help-26

[late crypt]

Wtf

[torpid sparrow]

That is why i wanna see how you did the partial fraction

[fiery badge]

B seems fine

A seems wrong

did you not plug in B = 5 into the equation for A?

[late crypt]

Uhm

Oh

[torpid sparrow]

Hold on

[fiery badge]

A should be 2C + 4

Not 2C - 1

[torpid sparrow]

There is no 5 here as b

[late crypt]

C=-4/3

[torpid sparrow]

B = 11/5

[fiery badge]

?

[torpid sparrow]

B i mean

[fiery badge]

Oh right lmao

You didn't write the equation properly

[late crypt]

?

[fiery badge]

The third one is missing C

[late crypt]

??

[torpid sparrow]

Exactly

[fiery badge]

Should be -B + 2 C

not just - B + 2

[late crypt]

Bruh

[fiery badge]

didn't even notice that lmao

[late crypt]

Wtf

[torpid sparrow]

Better

Now you split into 3 fractions and solve one by one

[late crypt]

Howwww

Theres a y²

[torpid sparrow]

Actually 2 is fine

[fiery badge]

Complete the square

in the first fraction

and then to a sub

[late crypt]

Wym

Complete?

[fiery badge]

Complete the square, become one with the integral, attain transcendence

Fulfil your destiny

[torpid sparrow]

Ok lets go one by one

The first fraction

[torpid sparrow]

You start by putting 1/5 out of the integral

And let the numerator as 2y+11

Come on, work out that

[late crypt]

Wtf

I never saw these formulas

[late crypt]

Why this help tho?

[fiery badge]

Cause you can then do sub

[late crypt]

But I already did sub previously

Double sub??

[fiery badge]

Yes, we're entering the meta game here

we're going deep

[late crypt]

WHATEHEEEELLL

[fiery badge]

2 subs deep

[late crypt]

Whats meta?

[fiery badge]

make sure not to cross the fractions

Ok, enough jokes

lemme write you what you gotta do

I maaaaaaaaay have overcomplicated this

but like, what's 4 more subs amirite

Now just solve as table integrals and return all the subs in order

[fiery badge]

.

[late crypt]

WOAH

[fiery badge]

Your final solution should look something like this

[late crypt]

Omg

[fiery badge]

eh, this can be simplified, I can't be bothered to do so though

[late crypt]

Dw

[fiery badge]

I may have made a mistake somewhere, this function behaves weirdly

[late crypt]

Alr alr

.close

[topaz sinew]

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[topaz sinew]

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[broken fulcrum]

what is this even supposed to mean

[ionic oar]

Do you understand what a rational number is?

[broken fulcrum]

i do understand what a rational number is

[ionic oar]

Right

And in general the square root of any rational number is not always rational?

[broken fulcrum]

yes

[ionic oar]

Do you have a problem in understanding how you'd proceed?

[broken fulcrum]

yes

[broken fulcrum]

i cant understand what this question wants me to do

[ionic oar]

What part exactly?

n is an integer

And that expression needs to be rational

You should consider the fact that the square of every rational number is also rational
nvm

[broken fulcrum]

oh wait yes my bad

[torpid sparrow]

You have to prove the opposite

[broken fulcrum]

?

how do u find all positive n

[torpid sparrow]

Prove that there are no possitive number that satisfy that

[ionic oar]

yeah that makes sense

[broken fulcrum]

i cannot understand the 3rd step of this proof

[torpid sparrow]

You are suppose to make the prove yourself…

The third step is just rationalizing

[broken fulcrum]

bro today is the first time ive studied proofs seriously

[torpid sparrow]

With more reason to give a try

[broken fulcrum]

i need some practice before making my own

[pulsar kindle]

Take it slowly

[broken fulcrum]

okay

[broken fulcrum]

are the numerator and denominator multiplied by sqrt(n+1)-sqrt(n-1) in the 3rd step?

[pulsar kindle]

you can let √(n-1) = k
and √(n+1) = h

which will make it easier

[torpid sparrow]

The opposite

Sqrt(n-1)-sqrt(n+1)

[broken fulcrum]

but like

the answer after the one is multiplied is shown as sqrt(n+1)-sqrt(n-1)

[torpid sparrow]

Oh yeah it is the same

Double -

Anyways, u get sqrt(n-1)-sqrt(n+1)/-2

[broken fulcrum]

yes

[torpid sparrow]

Or sqrt(n+1)+sqrt(n-1)/2

It is the same

That is q/p

So 2q/p = sqrt(n+1)-sqrt(n-1)

[broken fulcrum]

oh

how does that make (n-1) and (n+1) perfect squares

[torpid sparrow]

Because

p/q = sqrt(n-1)+sqrt(n+1)

[torpid sparrow]

And this

So

Do this

p/q+2q/p

[pulsar kindle]

you'll get 3/2

@torpid sparrow is it proof by contradiction?

[torpid sparrow]

You prove that for this to be true both sqrt(n+1) and sqrt(n-1) are rational

[pulsar kindle]

Obviously for n>=1, it's irrational

[torpid sparrow]

The exercise says Positive integers

n cannot be other than that

[pulsar kindle]

So it's basically asking to prove there are no positive integers

[torpid sparrow]

Yes well the exercise asks to find all possitive integers

But the real question is to prove that there are none

[pulsar kindle]

Yup

This is easier to digest I believe

[torpid sparrow]

Anyways, i have to leave now. I think it is pretty easy from here to understand @broken fulcrum

[broken fulcrum]

yes

[pulsar kindle]

Yeah and take your time, proofs take long to understand

[broken fulcrum]

yeah

[broken fulcrum]

wait why is h = 3/2 and k = 1/2

[topaz sinew]

@broken fulcrum Has your question been resolved?

[broken fulcrum]

<@&286206848099549185>

[pulsar kindle]

(h+k)(h−k)=2
h+k and h−k are integers and h>k
⇒h+k=2 and h−k=1
Solving, we get h=3/2 and k=1/2, which is a contradiction.

[broken fulcrum]

how is h+k=2 and how is h-k=1

and what was solved to get 3/2 and 1/2

[sonic escarp]

n+1 = h^2, n-1 = k^2 -> h^2-k^2 = 2 -> (h+k)(h-k) = 2 as h andk are integers h+k must divde 2 which means it is 1 or 2. same for h-k, so
h+k = 2
h-k = 1
sum them up -> h = 3/2

[broken fulcrum]

how did u get that it must be 1 or 2 after dividing h+k with 2?

[sonic escarp]

which natural numbers divide 2?

[broken fulcrum]

(p.s i might ask dumb questions cuz im still in 8th)

[broken fulcrum]

even numbers?

[sonic escarp]

2 is a prime number, right?

[broken fulcrum]

yes

[sonic escarp]

what is the property of prime numbers?

[broken fulcrum]

which property

[sonic escarp]

when do you call a number a prime number?

[narrow cove]

irrelevant to your question but im in 12th and i still ask the stupidest questions

you wont learn unless you ask, so feel free

[broken fulcrum]

when it has 2 factors

[sonic escarp]

which one?

[broken fulcrum]

1 and itself

[sonic escarp]

well (h+k)(h-k)=2, so what can h+k be?

[narrow cove]

oh wait thats smart i didnt think of that

[broken fulcrum]

i am still clueless

wait

2 or 1?

[sonic escarp]

h+k divides 2, the only numbers who do this are 1 and 2.

[broken fulcrum]

ohhhh

[broken fulcrum]

so why is h+k=2 and why is h-k=1

[sonic escarp]

which one is bigger h+k or h-k?

[broken fulcrum]

h+k

oh okay

[broken fulcrum]

do u find 3/2 by simultaneous equations?

[broken fulcrum]

thanks!

[sonic escarp]

but to be fair, i woudl argue in a different and i think easier way.

h^2-k^2=2, we know the smallest difference of two integer squares is 3 (2^2-1^2). so we have the contradiction easier.

[broken fulcrum]

that makes sense

damn

thanks again

.close

[topaz sinew]

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[noble marsh]

How do I find the sum of this series through telescoping?

[crystal goblet]

$\sum_{n=1}^{\infty} \frac{1}{2n} - \frac{1}{n+1}+\frac{1}{2n+4} = \frac{1}{2} \sum_{n=1}^{\infty} \frac{1}{n} - \frac{2}{n+1}+\frac{1}{n+2} \newline = \frac{1}{2} \sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1} - \frac{1}{n+1} +\frac{1}{n+2}$

[thorny flame]

quickdoom

[crystal goblet]

I hooe you can continue from here

[noble marsh]

all the three terms are within the sum btw

[crystal goblet]

Ik

[noble marsh]

oh ok

[noble marsh]

where did the 1/2 come from?

it came from 1/2n but since all 3 terms are part of the sum, isn't that wrong?

[crystal goblet]

It came from the other terms also

Read it

[noble marsh]

oh i see

[noble marsh]

we have 4 terms now but I don't see what I could do next with them

I thought telescoping was writing all the terms out and seeing which cancels with which but apparently that's wrong

[crystal goblet]

It dors

[thorny flame]

quickdoom

[crystal goblet]

How about now

Can you see how to telescope the sums individually?

[noble marsh]

i can kinda see it yea

im gonna try the left one rn

[noble marsh]

ok i have just 1 for the first sum

is that right?

[crystal goblet]

Yeah

[noble marsh]

ok ok epic let me do the second

[noble marsh]

for the second i have -1/2 left

but

[crystal goblet]

Yes again

[noble marsh]

1 - 1/2 = -1/2 right and i cant take the limit of that so that's supposed to be my sum answer

but the sum answer is 1/4

[crystal goblet]

Uh

The left one is 1

The right one is 1/2

So you are left with 1/2(1-1/2)=1/2(1/2)=1/4

[noble marsh]

Oh

right right i forgot about the 1/2 before the sum

what do you think is most important when doing telescoping?

like what should I do if I encounter another excersise similar to this one

should i attempt to simplify it as much as possible?

[crystal goblet]

Im not sure there are any tips i can give other than practice

Do a few of them and you should get the hang

[noble marsh]

alright fair enough

thank you for your help : )

.close

[topaz sinew]

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[noble marsh]

How do you solve a series like this where ln is everywhere?

[topaz sinew]

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[mental hatch]

The actual answer is 9/2

Could anyone give me a little hint about my mess?

[pastel oracle]

What are you trying to find

[mental hatch]

The area between the curves

between x = y^2 and x = y + 2

[mental hatch]

So, could you give me a hint?

[keen venture]

@mental hatch
It's correct until the last addition

Check the bottom line

[topaz sinew]

@mental hatch Has your question been resolved?

[topaz sinew]

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[magic grail]

Hello, good afternoon, I need help with this combinatorics exercise please. I don't know how to approach the exercises.
Ex.20) The elevator of a building carries 10 passengers and can stop at any of the 12 floors of the building.
a) Distinguishing between people:
In how many ways if on the 10th floor exactly 3 people descend?
In how many ways if at most one passenger descends on each floor?
b) If no distinction were made between people, what would be the answers to the questions posed in a?

[topaz sinew]

@magic grail Has your question been resolved?

[magic grail]

pls

[velvet garnet]

hmmm i dont have an answer but we can try togehter!

[velvet garnet]

how about that?

how much work do you have so far?

[magic grail]

hi

[velvet garnet]

hi there

[magic grail]

I don't understand how to approach it

[velvet garnet]

ok, so how many ways can 1 person descend?

[magic grail]

is a different exercise from those I have done before

[magic grail]

12

[velvet garnet]

oh my bad, if on the 10th floor*

[magic grail]

12?

hmm

[velvet garnet]

the key word is descend

so (depending on the prof) you can either get off 10th, 9th, 8th, ... 1st.

[magic grail]

10?

[velvet garnet]

Yup

Now how does it work for 2 people?

(Assuming they can get off on same floors)

[magic grail]

also 10?

[velvet garnet]

They can also get off on different floors

[magic grail]

10 . 10?

[velvet garnet]

Yup

[velvet garnet]

So 3 people would be…?

[magic grail]

10 . 10 . 10

[velvet garnet]

Nice!

[magic grail]

then?

[velvet garnet]

So the second part of a is determining the related

First person has 10 choices

But now the second person cannot get off wherever the first person got off

[velvet garnet]

So how many choices?

[magic grail]

I'm a little confused, but they say that on the 10° floor 3 people go down.

[velvet garnet]

We’ll get there

[velvet garnet]

But first think about 2nd person’s choices

[magic grail]

But wouldn't those 3 people have only one chance to get off? they get off on the 10th floor.

[magic grail]

hmm

is a bit strange

[velvet garnet]

i have to get off discord but here is what i was getting at:

https://math.stackexchange.com/questions/3758034/combinatorics-problem-getting-off-a-elevator

[magic grail]

😦

thanks

[topaz sinew]

@magic grail Has your question been resolved?

[topaz sinew]

@magic grail Has your question been resolved?

[topaz sinew]

@magic grail Has your question been resolved?

[topaz sinew]

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[dusk stone]

calculus help needed dealing with limits, im not sure HOW to solve the problem, or what steps to take to arrive at the solution.

[topaz sinew]

Please don't occupy multiple help channels.

[astral blaze]

you use graph or table as noted.

plot that function on desmos or something

[dusk stone]

ok thanks

[thorny remnant]

Have u tried using lim property

[restive inlet]

double channel

.close

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[royal sky]

the mclaurin serie for sinx

is

x^2n+1 /(2x+1)!

so if i time 9x to it isnt it just x^2n+10 /(2x+1)!

[abstract wadi]

this is x^9 times that, not 9x.

[royal sky]

oh

oh

oh

riht

oops

[astral blaze]

yeah, you can check this by notice that there is no 9

in coefficient

[royal sky]

is it just

wait no

[astral blaze]

$\frac{d}{dx}9x\sin(x) = 9(x\cos(x) + \sin(x))$

[thorny flame]

print("NAME")

[royal sky]

is there a way to do it without like

determining the derivative

this for example

[astral blaze]

you can convolute it

and you can basically do that

[royal sky]

what does that mean

[normal tapir]

you had the right idea here

[astral blaze]

I mean sum of something times 9 is 9 times the sum

[normal tapir]

you just multiplied by 9^x instead of 9x

[royal sky]

yeah 😭

[royal sky]

oh

i just need a way to plug 9 in

[normal tapir]

if you just join the x's it should be fine

[astral blaze]

your idea is good. it just does not work in the more general function

[royal sky]

rn i have (x^(2k+2))/(2k+1)!

but 9 is missing

and idk how to plug a 9 in

[normal tapir]

it's not plugging the 9 in, you just wanna multiply by 9 to that summand

[royal sky]

ah rip

[astral blaze]

here it works tho

[thorny remnant]

Just put it inside the sigma

[royal sky]

yeah i have no idea how to do that though 😭

[royal sky]

like

just put it?

[astral blaze]

anyways, intuitively when you differentiate it, each term will need to multiply by 9. so, you can put 9 in front of the sum

[normal tapir]

all of what you wrote, times 9

[royal sky]

so

[normal tapir]

[thorny remnant]

Yes it's right

[astral blaze]

send it and hope that webwork does not interpret this differently.... oh

[royal sky]

yeah-

[normal tapir]

oh reindex haha

[thorny remnant]

Yep that makes sense

[royal sky]

reindex?

oh im dumb

oh its actually so stupid lol

HAHAHAH

[astral blaze]

I think you see why lol

[royal sky]

yeah

ty

.close

[topaz sinew]

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[pseudo sonnet]

,ti syrexxx

[thorny flame]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[pseudo sonnet]

[normal tapir]

stalker

[pseudo sonnet]

I feel like syrex has been asking questions for 8 hrs

[normal tapir]

ABCD

[pseudo sonnet]

🔡

[pseudo sonnet]

do you not stalk the help channels?

[normal tapir]

not frequently

[pseudo sonnet]

not a true helper, I see

[normal tapir]

i did not choose helper

helper chose me

[pseudo sonnet]

just because helper chose me doesn't mean that I'm free to avoid the helpful life

[normal tapir]

i am helpful when i am

[pseudo sonnet]

[wary tulip]

i am not a true helper

[wary tulip]

i think she's speedrunning after not going to class in a few months

[pseudo sonnet]

I saw

but still, 8 hrs is a damn lot

(has it only been 8 hrs?)

it could be a lot more idk

[pseudo sonnet]

you are better than us

[wary tulip]

i'm not even helpful

[normal tapir]

nor am i unless i am

[pseudo sonnet]

yes you are

[topaz sinew]

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[subtle kiln]

for number 6 can i just use the root test? My class has only covered the root and ratio test so far

[topaz sinew]

@subtle kiln Has your question been resolved?

[keen venture]

You guys have also covered the alternating series test

Well, then again maybe the ratio test is the right way to go anyway

"interval of convergence" is commonly done with ratio test

[topaz sinew]

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[honest quiver]

can someone help me with this

[pulsar kindle]

are N and M midpoints of AD and DC?

[honest quiver]

yes

[pulsar kindle]

Great it's easy to solve then

@honest quiver you need the length of EF right

[honest quiver]

yeah

[pulsar kindle]

is the answer 4.61

@honest quiver

[hollow plover]

Eqn of line be x/8 + y/4 = 1

[restive inlet]

/4 not 6

[hollow plover]

Eqn of parabola is (x-4)² = a(y-0)

[hollow plover]

I am considering AD x acix

[restive inlet]

oh

[hollow plover]

And DC y axis

[pulsar kindle]

the eqn of the line I found is y=-(1/2)x + 4

[hollow plover]

Now parabola satisfies (0,8) so we can get eqn

[pulsar kindle]

and the curve is y=(x-4)^2

[hollow plover]

Yeah both are correct

it varies on the assumptions

[pulsar kindle]

what length did you get cairo

[hollow plover]

I am solving

[restive inlet]

continue with your work

equation of the curve is parabola though

[hollow plover]

,w solve x/8 + y/4 = 1 and (x-4)² = 2 × y

[pulsar kindle]

That doesn't look right

[deft crow]

tbh yh u true

[restive inlet]

the eqn of the line I found is y=-(1/2)x + 4
based on that, you seem to be setting D to be the origin
however with
and the curve is y=(x-4)^2
when x=0, y = 16 not 8

[deft crow]

because u need to solve it first before u going do it in (..)

[restive inlet]

what you actually want is y = (x-4)^2**/2**

[pulsar kindle]

You are right the curve is wrong

[pulsar kindle]

Yes

there

[restive inlet]

i still don't know/see why you're using "6"

[hollow plover]

AD midpoint is N

Ahhh sry

[hollow plover]

Mb

[honest quiver]

tyall

.close

[topaz sinew]

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[dapper vapor]

I'm learning how to verify Trigonometric Identities and while I can solve some identities some are harder for me. This one I just cannot figure out for the life of me and I was wondering if someone more experienced than me could walk me through solving it. I am pretty sure that the reason I can't solve it is because I don't know enough algebra, but I'm not 100% sure.

[astral blaze]

Let me see whether I got your question right or not: $\sec^6(x) - \tan^6(x) = 1 + 3\tan^2(x)\sec^2(x)$?

[thorny flame]

print("NAME")

[dapper vapor]

Yes

How did it work for you but not me?

$ \sec^6x-\tan^6x=1+3\tan^2x\sec^2x $

Weird...

Anyway

Wait

$\sec^6x-\tan^6x=1+3\tan^2x\sec^2x$

[thorny flame]

BlueTint

[dapper vapor]

I'm dumb

[astral blaze]

there you go

I did not solve this yet but my gut tell me that you can write the left side as something times sec^4 which will be the same as another side.

hopefully

I think about that because we usually have a nice identity when it is squared.

[dapper vapor]

Is there a reason you think that? Or is it just from lots of practice?

Oh there we go

when it is squared
What do you mean by it?

[astral blaze]

Like, I deal with $\tan^2(x)$ a lot so I want to make whatever it is into $\tan^2(x)$ for example

[thorny flame]

print("NAME")

[dapper vapor]

Okay

[astral blaze]

and 6 - 2 = 4

that is my guess

I have to write it down and spend some time with it tho

[dapper vapor]

My current Trig Identity skills involve moderate algebra and converting everything to sin/cos

[dapper vapor]

No worries if you don't want to

It's an annoying one

[astral blaze]

ah I see. another simple way

[dapper vapor]

Ooh okay

[astral blaze]

notice that it is difference of the cubic, right?

the LHS

so you can expand it out

[dapper vapor]

Like difference of squares type thing?

I tried expanding that out

This is LHS:

[astral blaze]

$\sec^6(x) - \tan^6(x) = (\sec^2(x))^3 - (\tan^2(x))^3$

[thorny flame]

print("NAME")

[dapper vapor]

Oh, I see

That's not what I did but I can see that working

Because $\sec^2x=1+\tan^2x$

[thorny flame]

BlueTint

[astral blaze]

and you should have square term first then some long polynomial as a second term. $\sec^2(x) - \tan^2(x) = 1$ so...

[thorny flame]

print("NAME")

[astral blaze]

it should be something like $(\sec^4(x)+ \sec^2(x)\tan^2(x) + \tan^4(x))$, $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ if I still remember the formula correctly

[thorny flame]

print("NAME")

[dapper vapor]

Wait I do know difference of cubes

That seems like the right path

Let me try that and I'll get back to you?

[astral blaze]

sure

the rest is... I think substitution and that should be it

[topaz sinew]

@dapper vapor Has your question been resolved?

[dapper vapor]

Okay I've gotten to the point where the denominators are equal. I think that's a start.

[thorny flame]

BlueTint

[dapper vapor]

The 3 and the 1 + are really tripping me up

<@&286206848099549185> Is anyone available?

[astral blaze]

I think the rest is expansion

if you got that

[dapper vapor]

I don't got that

[astral blaze]

notice $\cos^4(x) = (1-\sin^2(x))^2$

[thorny flame]

print("NAME")

[astral blaze]

and the rest is algebra

[dapper vapor]

That doesn't fire any cylinders in my brain

I think I might just be bad at algebra

[astral blaze]

no you are not. it just takes experience

[dapper vapor]

Like I understand why this is true and that I could replace $\cos^4x$ on the denominator with it, but I don't see why it helps me

[thorny flame]

BlueTint

[dapper vapor]

Oh totally but just right now I might not be good enough

It's okay

[astral blaze]

it helps because you can just ignore it now

[dapper vapor]

I'll try algebra-ing it

[dapper vapor]

What do you mean by ignore it?

[astral blaze]

because both side has it. as long as $\cos(x) \neq 0$ then you know your identity is true

[thorny flame]

print("NAME")

[dapper vapor]

Oh, I see!

Of course

Man I really can't algebra this at all. Like I can't even think of a next step.

Even ignoring the denominator

What am I supposed to do with $1+\sin^2x+\sin^4x$?

[thorny flame]

BlueTint

[dapper vapor]

Nevermind I have an idea

Okay the idea has been half-successful

$\frac{1-\sin^2x}{1-\sin^4x}=\frac{1-\sin^4x+3\sin^2x}{1-\sin^4x}$

[thorny flame]

BlueTint

[dapper vapor]

Any hints on the algebra needed from here?

[dapper vapor]

<@&286206848099549185> I will ping since it's been 15 minutes

[trim owl]

Try making perfect square

[dapper vapor]

Like $(1-\sin^4x)^2$?

[thorny flame]

BlueTint

[trim owl]

Yeah

[dapper vapor]

Or do you mean

[trim owl]

Maybe u can do some thing from this

[thorny flame]

BlueTint

[trim owl]

Try all different squares

There is (1-sinx+sin2x)(1+sinx+sin2x) also

[dapper vapor]

$(1-\sin x+\sin^2x)(1+\sin x+\sin^2x)$

[trim owl]

Yeah

[thorny flame]

BlueTint

BlueTint

[dapper vapor]

Is this what you mean? Is this even true?

[topaz sinew]

@dapper vapor Has your question been resolved?

[dapper vapor]

No but I'll close it

.close

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[nimble hearth]

Given
0.60 mol CO2, 0.30 mol CO, 0.10 mol H2O
What is the partial pressure of CO if the total pressure of the mixture was 0.80 atm?

[ruby mural]

Is the volume and temperature constant?

[nimble hearth]

Yes

[ruby mural]

Ok then we can say that Pressure is directly proportional to number of moles
(Coz PV=nRT)

Or we can say P=kn, k is a constant

And total pressure= sum of partial pressures of gases
Use these two things to find it

[nimble hearth]

Ty

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[indigo salmon]

What should be my next step?

[tough nest]

Sum of squares means that you have to write them as a^2 + b^2

the goal is to find a and b for all four of the numbers

45 for example

if you take 6^2

you get 36

and 45 - 36 = 9

which is 3^2

so 45 = 6^2 + 3^2

[indigo salmon]

Is there any of them that can be eliminated? We are working with number theory "Representation as sums of squares"

[tough nest]

eliminated?

[indigo salmon]

Like is are there numbers were the idea of this won't apply? Or am I over thinking it.

[tough nest]

what a terribly written sentence that theorem is

[indigo salmon]

Its the module given to me xP

[tough nest]

oh wait i get it

so the prime factorisation

[indigo salmon]

Example of it.

[tough nest]

any prime in that that is of the form 4k+3

for some k

has to be part of the factorisation either 0 times, 2 times, 4 times etc

[indigo salmon]

I believe so.

Which I already did the prime factorization of the numbers earlier.

[indigo salmon]

.

[tough nest]

so 90 cannot be

[indigo salmon]

90?

[tough nest]

because 11 is of that form

99

sorry

[indigo salmon]

Yeah.

[tough nest]

11 is only once

and 4 * 2 + 3

so it's impossible to write 99 as the sum of 2 squares

45 i gave you :D

[indigo salmon]

Yup.

[tough nest]

80 has no prime factor of that form

490 idk

i think same as 80

but to find them you just have to take the squares of numbers up until they get to the size of the square root of the number

and see which of them sum to the number

[indigo salmon]

I

'll try. Thanks.

.close

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[versed cairn]

just google it

it can vary on school to school / country to country

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[patent light]

should be correct, right?

[topaz sinew]

@patent light Has your question been resolved?

[tough nest]

if h = 0 doesn't A become rank 3?

[patent light]

Yes, I wrote it wrong, it was for h = 1

Right ?

[tough nest]

yes

if h = 1 then rank(A) = 2

[patent light]

Yes

[tough nest]

anything else rank = 3

[patent light]

Can I ask you a question

[tough nest]

yes?

[patent light]

Just one thing but why can I say that dim Im f = rank(A) ?

So in this case , for h = 1 , dim Im f = rank(A) = 2

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[tough nest]

.reopen

[topaz sinew]

✅

[patent light]

I don't understand why I can say this, Is there any theorem?

[tough nest]

i remember there being something relating things

lemme look it up

https://en.wikipedia.org/wiki/Rank–nullity_theorem?useskin=vector

it's this lol

so convenient the name

[patent light]

Thanks !

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[tawdry orchid]

Hi, I integrate the formula by parts, but for some reason I only get 2x cos + x^2 * sinx
I'm not sure how x^2 - 2 is derived in H(x) or how it's - x^2 * sinx in K(x)?

[dapper lantern]

Can you show your work? @tawdry orchid

[tawdry orchid]

It looks horrible, but sure, give me a sec

Oh, I don't know why it posted like that, lemme retry

Not sure if it's legible, sorry

[dapper lantern]

First step is not correct

"ILATE" is not applied

Also it's weird how you do it

Usually you convert u -> du and dv -> v

[tawdry orchid]

So u' = cosx and v = x^2 instead?

[dapper lantern]

Yep

[tawdry orchid]

I still get the same answer, though

[gritty birch]

you need to do integration by parts again for $\int \sin{x} \cdot 2x \ dx$

[thorny flame]

lgkoo

[gritty birch]

also that's integral of (sinx times 2x), not integral of sinx, then times by 2x

[topaz sinew]

@tawdry orchid Has your question been resolved?

[tawdry orchid]

Ooh, that makes sense

Thanks, I got the answer to be H(x) then 👍

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[polar oracle]

What’s the difference between midsegment theorem of a trapezoid and a triangle and the converse too

[neon iron]

there is only one major difference

hint: how many can u draw in a triangle and how many can u draw in a trapezoid

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[fallen nimbus]

I want to see if my answer is correct by comparing with someone elses answer if u are able to solve this, and seeing where i went wrong if I did go wrong somewhere

[topaz sinew]

@fallen nimbus Has your question been resolved?

[urban kite]

am getting a different ans

@fallen nimbus

look at the 3rd step from the bottom

i think u missed the sqrt(x)

am getting :-

$$\frac{2a\sqrt{am}}{k} \left( \frac{1}{2} - \frac{\pi}{4} \right)$$

[thorny flame]

notcarlfriedrichgauss

[urban kite]

i did it in a really weird way , idk much of calc so...

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[mighty nacelle]

can you write 7tan as 7sin/7cos

[mighty nacelle]

or is it 7sin/cos

[fiery badge]

I mean

7sin / 7cos

is literally just

(7/7) * (sin/cos)

which is 1 * (sin/cos)

so no

that's not it

7 * tan

tan = sin/cos

7 * (sin/cos)

which is the same as

(7 * sin) / cos

[mighty nacelle]

ok thanks

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[exotic furnace]

y cant we use u=x^2/2 instead so we get du=xdx & then we get arcsin(u) + c?

[haughty wren]

If you let u=x^2/2, your x^2 in the denominator becomes 2u, no longer an arcsin form

[exotic furnace]

ah right

what if u=x/2 and let x=2u wouldnt that work

oh no it wouldnt oops

[haughty wren]

Then yeah you wouldn‘t get an xdx to cancel the top

[exotic furnace]

okay thank you

[haughty wren]

You‘re welcome

[exotic furnace]

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[polar oracle]

I don’t get it

U can draw

One line

Connecting 2 midpoints

In the 2

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[pallid anvil]

the partial derivative on y is incorrect right?

it should be 5x/(y^3)

[rigid ivy]

why?

[pallid anvil]

because (y^-2)'= -1/2 (y^-3)

taking the derivative gives -1/2 as a factor, not -2

[normal plover]

y^-2 derivative is -2y^(-3)

[pallid anvil]

when you do integrals and derivatives your brain can get scrambled up

i think i confused it with y^(1/2)

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[shut obsidian]

Wrong one

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[devout agate]

I have an end of year test coming up and one question will be trial and improvement

[devout agate]

Are there any tips to make finding the solution faster

This will be on calculator

This is an example question

[digital river]

There are algorithms for this sort of thing, but I don't think you are expected to know them

you could look into Newton's method if you're curious

[devout agate]

It’s a test for end of year 8-

[digital river]

Yeah, most of these require calculating derivatives afaik

[devout agate]

•-•

How do I make reasonable estimates

To then get the answer

or do I have to actually do trial and improvement properly

[digital river]

Just intuition I suppose? We never learned this in my school

[devout agate]

ah ok

[digital river]

5 is too low, 6 is too high, so just having a sense for where exactly in the middle to guess

[devout agate]

yea

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[warm swift]

Can someone check my work plz

[rigid ivy]

$y=4^{x^2+\log 4x-g(\sec x)}$?

[thorny flame]

SWR

[warm swift]

Yes

[tawdry skiff]

i think its y'??

[warm swift]

Yes finding y prime

[rigid ivy]

Looks good but you're missing some parentheses. Also, are you sure that $\log$ means $\log10$? It can sometimes also mean $\ln$, so just be sure you know which one your teacher wants

[thorny flame]

SWR

[warm swift]

Yeah it’s base 10. Thank you

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[wise anchor]

I understand how to do a part but idk how to do b part

[neon iron]

for a quadratic equation having roots of oppsite sign

what sign would the products of roots have ?

[fluid compass]

-ve

[wise anchor]

wait what

[fluid compass]

woah we have same person on our dp

[neon iron]

?

[meager dawn]

who taught y’all this abbreviation

i saw this in my calc 2 students work

and it drove me crazy

[cinder sequoia]

i was so confused reading this at first and it's nauseating

takes same effort to just say > 0 or < 0

pos vs neg

idk

[rapid wyvern]

oh that means negative

[fluid compass]

negative mb

[wise anchor]

wait so how do yousolve this 😭

[loud oasis]

it's apparently used in engineering

[cinder sequoia]

ah this explains everything

[meager dawn]

sorry we derailed your help channel

[neon iron]

so they used c/a <0

and after that they used wave curve method

[wary tulip]

i think it's an india thing

everyone i've ever seen use it has been indian

[wise anchor]

what is the wave curve method

[neon iron]

yes

[hollow plover]

Product of roots is (9+2k)/k no?

[neon iron]

you missed the 2k

[hollow plover]

I confirm !

[neon iron]

cairo

you are indian ?

[wary tulip]

@noble laurel see i told you

[neon iron]

i thought you were from egypt

"Cairo"

[hollow plover]

What

[neon iron]

capital of egypt

[hollow plover]

Cairo is the capital of egypt

Have you ever seen someone named after a capital

[neon iron]

you are the first

xD

leave it

[normal tapir]

George washington was named after washing dc

[neon iron]

it is used to determine for what range of K the given function is positvie or negative

[wary tulip]

catgirl pee must be from catgirl pee

[normal tapir]

I'm from ure mum

[hollow plover]

I think itz getting worse

[wary tulip]

i'm not gonna gonna be able to recover from that one

[neon iron]

@wise anchor

you can use any other method you are aware of

[hollow plover]

Bro casually left the chat

[neon iron]

?

[normal tapir]

slayla, receiver of being slayed

[hollow plover]

@wise anchor

[normal tapir]

[wary tulip]

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[latent solar]

i dont understand question b

[hollow plover]

It says

To find two points

Where f'(x) =20

[pearl fog]

im pretty sure the way you find them is to find f'(x)=20 for the 2 x'es

[hollow plover]

@latent solar ^

[latent solar]

but if it says f is 20, do i automatically know that it's asking for f'(x) = 20?

i thought it mean when f(x) = 20

[hollow plover]

,w 3x²-12x+5 =20

[thorny flame]

Results provided by WolframAlpha

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

Requested by itzmecairo

[muted crypt]

It says gradient of the graph f

[hollow plover]

Gradient refers to slope

[pearl fog]

its saying the gradient of it is 20, and f'(x) is just the gradient of the function at point x

so, by searching the x where f'(x)=20 your searching the x where the gradient of f(x) is 20

[latent solar]

how would I solve for this on my calculator to find two x points?

or i can js trace on the graph

[pearl fog]

by question a, you already know the function that f'(x) is

could you show what you got for a?

[latent solar]

3x^2 - 12x + 5

[pearl fog]

yes, f'(x)=3x^2-12x+5, so if we plug in 3x^2-12x+5=20, you can change it so that it becomes
3x^2-12x-15=0
x^2-4x-5=0
and you can solve this quadratic
(x-5)(x+1)
x=5, x=-1

[latent solar]

ooh ok got it now

tysm!

[pearl fog]

if you dont have any more questions you can close this channel

[topaz sinew]

@latent solar Has your question been resolved?

Channel closed

Closed by @latent solar

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[valid ermine]

Can someone help me intuite what B is here?

[wary tulip]

not sure what you're looking for. do you understand all the things defined there?

[valid ermine]

Yes except B

Its a proof for for a compact sub set

Compact Set sorry

B is x such that F contains a finite subcover of Sx

So is B a subset of x, that always covers $S_x$?

[thorny flame]

Sands

[wary tulip]

B is a subset of x?

B is a subset of S

[normal tapir]

elements of B are x values

[valid ermine]

so the set Sx is growing as x increases

[wary tulip]

as in S_x is a subset of S_y if x < y?

[valid ermine]

F is a open cover of S

I have no idea what S_y is

It literally says it there lol

F is an open cover of S

[wary tulip]

sorry i misread that shouldn't have 'd it

[valid ermine]

Okay so B contains the elements of x such that F contains a finite sub cover of Sx

so B is the finite cover of S?

where F could be infinite?

[wary tulip]

that's the one i wanted to

[valid ermine]

So Sx is growing right?

as s increases

[wary tulip]

yes growing in this sense

[normal tapir]

if $x < y, S_x = S\cap (-\infty, x) \subseteq S\cap (-\infty, y) = S_y$

[thorny flame]

catgirl pee

[normal tapir]

that's what slayla is saying

[valid ermine]

So basically S_y is some other later point in S and S_x is growing toward S_y?

[wary tulip]

sure

if you increase x

[normal tapir]

[wary tulip]

you're saying it kinda weird tho

[normal tapir]

S_x, and S_y are sets

x, y are real numbers

[valid ermine]

Sure okay got that bit

[normal tapir]

as x -> infinity, then S_x -> S incest reals

[valid ermine]

okay, so S_x grows to S

So eventually S_x will equal S ?

[wary tulip]

yep

for any x greater than or equal to the largest element in S

[normal tapir]

i just realized

[valid ermine]

Ack got that

[normal tapir]

S_x

i could have been saying sex this whole time

[wary tulip]

no sex here just proofs about compact sets

[valid ermine]

Okay, I understand what S_x is doing

But what is B ?

I get that F is an open cover of S as well

[normal tapir]

so for a particular x, consider Sex

then ask the question

does F have a finite subcover of Sex

if the answer is yes

put the x in the B

if the answer is no, then goodbye ex

[valid ermine]

Hows that possible because its already assumed that F is an open cover of S_x? so wouldnt B just contain every element of x?

[wary tulip]

you don't really know what you can cover with only finitely many sets from F at this point

if you could use infinitely many then yea you can just use all of them and cover S so you also cover S_x for any x

[normal tapir]

^

F covers S

[valid ermine]

Thanks for your help. I hjave no fucking idea wqhat your talking about.

I have no respect for this branch of math, just because of this reason.

.close

[topaz sinew]

Channel closed

Closed by @valid ermine

Use .reopen if this was a mistake.

[normal tapir]

we don't know if F has a finite covering of S

oh.

we failed

[wary tulip]

i have never seen a math ragequit like that before

[normal tapir]

i don't think i've ever seen a math rage quit in real life

then i join mathcord and i see so many

[wary tulip]

[normal tapir]

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[topaz sinew]

Please don't occupy multiple help channels.

[onyx lance]

oops sorry

anyway

where did I go wrong

tho?!

[ornate magnet]

In 2nd line

9-9a-3b

[neon iron]

...what?

Go through what I did pls, I'm questioning my process now. Did I get your question right? I thought I had to find the values of A, B and C. That is the question right?

[topaz sinew]

@onyx lance Has your question been resolved?

[onyx lance]

what’s wrong with my approach tho

sorry pls disregard my answer for B and C

noticed an error

but what’s wrong with my answer for A

[neon iron]

You didn't multiply properly in the sub into 1 part

Look carefully

You didn't multiply 18 by 2 when you were opening the brackets

4A + 2(6A -18) is 4A + 12A - 36

You wrote 4A +12 A -18

[onyx lance]

copy pasting what I wrote in another server

even after correcting it

I still don’t get A = 1

[neon iron]

Hmm

[onyx lance]

which seems to be the correct ans

[neon iron]

Now continue from there and show me what you did

[onyx lance]

this is not looking good man I was learning complex numbers and integration by parts just a few days ago and now I’m struggling with basic simultaneous equations

[neon iron]

Haha

See, always try to simplify before you solve

And try not to take it into fractions

And use the elimination method before the substitution method

And you'll get there

Go through what I did. I started with the simplest expression and tried to simplify it further

[onyx lance]

,rotate

[onyx lance]

ignore the ones split by the line at the bottom

C = 2.25, B = -2.25, C = -18

[onyx lance]

what I don’t get is how sometimes when I use substitution it just does not work and sometimes comparing coefficients work

which is kind of confusing because shouldn’t they all work?

[neon iron]

Why don't you substitute these values back into those expressions and see if the equations hold

[onyx lance]

no they don’t 🥹

[neon iron]

Yeah

I tried with my values and the equations hold

[onyx lance]

wat went wrong with my methodology though

[neon iron]

You are making it too complicated and getting lost in it yourself