help-27

[timid isle]

Also the general idea is that a disparity in the even indices can “cancel out” a disparity in odd indices

[bitter halo]

I dont know how to start

C++ or python

int main() {
     array<array<int,4>,3> arr = {{
      {0,5,2,1}, {0,17,0,3}, {2,4,6,7}
    }};
    int m = 0;
    for(array<int,4> &a : arr){
      for(int i = 0; i < 4; i++){
        (i % 2) == (a[i] % 2) ? m += 1 : m += 0;
      }
      m == (4-1) ? cout << "GOOD\n" : cout << "BAD\n";
    }
    return 0;
}

do you see this? y/n @timid isle

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[abstract moss]

Problem 17.. I have tried using bezout's theorem on gcd part but it's not working.. Any hints??

[livid geyser]

,rotate

[livid geyser]

ok so yeah bezoutvs identity does help

[restive river]

yea

it does

PAYA

[abstract moss]

.. That means I have done some other mistake?

[livid geyser]

Whatd u try doing with bezout's exactly?

[restive river]

Yes you have

What were u doing?

like with the identity

[abstract moss]

Wait leeme send my work..

[restive river]

k

[abstract moss]

I got stuck after that... And maybe I think there are many mistakes in this too:/

[livid geyser]

yeah my sln is like 6 lines and i can probably simplify it a lil still

I'd suggest working with modular arithmetic

Rather than the definition of mod directly

[abstract moss]

Yeah😅 whenever 'mod' appears I just write it like that :/

[abstract moss]

Can you send it?

[livid geyser]

hint: if bx + ny = 1, what's bx + ny (mod n)

Can't give slns in this server 😐

[abstract moss]

How does that help?
I am really dumb://

[livid geyser]

well ok i shouldve asked first

Simplify bx + ny (mod n) as much as possible

remember n = 0 (mod n)

[abstract moss]

Hmm so n+1= bx+ny(mod n)?

[livid geyser]

hmmm not what i was going for

but it is true

what's 0 times something

[abstract moss]

0

[livid geyser]

yeah

Can u simplify bx + ny (mod n) now

... can u simplify just the ny part?

[abstract moss]

Umm 0? That's the best I can think of

[livid geyser]

yeah but i don't like how unconfident that was >. >

[abstract moss]

My confidence is in negative after that -_-

[livid geyser]

Here's a crash course in modular arithmetic

[abstract moss]

Ok

[livid geyser]

If a = c (mod n) then ab = cb (mod n)

[abstract moss]

Ok

[livid geyser]

so if n = 0 (mod n) then ny =?y (mod n)

fill in the question mark

[abstract moss]

mn, m is integer

[livid geyser]

a = n, c = 0, b = y

Make the substitutions

[abstract moss]

So it's just 0?

[livid geyser]

yeah

[abstract moss]

But why not mn? Like they both give remainder 0 when divided by n?

[livid geyser]

could work too but i was just tryna get you to recognize the pattern from the rule

[abstract moss]

Ohhk

[livid geyser]

So yeah ny = 0*y = 0 (mod n)

[abstract moss]

Hmm

[livid geyser]

then z + 0 = z (mod n), so bx + ny =? (mod n) (z = bx)

[abstract moss]

bx

[livid geyser]

Yuuuup

and we also know bx + ny = 1

So now we have bx = 1 (mod n)

[abstract moss]

hmm

[livid geyser]

from there just try playing around with the expression

So like for instance if you multiply borh sides by a u get abx = a (mod n)

Then using the given hypotheses and arithmetic properties like associativity, try to go from "abx" to "c"

[abstract moss]

hmm wait i am trying..

[livid geyser]

bet

[abstract moss]

i can't 😐 its not working

any more hints?

[livid geyser]

abx = (ab)x

well actually

firstly let's see what you tried and see if i can give a hint from there

[abstract moss]

no.. wait.. i think i got it.. form b(dx-1)=n(-dy+k) and gcd(b,n)=1 it implies dx-1=n == dx=n+1 ==abx=cdx (mod n)== abx=c(n=1) (mod n) == abx=c (mod n) == now subtituting in abx= a (mod n)== c=a (mod n)

is it correct ?

[livid geyser]

hmm honestly I can't completely follow what u did, but abx == cdx (mod n) is on the right track

ping me when u reply pls ty

[abstract moss]

hmm.. i pluged in the value of dx as n+1 i got it from b(dx-1)=n(-dy-k) as their gcd is 1 so they are co prime that means dx-1=mn == dx=mn+1 and then just substute...

That's what I did now.. Is it correct? @livid geyser

[livid geyser]

oic yeah that works

There's a simpler way with modular arithmetic but your work is correct

[abstract moss]

i have a little doubt in step abx=c(nm+1) (mod n) == abx= c*1(mod n) is it allowd i just write the remainder when nm+1 is divided by n?

[livid geyser]

yeah

[abstract moss]

what's that?

[livid geyser]

a == (ab)x == (c(d)) x == c((b)x) == c*1 == c (mod n)

first replace ab with cd

Then d == b (mod n)

So replace d with b

Then we go back to bx == 1

So replace bx with 1

[abstract moss]

got it (:

it is way simpler

thankyou

[livid geyser]

np

[abstract moss]

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[steel knoll]

Please, check my answer)

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[steel knoll]

<@&286206848099549185> )

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[strange arch]

ys

is right

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[boreal plume]

If ^2 is a square, ^3 cube, then how named ^4, ^5, ^1, etc.?

[stone stump]

they dont really have names like that

[boreal plume]

I find name for ^4, it`s bisquare(can be wrong translate, in Ukrainian: Біквадрат)

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[unborn atlas]

67

[river solar]

lhopitals

may help

im not sure

oh no ahahaha

try rationalising the fraction first maybe

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[unborn atlas]

.reopen

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✅

[unborn atlas]

I don’t know how to do it still

I get this

[restive river]

divide by sqrtx

[unborn atlas]

Wdym

[restive river]

denominator and the numerator

[unborn atlas]

What does that do

[restive river]

what do u have rn

[restive river]

change that to 1 + 1/x

and 9 + 1/x

btw do you play jtoh

[unborn atlas]

?

[unborn atlas]

3

[restive river]

ye

[unborn atlas]

Ty

[restive river]

nice

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[summer dune]

.close

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[summer dune]

hello

[summer dune]

what does this point mean

are these exponents?

[azure fog]

yes

the y coordinate is $\frac{-7}{5}\sqrt{3}\sqrt{17}$

[woven radish]

Raiden

[twilit comet]

aka $-\frac 75 \sqrt {51}$

[woven radish]

ren

[azure fog]

it looks like it

[summer dune]

ohhh gotcha

thanks

[twilit comet]

!done

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[summer dune]

.close

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[uncut vine]

consider this example
what is the convention for ordering this polynomial
for example both -4ab and +6ac have the same degree, so how do I order them? and how do I order this entire polynomial

<@&286206848099549185>

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[spark cove]

how can i find the values of p for which this denominator is equal to 0

i tried finding the discriminant D= p^2 -14p +9

then i wanted to find s1,2 = (-(p+1) +-sqrt(D))/2

but i don't know how to solve this

[quaint citrus]

hmm

The denom is 0 for all s that are equal to$\frac {-(p+1) \pm \sqrt {(p+1)^2 - 4(1)(4p-2)}}{2}$

[woven radish]

Stephen

[quaint citrus]

@spark cove

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[inland pawn]

For this problem here why do you have to use chain rule for second derivative

but for other derivative notations like with ' there's no chain rule involved for this derivative

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[hushed lance]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[inland pawn]

I just need help on b)

[hushed lance]

ah i see

because h itself is a function of t

what youre doing is taking that given equation and d/dt both sides, not d/dh

[inland pawn]

because it's different variables. I need to use implicit differentiation and use chain rule?

[hushed lance]

kind of

yeah pretty much

[inland pawn]

ok got it ty so much

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[keen moss]

A club with 15 women and 12 men needs to form a committee of size 6, How many committees are possible if the committee must have at least 3 women?

I'm struggling to understand the answer to the question. My intial approach was to do 15C3 to guarantee at least 3 women and then move the remaining group to be grouped with the men resulting in 24C3 and my final answer being 15C3 * 24C3. However the answer is something along the lines of assuming different scenarios like so:

3 women , 3 men: 15C3 * 12C3
4 women, 2 men: 15C4 * 12C2
5 women, 1 men: 15C5 * 12C1
6 women, 0 men: 15C6 * 12C0
all summed up. Why is my approach incorrect?

[topaz axle]

it makes the same commitee over and over and over

[keen moss]

I thought about it for a bit and I think the reasoning might be due to I'm treating it as individual people but what matters is the gender and not the unique identification of each person

[topaz axle]

for example there's 3 women and 2 men
W1 W2 W3 M1 M2
the commitee should have at least 1 woman and 3 total people
3c1 * 4c2 creates these commitees, among others
W2 + W1 W3
W1 + W2 W3
W3 + W1 W2

so it's useless

[keen moss]

okay so there's repetition

okay

I get it now thanks

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[keen moss]

one last question would the total combinations be (15+12)C6?

[solid bolt]

wdym

wait ill let him answer that mb

also use .reopen

[keen moss]

.reopen

[devout snow]

✅

[keen moss]

Was also looking to solve the problem by taking total combinations - cases in which there was not at least 3 women

So was wondering if the total case would be 27C6

[topaz axle]

yes (15+12)C6 would be all different commitees

[keen moss]

Alright thanks

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[neat kelp]

im kinda stuck

nvm figured it out

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[dry lotus]

Please tell me how

@neat kelp

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[thorny pawn]

Is it true that every convex and differntiable function f:(a,b) -> R has at most one critical point which must be a global minimum?

[thorny pawn]

I'm not sure if this is true but also can't really find a counter example

[spare crypt]

that's right, essentially convex means you're only turning in one direction along the graph

[thorny pawn]

Ah okay yeah that makes sense. Thanks. I'm basically doing a self-test and I have to select all the right ones.

1. Every convex function is continous.
2. Every convex function is differentiable.
   Wrong. take f(x) = |x|
3. Every convex function is integrable.
   Wrong. Take f:(1,2)->R f(x) = 1/[(x-1)(2-x)]
   4)If f:(a,b) -> R is convex then it has a global minimum.
   Wrong. take f:(1,2) -> R f(x)=x^2
   5)every convex and differntiable function f:(a,b) -> R has at most one critical point which must be a global minimum
   6)Every convex function f:(a,b) -> R must have a nonnegative second derivative.

I think 1), 5) and 6) are right but it's apparently wrong and I'm not sure where I went wrong.

Oh I guess 6) is wrong because the second derivative doesn't necessarily exist...

Should've known that

And the answer is 1) 3) and 5) but I don't get why 3) is correct...

[spare crypt]

hmm your counterexample seems to work

it's true when it's continuous on a closed interval because then that implies integrable, but yea you can take an open interval that diverges at the ends

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[vivid kite]

I have a question

For 2 the radius is 1

Because of the ratio test right

Because it only converges if it’s less than 1

So R has to be 1

[inland seal]

yes

If |x + 5| < 1 you mean

[vivid kite]

Yes

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[earnest zinc]

hi! i need help identifying two functions in 2 different composite functions. i’ll send a pic of them in just a sec.

[lavish nimbus]

Think the question as denominator/numerator.

[earnest zinc]

for part a?

[lavish nimbus]

b

[earnest zinc]

so, denominator/numerator so would f(x) = square root x - 2?

okay, and would g(x) be 1/ square root x?

[lavish nimbus]

Just 1/x

[earnest zinc]

thank you for your help! does a look okay too?

[lavish nimbus]

The parenthesis around g(x)’s x could be removed.

[earnest zinc]

so it would just be x^7?

in that case would a parentheses be needed around the f(x)?

[lavish nimbus]

The functions are independent, putting a function to another function is to have a more bizarre variable/argument.

[earnest zinc]

ohhh okay, thanks again

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[uncut yew]

Can someone explain this to me

[heady tulip]

https://www.youtube.com/watch?v=S-agS4YaxxU

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[uncut yew]

i dont get how they got sqrt2/2h * sqrt2/2h * 1/2

Cause i thought the formula of a triangle was base * h * 1/2

[heady tulip]

yes

h is height

not the side

you dont have height

you have the side

[uncut yew]

how do u find the height?

[heady tulip]

equilateral triangle --> 60 deg each angle

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[restive river]

i dont get this question

need someone to help solving

[olive condor]

okay

well what is the definition of trapezium

[restive river]

quadrilateral

[olive condor]

that is what

it has 2 parallel sides iirc right

[restive river]

a quadrilateral with one pair of sides parallel.

yep

[olive condor]

so your goal is to prove PS and QR is parallel i guess

[restive river]

ye

i think so atleast

what next?

[olive condor]

hmm

im seeing

[restive river]

oki

[olive condor]

is 2a + 4b supposed to be

the length of QX

[restive river]

yes

[olive condor]

ill brb

nvm i gtg im sorry 😭 maybe you can try an arguement with diagonals and similar/congruent triangles

thats what i was going to attempt b4

[restive river]

okayy

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[unkempt quiver]

Idk where to start with this

[unkempt quiver]

But isn't sin(2x) = 2sinxcosx

And

And cscx = 1/sinx

I'm trying to relearn trig and I haven't done it in a year if anyone could help me out that'd be great <3333÷

[unkempt quiver]

With that problem above

[strange arch]

yes so let's start by inserting the formulas you mentioned

well and if that product is 0

then we know at least one of the factors on the left is 0

and cos(x) is 0 in [0, 2pi) for x=pi/2 and x=3pi/2

so we already know 2 solutions

and then we have 4sin(x)²-1 = 0

4sin(x)² = 1

sin(x) = 1/2 or -1/2

which is true for

x = pi/6 or x = 5pi/6 or x =7pi/6 or x = 11pi/6

@unkempt quiver

[unkempt quiver]

Hi!

[unkempt quiver]

Thank you so much!

[unkempt quiver]

Wow you're the best <333

That was explained so well

[strange arch]

🦇

[devout snow]

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[devout snow]

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[tame chasm]

May someone check if I got question 2 correct?

[thin fern]

that looks correct

[tame chasm]

Alright thanks

.close

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[tame chasm]

.reopen

[devout snow]

✅

[tame chasm]

May someone confirm if I’m doing 8 right with my answer

[devout snow]

@tame chasm Has your question been resolved?

[tame chasm]

<@&286206848099549185>

[urban harbor]

,rotate

[urban harbor]

at theta = pi/2 the function doesn't change signs even though there is a 0, (sin theta - 1) is negative on either side of pi/2

but your way to approach this is correct, you just need to make sure you figure out what the correct signs are between those key values

[tame chasm]

Wait so is my answer correct?

[urban harbor]

no

[tame chasm]

Darn

What website is that?

[urban harbor]

it's called google, it's a bit obscure 🙂

https://www.desmos.com/calculator
is also a good online grapher

[tame chasm]

so it would be negative from 0 to pi/2

[urban harbor]

right because the (sin theta - 1) factor is negative and the other is positive

then it stays negative (pi/2, 7pi/6) because nothing changes

[tame chasm]

that makes sense

[urban harbor]

at theta = 2pi, (sin pi - 1) becomes 0 again, but (11pi/6, 2pi) is also negative

[tame chasm]

Wait how would I approach this question if I didn't have a graphing calculator to look at the points

[urban harbor]

your approach was approximately correct, what you can do is make a table for each factor individually, (2sin+1) and (sin-1) and well you found out where they are 0, then check on either side of those zeroes what the signs are of the individual factors, then the function overall will be negative when there is 1 negative factor, or you could do test points of the overall function but itd be a bit more algebra maybe

[tame chasm]

Ow alright thanks

That

something I never though of

[urban harbor]

i thought thats what you were doing with the + - table 🤔

[tame chasm]

I was, but I was confused on how the graph would look

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[opaque helm]

https://cdn.discordapp.com/attachments/1018700472988749904/1218977725059039232/Screenshot_20240317-094937_Chrome.jpg?ex=6609a079&is=65f72b79&hm=252e1ce7f3f4853ccc752e6ad5092289ca36e20f58dc50587e39f32f02894931&

[opaque helm]

retweet

[oblique mirage]

What is your question?

[opaque helm]

How did the computer evaluate this 😭

[dense lynx]

by approximating

[opaque helm]

taylor series?

[kindred agate]

It just approximated the limit

You know the limit expression for the integral right, it just chose a high valie

[uncut crow]

i doubt it

[uncut crow]

i also doubt it did it like that

[opaque helm]

I think the taylor series is easier

Hold on

it's so not

[kindred agate]

How did it do it then

[opaque helm]

I'm stuck on the series 1 / ln (5 + i) * (1 + i)

Yeah Slayla

How then

[kindred agate]

I doubt it solved it algebraicly

[opaque helm]

Slay the question slayla 🙏

[uncut crow]

look i do not know what it did lmao, just that there are much better numerical integration methods than that

[opaque helm]

Can you give an example

[uncut crow]

simpson’s rule

[opaque helm]

To be honest that wasn't the question on my exam

It showed that integral from 5 to infinity and asked whether it diverged or converged

When I asked my TA about it later he said we needed to evaluate it to know

[uncut crow]

[kindred agate]

Big brain TA

[uncut crow]

you def don’t need to evaluate it

[kindred agate]

Whats the point of algebra when you have computers, right

Hell whats the point of calculus if you have desmos and a sharp eye

[opaque helm]

He said the first step was to set lim n to infinity and set the upper bound of the integral to n

[magic pine]

the government doesn't want you to know this, but there is no point to calculus if you have desmos and a sharp eye

[opaque helm]

Are there any divergence or convergence tests that work here?

[uncut crow]

wolfram language has a lot of numerical integration algorithms built in. it’s hard to know exactly which one it chose to use here

https://reference.wolfram.com/language/tutorial/NIntegrateIntegrationStrategies.html

[opaque helm]

I was reading through them

No way

This was an exam for an intro to calc class

[uncut crow]

dawg

the question you asked is totally different than the question on the exam

[opaque helm]

I know but my TA said to evaluate it

[magic pine]

doesnt matter as long as you have desmos and a sharp eye

[uncut crow]

“what numerical integration algorithm did wolframalpha use here” vs “does this integral converge?”

[opaque helm]

Are there any convergence tests to use here?

[robust dust]

the integrand doesn't have any singularities over [5,10], so the area doesn't blow up and you know its integrable

[uncut crow]

no this is an xy problem

the question on the exam was whether $\int_5^\infty \frac{1}{(x-4)\ln(x)}dx$ converges

[woven radish]

slayla

[opaque helm]

I got it

$\frac{1}{(x-4)\ln(x)}$

[woven radish]

AIDEN HONG

[opaque helm]

Just divide it by 1/x^2 and evaluate lim x -> infinity

Which resolves to infinity

Therefore both integrals must be convergent

[uncut crow]

we should have $\int_5^\infty \frac{1}{(x-4)\ln(x)}dx > \int_5^\infty \frac{1}{(x-4)x}dx$ right

[woven radish]

slayla

[opaque helm]

Yeah but the original integral is larger so the comparison test can't be used

[uncut crow]

nvm the one on the right converges

so not helpful

[opaque helm]

$\frac{1}{(x-4)\ln(x)\frac{1}{x^2}}$

[woven radish]

AIDEN HONG
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[opaque helm]

damn

[uncut crow]

did you learn like, a "limit comparison test"

[opaque helm]

Yeah

[uncut crow]

ok i think you should use that then

[opaque helm]

We only learned it for series but this is fine I guess

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[uncut crow]

by some limit comparison shenanigans the original has the same convergence status as $\int_5^\infty \frac{1}{x\ln(x)}dx$

[woven radish]

slayla

[uncut crow]

and this one you can "evaluate" to find it diverges

by finding an antiderivative

ln(ln(x)) is an antiderivative

and ln(ln(x)) - ln(ln(5)) diverges as x goes to infinity

@opaque helm

[opaque helm]

You're right

That's confusing

@uncut crow I think it has to do with that the original integral is only continuous, positive, and decreasing from >4

[uncut crow]

well yea that's why they chose 5 for the bound

[opaque helm]

That limit comparison would resolve to 1

[uncut crow]

if it was, e.g., 4 then the problem would be a lot different

[devout snow]

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[fervent jewel]

I guess, it makes sense if L1 = L2, so you basically reflect across L1 first then the reflection across L2 takes you back?

[magic pine]

that's 1 specific case yes

[fervent jewel]

hmm thats the only one i can think of in R2

[magic pine]

consider just a single reflection. when does that have a fixed point?

well always, but which points are fixed?

[fervent jewel]

the line is on the point

[magic pine]

other way around but yes

so if we go through 2 reflections and stay fixed, what is one possibility for that point

[fervent jewel]

if a point goes through 2 reflections and remains fixed, still L1 = L2 is one way that would work. Or the point could be the intersection of the two lines

[magic pine]

there you go

so the condition you want is an intersection

[fervent jewel]

ah

yes

thank you

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[reef sparrow]

hallo

[reef sparrow]

i have math question

i understand that we flip it and multiply

i do NOT understand where we get (x+1) from

HUH

[icy glen]

Haven’t looked at the whole thing but probs cause ax+a = a(x+1)

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[plain schooner]

Are the points I highlighted in red also considered h'x = 0?

[plain schooner]

I know f'(x) = 0 when its U or ∩

but i dont know if those ones count since the slope goes back up

[spare crypt]

left one yes, right one has a bunch of tangents so you say the derivative doesn't exist

[plain schooner]

Oh okay so other than if its a sharp turn, if a turn has different types of tangent its a DNE too?

[spare crypt]

I think it's always sharp turns

[plain schooner]

oh yea im aware of the sharp turns, but the one on the right just didn't look sharp to me that's why I'm a bit confused

[spare crypt]

oh sure, yea any turn at all

I guess there's other scenarios where the derivative doesn't exist but it's kind of wild edge cases

[plain schooner]

Makes sense, thank you boss

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[latent hazel]

how can i prepare for a tech active polynomials test its on graphing, solving and factorising polynomials, i am okay with graphing solving and factorising but am unsure how to do extended response questions where it asks to find the domain of a function, the maximum and minumum value

[latent hazel]

<@&286206848099549185>

i think i got a)

is it V=x(96-2x)(48-2x)

V=8x(24-x)^2

does anyone know how to find the domain for b?

can anyone please help i have a test tomorrow

CAN SOMEONE HELP ME

<@&286206848099549185>

[stark storm]

Which question

?status

@latent hazel Do you have any idea where to start or have you already done some work

[latent hazel]

b please

i dont know how to do the domain or find the maximum with out calc

[stark storm]

Do you have a CAS calculator

[latent hazel]

yea

[stark storm]

I just going to think what is the best way to explain to you

@devout snow

@latent hazel Ping the helpers again cuz i cant explain why although i can do it

[latent hazel]

<@&286206848099549185>

np thanks for your time tho

[stark storm]

Also because i can give you straight answers

Are you new

?

[latent hazel]

yes

[high coral]

Dv = R+

I think

[latent hazel]

dv?

what is dv

[high coral]

domain v

[latent hazel]

k

what is r+

[high coral]

You can't have negative dimensions can you ? so bearing that in mind

[latent hazel]

yeah

i just don't knnow how to find domain

[high coral]

you get all the reals that are positive

[latent hazel]

i understand the general theory

[high coral]

R+

I suppose you know how to find the domain of a function

[latent hazel]

not without cas

wait do you just use 8x(24-x)^2 and solve for x and use as domain

[high coral]

ok so for polynomials it is always all the reals but you want your V=8x(24-x)^2 expression to be > 0 so solve 8x(24-x)^2 > 0

[latent hazel]

so it would be 0<x<24

[high coral]

isn't the expression 8x*(24-x)^2 > 0 ?

[latent hazel]

yeah

so it 0<x<24 right

[high coral]

ok because (24-x)^2 is always >= 0 because it is a perfect square you only care about your 8x so you have for x (=/=) 24 8x > 0 which is x∈(0,24)u(24,+oo)

https://www.desmos.com/calculator/lmgabgzcrw

[latent hazel]

how do you find the maximum

[high coral]

just plot your 8x*(24-x)^2 and see where it peaks

[latent hazel]

my calc is only showing 1.64x10^4 is there any other way i can do this

[high coral]

well the other way I know to find the maximum of a function is using derivatives, do you derivatives?

[latent hazel]

no

so i really need to sort out my calc

[high coral]

your calc is showing you the correct result

I believe

[latent hazel]

but its not precise to the exact cm^3

i need it so it shows 16384cm^3

i am fine i think as my calc shows the x coordinate as 8

[high coral]

your problem says that approximate values are required so I think it's okay to leave as is

[latent hazel]

i can sub it into the equation

and find the exact solution so its 16384

[high coral]

yea why not

[latent hazel]

all good thank you for your help

[high coral]

you're welcome

[devout snow]

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[devout snow]

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[modern kelp]

how do i do it

[devout snow]

Please don't occupy multiple help channels.

[modern kelp]

Here we go

Sorry everyone

is this normal for year 8 maths. I find this hard. could someone explain please👍

[thorny lily]

Lol is that dy as in the differential or just d*y

[modern kelp]

huh

expand please

[thorny lily]

Dont worry its a calculus thing

But anyways what are you confused about

[modern kelp]

how to solve

[thorny lily]

Do you know what the numerator of the first fraction becomes

[modern kelp]

just saying im maths extension but not that big off a deal but the numerator would be all powers added together and i dunno rest

so ye id appreciate if u could help me solve it step by step

[thorny lily]

The way to solve is to expand everything and make it one fraction

[modern kelp]

expand what tho?

[thorny lily]

d3e3y5 squared

and dy to the 6

[modern kelp]

what would it be then over e to the power of 7

[thorny lily]

Divide the e terms

[modern kelp]

equalling what

[thorny lily]

You have a go

What do you think

[modern kelp]

zero clue

[thorny lily]

what is 2^3/2^7 its the same concept

[modern kelp]

ohh

i luv u so much

not in a gay way

[thorny lily]

Pause

[modern kelp]

ye continue

not understanidng the rets

rest

[thorny lily]

Show me what you got so far

[modern kelp]

nothing cause im dumb. if you do d^6 e^6 and y^10 x e i dunno what u get

22e?

[thorny lily]

You got the expansion right

[modern kelp]

so now denomonatars?

[thorny lily]

But you cant just combine them all to e^22

[modern kelp]

ye i dunno then

i gtg soon so u can explain real quick bottom and top thanks

[modern kelp]

thanks i apprecate it

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[gloomy sparrow]

Hi

[restive river]

hi

[gloomy sparrow]

where did the +1 go

the +1 in the formula just poofed

[gloomy sparrow]

also why 52 and 56 why cant it just be 52

since its the 4th term

[devout snow]

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[gloomy sparrow]

<@&286206848099549185>

[devout snow]

@gloomy sparrow Has your question been resolved?

[surreal junco]

Yo @gloomy sparrow

Sorry to interrupt just wanted to say I found your document really helpful and interesting!

Could you send me the link for it so I can also revise for my upcoming exams?

God bless

[devout snow]

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[random glade]

can anyone help me on how zvalue is 0.3121 became 0.7549 in pvalue

[random glade]

any specific methods without using softwares

[snow leaf]

define zvalue and pvalue?

[random glade]

statistics

z value for test statistic value

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[hollow snow]

whats this?

[devout snow]

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[narrow prairie]

How do you find the value of x after u get the equation of the dy/dx? (No 9)

[devout snow]

@narrow prairie Has your question been resolved?

[gaunt matrix]

Use quotient rule to find dy/dx. Stationary point implies derivative=0, solve dy/dx=0 and that is your value of x

Substitute that value of x into the equation for y to find y, and that makes up your coordinates for the stationary point

To determine the nature of these points, you can use the first/second derivative test

[narrow prairie]

i tried to use quotient rule, but the prob is tht i cant find the value of x, just that, i got ln7/4 but apparently the correct ans is -0.988, so is there a way to achieve tht result?

[gaunt matrix]

Make sure ur doing quotient rule correctly

Think your quotient rule formula might be wrong (not 100% sure) but just search up the correct one to make sure

[narrow prairie]

Pretty sure I did it bcs ive done it multiple times and my friends also got the same result, can you try doing it please so I can see which part is incorrect or how to get it?

[devout snow]

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[narrow prairie]

<@&286206848099549185>

[spare crypt]

here's the derivative but there's no good answer for the value of x where dy/dx=0, it's the log of a degree 5 polynomial

like there's no way to get x without a calculator

best you can do is say a calculator gives (-0.9888,2.1223) and it's a local minimum

[narrow prairie]

hmmm what do u think i should do so i can get liek the result of x with the working as well, is tht possible? ive just been trying to do for liek hours but no result 😓

[spare crypt]

I'm not sure I see you taking the derivative on the paper you linked

[restive river]

best to simplify as much as you can, then just provide the answer

that way you could minimise your mark loss

since the question didnt ask for exact values, i think youd be okay as long as you showed all working prior to using calculator

good luck determining the nature tho 💀

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[mystic arrow]

What exactly is a domain and range of a f(x) function?
Is the range the lowest value of f(x) and the highest value of f(x) like 2< f(x) < 5 and the domain all the values of x like 3 < x < 5?

[devout snow]

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[mystic arrow]

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[frail sun]

I guess I'm just a bit confused on the wording here.

[frail sun]

I get the first derivative and then find the x values, which are 0 and -5, right?

[quaint citrus]

yea

[frail sun]

what do I do from there?

[quaint citrus]

are u familiar with the second derivative test

[frail sun]

yeah, i'm pretty sure

[quaint citrus]

alright, find f''(0) and f''(-5) and then apply the second derivative test

[frail sun]

f''(0) = 30?

[quaint citrus]

uh lets see

yea

[frail sun]

that means f''(-5) is the local min and f''(0) is local max?

[quaint citrus]

no

if f''(x) < 0, its a local max

and vice versa

[frail sun]

huh?

oh i see what i did

what's the point of the second derivative

yeah, can't I just do this? @quaint citrus

no need for second derivative

[quaint citrus]

lol

u can

but ur question asks u to do 2nd derivative test

soooo

[frail sun]

that's fair

buttttt this is for an exam, which is online so no way to show work

lol

[quaint citrus]

oh nah jit

we cant be helping w exams

[frail sun]

noononooo this is the practice

I have one more question

How could I determine these things?

[devout snow]

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[frail sun]

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[restive river]

hi

[restive river]

Pls help

Can anyone give me the shortest solution?

<@&286206848099549185> ?

[gaunt matrix]

2/5 of the total number of balloons are left. half are blue, and so half are red. so the number of remaining blue balloons = the number of remaining red balloons. there are 20 red balloons left, implying that there are 20 blue balloons left. so there are 40 balloons left in total. this is 2/5 of the total number of balloons. start with this and hopefully you will get the answer

[restive river]

Uhh oki

100?

over s?

oop

.close

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[placid kraken]

i need help with this equation

[tough storm]

u x ??

[placid kraken]

what

[tough storm]

what is that symbol

[placid kraken]

oh a 4

and the last numerator is a 7

[final token]

$\frac{2x}{(x-1)^2} - \frac{4x}{x^2-1} + \frac{7}{2x-2}$

[woven radish]

dqvidutzul

[final token]

is this right?

[placid kraken]

its a division symbol not minus

everything else yes

[final token]

ohh alright even better

[tough storm]

flip

[final token]

you know how fraction division works right?

[placid kraken]

ok so i have the answer to it that my teacher made but i was confused on some steps

[placid kraken]

yes\

[final token]

what steps confused you

[placid kraken]

why didnt she make that (x-1)^2 a perfect square

[final token]

you mean why didnt she use x^2-2x+1?

[placid kraken]

yes

[final token]

because when multiplying, at the numerator was (x-1) which was easy to simplify

[placid kraken]

but my teacher says to always factor when possible

wait a sec

im dumb

that is factored

[final token]

here (the green line)

[placid kraken]

yeha i get it now

bc (x-1)^2 is already factored

i was unfactoring it

[final token]

yeah that would still work but made it harder and like 10 extra steps

[placid kraken]

oh

[final token]

your teacher used the easiest and best method

yep what’s up

[placid kraken]

nvm

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[regal wagon]

hey, im not really sure where to start for this. could someone point me in the right direction?

[devout snow]

@regal wagon Has your question been resolved?

[regal wagon]

<@&286206848099549185>

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@regal wagon Has your question been resolved?

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@regal wagon Has your question been resolved?

[magic pine]

draw it out @regal wagon

do you understand, geometrically, what this is saying?

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[solar goblet]

square root is a function

[solar goblet]

for example, sqrt4 = 2, not plus minus 2, because its a function

but why does sqrt{i} output 2 values?

[topaz axle]

because whoever outputs it to you wants that

[solar goblet]

we always meme this and most of the time, this is an explanation, yet somehow its okay to do so with imaginary number?

[dense lynx]

says who

[wooden zodiac]

,w sqrt(i)

[woven radish]

Results provided by WolframAlpha

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

Requested by fractalogist

[dense lynx]

ur supposed to take the principal sqrt (looks like wolfram does that as well)

[solar goblet]

https://youtu.be/Z49hXoN4KWg?si=wIr29dOPsfLjMQP4

[dense lynx]

most reliable source

[solar goblet]

yes

my teacher also arrives to the same answer

and stackexchange as well

[dense lynx]

that's fine

it's normal to say "there are two square roots of [whatever number]"

but when u write sqrt(number) it's implied ur taking the principal sqrt

[urban harbor]

just like with real numbers, there are two complex numbers that square to a certain complex number (except for 0), but the square root function (sometimes called principal root function) is by convention the one with positive real component i think so that it is indeed a well defined function

just like (-2)^2 = (2)^2 = 4 there are two numbers that square to 4 but we define the square root real function to give the positive version sqrt(4) = 2

i think its just same thing

[solar goblet]

thats my thought as well

but often times i see its misworded and people just say sqrt i has 2 results

when really theres just 1

a number has 2 square roots, but the square root of that number can only have 1 value

[urban harbor]

its probably better avoid saying "i has two square roots," i would instead use language like "there are two numbers z such that z^2 = i" but i think its technically correct to call them square roots. i dunno what the technically correct name for the "secondary" root is, but the one for the main one is principal root

but its definitely technically incorrect to say that the square root function has two values/outputs

[solar goblet]

non-principle root

i think

[solar goblet]

yes

yeah that should clear up my doubt

alright, thanks!

.close

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[bold bluff]

is anyone able to explain this for me?

[bold bluff]

Where did the 2^2 go

and how did he just bring the 5 out

[proud adder]

Expand the (5x-1) - 2²

[scarlet mauve]

(5x-1)-2^2

where 2^2=4

=> 5x-1-4

=5x-5 = 5(x-1)

[bold bluff]

huh

ohhhh

thanks

got it

.close

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[rugged latch]

Need help with last question

[devout snow]

@rugged latch Has your question been resolved?

[rugged latch]

<@&286206848099549185>

what should i do first

[solid bolt]

draw a fresh diagram

[rugged latch]

ok

@solid bolt

not the best drawing

[solid bolt]

mb sorry i was afk

[rugged latch]

still need help with this lol

[solid bolt]

yeah im having a look at it

now

with a clearer diagram

[rugged latch]

do i need to redraw?

[solid bolt]

nonono

its fine

[gleaming forum]

yo anyone know this question?

[solid bolt]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[solid bolt]

see #❓how-to-get-help

not that sure about this one

sorry

its an annoying problem

[rugged latch]

hmm

[solid bolt]

wait lemme think

<@&286206848099549185>

[rose berry]

10

[solid bolt]

.

[twilit comet]

trig?

[devout snow]

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[rugged latch]

.close

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[strong willow]

what does they say here?

[devout snow]

@strong willow Has your question been resolved?

[strong willow]

<@&286206848099549185>

[jade oak]

What do u mean

[strong willow]

i don't understand what this question means

like where is the pyramid located

[jade oak]

It is below the tangent plane

Bounded between the curve and all 3 axis planes

[strong willow]

i don't understand

[jade oak]

I will try and get an example 1 sec

[strong willow]

what is below?

[jade oak]

The pyramid is there

All tangent planes to the given curve will form a pyramid like this

[strong willow]

ooo i see

ok tnx

[jade oak]

np

[strong willow]

good job

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[solar goblet]

how many complex number $z$ exists such that $|z+2-i|=2\sqrt2$ and $(z-1)^2$ is a pure imaginary number

[woven radish]

Fungus 34A05

[solar goblet]

expanding the modulus i get a circle whose center is (-2, 1) and radius 2sqrt2

expanding the square i got:

$a^2-b^2-2a+1=0$

[woven radish]

Fungus 34A05

[solar goblet]

whats left is to find the intersection between the two graphs

but i struggle to do so

[devout snow]

@solar goblet Has your question been resolved?

[solar goblet]

<@&286206848099549185>

[devout snow]

@solar goblet Has your question been resolved?

[rain fjord]

$b^2 = (a-1)^2$

[woven radish]

[ᴛʜᴇ ᴇᴍᴘᴇʀᴏʀ]

[rain fjord]

then you can substitute b in the other equation

[crisp niche]

etc

[devout snow]

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[lost laurel]

If the sum of the first 2n terms of an AP is $\alpha$ and the next n terms in $\beta$ find the common difference

[woven radish]

Why am. I here

[lost laurel]

*is

I started by writing the general formula for an AP

$\alpha=2\left(\frac{n}{2}\right)\left(2a+\left(2n-1\right)d\right)$

[woven radish]

Why am. I here

[lost laurel]

and

$\beta=3\left(\frac{n}{2}\right)\left(2a+\left(3n-1\right)d\right)-2\left(\frac{n}{2}\right)\left(2a+\left(2n-1\right)d\right)$

[woven radish]

Why am. I here

[lost laurel]

which basically means the sum to the 3nth term is $\alpha+\beta$

[woven radish]

Why am. I here

[stark anvil]

You can find a_n

[lost laurel]

how

I solve the equations, I guess?

ah yes, two unknowns , two equations

it will be a mess though, is there no way around it

[stark anvil]

There is a property

Idk if you can maks use of it somehow

"A sequence is an AP iff the sum of its first n terms is of the form An^2 + Bn where A,B are constants independent if n. In such a case common difference is 2A."

[lost laurel]

hmm

[stark anvil]

If it's nth term is a linear expression in n
a_n = An + B then A is the cd

[lost laurel]

I see

I'll think about these properties

TYSM

[stark anvil]

I'll too

[lost laurel]

.close

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[nova whale]

.close

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[graceful cipher]

maximise $\frac{x}{(x+a)^{\frac{3}{2}}}$, where a is an arbitary constant

[graceful cipher]

the 3/2 is in power

[twilit comet]

u mean
$\frac {x}{(x+a)^{1.5}}$

[woven radish]

ren

[graceful cipher]

yeah

[twilit comet]

differentiate

[woven radish]

therealtdp

[twilit comet]

yes yes anyway differentiate

[graceful cipher]

i did and i got some funky quadratic

[twilit comet]

gib

[graceful cipher]

im getting $x^2 + a^2 = \frac{3}{2} x$

[woven radish]

therealtdp

[twilit comet]

!show

[devout snow]

Show your work, and if possible, explain where you are stuck.

[graceful cipher]

im on a pc

i cant take pics

[twilit comet]

latex?

or desmos

[graceful cipher]

okay wait