices shoe 5 2 and 4 in no order

if it should be a valid toss what is x1 x2 x3?

2 4 5 right?

[merry willow]

yes

[stark rampart]

it's like thinking of the numbers that come up (without order first)

[merry willow]

ok

[stark rampart]

we can get those combinations of numbers from 6C3

153, 234, 521, etc

the thing is that u need to have x1 x2 x3 right

that's the main concern

[merry willow]

yes yes i m with you

[stark rampart]

well once u get a combination of numbers that come up(without order still)

[merry willow]

main concern is toss 1 < toss 2 < toss 3

[stark rampart]

u can just arrange it to let x1 be smallest then x3 be largest

[stark rampart]

e.g. is this one from a while ago

for example

[merry willow]

i c

[stark rampart]

combination 2 4 1 => (1,2,4)
combination 5 2 3 => (2,3,5)

it's a one to one relationship

[merry willow]

can just ignore the order statement

[stark rampart]

hmmm not exactly ignore

[merry willow]

i see your point, get distinct set

[stark rampart]

coz i did order them at the last point

[merry willow]

where in 6c3 did you order them

[stark rampart]

but u can refocus your solving to distinct numbers rather than worrying about order

[merry willow]

😦

[stark rampart]

6c3 gives u the combinations

[merry willow]

yes yes

why can i ignore the order

ik bc i can arrange it myself

[stark rampart]

the combinations on the right are from 6c2 aka 3 distinct numbersin no particular order

yep yep u can arrange it yourself

andddd it doesnt overcount because a die combination wll always have one ordering

2 4 1 ca only have (1,2,4) as your valid outcome

[merry willow]

yes

tyty ian

why were you able to tell 6c3 is good enough

6c3 suffice the x1<x2<x3 statement

as x1,x2,x3

[neat merlin]

$\left{\begin{array}{l}6 x z+3 x=2 z-2 \ x y+z y=2(z-x+1) \ z y-6 x z+y=3 x+3\end{array}\right.$

[stark rampart]

oh because once u get three unordered distinct numbers, u can always find an arrangement of those three as x1 x2 x3

[ocean seal]

qcanser

[stark rampart]

it's like

instead of countng the number of people in the room, if u know the number of chairs ad everyone sits on a chair and all is unoccupied, then u just count the chaira

chairs

[merry willow]

lol

😦 why i couldnt see chairs

tyty ian!

https://tenor.com/view/flowers-cute-dog-bouquet-dog-flowers-for-you-gif-16843946

um.. maybe another question

i dont get p value..

[stark rampart]

haahahahah

it's a different way of counting

[merry willow]

feels like p value is always at least as large as probability

if we toss coins

[signal drift]

Lets say I have a data table showing a growth rate

Year 2 +3%
Year 3 +7%
Year 4 + 15%
Year 5 + 40%```

How can I calculate the average growth rate per year so I can use it to see "estimated" +% in  X amount of years

<@&286206848099549185>

[noble sinew]

same way you would fine the mean of some numbers

[signal drift]

I dont think that would work for this data

[tepid otter]

does anyone know if there's a calculator for this?

[signal drift]

Occupied

[signal drift]

The mean wouldnt work for this because it seems to be an exponential growth rate

not a fixed average growth rate

[signal drift]

Still waiting for help on this question

#help-0 message

[noble sinew]

then fit exponential function to the data

[placid zinc]

It's not clear what you're asking. I don't know that that list of numbers was supposed to tell us.

Are those numbers
year 6
year 7
...?

And were those given to you? Or are you using some method to get them?

[signal drift]

like its the growth rate of the bacteria
at the end of year one the number grew by 224% then year 2 984% and so on

so this table only goes to year 10 and I want to try and create an equation that will allow me to put in X amount of years to see the percentage change

[noble sinew]

do this my friend

[placid zinc]

The numbers seem to contradict your original message

Anyway yeah do that

[signal drift]

Idk what that means

[noble sinew]

exponential function is on the form y=a*b^x

[placid zinc]

Honestly go into excel and fit an exponential to those numbers

[noble sinew]

you mentioned yourself it has exponential growth

[alpine sable]

yo what is wrong here

[placid zinc]

@alpine sable
What's the work look like? Possibly a calculation error?

Remember to take the unit vector in that direction

[alpine sable]

unit vector

2/3, 2/3, -1/3

[placid zinc]

3² when it should be 3

On the last component

[alpine sable]

holy shit

your eagle eyed

tysm!!

[placid zinc]

Haha I get practice. Glad it works!

[sterile beacon]

(3^x + 3^x)^2

[oak chasm]

@sterile beacon What's the question?

[sterile beacon]

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

[oak chasm]

OK, do you know how to do the addition in the parentheses?

[sterile beacon]

no

[oak chasm]

OK, do you know that a + a = 2a?

[sterile beacon]

yes

[ocean seal]

Chai T. Rex

[sterile beacon]

6^x?

[oak chasm]

Not exactly.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

You multiply the thing you added to itself by 2.

[sterile beacon]

Okay yes

add the same

it's the same thing twice

*2

[ocean seal]

Chai T. Rex

Chai T. Rex

[sterile beacon]

a^2b^2

[ocean seal]

Chai T. Rex

[sterile beacon]

2^2 * 3^2x

[oak chasm]

Right!

[ocean seal]

Chai T. Rex

[sterile beacon]

4 * 9^x?

[oak chasm]

Right!

That's your answer.

[sterile beacon]

Thank

s

[oak chasm]

You're welcome.

,w simplify (3^x + 3^x)^2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[pearl folio]

I don't know what I am doing wrong, but I'm not getting the same as the answer

[oak chasm]

What answer are you getting?

[pearl folio]

e^2t

And c=0 I'm getting

[oak chasm]

OK, when you take the antiderivative, you have a constant term, usually C, right?

[pearl folio]

Yes

[oak chasm]

OK, so when you take the first antiderivative to get velocity, what should that C be?

[pearl folio]

Uh

Yeah forgot about that

But idk what that'd be

[oak chasm]

Well, the velocity at time zero is what?

According to the problem.

[pearl folio]

0

?

[oak chasm]

Right, and what's the antiderivative of the acceleration?

[pearl folio]

2e^2t

+c

[ocean seal]

Chai T. Rex

[pearl folio]

c=-2

Yes?

[oak chasm]

OK, good.

[ocean seal]

Chai T. Rex

[pearl folio]

e^2t - 2t

+c

[oak chasm]

OK, same thing as before. This is position. What's the starting position?

[pearl folio]

1

[ocean seal]

Chai T. Rex

[pearl folio]

Yeah I get it now

c= 0

[oak chasm]

Oh, sorry, with ts filled in with 0s

OK, good.

[pearl folio]

Equation is e^2t -2t

Yeah thanks

[oak chasm]

No problem.

[upper kayak]

what's the equation relating speed, distance and time?

[stark lantern]

probably km/hr

[upper kayak]

yeah

plug in the values you know

that's what you have to find

set s to 25

km/hr

d is distance

set that to 120km

now solve for t

$4 \cdot 3^x - 9 \cdot 2^x = 5 \cdot 3^{\frac{x}{2}} \cdot 2^{\frac{x}{2}}$

[ocean seal]

gang

[upper kayak]

can anyone help me with this?

[alpine sable]

$2^2 * 3^x - 3^2 * 2^x = 5(3*2)^{\frac{x}{2}}$

[ocean seal]

ajuze

[upper kayak]

mhm

[alpine sable]

idk someone else do it

[upper kayak]

lol

[stark lantern]

you can make this into a quadratic in y = 1.5^(x/2)

$4\frac{3^{0.5x}}{2^{0.5x}} - 9\frac{2^{0.5x}}{3^{0.5x}} = 5
\implies 4y - \frac{9}{y} = 5$

[ocean seal]

error 404

[stark lantern]

solve for y then solve for x

[alpine sable]

wow this is a very interesting technique

bravo

[upper kayak]

how did you get there from the original problem

[stark lantern]

divide both sides of original problem by $3^{\frac{x}{2}}2^{\frac{x}{2}}$

[ocean seal]

error 404

[upper kayak]

ok

[stark lantern]

120/25 = 4.8 hours = 288 minutes

[upper kayak]

got that

no

that's where the division comes from

$$s = \frac{d}{t}$$
$$25 \frac{km}{hr} = \frac{120 km}{t}$$
$$t = \frac{120 km}{25 \frac{km/hr}}$$

of course

$$s = \frac{d}{t}$$
$$25 \frac{km}{hr} = \frac{120 km}{t}$$
$$t = \frac{120 km}{25 \frac{km}{hr}}$$

[ocean seal]

gang

[upper kayak]

there

the kms cancel out, and 120/25 is 4.8

you know canceling right?

common factors in the numerator and denominator cancel out

$$\frac{2 \times 2}{2}$$

[ocean seal]

gang

[upper kayak]

bottom two cancels out with one of the twos in the numerator

units are treated the same way

[alpine sable]

Anyone help?

For which numbers $n$ does $$\sin^{2}\left(\frac{\pi x}{n\left(x+1\right)}\right) + \sin^{2}\left(\frac{\pi}{n\left(x+1\right)}\right) = 1$$?

[ocean seal]

macoro

[alpine sable]

<@&286206848099549185>

ok it seems to do so for all numbers n = 2/(2z+1), where z is an integer

why tho?

$\sin^{2}\left(\frac{\pi x}{n\left(x+1\right)}\right) = 1 - \sin^{2}\left(\frac{\pi}{n\left(x+1\right)}\right)$

[ocean seal]

sshaagar

[alpine sable]

$\sin^{2}\left(\frac{\pi x}{n\left(x+1\right)}\right) = \cos^{2}\left(\frac{\pi}{n\left(x+1\right)}\right)$

[ocean seal]

sshaagar

[alpine sable]

I dont understand why thats true

[oak chasm]

Do you see the steps they took from your original question?

[alpine sable]

yep

[oak chasm]

OK, which step do you get stuck on?

[alpine sable]

Just understanding the last equation

$\sin^{2}\left(\frac{\pi x}{n\left(x+1\right)}\right) = \sin^{2}\left(\frac{\pi}{2} - \frac{\pi}{n\left(x+1\right)}\right)$

[ocean seal]

sshaagar

[alpine sable]

Compare the inner parts

oh thanks

[brazen dragon]

"A student ticket to the zoo costs $C. An adult ticket to the zoo is double the cost of a student ticket. If taking 25 students and 3 teachers (adults) to the zoo costs $474.30, find the cost of an adult ticket"

[oak chasm]

@brazen dragon Sorry, channel is still busy.

[vale wigeon]

mb

didnt see the timestamps

yeah hlee you will have to move

[alpine sable]

Nah it's open I got it

[vale wigeon]

oh

[alpine sable]

Thanks sshaagar

[brazen dragon]

oops sorry

[vale wigeon]

well in any case, you should tell us what you've tried so far

@brazen dragon ?

[brazen dragon]

well for some reason i can't seem to solve it

[vale wigeon]

have you made any progress?

if you've gotten yourself stuck somewhere, please tell us where

so that we can help you

[clever locust]

show us what you've done so far, even if it didn't get you very far

[brazen dragon]

i forgot how to write a formula for it

idk im brain dead rn

[vale wigeon]

well, there is a way to do this problem that doesn't rely on formulas.

at least, not very explicitly.

if you want, i can share.

[brazen dragon]

sure go ahead

[vale wigeon]

imagine that instead of an adult ticket, we just give each adult 2 child tickets.

[brazen dragon]

ohh

[vale wigeon]

since the problem says an adult ticket costs double a child ticket, the value will be the same.

[brazen dragon]

yea that makes sense

[vale wigeon]

so now, ask yourself: this group of 25 children (with 1 ticket each) and 3 adults (with 2 tickets each)

how many tickets do they have in total?

[brazen dragon]

31

[vale wigeon]

great

and we know they're all the same price

and together they all cost $474.30

so how much does one of them cost

[brazen dragon]

mm its 15.30

thanks

[vale wigeon]

(notice that 15.30 is not the answer to the question you're actually being asked here)

(you're asked for the cost of an adult ticket, but here we're only dealing with child tickets)

[brazen dragon]

i mean yea you times it by 2

[vale wigeon]

yes good

[brazen dragon]

so its $30.60

[vale wigeon]

i wanted to ensure this didn't slip by you

[brazen dragon]

ah ty

[woeful tartan]

help, O = 2 x π x r. how do i solve this

[vale wigeon]

what do you mean by 'solve'?

[woeful tartan]

it says find out r

[vale wigeon]

okay...

do those x's stand for multiplication?

[woeful tartan]

sorry had to translate from another language

yes

[vale wigeon]

so you have O = 2pi * r...

r is being multiplied by 2pi

how do you undo that?

[woeful tartan]

division maybe?

[vale wigeon]

why maybe

yes, divide both sides by 2pi.

it really is that simple

[woeful tartan]

wait

so the answer is O/2pi = r??

[vale wigeon]

yes

[woeful tartan]

okay

[vale wigeon]

parentheses, but yes

[woeful tartan]

i was making it complicated

thanks

what about ,w 9a^2 + 2ab + b^2/ a + b

,w

Sorry i was trying to use the bot so i can show the thing

[oak chasm]

@woeful tartan You'll need parentheses around the whole numerator and the whole denominator.

,w (a^2 + 2 a b + b^2)/(a + b)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[woeful tartan]

ah okayy

[oak chasm]

See the top here ^

[woeful tartan]

yeah

did that give bot give me answers

[oak chasm]

What do you want Wolfram Alpha to do?

[woeful tartan]

just show what i wrote

[oak chasm]

Oh, that's better for LaTeX.

$\frac{9a^2 + 2ab + b^2}{a + b}$

[ocean seal]

Chai T. Rex

[oak chasm]

$\frac{top}{bottom}$

[woeful tartan]

ahhh

okayy thank you

[oak chasm]

No problem.

[woeful tartan]

can i repost the question now?

[oak chasm]

Is it from this channel?

[woeful tartan]

yeah

[oak chasm]

Sure.

[woeful tartan]

Help, $\frac{a^2 + 2ab + b^2}{a + b}$

[ocean seal]

mishri

[oak chasm]

OK, so factor the top.

Or, I guess, do long division.

[woeful tartan]

(a + b) + (a + b) + 2ab/a+b

like this or?

[oak chasm]

Don't forget parentheses around the whole top and the whole bottom.

No, that's not correct factoring.

[woeful tartan]

umm

i don't know factoring apparently

[ocean seal]

Chai T. Rex

[oak chasm]

Which isn't what you started with.

[woeful tartan]

ahhh that

okay

sorry i am a bit confused

would it be 2* 2 *2 + a + b + ab

[oak chasm]

What full expression do you mean?

OK, what does that simplify to?

[woeful tartan]

8 + a + b + ab

[alpine sable]

explain why the surface area of a right prism can be found using the formula a=ph+2b

[oak chasm]

@alpine sable Sorry, channel is busy.

@woeful tartan OK, so that's not correct.

Are you OK with watching YouTube videos?

[woeful tartan]

Yes, I am if it helps me

[oak chasm]

OK, watch this one: https://www.youtube.com/watch?v=kKE4t7R_KWc.

[woeful tartan]

Okay, Thank you.

[oak chasm]

No problem.

[alpine sable]

explain why the surface area of a right prism can be found using the formula a=ph+2b ?

[next hatch]

bro u posted that in another channel

[oak chasm]

@alpine sable Sorry, this channel is still busy (they'll be back shortly, I think).

[alpine sable]

oh ok

[woeful tartan]

it is a bit confusing but i understood factoring

[ocean seal]

Chai T. Rex

[woeful tartan]

a * a?

[ocean seal]

Chai T. Rex

[woeful tartan]

hmmm

2a?

[ocean seal]

Chai T. Rex

[woeful tartan]

2

[next hatch]

bruh

[ocean seal]

Chai T. Rex

[woeful tartan]

it doesnt

[ocean seal]

Chai T. Rex

[woeful tartan]

it doesnt

[ocean seal]

Chai T. Rex

[woeful tartan]

yes

[oak chasm]

OK, we take all the variables put together in a term and we call it the those variables term.

[ocean seal]

Chai T. Rex

[woeful tartan]

yes, it does

[ocean seal]

Chai T. Rex

[woeful tartan]

yes it does

[ocean seal]

Chai T. Rex

[woeful tartan]

hm, it's ab?

[ocean seal]

Chai T. Rex

[woeful tartan]

hmmmm

wait no

a^2 is the single term?

[ocean seal]

Chai T. Rex

[oak chasm]

What's its coefficient?

[woeful tartan]

hmm

a^2 or a is its coefficient since i dont see a number at start

[oak chasm]

OK, so here's the trick when you don't see a number.

[ocean seal]

Chai T. Rex

[woeful tartan]

yes

[ocean seal]

Chai T. Rex

[woeful tartan]

okay

so coefficient of b^2 is 1

[oak chasm]

Yes, but hold on.

[woeful tartan]

okay

[oak chasm]

We're pretending that a is the only variable and b is just some number.

Does that make sense?

[woeful tartan]

somewhat

[ocean seal]

Chai T. Rex

[woeful tartan]

hm b^2

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[woeful tartan]

1b^2

[oak chasm]

And what does that simplify to?

[woeful tartan]

b^2

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[woeful tartan]

which video

ahh yesss

yes it does

[ocean seal]

Chai T. Rex

[oak chasm]

What's that?

[woeful tartan]

bottom of the x?

2?

[oak chasm]

Yes, this X:

2 is good.

[woeful tartan]

oh that x

[oak chasm]

But it's not exactly what we want.

We're pretending that b isn't a variable, it's just another number, right?

[woeful tartan]

yes

[ocean seal]

Chai T. Rex

[woeful tartan]

right

[oak chasm]

So what's the coefficient of the a term?

[woeful tartan]

hmm

3 maybe?

[oak chasm]

What's the a term?

[woeful tartan]

a^2

[ocean seal]

Chai T. Rex

[woeful tartan]

a term is 1a

[oak chasm]

No.

What's the a term?

[woeful tartan]

a + b^2???

[oak chasm]

That's two terms.

What's the a term?

[woeful tartan]

a

[oak chasm]

No, that's not one of your three terms.

[ocean seal]

Chai T. Rex

[woeful tartan]

2ba ?

[oak chasm]

Right.

[woeful tartan]

so 2b?

[oak chasm]

Right.

First, you get the term.

Then you get the coefficient.

[woeful tartan]

so 2ba is the term and 2b is the coefficient

[oak chasm]

Right, if a is a variable and we're treating b like just another number.

[woeful tartan]

ahhhh

so if its 7xy

7xy is the term

and 7x is the coefficient?

[oak chasm]

Of x and y, which are variables, which are we treating like numbers?

[woeful tartan]

x

[oak chasm]

x is the variable or the number?

[woeful tartan]

number

[oak chasm]

y is a variable or a number?

[woeful tartan]

y is the variable

[oak chasm]

OK, then yes.

7x is the coefficient of the y term.

[woeful tartan]

okay understood that

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[woeful tartan]

okay

yes

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[woeful tartan]

hmm

1 and b^2??

[oak chasm]

Right. What else?

[woeful tartan]

hmm

b and b?

[oak chasm]

Right!

So, those are the factor pairs we care about because we only want integer coefficients on b.

[ocean seal]

Chai T. Rex

[harsh acorn]

Can I share a question too if you guys are done

[oak chasm]

@harsh acorn Sorry, channel is still busy.

[ocean seal]

Chai T. Rex

[oak chasm]

What does it simplify to?

[woeful tartan]

1b^2

[oak chasm]

Nope.

• doesn't mean multiply.

[woeful tartan]

1 + b^2?

[oak chasm]

Right.

Is that 2b on the bottom?

[woeful tartan]

yes

[ocean seal]

Chai T. Rex

[woeful tartan]

uhh no?

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

Chai T. Rex

[woeful tartan]

hmm

i dont know i dont think it can be simplfied??

[ocean seal]

Chai T. Rex

Chai T. Rex

[woeful tartan]

2b?

[oak chasm]

Did you actually draw the X and write the numbers on top and bottom?

[woeful tartan]

i drew the X with the numbers you told

[oak chasm]

OK, so what number is on the bottom of the X?

[woeful tartan]

2b???

[oak chasm]

You wrote it. You tell me.

[woeful tartan]

it is 2b

[ocean seal]

Chai T. Rex

[woeful tartan]

no

its on the top

[oak chasm]

Right, so that factor pair doesn't work.

No, it's not.

[ocean seal]

Chai T. Rex

[woeful tartan]

sorry i meant b^2

it doesn't work

[oak chasm]

OK, so we've done two of our factor pairs.

What about our third (b, b)?

What's b + b simplified?

[woeful tartan]

2b

[oak chasm]

Is that what we have on the bottom?

[woeful tartan]

yes

[oak chasm]

OK, so write the first number in the factor pair on the left of the X and the second number in the factor pair on the right of the X.

(b, b) is the factor pair.

[woeful tartan]

okay

i wrote it

[oak chasm]

OK, so we have (a + left of X)(a + right of X).

Fill in the left of X number and the right of X number.

What do you get?

[woeful tartan]

a + b+b

[oak chasm]

Nope.

[woeful tartan]

a + 2b

[oak chasm]

Nope.

[woeful tartan]

what

[ocean seal]

Chai T. Rex

[oak chasm]

Do it step by step.

What number is left of X?

[woeful tartan]

b+b

[oak chasm]

No.

[woeful tartan]

huh

[oak chasm]

What was the factor pair that worked?

[woeful tartan]

b+b

(b,b)

[oak chasm]

No, it was (b, b).

What's the first number in that?

[woeful tartan]

b

[oak chasm]

Write that to the left of the X.

[woeful tartan]

okay

[oak chasm]

What's the second number in that?

[woeful tartan]

b

so a+b and a+b

[oak chasm]

Write that to the right of the X.

Right.

Now, do you know FOIL?

[woeful tartan]

I don't

[oak chasm]

Do you know how to expand?

[woeful tartan]

yes

[oak chasm]

Expand (a + b)(a + b).

[woeful tartan]

a^2 + ab + ba + b^2

[oak chasm]

Simplify that.

[woeful tartan]

a^2 + 2ab + b^2

[oak chasm]

That's what we started with, right?

[woeful tartan]

yess

what about the divison

[oak chasm]

So, (a + b)(a + b) is that factored.

[alpine sable]

Hey

[oak chasm]

@alpine sable Sorry, channel is busy.

[alpine sable]

Oh alright my bad

[ocean seal]

Chai T. Rex

[woeful tartan]

wait

so

[oak chasm]

@woeful tartan ^

OK.

[woeful tartan]

(a+b)^2/a+b

can i cancel out the 2

with a+b

and it leaves me with a+b

is the answer a+b

[pure temple]

Can anyone please help me with this once you are done

[ocean seal]

Chai T. Rex

[oak chasm]

@pure temple Sorry, channel is busy.

@woeful tartan ^

[woeful tartan]

okay

thank you very much, I learnt new things

[oak chasm]

You're welcome. If you want, rewatch that video while using its ideas is fresh in your mind.

[woeful tartan]

ah yes i saved it, i will rewatch it

Got a math test today so gotta prepare for other things

[oak chasm]

Oh, OK.

[woeful tartan]

thank you again

[oak chasm]

You're welcome.

[pure temple]

Can I get help now?

[oak chasm]

@woeful tartan Are you done with this channel for now?

[pure temple]

I think they left

Please my exam is in an hour this is very urgent

[oak chasm]

Is this practice or the exam?

[pure temple]

practice

[oak chasm]

,rotate

[finite ingot]

Can anyone help me in Linear equations

[oak chasm]

@finite ingot Sorry, channel is busy.

[finite ingot]

Ok ;{

[oak chasm]

@pure temple How does the grading work?

[pure temple]

?

[oak chasm]

What part of the final grade are each homework? What part of the final grade is the final assessment? Are there any other parts of the final grade?

[pure temple]

This is the practice test, it is for preperation

[oak chasm]

Right, but read the question.

Do you see how it mentions a grade, homeworks, and the final assessment?

[pure temple]

oh no there aren't

that's all the info given

[oak chasm]

How many homeworks have you done in real life for this class?

[pure temple]

First one

this is the first of this type

[oak chasm]

This is a practice thing, so it probably doesn't count towards your grade.

Have you done other homework?

[pure temple]

yeah

no

Are you aware of how to solve the question?

[oak chasm]

Not without knowing what weight each homework and the final assessment has toward the final grade.

[pure temple]

In real life or in the question?

[oak chasm]

In the question.

[pure temple]

Oh okay cheers

[oak chasm]

In real life might apply to the question, though.

Like if you had 6 homeworks and a final assessment, they might be asking about the grading scheme used for you.

[pure temple]

Yeah

[oak chasm]

Oh, I see.

I see a way to do it.

Apparently, they're all called assessments.

So, if we assume each assessment is worth equal weight and the assessments are all that count toward the final grade, then we can do the problem.

[pure temple]

ohh okay

[oak chasm]

So, she got 73% on her first 5 assessments.

[pure temple]

That's the average yea

[ocean seal]

Chai T. Rex

[oak chasm]

Does this inequality make sense?

[pure temple]

Ohhh yes it does

[oak chasm]

OK, solve it for x.

[pure temple]

okay I'll write the equation down and do it shortly as I have to go

Thabks

[oak chasm]

No problem.

[pure temple]

Would it be 85%

@oak chasm

[oak chasm]

It would.

[pure temple]

Thanks

[oak chasm]

No problem.

[tight locust]

@grizzled garden sj is 1 and sj+1 is 1

maybe you guys can help with this question. more CS but the programming server i'm in isn't that smart lmao

given a function fib(n)

fib(0) returns 0

fib(1) returns 1

fib(n>=2) returns fib(n-1) + fib(n-2)

for a given input n>=2, how many calls to the function are made?

[upper kayak]

seems like a geometric progression

2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
16 3193
17 5167
18 8361
19 13529```

left column is n, right is number of calls

or maybe not

hold on

[upper kayak]

looks exponential

but the base is changing

or it might just be lack of precision

[tight locust]

can you make another column

that is the value of fib(n)

[upper kayak]

ok

btw

before that

i said the base changes

starts out as 1.7 and decreases

looks like it's approaching the golden ratio

2 3 1
3 5 2
4 9 3
5 15 5
6 25 8
7 41 13
8 67 21
9 109 34
10 177 55
11 287 89
12 465 144
13 753 233
14 1219 377
15 1973 610
16 3193 987
17 5167 1597
18 8361 2584
19 13529 4181
20 21891 6765
21 35421 10946
22 57313 17711
23 92735 28657
24 150049 46368
25 242785 75025
26 392835 121393
27 635621 196418
28 1028457 317811
29 1664079 514229
30 2692537 832040

using that as base is a pretty bad estimate

so ig not

[main zephyr]

okay im trying to find angle c, the information that the question gave me is
angel D = 56
a = 3
b = 7
c (the right side) = 4

right side c doesn't equal to left side c
a and b are both straight lines

what i've found so far:
angel A = 134

im stuck and could someone verify if angel A = 134?

[oak chasm]

@main zephyr You're trying to find angle C, right?

[main zephyr]

yes

i dont know what angle B is tho

[oak chasm]

OK, and you see how it's marked as congruent to angle D, right?

[tight locust]

@upper kayak are you sure you're not using memoization or anything?

[main zephyr]

angle D = angle B
meaning B is 56?

[oak chasm]

No.

[main zephyr]

OH

[oak chasm]

Do you see the two curve marks next to D?

[main zephyr]

180 - 56?

[oak chasm]

No.

Do you see the two curve marks next to D or not?

[main zephyr]

yes

180 = d + c

[oak chasm]

OK, do you see the two curve marks next to C?

[main zephyr]

yes

[oak chasm]

That means that C is congruent to D.

That means they have the same measure.

So, what's the measure of D?

[main zephyr]

56?

[oak chasm]

Right, so if C has the same measure as D, what's C?

[main zephyr]

56?

[oak chasm]

Right.

[upper kayak]

what?

[main zephyr]

hm the answer says 68

lemme send u a pic of my question

[upper kayak]

what do you mean

[main zephyr]

(the pic above is from google)

[upper kayak]

how can i memorize that

[tight locust]

memoization is when you save the results of function calls

[main zephyr]

@oak chasmhere

its question J

[tight locust]

to an array or something and then just return the value at that index.. which would affect the number of calls depending on how many times you use the function

[main zephyr]

wait angle D isnt equal to C since their length are not the same

i stated that in my message

[oak chasm]

You also showed a picture where C was the same as D.

[main zephyr]

yes cuz i cant find any ones same as my question

when googling it

[oak chasm]

You found one here.

[main zephyr]

tho heres my question

yes

so my brain stops at here

since the teacher didnt teach us how would we find angles using length

[main zephyr]

would anyone help me?

[upper kayak]

no

just updating a counter each call

[tight locust]

ooh i got it

calls(n) = 2*fib(n+1)-1

i think my confusion arose from the fact that some people say fib(0) = 1

personally i think fib(0) = 0

Wolfram alpha agrees

[upper kayak]

bruh

[cunning lynx]

what grade are you in?

[tight locust]

i'm not in school anymore

[cunning lynx]

oh so you finished it

[tight locust]

yeah just finished hs

[cunning lynx]

So what do you want to become?

also good luck !!!

[tight locust]

i'm looking into EE

[cunning lynx]

alrighty 🙂

[upper kayak]

omg

i've ended up in recursion hell

almost done

now i know what they have supercomputers for

@tight locust

pretty close, no?

[tight locust]

what is orange and green

[upper kayak]

red is actual no. of calls

green is my model

probably could get better accuracy but i can't do that on my laptop

$$f(n) = e^{1.1 + 0.4898581513529545(n-2)}$$

[ocean seal]

gang

[tight locust]

what even is that number

[upper kayak]

the natural log of each number of calls increases by around that number (0.48985) for each increment of n

ln(calls(fib(2))) is 1.1

roughly

ln(calls(fib(2))) is 1.5

and so on

[upper kayak]

this gets closer to 0.481212

so i guess that's why it goes off around the end

[small holly]

how do i get the surface area

this is the answer

i want to know the working out

[plucky crow]

1/2 *a+b *h *5.3

oh

surface area

nvm

[vale wigeon]

parentheses!

[small holly]

yeah

its 1/2(a+b)

[plucky crow]

i cba to write it out but area of the trapezium

twice

[vale wigeon]

@small holly so you know that to find the surface area of a shape, you find the area of each face & add them together

right?

[small holly]

yeah ik that

[vale wigeon]

yeah so

[small holly]

but the diagram is just confusing