help-38

[sharp gust]

Yeah haha

I will try to erase it bettrr

[lilac cloud]

Try to move the 1 term to the other side of the equation and rust do regular algebra to solve for t

[sharp gust]

If I do that can’t I just multiply the 1 by 2/3 and get 1/3t on the right side?

[lilac cloud]

You can divide the 1 by 1/3 then you will have t^(-2/3)=3

[sharp gust]

Then take a log of both sides?

[lilac cloud]

I don’t think so. I would just take reciprocal of both sides

Then t=1/3^(3/2)

plus and minus

[sharp gust]

Gah I'm so rusty with everything, thanks

But this is why I'm practicing I guess

I got it half right, but my minimum is wrong?

The maximum is just f(6), but when I put in f(2) I get 2- 3root(2) which gives 0.741 but that's not the minimum?

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[verbal iris]

Need some quick help (this is integration btw)

The whole question makes sense to me and makes sense however i am missing a lot of my foundation maths stuff and need help understanding how the sin(pi/6) becomes 1/2

I type sin(pi/6) into my calculator and it doesnt come up with 1/2 and i just want to know how that change was made and why, ty!

[twilit meteor]

is ur calc in radians or degrees

[verbal iris]

degrees i think

[rugged latch]

thats why

[twilit meteor]

ok well for this it needs to be in radians

[verbal iris]

ah, should i have it in radians for all of integration and differentiation or would degrees be better

[twilit meteor]

pretty much always radians

unless there's somehing specificc suggesting degrees would be sensible

[verbal iris]

right that makes a lot more sense,thank you very much!

[twilit meteor]

💜

[verbal iris]

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[fringe marsh]

is [kn] the equivalence class of z/12z?

[fringe marsh]

also could you say f(6) = f(2) when k = 2 and 6 respectively, or must k be the same value both times

[austere cedar]

[kn] would usually refer to the equivalence class that kn is in

[fringe marsh]

okay so for this its 12 mod n

also must k be the same value for both functions

im trying to think if this is injective or surjective

[austere cedar]

In order to make this a proper function between Z/Z12 and Z/Z12, you'd need to choose k ahead of time yeah

So there's 11 different functions we are discussing here

[fringe marsh]

tbh i dont get that, could you explain

is it because k can be uh 11 options

[austere cedar]

Yeah

x -> [2x] is a different function from x -> [5x] for example

(Or is it?!)

(Yeah it probably is)

[fringe marsh]

sorry this might be stupid but do I need to check all Ks

[austere cedar]

There's a nice result. The k's that cause a bijection have a clear property

[fringe marsh]

can you give me a hint

[fringe marsh]

k = 1 is bijective

k = 6 is not

i know 0 mod 12 = 12

2 x 6 = 12 and 12 mod 12 = 0

[austere cedar]

0 = 12 (mod 12) yes

[fringe marsh]

that sthe bets guesses i have though

hold on

its coprimality

thank you for helping

: )

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[fringe marsh]

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[fringe marsh]

do you need to use multiplicative inverse

or is there another reasoning i can use

we did not really use that definition, im not sure if i can use it

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[austere cedar]

What definition?

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[sour talon]

how can this be true using

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[barren crescent]

can someone explain how to solve this?

[prime crystal]

you're given an arithmetic progression

general term of an ap is written as Tn = a + (n-1)d

where a is the first term and d is the common difference

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[flint fox]

4,5,6

I have no idea how to solve these

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[flint fox]

@wild quail

stfu

<@&286206848099549185>

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<@&286206848099549185>

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[analog shale]

question 4 should be relatively easy if you know how to manipulate 2/x

question 5, you might have a better time keeping the 2 in the right-hand side until you've done manipulating 4/(x-1) + 5/x

question 6, notice the relationship between the two denominators and do stuff from there

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[candid aurora]

ok guys i should do 1 more

[trim jolt]

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[candid aurora]

tell me the easiest out of these

need to find the limits

[whole coral]

7 probably the easiest

(6 is basically also very similar to one problem [4] you did already, so you could make use of that too)

[candid aurora]

well for 6 i would need to use e?

[limpid dawn]

german interesting

i got hehe'ed from chartbit before gta 6

[whole coral]

(and would be a very good idea, then you should notice something...)

[supple bluff]

Which course is this?

[tepid rock]

Limits.

[supple bluff]

Is it standard pre-calculus

[tepid rock]

Yes.

[supple bluff]

Oi

[candid aurora]

cs analysis course 1 of the many topics

[supple bluff]

lim (sin x)^x as x ->0 is |sin infty|^0 = 1

[limpid dawn]

7 kannst du log eigenschaft nutzen log(a/b) = log(a) - log(b)

[supple bluff]

does cs mean computer science

[candid aurora]

ye

[supple bluff]

Ok

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[sinful pawn]

Hello, i'd like to have this one pls :

$\displaystyle w( t) =\begin{cases}
1\ if\ 0\leqslant t\leqslant T\
0\ else
\end{cases}$ what is $\displaystyle ( w\ast w)( t)$

[solid kiln]

Sakai

[sinful pawn]

Firstly I wrote this :

[solid kiln]

Sakai

[sinful pawn]

by definition

Is that correct ?

[solid kiln]

Sakai

[strong zinc]

Not sure, but uniform convolved with uniform -> 2 sounds right

[lean prawn]

Well first, you know the integrand is certainly zero when theta is outside [0, T]

This means that you can simplify the integral to be from 0 to T

But what about the t-theta one?

~~0 <= t - theta <= T

<=> -t <= -theta <= T

<=> -T <= theta <= t~~(garbage)

This means that the integrand will also be zero outside of that interval. So therefore we want to integrate from 0 to min{t, T}

[sinful pawn]

You forgot T-t

lines 2

[lean prawn]

oh yeah true

0 <= t - theta <= T

<=> -t <= -theta <= T - t

<=> t - T <= theta <= t

So the upper bound of integration will certainly be t

The lower bound will be max{t-T, -T}

if t>=0 then t-T>=-T, in which case you integrate from t-T to T, which I think should give 2T-t

And I think that's starting to make sense because I think the graph of the function should be like a triangle

[sinful pawn]

Yeah I agree

[lean prawn]

if t<0 then t-T<-T, in which case we integrate from -T to T, which I think should give 2T, which is kinda sus(garbage)

aha

[lean prawn]

this should be from t-T to t, which gives T

[lean prawn]

and then this should be t-T to t, which gives T(garbage)

idk if that makes any more sense tbh xd

I mean, I know it doesn't because it should be a triangle arghhh

ah shit I'm stupid

I forgot that we must be inside [0, T]

so the upper bound is min{T, t}

And the lower bound is max{t- T, 0}

oh yeah I see what happened, I should've deleted my incorrect calculation

righttt okay

for t<=T, the upper bound is t and the lower bound is 0

So for t <= T, we get t as the value of the integral

For t > T, the upper bound is T and the lower bound is t - T

So for t > T, we get 2T - t as the value of the integral

And note that the function is continuous at t=T so that's a sign that stuff might actually add up

@sinful pawn sorry for making a bit of a mess but I hope that makes sense

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[ripe topaz]

try polynomial long division

[pearl spade]

That's too much work

I was thinking bring the x^2 up

x^-2 (x-1)^3

Would I just expand and go on

[limpid dawn]

you can expand the numerator

[pearl spade]

Or is there a simpler way

[limpid dawn]

it's not a big deal

[pearl spade]

What if the 3 was a 7 or something

[limpid dawn]

then it gets lengthy

i know what you did

[pearl spade]

Would there be a simpler way

Or only way is to expand

I have no problem but if that 3 was a bigger number I'm just wondering how I'd go about it

[limpid dawn]

another thing that i notice is (x-1)³ = (x-1)²(x-1)

,,\int_1^3 (x-1) \cdot \left (\frac{x-1}{x}\right)^2 \dd x

[solid kiln]

𝔸dωn𝓲²s

[pearl spade]

Ah I see

[limpid dawn]

but i dont thimk it's any better

maybe by 1 %

[pearl spade]

Yeah I think the only way would just be to expand

[limpid dawn]

i dont see a suitable substitution honestly

[pearl spade]

u substitution would make it more complicated

[limpid dawn]

Maybe if it was ^7 polynomial division might help

[pearl spade]

I'll just try expanding

so x^-2 * (x-1)^3

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

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

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

x-3+\frac{3}{x}-x^{-2}

then indefinite integral would be

\frac{x^{2}}{2}-3x+3\ln\left|x\right|+\frac{1}{x}

how do u display the equation

[limpid dawn]

use $ code $

[pearl spade]

$ \frac{x^{2}}{2}-3x+3\ln\left|x\right|+\frac{1}{x} $

[limpid dawn]

try without space

[pearl spade]

$\frac{x^{2}}{2}-3x+3\ln\left|x\right|+\frac{1}{x}$

[solid kiln]

shaqiqi

[pearl spade]

is that right

then just evaluate on the interval 1 to 3

[limpid dawn]

seems like it

[pearl spade]

actually it wouldn't need to be ln|x| just ln(x) cus the interval only positive values

[limpid dawn]

yea technically but it isn't wrong

[pearl spade]

I got

$3\ln\left(3\right)-\frac{8}{3}$

final answer

[solid kiln]

shaqiqi

[pearl spade]

alright it's correct thanks

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[buoyant grail]

The first line of the solution manages to come up with this as the value for T and I'm very confused as to how

Where D'(R) denotes the space of distributions

the following bit of the solution does this which I understand but I was unable to actually simplify it since I didn't have the general form of T, I just left it as T and T'

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[wooden plover]

@buoyant grail you should try asking in one of the advanced channels

[buoyant grail]

I'm not really sure what field it would come under in the sections

i suppose advanced analysis actually

[wooden plover]

prolly the best fit yeah

[buoyant grail]

ok thanks

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[cobalt sapphire]

I'm confused what i did wrong

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[pine mortar]

Hello I’ve worked this out the other day but now my brain has been shutting down, of course I’m not looking for answers but could I get assistance on how to solve these?

[pine mortar]

<@&286206848099549185>

Does anyone know how to do geometric probability?

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[shrewd pebble]

how does this become that??

[marble flare]

Basically, notice that sin^2 = 1-cos^2 then let u = cos

[shrewd pebble]

so if u is already a u-sub, is v a second variable to another u-sub? and then we are using cos as the usub for v?

how did we turn cos into sin, is it using the trig identity cos^2+sin^2=1?

[marble flare]

Indeed

[shrewd pebble]

when you do that wouldn't you get a square root thing?

[marble flare]

Not sure I’m following.. you want to change the -sin^2 + 2 on the bottom to cos^2 + 1

Actually I’m not even sure what the computer was doing it did this then it did another u sub by making w = v^2 lol

[shrewd pebble]

ooh

the inception of math hurts my head

[marble flare]

Lol

@knotty locust did I ABCD?

[knotty locust]

ABCD

[shrewd pebble]

✈️
🧑

neeew question

is u 41x or the denominator

or maybe just cos(41x)

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[knotty locust]

@marble flare sir

pls

[marble flare]

Hmmm

(a) looks wrong (?) You showed that A <= infinity?

[knotty locust]

oh

good point

how to clear it then

[marble flare]

Maybe you can let z = e^itheta and break it into two cases if theta = rational or not

[knotty locust]

[marble flare]

The problem is that an n+1 could cancel n if tthe e^intheta is -e^(i(n+1)theta) in the next term

Wait

Isn't this just test for divergence

[knotty locust]

🦦 yes

[marble flare]

Like if a series converges => terms go to 0

🔠

[knotty locust]

oh right
for the series to converge
we need
nz^n -> 0
i.e |nz^n| -> 0
and
|nz^n| <= |n||z|^n = n
does not go to 0
qed
Ultimate Chad

[marble flare]

https://tenor.com/view/minion-gif-4256583569949039458

[knotty locust]

thank you sir!

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[knotty locust]

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[knotty locust]

@marble flare BUt

green looked good?

[marble flare]

Im actually not sure

You showed its ROC is 1 and that it has bounded value on the boundary

Does this mean it converges?

[knotty locust]

uhhh

limit comparison

sir

right

[marble flare]

What are you comparing it to?

[knotty locust]

lim n - > inf in the partial s of z/n^2

it will be less than lim n-> inf in the partial s of 1/n^2

which converges

so the limit of partial sums

also converges

for original sm

sum*

[marble flare]

Isn't limit comparison if the terms a_n/b_n -> L and b_n converges then a_n does

[knotty locust]

my sir is washed

[marble flare]

Fuck bro

[knotty locust]

if an <= bn for all n

and lim bn converges

so does an?

[marble flare]

What if a_n -> -infinity

and b_n = 0

[knotty locust]

0 <= an <= bn

:p

[marble flare]

Is this real

What if a_n oscillates

0 <= (-1)^n + 1<= 2

[knotty locust]

no

Idk if it's real

I am questioning everything now

did I just try to use monotone sequence theore

without it being monotone

[marble flare]

Correct.

[knotty locust]

but sir this has to be true

[marble flare]

Maybe try showing its cauchy

This actually works pretty easily i think

Same idea as ur proof too

[knotty locust]

absolute

convergence

implies

convergence

Q

E

D

A

B

C

D

[marble flare]

No

Wait?

[knotty locust]

:)

[marble flare]

Does it?

Yes

[knotty locust]

:)

[marble flare]

🔠

I actually proved that too

[knotty locust]

doubt

fucking

slaughtered

[marble flare]

AAAAH YEAH

https://tenor.com/view/minion-gif-4256583569949039458

[knotty locust]

I'll keep this incase I have another doubt sir

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[wraith hinge]

for b) im a bit unsure about the boundary conditions that the electric field experiences between two different media

oh gosh nvm im an idiot

i got it while typing lmoa

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[nimble panther]

I have defined the function g = f'(x)/x-a - (f(x) - f(a))/(x-a)^2

[nimble panther]

And tried to prove g' must be 0 at some point

To contradict this I have taken the min to occur at a and max to occur at b

But this gives extremely lengthy calculations I cannot keep up with

If anyone has an alternate approach or can work out the calculations it would be helpful

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[arctic geode]

is here anyone who is available to teach me how to do these kind of questions?

[fringe zealot]

can anyone help with mutiple angle identities

[delicate belfry]

Use the log properties.

[arctic geode]

even with the log properties i cant seem to get my head around these questions

the first one was fine but i have no clue what to do on the 2nd?

[delicate belfry]

Do it from outside.

[arctic geode]

alright let me try!

well i solved the outermost and got 1/2 x log3(1 +log 2 ( - - - - - - - - -

i dont really know how to do it from here

[arctic geode]

what do you think i should do?

[delicate belfry]

Did you get rid of log4?

[arctic geode]

yes

[delicate belfry]

Then you do the same with log3.

[arctic geode]

but how?

[delicate belfry]

$x^{ab}=x^a \cdot x^b$

[solid kiln]

Good

[arctic geode]

but its like

1/2 x log3 + 1 + log 2

how do i get rid of log3 with that

[delicate belfry]

$$\log_4(2\log_3(1+\log_2(1+3\log_3 x)))= \frac12$$ $$ 2\log_3(1+\log_2(1+3\log_3 x))= 2$$

[solid kiln]

Good

[delicate belfry]

You apply 4 as base to get rid of log4.

[arctic geode]

wait how do u still have 2 infront of log3 when u got rid of it by sending it to the other side

shouldnt it be log3(1+log2( ----

[delicate belfry]

4^log4 = 1, 4^1/2 = 2

[delicate belfry]

All in parenthesis doesn't get affected by that.

[arctic geode]

wait let me show you how i got rid of the log4 so you know what i am doing

This is how i got rid of the log4

[delicate belfry]

This is another one $\log_x ab = \log_x a + \log_x b$

[solid kiln]

Good

[delicate belfry]

Look over all properties, and be aware of those.

[arctic geode]

i know this one but how did u do it with this one?

[delicate belfry]

As I mentioned.

$$\log_4 = \frac12$$ $$4^{\log_4} = 4^{\frac12}$$ $$1 = 2$$

[solid kiln]

Good

[delicate belfry]

Although this equation is not true, I've just shorten it from the original question.

[arctic geode]

but the way i did it was it wrong?

[arctic geode]

wait did u just multiply both sides by 4 to remove log4??

[delicate belfry]

Not multiply, but put 4 as base.

[delicate belfry]

My bad, should've put log4(4)

[arctic geode]

isnt 4 already the base?

[delicate belfry]

Not certainly, it might work, but the use of log property was wrong.

[arctic geode]

wait why was it wrong?

[delicate belfry]

That's logbase.

[arctic geode]

what base are u talking about

[delicate belfry]

$$\log_4(2 \cdot \log_3(x))$$ $$\log_4(2)+\log_3(x)$$ $$\frac12 + \log_3(x)$$

[solid kiln]

Good

[arctic geode]

ohhhhhhhhhhh

[delicate belfry]

Like the way you applied it in i.

[arctic geode]

so since its being multiplied i have to use this property is what you are saying?

[delicate belfry]

Yeah, or the way you did it in i.

[arctic geode]

OMG

I GOT IT

WE USED THE BASIC PROPERTY

TO GET 2

logba = k

a = b^k

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[inner talon]

<@&286206848099549185>

[inner talon]

Hello I need help with a question

<@&286206848099549185>

[normal crest]

[inner talon]

I need help with phisics

[normal crest]

Show the question

[inner talon]

I am clueless

[normal crest]

Show the statements

[inner talon]

It is their

In the question

nvm O I GOT IT

[normal crest]

“Which of the following statements are true?” But no following statements are shown

[inner talon]

no its says the radii of the following

like gives me 2 statements

28m and 19

answer is 28

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[inner talon]

ty

.close

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[inland bear]

How did they figure out the values of y1, y3.. etc?

[past comet]

Split [1,4] into 7 points evenly spaced

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[frosty slate]

💀

Do u even know whats the Simpson rule trying to solve

[past comet]

No

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[brave anchor]

am i doing this right?

what does #4 mean?

Sequence: 2, 4, 8, 16, 32, 64...

Formula: S(k)=2S(k-1)

that?

<@&286206848099549185>

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[waxen trail]

heyo is my solution correct so far?

[waxen trail]

its about differential equation

i have to solve for the particular solution

y(3)=1

[kindred pier]

Looks good so far

[waxen trail]

awesome :) how do i isolate y from there on tho?

[waxen trail]

this is what i did

is it correct?

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[kindred pier]

Yes. Now do initial conditions

Also don't forget $\pm$ when doing square root

[solid kiln]

SWR

[waxen trail]

oh right

ill try

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[waxen trail]

is it correct?

.reopen

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✅

[waxen trail]

how do i isolate the c? i think i have to flip it somehow

[sly pewter]

Multiply by the denominator

[waxen trail]

like this?

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[tiny spoke]

Problem I am having trouble with: "A trapezoid of area 100 cm^2 has bases of 5 cm and 15 cm. Find the areas of the two triangles formed by extending the legs until they intersect."

[tiny spoke]

I already found the height of the trapezoid, which is 10 cm

I guess the problem is that this question is a bit vague and doesn't have any clarification in the textbook.

I think it's referring to to triangles above the trapezoid

nvm There is clarification

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[tiny spoke]

.reopen

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[tiny spoke]

So actually there isnt any clarification

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[tiny spoke]

.reopen

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[tiny spoke]

Oops my bad

How on earth am I supposed to solve this without know any of the angle measures in the trapezoid?

There is no indication of whether it's isosceles

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[marsh hare]

I don’t know how to do number 4

[kindred pier]

... you have to tell us what number 4 is

[marsh hare]

Is there some formula?

I know the period is the distance which is 12

[marsh hare]

Sorry!! The picture didn’t send

The school wifi is so bad

[kindred pier]

if the period is 12, that means the f(x) values repeat every 12 steps. So f(x)=f(x+12)=f(x+24)=f(x+36)... and so on

And in the opposite direction too: f(x)=f(x-12)=f(x-24)=f(x-36)...

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[blissful sparrow]

There is a surjective map f : IR6 → (\mathbb{Z}^{24}) with dim core(f) = 3.

I need to explain whether the statement is true or false. Maybe you can help me with my solution and understanding.

surjective is when all the elements of the value area have an element connected to the definition area (IR6 in this case)
so now I wonder what exactly is the core(f), how can I imagine it, I know it is the set of all vectors that can be zero with the main matrix A?

so there is a formula to calculate the dim core
rank(A) + dim(core(f)) = dimV
not sure if this is correct for this exercise but maybe...
dim(core(f)) = 6-1
dim(core(f)) = 5

so the statement is false because the dim core is 5 and not 3

[solid kiln]

skenox

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[strong granite]

is this answer backwards? i thought (a,b) exists in the composition S ° R if there is a c s.t. (a, c) exists in S and (c,b) exists in R which isn’t consistent with this answer

[edgy willow]

looks like the right order to me, SoR is aSx so a is a sibling of someone, and xRb so x is a parent of b, which means uncle/aunt to me

[strong granite]

that’s the answer for R°S tho

[edgy willow]

oh did I swap it haha

then you're right yea

[strong granite]

yeah this is a textbook answer key that my prof also gave out lol but def seems wrong

[edgy willow]

I see stuff online that agrees with you ok weird https://data.testprepkart.com/Online_Preparation/JEE/JEE Maths/1_JEE_Maths_Relations/5_JEE_Maths_Relations_Composition of Relations.pdf

[strong granite]

yeah i’m not sure this is a very trivial topic but the answer has me confused

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[edgy willow]

each starting gossiper is like a 3^n

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[ionic pendant]

http://galileo.math.siu.edu/Courses/251/S12/vpot.pdf

[runic pumice]

What confuses me in this is how the following is determined:

Why can we assume that the partial in y of G_3 is 0?

[ionic pendant]

they address this at the start, but basically there are infinitely many functions with the required curl, so we can just choose a convenient assumption and work from there

[runic pumice]

And it follows through Stokes that no matter what f turns out to be, it will always follow that the closed line integral equals the surface integral of F?

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[runic pumice]

The proecss doesn't seem to fully help

Tried it and didn't get F back when taking the curl

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[runic pumice]

I think I'll give up here

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[steel socket]

im reviewing for a test i got tomorrow and lowkey after everything i've reviewed, i forgot how to solve this by hand, with calculator sure easy peasie but can someone tell me the formula to solving it or im just too sleep deprived

[vague citrus]

sum of GP for finite terms

[steel socket]

sum=(first-one past last)/(1-r)

thanks man

.clsoe

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[naive geyser]

so

i think this answer key is actually wrong

take a look at this part

i think it's incorrect but correct me if im wrong

[ionic pendant]

that part seems to be linear, so you would expect the derivative to be constant there

[naive geyser]

yeah

it should be horizontal

right?

my teacher always makes dumb mistakes like that

it's not even funny

😭

[neon dirge]

One could say it very slightly curves downwards

which is why he may have sketched that the derivative decreases

but it's too subtle to argue against or for

definitely not a factor of 2

[arctic mountain]

it's weird how he made that mistake, when right next to it he correctly drew the upward linear part as a constant

but 🤷‍♀️

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[sharp mantle]

what does it mean to "restrict to linear transformatoins ..."

I have no idea what the question is asking me to do lol

[marble wharf]

theta normally allows all inputs from V and you get outputs from V. if you now only allow inputs from im tau, then the claim is that you also only get outputs from im tau

[stark bison]

Restricting a function means restricting its domain and codomain, but keeping the same rule of assignment, so in this case you need to show that $\theta(x) \in \im\tau$ given $x \in \tau$ and $\theta(x) \in \ker\tau$ given $x \in \ker\tau$

[solid kiln]

A Lonely Bean

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[sharp mantle]

https://tenor.com/view/sending-love-gif-25755600

THANK YOU

[sharp mantle]

wait, restricting both the domain, and codomain, or either?

for e.g., if we were only restricting the codomain, but keeping the same domain, would that still be considered as "restricting the map"

[stark bison]

One or both

Yeah

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[short trellis]

from point A to the circle there are 2 tengents need to find a

[short trellis]

So ik that the tengents are equal

But thats where im stuck at

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[flint fox]

can you not simplify the 4 and 2

[past depot]

No, to simplify it has to divide all the terms, if you expand out the top you get $\frac{4p^2 - p}{2(p+2)}$ but 2 doesn't divide p

[solid kiln]

JJP

[flint fox]

got it

ty

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[keen void]

"Determine the points (x,y) on the ellipse for which the area of the triangle with the corners (0,-b), (x,y) and (0,y) gets the largest area"

[keen void]

Does someone know how i go about solving this?

[wraith hinge]

I would find the function that gives you the area and then the stationary points

The other points are moving or just (x,y)?

[keen void]

What do you mean by moving?

[wraith hinge]

if the other vortices can change their position

[keen void]

Nothing is moving

[wraith hinge]

Well (x,y) is moving so that you have greater triangle

[keen void]

I'm supposed to determine (x,y) which gives the triangle it's maximum area where (x,y) is on the ellipse

[wraith hinge]

are you comfortable with elliptic coordinates?

[keen void]

No

Do you know how to solve it? This is multivariable calculus

[wraith hinge]

what are the coordinates of the tallest point?

[keen void]

(0,b)

[wraith hinge]

I don't think so

[keen void]

you can quite literally see that it is (0,b)

[wraith hinge]

I mean the tallest vortice

The y coordinate is unknown

it's in exercise (0,y)

So that point is also moving along with point (x,y)

[keen void]

Absolutely nothing is moving

[wraith hinge]

to give you the height of the triangle

[keen void]

I'm given three points which of i'm supposed to determine 1 point

[wraith hinge]

Wait I'll try to draw

[keen void]

Have you done multivariable calculus with optimization in 2d/3d?

[wraith hinge]

those points are movable in order to vary the area

you need to find the position where the triangle gets the greatest area

[keen void]

Yes but all three points are already fixed

That triangle already has the largest area

None of the points are moving

[wraith hinge]

they aren't "fixed" when the points have variables in the coordinates

the figure is just an example

what you know is that 0 < x < a

and 0< y < b

For example when X=0 -> y=b

And you are near the minimum area

Which is just a straight line

[wraith hinge]

Why don't you write y as a function of x?

And you triangle will be a f(x)

f(x) = Area = y(x) * x / 2 , for all 0<X<a

then find the maximum value with f'(x)

[keen void]

Sorry something came up, thanks tho

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[umbral lily]

Hey there can someone explain how it become 8 tho ?

[turbid leaf]

Have you tried anything

[umbral lily]

add up all numerator n denominator

[wraith hinge]

lmao

[onyx ferry]

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)

[turbid leaf]

!occupied

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[wraith hinge]

yea

anything else

[umbral lily]

nah i hv no idea bro, cross multiple does work ?

[wraith hinge]

?

put x/4 = k

y/5 = k

z/6 = k

[umbral lily]

then what to do with 2x - 3y + 4z = 34 ?

[wraith hinge]

substitue c:

see if you can solve it yourself

you prob just need the value of k

put it in some equation

[umbral lily]

get it

How bout this situation?

[wraith hinge]

uh wait

[umbral lily]

ans given is B idk how it went to

[wraith hinge]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

you can uh

shit, idk the term

factorisse it?

both are square

s

[umbral lily]

get it

[umbral lily]

One more to go

[wraith hinge]

@_@

,rotate

[wraith hinge]

equate

[umbral lily]

Wdym pal ?

[wraith hinge]

try to equate smth with smth

if doesnt work, ill say

[umbral lily]

I did simultaneous

[wraith hinge]

i have no idea what that means

💀

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[marsh forum]

<@&268886789983436800> spam/malicious link perhaps

or advertisng

[rapid mirage]

THANKS

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[rapid mirage]

thanks*

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[shut lichen]

please help

[shut lichen]

.close

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[dusk canyon]

how did this happen?

[dusk canyon]

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[coarse hound]

Can anyone help me with the Laurent series, I tried my best but stuck at that part

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[coarse hound]

<@&286206848099549185>

[vague thistle]

Nah this some freaky maths

Sorry I can't help

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[silk anchor]

.open

[cold sphinx]

can someone help me understand this

[pseudo grotto]

which part do you not understand

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[cold sphinx]

dw i found it

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[sharp mantle]

Is the ODE $y'(x)=\frac{f(x)}{g(y)}$ always separable?

[solid kiln]

Kakaka

[sharp mantle]

might it be non-separable?

[marble flare]

Looks always separable

You get g(y) * y' = f(x) this is by definition separable

[twin mist]

@sharp mantle

[sharp mantle]

wait, is the converse of this staementr true?

for the wronskian

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[wooden plover]

@sharp mantle no, here's a counter example there https://math.stackexchange.com/a/4518815

intuitively, wronskian(f, g) = 0 for some point x tells you there's a linear dependence between f(x) and g(x)

but it doesn't tell you which dependence it is

so that you could end up with 2 different dependences for different inputs

that's how the counter-example was thought of

$$f(x) = x^2 = \begin{cases} x^2 & x \leq 0 \ x^2 & x > 0 \end{cases}$$
$$g(x) = x|x| = \begin{cases} -x^2 & x \leq 0 \ x^2 & x > 0 \end{cases}$$

[solid kiln]

aPlatypus

[wooden plover]

the linear dependence between the outputs switches around x=0

so globally, the functions aren't linearly dependent

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[pale badger]

How do i prove this?

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[wild imp]

Is u a unit vector?

If it is, then just taking the dot product should work

[pale badger]

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[wraith hinge]

<@&286206848099549185>

[wraith hinge]

Please help

<@&286206848099549185>

Please provide some questions for linear equations class 8

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[steady tulip]

How to solve this

[steady tulip]

3rd one

[wild imp]

chain rule

[steady tulip]

Why not directly applying power rule

[wild imp]

power rule only works directly for x^n

[steady tulip]

Isn't this the same

[wild imp]

this is (sinx)^3

[steady tulip]

(sinx) cube

[wild imp]

you have an outer and inner function

[steady tulip]

Yea

[wild imp]

so you use chain rule

[steady tulip]

What's that

I don't understand

[wild imp]

,, \dv{}{x} / f(g(x))=f'(g(x))\cdot g'(x)

[solid kiln]

Prof. Rosswell

[wild imp]

its a composition of 2 functions

[steady tulip]

Ohhhh so the functions here are sin and x right

[tired shoal]

i think its time to revisit functions

[steady tulip]

My teacher is trash

He can't teach

💀

Ty tho @wild imp

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[wild imp]

they're f(x)=x^3 and g(x)=sinx

[steady tulip]

Ohhhh ty

.close

[prime crystal]

its already closed

[steady tulip]

Mb

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[lavish jackal]

Is the answer 12C3+8C2...or 12C3×8C2??

[sweet turret]

x

[lavish jackal]

And when its not independent events then its addition?

Thanks

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[obsidian nimbus]

do coordinates in a vector correspond to its i and j components e.g is (2,4) = 2i + 4j

[tired shoal]

yes

[obsidian nimbus]

cheers

can someone tell me why im wrong

im trying to do the vector resolute

a on b

a = 2i +4j and b= 2i

when i do a on b perpendicular it is wrong

<@&286206848099549185> i gtg in like 10m

[marble flare]

!15m

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[vapid pawn]

Did u find the equation between (0,-1) and (2,0) and then find the distance between that line and the point?

[vapid pawn]

^

[obsidian nimbus]

Why do I Need to find the equation between those 2 points?

If iT said find the distance with the cat?

<@&286206848099549185> it's been 15 minutes please help I'm strugglong

[quartz fulcrum]

so like

i cant help u but

its an advice

to use chat gpt

[knotty locust]

!nogpt

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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[quartz fulcrum]

because it explains to u

[quartz fulcrum]

IT WAS WRONG THE WHOLE TIME

[obsidian nimbus]

Mb

[knotty locust]

Please do not recommend people to use ChatGPT for their problems, it is against the server rules

[quartz fulcrum]

EVEN FORMULAS?

no cus i was suggesting them to grab formulas out of it

not the answer and stuff

[obsidian nimbus]

But can someone tell why I'm wrong when I do a perpendicular to b

[knotty locust]

If you're going to do that it'd be better to use a textbook or wikipedia

[quartz fulcrum]

honestly yea true

[quartz fulcrum]

example theres an example page for everything

in a textbook

👍👍👍

[obsidian nimbus]

It's not from a textbook

From onenote page

From another teacher

[quartz fulcrum]

holy shit u use one note

wow

me too

[quartz fulcrum]

isn't there lessons

[obsidian nimbus]

Nope

I just need worked solution for this question

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[turbid coral]

Not sure what to do next

I know that you use gradient function to find a vector normal to a point then use point-normal equation of a plane

wait

[wraith hinge]

you are pretty much done

[wraith hinge]

P_1P_0 is any vector formed here

so like

you have ur general equation be [
F_x(x-x_0)+F_y(y-y_0)+F_z(z-z_0) = 0
]

[turbid coral]

I'm not sure how Fz is derived

partial derivative df/dz

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[arctic matrix]

Write the following equation in Cartesian coordinates:
r cot θ = 3

I did:

r cot θ = 3 <=> r cos θ = 3 sin θ

=> r² cos θ = 3r sin θ

=> y sqrt(x² + y²) = 3x

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[silver furnace]

how do you know it equals 3?

[arctic matrix]

Ow sorry that's part of the original question.

Edited now

[wild imp]

how did you get the last equation?

i think instead of multiplying r, you should square both sides to get r²cos²θ=9sin²θ
=> r^2=9tan²θ

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[lapis blade]

can someone explain how area is being calculated

here

and also why is x from 1 to 0

i understand the y and z because they are pretty self explanitory but i am confused about x

and also I thought the area was all of the uppers multiplied by each other

which to me doesnt equal 2

[tall kernel]

You're supposed to ping after 15m also this channel is occupied

And do u mean area

It's just 120 cm btw

Just delete ur messages

[lapis blade]

<@&286206848099549185>

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[lapis blade]

When someone answers dis can they ping me im going to sleep

Or dm me idk something like that

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[ashen crypt]

how do i do this? im confused on the determine the least squares estimator part

Do i have to just write the regular formula?

this one?

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[elder pond]

Hi guys can someone help me with the ii and the iii please

I did the inequality with the condition and it gave me that a is greater than three and a is greater than 4

so I expect that the answer would be a is greater than or equal than 4

but

why is equal to 4???

I would say that it doesn't touch the 4

like (3, infinite) but with the exception of 4

but the answer is greater or equal than 4

I

am

confused

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[elder pond]

<@&286206848099549185>

[shy nacelle]

Hi

[burnt mulch]

We need -2<x<5

Which means x is at least 4 units away from 2 (which is what |x-2| represents)

Hence a__>__4

@elder pond

[elder pond]

Sorry but I don't get it