help-27

[soft umbra]

You have to distribute the negative sign to 4

[severe pasture]

yeah thats what i thought but arent u subracting\

or is it formatted like -(m+4)

[soft umbra]

Correct

[severe pasture]

oh so its like that always

[soft umbra]

yeah

Certainly

[severe pasture]

alrr thanks

.close

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[devout snow]

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[manic robin]

Not sure how to solve this

[magic pine]

have you heard of implicit differentiation

[manic robin]

No

[magic pine]

try writing this as [g(t) = e^{\ln\left(t^{\sec t}\right)}]

[woven radish]

maximo

[manic robin]

It says I need to solve it with rules

[magic pine]

ok

did you see what i sent

[manic robin]

Yes

Oh wait I figured that one out

Close

.close

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[proper terrace]

this table is confusing

[uncut crow]

i don't think your answer for b is right

[proper terrace]

is it 2

[uncut crow]

yep lol

[proper terrace]

i got it

.close

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[manic robin]

I need help with this, I need to fix what the student did wrong and give suggestions as well as solve it but I’m confused

[violet pine]

derivative aint correct

cause its product ruke

rule

[manic robin]

Wdym

I have no idea how to even start this I’m lost

.close

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[weak cove]

if you submitted this as a test and got marked wrong on some work somewhere then u deserved that

[solar goblet]

Given the graph above. $f(x)$ is the third degree polynomial, $g(x)$ is the linear equation

[woven radish]

FungusDesu MSC2020 34A05

[solar goblet]

no lol its homework

[weak cove]

[solar goblet]

anyway

[solar goblet]

The shaded region's area is $\frac{250}{81}$

[woven radish]

FungusDesu MSC2020 34A05

[solar goblet]

Evaluate $\int_0^1f(x)dx$

[woven radish]

FungusDesu MSC2020 34A05

[solar goblet]

as you can probably tell from the screenshot i tried a lot of ways, but its pretty much deadend

tried a simul equation with 5 var, but can only find 4 equations

[devout snow]

@solar goblet Has your question been resolved?

[devout snow]

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[urban vector]

Hello all! Having a problem with this question, I honestly have no idea where to start simplifying

[urban vector]

I've looked for common factors

There isnt any

So i dont know where to begin with this integral

[ocean silo]

you could try to split the integral into 4 of them, as I believe you can use partial fractions for the latter two terms

[urban vector]

uh

sorry, whats partial fractions?

I haven't learned that

[violet pine]

first divide

you can do polynomial division

[uncut bay]

You do like f(x)/ x-2 + g(x)/ (x-2)^2

Just split that in the integral and find f(x) g(x)

[ocean silo]

https://youtu.be/QKkdYW77xNI?si=QcW5tACbUcQknqsQ

[violet pine]

i would still divide first...

just to make things easier

[urban vector]

i havent used that since like

algebra bro

lemme figure out how to do that LMFAO

[violet pine]

fr

[ocean silo]

basically a way of expressing fractions into simpler, actually integratable terms

and poly division for the first two terms obviously

looks like a disgusting integral all round but hey

[violet pine]

also goes into natural logs

which i honestly hate

[urban vector]

ok

2x + (x+1)/x^2-4x+4

is the new integral

makes sense

do i have to do this partial fraction thing now?

[violet pine]

yeah

[violet pine]

make sure that the other part

[urban vector]

I don't think there is one, no?

[violet pine]

when you divide you have the whole number thingy

[urban vector]

isn't it just (x+1)/(x-2)^2

[violet pine]

so like without remainder

[urban vector]

my brudda in christ what is da number thingy

LMAO

[violet pine]

ok

so when you divide

you get a number

with no denominator

like not the remainder part

[urban vector]

ok

ok so i i have to do partial fractions it not going to be on my exam

so i am moving on

[violet pine]

lol

[urban vector]

ok so for this:

would the final integral be x^2f'(x) - (2xf(x) - 2int(f(x)dx) ?

im just confused because the final protion ends up with f(x) in the integral and idk how we integrate that

oh wait im slow

no im not im confused

[urban vector]

have any ideas?

<@&286206848099549185>

got it

.close

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[eager lodge]

Use the formulae for gravitational force and circular motion

Yeah

[devout snow]

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[vernal briar]

is the first 1 actually 4

or undefined

[wicked turtle]

it's 4

the value of the function at x=0 itself does not have any effect on the limit

you only consider x values near zero but not actually at zero

[devout snow]

@vernal briar Has your question been resolved?

[vernal briar]

I see thanks

[devout snow]

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[restive river]

if i have an imaginary number (-2i)^n. can i do (-2)^n * (i)^n

[restive river]

is that a valid operation?

[wicked turtle]

yes

(-2i) just means a product of n copies of (-2i)

you can rearrange it since multiplication is commutative

move all the -2's to the left, and all the i's to the right, that gives you (-2)^n (i)^n

[restive river]

oh yea what you are saying does make sense now

thank you

.close

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[zinc rover]

how to solve this

[junior vigil]

answer is 0

[junior vigil]

👍

[solar goblet]

@zinc rover

[junior vigil]

Use the formula x^logay = y^logax

1st and 3rd terms are same , similarly with 2 and 4, therefore the answer is 0

@zinc rover

[zinc rover]

many times

[zinc rover]

yeah dont give out answers

[junior vigil]

For that explain what is your problem exactly ?

[heady eagle]

bro u need to tell me where u get these imagex

[solar goblet]

not mine

[heady eagle]

oh ok

[solar goblet]

i am merely the messenger

[heady eagle]

well im saving em

ah gotcha

[zinc rover]

i tried to do 3^log75-3^log57 first

well it was wrong attempt at first

[zinc rover]

how can you know or derive that?

[supple knot]

,rotate

[devout snow]

@zinc rover Has your question been resolved?

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[queen steeple]

Regarding the formula for volumes using shell method, will r(x) = x and r(y) = y always?

[supple knot]

do more problems and find out

[queen steeple]

I did and they always seem to be equal
it is possible that my prof has given us easier problems

[supple knot]

do even more

[queen steeple]

Can you give me an example problem where r(x) ≠ x

.close

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[devout snow]

Please don't occupy multiple help channels.

[snow tundra]

i need help with this problem

[twilit comet]

groovy close your other channel

[twilit comet]

is fine we clogged it up, our fault

[snow tundra]

okay

[soft umbra]

Why people are using these meme recently 😂

[solar goblet]

cause funny

[tender cobalt]

1. its funny as hell

[soft umbra]

What have you tried so far?

[wicked turtle]

these are the new helper factoids

[snow tundra]

i have the solution but i dont understand it at all

[soft umbra]

Could you exhibit it?

[twilit comet]

wait wat

[snow tundra]

if i can get to that point ill be good but idk how he did

[tender cobalt]

always have been

[tender cobalt]

at what point did you get lost

[snow tundra]

where did he get (1-y)^2 to sub in for A

then turn it negative in the next line

[tender cobalt]

do you know where int 0 1 A(y) dy comes from?

[snow tundra]

ay dy is the volume when calculating volume using cross section method

if thats what ur asking

[tender cobalt]

do you know what that means?

[snow tundra]

nah

[tender cobalt]

now reread the problem closer

youll notice that you dont really need to care about what the actual 3D shape looks like

you only need to know that:

• the base looks like this triangle

[restive river]

LMFOAOO

[tender cobalt]

• if you slice the 3D shape into slices, each slice has a "base" of the purple strip and is a square like in the upper-right

[snow tundra]

so woulndt that be

1*1

cause thats the length of the base and height

[tender cobalt]

first of all

there is more than one slice

isnt there

so you cant just calculate the area of one slice and call it a day

[snow tundra]

okay

so what do i do

[tender cobalt]

do you see the shape's slices

[snow tundra]

the square?

or the line called x?

[tender cobalt]

here's the shape

[snow tundra]

that looks like it has a base of a square no?

[tender cobalt]

youre looking at it from the wrong angle

[twilit comet]

okay mtt don't kill me if i'm wrong

but instead of z = f(x, y)
why don't we just set this y = f(x, z) then integrate

[tender cobalt]

the shape is not sideways

[twilit comet]

never mind then

[tender cobalt]

they were specifically instructed to integrate it this way

[snow tundra]

oh okay so its laying down rn

[tender cobalt]

to practice a method

you can see that its a pyramid so that gives an alternate way to find the volume to check our answers

[twilit comet]

shrugs

[tender cobalt]

but really we're here to practice

alr the shape was turned around in the picture though

it should look like this

back:

side:

now imagine you take slices like this

these slices are perpendicular to the y-axis

can you see that the slices are perpendicular to the y-axis

[twilit comet]

mtt i have one question

[snow tundra]

yup

[twilit comet]

how are you so good at this

;-;

[tender cobalt]

I paid attention in class

[twilit comet]

no no no

i meant with the quick graphing skills

i know how to multidim integrate too

[tender cobalt]

go to https://desmos.com/calculator

click the (?)

then click Restrictions

[twilit comet]

bro's fr a Van Gogh for desmos

[tender cobalt]

ren has not seen actual Van Goghs do this better than I can

bro is easily impressed

[tender cobalt]

then go to https://desmos.com/3d and you can do the same

[twilit comet]

fr fr

[tender cobalt]

now we can go back to what an integral is

and integral needs a lot of parallel, evenly spaced slices

and its capable of adding them together

right

[snow tundra]

yup

[tender cobalt]

now lets consider our slices here

first, each slice represents the area of a square

that way, when we add the slices together, we get volume

wait I need to make this look better

those slices need to have thickness

alr here we go

the slices should really look like this

as the slices get thinner, the squares become more accurate to the real volume

do you get these slices

[snow tundra]

yea

[tender cobalt]

nice

now taking a look at one of the slices,

this slice has a thickness

and also has a length and height

right

[snow tundra]

yes

[tender cobalt]

now since we're slicing it y-wise,

the little thickness is dy

right?

[snow tundra]

yup

[tender cobalt]

now we need to figure out the length and height

for the sake of convenience, we'll instead do A(length)

after all you only need the length to calculate the area

so you figure out the length,

then A(length) will figure out the area of the square given the length

(A(x) = x^2)

does that make sense

[snow tundra]

yes

[tender cobalt]

so we have the area of the square figured out by doing that

now we just need the length

this is where the method gets looser

notice here that from above, the slices go from 0 to the edge

lets call this length "X"

now we know the y-coordinate, y, of this slice

we also know what x + y = 1 looks like

as shown with this green line

the line can be rewritten as x = 1 - y

since we know that X goes from the left at x=0 to the right at x=1 - y,

the length X must be 1 - y

this might not be what you expected, do you understand this

[snow tundra]

nop

[tender cobalt]

do you need a few minutes

[snow tundra]

ill be honest

my midterm is in 3 hours

i need some sort of sleep before it

[tender cobalt]

bro is withholding information

go sleep

[snow tundra]

so idk i think i got shell and disk method down

[tender cobalt]

this is also a separate method

[snow tundra]

but cross section i just dont understand it

[tender cobalt]

its the 3rd one

yea and its your fault for doing it sleep deprived 3 hours before the midterm

had we done this like 7 hours earlier

[snow tundra]

i tried way before

[tender cobalt]

had we done this like 7 hours earlier

[snow tundra]

thats not my fault 😭

[tender cobalt]

bro your midterm was in 4 hours and you chose to ask a question instead of go to sleep

it aint that easy

[snow tundra]

ik but it was my last hope of understanding cros section cause there will be a cross section question 100%

dont wanna just lose the marks

[tender cobalt]

manage your time and just sleep on this if all youre going to say to "do you want to understand this" is "ngl"

[snow tundra]

whaaat

[tender cobalt]

your words

[snow tundra]

bro i appreciate ur help t

[tender cobalt]

take them back

or leave

[snow tundra]

i rly do trust

[tender cobalt]

youll need the sleep man

every minute counts

[snow tundra]

yea just keep going wtv

lemme finish this then ill go

[tender cobalt]

then answer the question

do you want a few more minutes

with a yes/no instead of a ngl this time

[snow tundra]

bros upset at me

i dont think a couple of minutes will help me understand it id appreciate if ud help me

unless theres nothing else to be saidn ill just keep re reading it

[tender cobalt]

take a look at the y in this picture

I already told you all I needed to say

[snow tundra]

i understood everything but the last part why re arrange for x

[tender cobalt]

look at where the red length starts and ends

as a horizontal length it represents an x-coordinate

you can see it starts at x = 0 on the left, yes?

[snow tundra]

yes

[tender cobalt]

no problems

with x = 0

yes?

[snow tundra]

yup

[tender cobalt]

do you know

what x = 0 is?

[snow tundra]

the y axis

[tender cobalt]

so what's on the right?

you dont know

so instead

we draw this green line here for the right edge of the shape

we know the equation for this green line

it's x + y = 1

yes?

[snow tundra]

yes

[tender cobalt]

the left side begins at **x=**0

so the right side ends at **x=**1-y

[snow tundra]

ohhh

yea

i get it

[tender cobalt]

literally repeated myself there

told you you only needed a few more minutes

we're very close now

because we know the left and right side of this X,

we know how long X is now

the length of the red slice (X) is 1 - y, yes?

[snow tundra]

yup

[tender cobalt]

and so

A(1 - y) would be the area of the red slice, yes?

[snow tundra]

yup

[tender cobalt]

and so A(1 - y) dy would be the volume of the red slice, yes?

[snow tundra]

yup

[tender cobalt]

and so $\int_0^1A(1-y)\dd{y}$ would be the volume of every slice, yes?

[woven radish]

mtt07734

[snow tundra]

yup

[tender cobalt]

then that has to be the whole volume of the shape

its harder to consider at first, but its just like a regular integral but in 3D instead of 2D

so that's how you get $\int_0^1A(1-y)\dd{y}$

[woven radish]

mtt07734

[tender cobalt]

from there, you know the area of a square means squaring the length

so $\int_0^1(1-y)^2\dd{y}$

[woven radish]

mtt07734

[snow tundra]

sooo

last question

where does the negative come from again?

is that just chain rule

[tender cobalt]

yea

btw

(1 - y)^2 is the same as (-(y - 1))^2 or (y - 1)^2

you integrate (y - 1)^2, you get (y - 1)^3/3

this is the same answer as -(1 - y)^3/3

since -(1 - y)^3/3 = (-(1 - y))^3/3 = (y - 1)^3/3

what I mean by this is that you can do this integral either way

because even though they might look different theyre not

[snow tundra]

wait so to integrate a bracket u increase n by 1 put it over n+1 and multiply by the derivative of inside?

[tender cobalt]

no not like this

you divide by the derivative of inside instead

and you need to have nothing except the original after the division

this is reverse chain rule not regular chain rule

since youre integrating (reverse derivative)

[snow tundra]

oh okay

makes sense

okay man tyvm

[tender cobalt]

np

gl on your midterm

[snow tundra]

ur the only one in the server who helped this hard icl

[tender cobalt]

appreciate it

[snow tundra]

u mind if i add u and ask questions whenver or is that a no no

[snow tundra]

ty

[tender cobalt]

usually I dont respond but you can just DM me some questions and I might get back to you

not really that online is all

[snow tundra]

okay ill add u then

tyvm again and goodnight man ur crazy at this stuff

[tender cobalt]

np and gn

[devout snow]

@snow tundra Has your question been resolved?

[devout snow]

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[sullen meadow]

guys

[sullen meadow]

.close

[devout snow]

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[solar goblet]

[devout snow]

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[vocal robin]

x√7 = x√2 + √32 find the value of x and answer in (a + b√14) ÷ 5 form if a , b are integers.

[vocal robin]

i dont know where to start

[solar goblet]

did you try solving for x

[vocal robin]

do i do something like this x√7 = x√2 + √32 x(√7-√2) = √32

and then √32 / √7 - √2

?

[candid wing]

rationalize it

[vocal robin]

i saw this x√7 = x√2 + √32 x(√7-√2) = √32 somewhere but I'm not sure how to get to it

[candid wing]

rationlise this

[vocal robin]

(4√14 - 7√2) / 7?

[vocal robin]

i have a question where did the x go in this

[candid wing]

you need to rationlise this to find x

[candid wing]

(4√14 - 7√2) / 5

[vocal robin]

oh okayu

[candid wing]

you can find a,b by comparing it (4√14 - 7√2) / 5 with (a + b√14) ÷ 5

[vocal robin]

ohhh

so after i rationalise that, i just compare it with (a + b√14) ÷ 5?

to get a and b

[candid wing]

yes

a=4(14)^1/2 and b=-1

[vocal robin]

ohh okay thanks

.close

[devout snow]

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[devout snow]

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[steel escarp]

Is it correct so far?

I've never done a similar exercise where phi is not an integer so it felt like I did something wrong

[visual hazel]

yeah its good

[steel escarp]

Ok great! Would you kindly like to explain how I can compute (d) and (e) or just give me some tips? I haven't seen that kind of probability exercise before

[visual hazel]

use the fact that |X| > 1 is the same as X < -1, X > 1

and why does e seem to be exactly the same as d

[steel escarp]

So I would need to compute X < -1 and X > 1 separately before coming to a conclusion on that one?

[steel escarp]

because the X <- 1 and x > 1 holds true for x^2 aswell

[visual hazel]

yeah

[steel escarp]

Alrighty, I'll get to work then! Thank you

.close

[devout snow]

Channel closed

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[steel escarp]

.reopen

[devout snow]

✅

[steel escarp]

.close

[devout snow]

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[shell salmon]

what have i done wrong here for <-44,20,28>?

[low holly]

It’s a dot product, not a cross product

[shell salmon]

oh

how do i know

what one to do

oh

nvm sorry the dot and cross

thank you

[low holly]

if there is $\times$ or $\cdot$ between the vectors

[woven radish]

Tushar

[shell salmon]

can u help me with this other q

it is significantly harder

[low holly]

!1q

[devout snow]

It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.

[low holly]

you can open a new channel

[shell salmon]

ya ok come find me pls lol nobody helped before

.close

[devout snow]

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[feral bobcat]

i got 4ln(x^2+1)

i first removed 4 outside the integral

[sturdy yew]

differentiate ur ans

u wont get the question

[feral bobcat]

then got 1/1+x^2

[feral bobcat]

antiderivative of that

is ln(x^2+1)

[sturdy yew]

no

[feral bobcat]

tell me how am wrong

[sturdy yew]

u'll have x multiiplied to it

chain rule

[feral bobcat]

what

thats not differentiating

do you know integrals?

[sturdy yew]

bruh

d/dx (ln(x^2+1)) = x/x^2+1

[sturdy yew]

i legit told differentiate ur ans

[snow merlin]

lol

[sturdy yew]

not the question

[snow merlin]

i will say the integral of 1/(1+x^2) is special i think

[feral bobcat]

why differentiate??

i am using integrals

[sturdy yew]

oof

bro is high fr

[snow merlin]

i mean you might as well, just to sanity check yourself

if you differentiate it and get your original integral, you did it right

[sturdy yew]

he is obvi not

[snow merlin]

when you're doing integrals you can always check to see if your answer is right if you differentiate the result and get the integral back

[feral bobcat]

ohhhhh

[snow merlin]

in your case, if you differentiate your result and compare it, you get something else

[feral bobcat]

you mean my antidefrentiation

is wrong

[snow merlin]

uhhh

antidifferentiation is... integrating... so yes...

[sturdy yew]

i wudve expected a guy doing indefinite integration to know that

[snow merlin]

its also not really a word so

[feral bobcat]

how do i find the antiderivative of 1/x^2+1

[sturdy yew]

yea

[snow merlin]

this one is a special case

do you know the trig derivatives/integrals

[feral bobcat]

ohhhhhhh

well i do not have them memorized

ig its tan or smth

[snow merlin]

arctan yea

anyway thats basically it

lol

[feral bobcat]

bruh i msut memorize them?

[snow merlin]

i mean if you're not going to have a cheat sheet on a test then yeah

if you are then id just remember what they look like in general

ah wait no here's a complete one

anyway yeah that's basically it lol

you can .close if ur done

[devout snow]

@feral bobcat Has your question been resolved?

[devout snow]

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[devout snow]

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[rotund hamlet]

What's the order of operation for A∩B∪C? It's clear when (A∩B)∪C or A∩(B∪C) distributing, but not so much for the other one

[topaz axle]

intersection first is more likely

[gray flax]

I say left to right

So yeah like frownyfrog said its probly intersection first

[topaz axle]

but i didn't mean left to right

[gray flax]

No no I didnt say that

Just meant I'm giving the same answer as you lmao

[rotund hamlet]

does this imply that if it was A∪B∩C you'd also do the intersection first?

so far we agree tho, i'd do A∩B first in the original exercise

[rotund hamlet]

sorry, I meant to quote this

[topaz axle]

it's a guess

what did they mean, whoever wrote it

i would guess intersection first

[rotund hamlet]

got you

we're all kinda guessing here then. The other two exercises y mentioned (where you can distribute) follow this one, so it's supposed to make sense i guess

[devout snow]

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[digital ember]

how do i start this?

[restive river]

A couple of things first:

Var(aX+b) = a^2 Var(X) for any constants a,b

do you get why that is?

because Var(X) = E[ (X-E[X])^2]

[digital ember]

yes i understand that

[devout snow]

@digital ember Has your question been resolved?

[devout snow]

@digital ember Has your question been resolved?

[devout snow]

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[hot vault]

hI

[hot vault]

How can i find all X values in the interval [0, π] that verify the ecuation

I don't know how to solve this kind of problems

[solemn ruin]

what is sen

[twin thunder]

is sen = sine

[solemn ruin]

sin?

[twin thunder]

probably, that seems the most reasonable choice

[hot vault]

yes

its sin

[solemn ruin]

wait why it 7.sinx

or the point just mean multiply

[hot vault]

yes

[wheat pawn]

it means multiply

[solemn ruin]

then make sin as an x

[wheat pawn]

it's common writing when you dont have avaliable fancy formatting

[solemn ruin]

and find a x

[quaint citrus]

bring all terms to one side

then do the substituion

a=sin x

[solemn ruin]

ye

[quaint citrus]

then solve quadratic

[solemn ruin]

then u will get like 2 results

then just check in [0,pi]

[hot vault]

it worked guys

thank you!!

.close

[devout snow]

Channel closed

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[devout snow]

Available help channel!

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[full fractal]

.help

[devout snow]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[full fractal]

Help

[full fractal]

Pls help with this situation

[candid lance]

What question

[full fractal]

All😭

Actually I answered 1.

I chose D)

ab+BC=ac

I chose this one

[candid lance]

ok thats correct

[candid lance]

but do u see that option b is also true

[full fractal]

Whats the 2 and 3 one?

IS IT TRUE also?

[candid lance]

yeah

|6-1|

which is d(B,C)

[full fractal]

Ohh I understand

What's about the 2,3 i don't understand them

[candid lance]

What exactly dont u understand in it

its a protractor I hope u know that

[full fractal]

Yeah

But

All of them are trur

[candid lance]

Wdym

[full fractal]

True i think

[candid lance]

they arent

What is option a

[full fractal]

Mln is 120

[candid lance]

tel me

How is 120

Show me the angle

[full fractal]

One seocnd

[candid lance]

u see this is the angle MLN

right

[full fractal]

Yep I see

[candid lance]

Isnt it an acute angle

[full fractal]

It's 120

[candid lance]

Nooo

u measure it from the left

[full fractal]

So it's true

From where we measure then

M is from left side

[candid lance]

u have to measure the distance from M to N

not from Q to N

[full fractal]

I don't understand

[candid lance]

name the angle

[full fractal]

It says angle MLN

[candid lance]

what is the name of the angle

[full fractal]

mln

[full fractal]

This

[candid lance]

its an acute angle right?

do u know what is an acute angle?

[full fractal]

Yeaf

More then 90 degres

[candid lance]

Nooooo

its less than 90 degrees

[full fractal]

Oh yeah

[candid lance]

acute = less than 90
Right angle = 90 degrees
Obtuse = mroe than 90

then if its an **acute angle MLN **how can it be 120 degrees?

[full fractal]

MLN looks like acute angle

[candid lance]

yeah

[full fractal]

But it's 120

[candid lance]

Thats the measurement on the protractor

[full fractal]

Idk

OHH

So it's 60 degrees

[candid lance]

but u have to substract the lower limit from the upper limit

[full fractal]

Not 120

[candid lance]

yesssirrr

[full fractal]

Ohh

[candid lance]

180 - 120 = 60

[full fractal]

Then why do they confuse us with this

[candid lance]

thats how the basic works

[full fractal]

Why 189

180

Like BCS the Line is 180 degreees

[candid lance]

u see M is on 180 degree

right?

[full fractal]

Yeah

[candid lance]

and N is on 120

so it will be upper minus lower

180-120 = 60

[full fractal]

Ojh

Alr

It means

[candid lance]

lemme ask

[full fractal]

QLP=50

Is correct

[candid lance]

measure me the angle NLO

[full fractal]

30

[candid lance]

Right

[candid lance]

and yeah

this is right

now u get how measuring angles works?

[full fractal]

Yep thanks 👍🏽👍🏽

[candid lance]

Nicee

[full fractal]

Only B IS CORRECT

[candid lance]

how so?

Check option C

[full fractal]

Oh yeah and c

And d also correct

[candid lance]

Actually u can do it visibly

after a lot of practice

but for beginners

u can write dow the left hand side

with numbers

add

and then count the angle on the right hand side

[full fractal]

Ohh

[candid lance]

that makes it easier to understna

[full fractal]

Alr

Thanks

So b c and d correct only

[candid lance]

I didnt check d

and I cant rn sorry

I got my test rn

cyaaa

[full fractal]

Ohh alr

Xua

Cya

[candid lance]

I wil maybe help u out later

but I'll be busy for 40 mins

cya

[full fractal]

alr

Cya

[devout snow]

@full fractal Has your question been resolved?

[buoyant token]

64x8?

[devout snow]

Channel closed

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[short grail]

hi

[soft umbra]

What’s your question?

[devout snow]

@short grail Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

Available help channel!

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Remember:
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[vague vortex]

Can someone please help me with this

[twilit comet]

send again, it hasn't been pinned yet.

[vague vortex]

@twilit comet

[twilit comet]

ummm

[sturdy yew]

oof related rates question

i hate them'

[stable storm]

so first what is the surface area formula of a sphere

[vague vortex]

A = 4pi r ^2

[stable storm]

alright and what’s the volume formula?

[vague vortex]

V=1/3pi r^2h

[stable storm]

not quite

[twilit comet]

no

firstly

pi not pie

[stable storm]

yep

[vague vortex]

Ok

[stable storm]

now we have to relate the rate of change of the surface area

to that of the volume

[woven radish]

ren

[stable storm]

what can we do to each of these formulas to achieve this?

[vague vortex]

Derive them

[stable storm]

with respect to what

[vague vortex]

dv/dt

[stable storm]

with respect to time yes

so if we differentiate both of these formulas what do we get

knowing that dA/dt is 48pi

and the surface area is 36pi

[vague vortex]

Ok what next

[sturdy yew]

dA/dt = dA/dr * dr/dt

[stable storm]

what did you get after differentiating?

you have to use those two equations to solve for dV/dt

[vague vortex]

What do I derive

[stable storm]

the surface area formula

and the volume formula

with respect to t

[vague vortex]

4pi r^2

[stable storm]

we have to take the derivative of this

with respect to t

which would be?

note that r is changing with respect to time as well

so it’s not a constant

[vague vortex]

4pi r^2/t

[stable storm]

not quite

if i were to differentiate let’s say $4\pi x^2$ with respect to x

[woven radish]

y0shi

[stable storm]

what would i get

[vague vortex]

4pi x

[stable storm]

not quite either

it would give you 8pi x

because of the power rule yes

[vague vortex]

Oh I get it

[stable storm]

yep

but if we aren’t differentiating with respect to x

but rather a different variable t

such that x is a function of that variable

we have to apply the chain rule

[vague vortex]

8pi t

[stable storm]

and multiply it by dx/dt

i believe you meant 8 pi r yes?

[vague vortex]

Yea

[stable storm]

but due to the chain rule

and r is a function of time

we have to multiply by dr/dt

[vague vortex]

So what is the derivative of both equations

[stable storm]

well so you got the first one which would be $\frac{dA}{dt}=8\pi r\frac{dr}{dt}$

[woven radish]

y0shi

[stable storm]

yes?

[vague vortex]

Yea

[stable storm]

using the same concept here do the same for the volume formula

[vague vortex]

12pi r^2/3

[stable storm]

yes

and don’t forget to multiply by dr/dt

so since we know that the surface area at the instant of time we are observing is equal to 36pi

what would be the radius

since we have two unknowns currently

dr/dt and r

but we can solve for r using the condition given

[vague vortex]

Can you write it like that

The volume formula like that

[stable storm]

$\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}$

[woven radish]

y0shi

[vague vortex]

Like this

[stable storm]

yes

so notice how we need to solve for dV/dt

but we have two unknowns

r and dr/dt

using the fact that the surface area is 36pi, what would be r?

[vague vortex]

6?

[stable storm]

not exactly

how did you get 6?

[vague vortex]

How do I find r

[stable storm]

so since we know the surface area is 36pi

which equation above relates the surface area to the radius?

[vague vortex]

dv/dt = 4pi r^2 dr/dt

[stable storm]

not exactly

we just have to use the regular surface area formula

A=4 pi r^2

so we can just plug in A for 36pi and solve for r

[vague vortex]

3

[stable storm]

yep

now we just need to solve for dr/dt

which formula can we use for that?

[vague vortex]

4pi r^3 / 3

[stable storm]

uhh not exactly

there isn’t a dr/dt term in that equation

we actually have to use the differentiated surface area formula here

since it gave us the rate of change of surface area

[vague vortex]

4pi r^2 dr/dt

[stable storm]

but using this formula

do we know what dV/dt is?

no right since we are trying to solve for that

[vague vortex]

No

[stable storm]

yep so we have to use the other formula

[vague vortex]

dA/dt = 8pi r dr/dt

[stable storm]

yep

we know that dA/dt is 48pi

and now we know that r is 3

we can just solve for dr/dt here

[vague vortex]

2

[stable storm]

yep

[stable storm]

now we just have to plug it into the differentiated volume formula to solve for dV/dt

[vague vortex]

dV/dt = 4pi r^2 dr/dt

[stable storm]

yep

[vague vortex]

72pi

Is it finished

Was that it?

@stable storm

[devout snow]

@vague vortex Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[rain karma]

Can someone help me prove that this sum diverges

[rain karma]

I tried taking out 1/n from the root see if I get anywhere

I didnt reall

[supple knot]

what about multiplying by the rational conjugate

[rain karma]

I tried taking out n then doing it

[supple knot]

$\sqrt{n^2+n+1} - n = \frac{\sqrt{n^2+n+1} - n}{1}$

[woven radish]

riemann

[sage ridge]

can someone explain this....

[sage ridge]

ok

thanks

[rain karma]

I got it ty

.close

[devout snow]

Channel closed

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[devout snow]

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[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[charred tusk]

so yea how im thinking this problem is going to be about triangle similarity

but im not sure how this quiet works

having 1 same side means what exactly?

solely with line af and line fc i can get bf?

this should be a very easy question to many since its only a grade 9 problem but if anyone does have time please do help me on this

<@&286206848099549185>

[thin inlet]

,rotate

[charred tusk]

??

[thin inlet]

where are the questions

[charred tusk]

what are the possible areas of the rectangular sections of the wooden wall

[thin inlet]

well, let's focus on f(x)

f(x)=-floor(-x/4)

floor is just another name for greatest integer function

greatest integer function rounds down to the nearest integer

floor(1.4)=1, floor(-2.2)=-3, floor(2)=2, floor(1.9)=1

[thin inlet]

we're doing this to give us a range of values for what 'x' could be

i.e. we know 9=-floor(-x/4)

-9=floor(-x/4)

lets say we ignore the floor, and we have -9=-x/4

[charred tusk]

ok

[thin inlet]

what would x be?

[charred tusk]

-1

[thin inlet]

no...

[charred tusk]

-36

[thin inlet]

no, you're closer though

[charred tusk]

1 sec uhm

0

[thin inlet]

i'm just asking you to solve for x

[charred tusk]

im confused

[thin inlet]

okay, first we can multiply both sides by -1, yes?

so 9=x/4

then what does x=

[charred tusk]

oh right

36

[thin inlet]

yes. NOW

what happens if we nudge x to be a little bigger than 36, say, 36.1

[charred tusk]

right anything between 36 and 37 exclusive

would be 36

[thin inlet]

is -36.1/4 gonna be bigger or smaller than -9

[charred tusk]

smaller ofc

[thin inlet]

yes, so it'll get rounded DOWN to -10

which is not what we want

[charred tusk]

right

but uh

im a little confused by your approach

so i think what were tryna find rn is line bf

and to find it simply there is something about triangle similary which is what i dont get

somehow with line af and fc we can get bf

could u elaborte on that part

from my point i see that ac which is the same as ed which is basically the width is 8 as its given now only thing we need is the height

and yea thats the problem for me rn

and right once we get bf we can obv substitude another variable in for the remaining high line ae or cd

but yea the thing is

how do i get bf

ik its smth abt triangle similarity but cannot seem to get it

[thin inlet]

you can express each of the legs of the right triangle in terms of BF (call it h)

then you can write the area in two different ways

[charred tusk]

hm rly? we can use comparison like that?

or substitude

could u show me how its done, ive never thought abt doing that i didnt know that was possible

i thought there was only 1 way

[thin inlet]

let the length of BF=h

then what does AB=

what does BC=

use pythagoras