help-13

[wanton sail]

not fun

don't go for it xD

[simple flare]

I wrote

But not sure correct or not

[wanton sail]

I gotta go to a meeting but I'll prob be back in around an hour, I don't think the z limit is correct though

[simple flare]

Okay, nvm, I’ll just use back spherical coordinate first. Anyway thanks for your help

But I think this bot will close automatically?

[wanton sail]

np! wait I think I can just type it out

the z upper limit should be $$f(x,y)$$ where $$f(x,y) = \begin{cases}\sqrt{x^2+y^2}&x^2+y^2<\frac92\\sqrt{9-x^2-y^2}&\frac92\le x^2+y^2 < 9\end{cases}$$

[wraith dagger]

Eric Tao

[wanton sail]

it's not worth exploring that tbh

[simple flare]

Okay, it’s way complicated 🫠

Anyway, thanks for your help

.close

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[turbid harness]

i basically reached this after a lot of trying $\\ \frac{9-3e^{-i\theta}-3e^{i(N-1)\theta}+e^{i(N-2)\theta}}{10-3e^{-i\theta}-3e^{i\theta}}$

[wraith dagger]

LicensedDumbass

[turbid harness]

nvm its wrong i didnt expand the N-1 to the 3 and cancelled

<@&286206848099549185>

,rotate ccw

[cedar kiln]

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[open swallow]

I already solved a but for b should I be using division method on the formula I got for I'?

if so what do I do with the c when integrating because the formula I got for I'(t) was
I'(t) = C(I'(t) - I'(t)^2)

do I just have to treat it like a constant? but wont I went up with multiple c's after I integrate?

[cedar kiln]

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[open swallow]

<@&286206848099549185>

[cedar kiln]

@open swallow Has your question been resolved?

[dawn junco]

You shouldn't have derivatives on the right side of your equation

[dawn junco]

I think they want you treat it as a parameter of the problem

Like imagine a country asks you to give them the evolution of the infected population for whatever virus

They know c=0.05 for some reason

You just replace c by 0.05 before solving the equation

It's pretty lunch like when you're solving y' = ay

You don't want to solve for a

You just want to see the different solutions depending on the value of a

[open swallow]

oh yeah oops those slipped in by accident

[jaunty mural]

???????

No random ghost pings please.

[open swallow]

?

I only pinged helpers

[dawn junco]

What about the rest ?

[open swallow]

wym

[dawn junco]

Like the second part of your question

about C

@open swallow

[open swallow]

oh uh

actually I think I figured it out

[dawn junco]

okok

[open swallow]

sory tysm though

[crimson sedge]

meow

[dawn junco]

.close

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[ashen magnet]

how would u simplify these expressions

[crimson sedge]

factor

for the second one, you might need to test for roots in order to factor the numerator

[ashen magnet]

i’ll try that

[ashen magnet]

u can’t factor (a)

[crimson sedge]

yea (a) is already fully simplified

[cedar kiln]

@ashen magnet Has your question been resolved?

[ashen magnet]

do u know how b is done?

i was trying to work it out thru polynomials

[rapid wave]

@crimson sedge

[crimson sedge]

you use rational root theorem and synthetic division

do you know about that stuff?

[ashen magnet]

algebraic long division?

[crimson sedge]

yea

[crimson sedge]

(a) is already simplified, you just leave it

[ashen magnet]

ah

alright

[ashen magnet]

i’ll try doing this for b

[crimson sedge]

you don't just do long division

you use rational root theorem and test roots

[ashen magnet]

oh alright

thanks

🙏🏼

[rapid wave]

Ah I remember doing this in middle school

Memories

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[simple osprey]

hi i need help

[crimson delta]

hmm not sure if there is a smart way to do this. but as step 1 I would get a common denominator

then it's much easier to add them and check whether they add to 1

[cedar kiln]

@simple osprey Has your question been resolved?

[simple osprey]

ill try tyy

[cedar kiln]

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[tawdry sparrow]

I got another question i was confused with the prev i asked

Where does thr 1/2 comefrom again?

[ocean badger]

Because du = 2x, and you only have x in the integral. So you multiply by 1 (2/2)

and leave the 2 in the integral for the 2x

and pull 1/2 out

Would you like me to write it down and send a picture of each step ?

[tawdry sparrow]

Alright i got a little confused

This is substitution right? Or do you do this with other methods aswell

[ocean badger]

This is usbstitution

[tawdry sparrow]

Ahh i seee now thanks

I gotta go rn to school thanks so much

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[jade vessel]

Need help with an exercise, it should be solved with the extremal principle, seems obvious, but i dont know how to apply it here. There is a finite amount of points on a plane with a property such that every line connecting 2 points from the set B also connects the 3rd point from set B. Prove all the points are collinear

[cedar kiln]

@jade vessel Has your question been resolved?

[dire geode]

probably proof by contradiction

if there isn't a point on the line, then the slope with this point with any other point doesn't intersect the other collinear points

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[reef lynx]

So Im basically bringing this back up as im stuck on what the question wants

[reef lynx]

this is how far ive gotten

we know that p=-3 or p=2

making
a=1/8 if p=-3
and
a=4 if p=2

which one do I use and can someone tell me what "the quadratic equation which has the roots..." means?

[cedar kiln]

@reef lynx Has your question been resolved?

[reef lynx]

<@&286206848099549185>

[cedar kiln]

@reef lynx Has your question been resolved?

[grave pumice]

Uhh..well,there's a bit of mistake there.

Loga.logb should be log(a+b)

Not log ab

[grave pumice]

I think,question wants u to find out the equation from roots

Usually we solve an equation,and get its roots..but here,instead of that,the roots are given and u need to find out the equation

Quadratic signifies that,the equation we have has highest power of 2

I think,it can be solved using properties of polynomial equations

[grave pumice]

Uhuh..sorry.I thought u wrote it wrong in the second line,I didn't notice the other mentioned info 🥲

[reef lynx]

thats alright I am just very lost at this point :/

[grave pumice]

Usually,such kinds of problem have a type of arrangement and we dont need to find everything inorder to find the equation..but for this one,i see no pattern

Do u know properties of polynomial equations?

[reef lynx]

I wasnt taught using english so Im not sure what that is

could you give an example?

[grave pumice]

Yes,I was just thinking of giving out an example

Wait

[reef lynx]

oky

[wraith dagger]

saintpuchi

[grave pumice]

This one is similar to your problem,just that,its way more simplified

Inorder to solve such kind of problem,we use properties of polynomial.Let me show u how to approach this one,then maybe u will get an idea about how to solve yours

[wraith dagger]

saintpuchi

[grave pumice]

This is the property of polynomials.(similarly,there are properties for cubic and more powered equations,but yours is a quadratic one,so this should do)

[wraith dagger]

saintpuchi

[grave pumice]

Now,the equation we want to find out,has roots 1/alpha^3 and 1/beta^3 ...we can find portion indicated by "a" and "b" in the standard equation using these roots

We had a format over here,we didnt need to go through trouble of finding alpha,beta inorder to solve it.Rather we could way easily, solve it by replacing values.
I was trying to search for similar pattern in your problem

But I couldn't see any,so :((

[grave pumice]

Ohho ,what is wrong with me today..I wrote formula for alpha^3+beta^3 wrong..it should be -alpha beta..not +alpha beta

But i hope,u got my point,tho the calculations here are wrong :/

[reef lynx]

Im sorry for the late reply

I am just very lost

I'll close this for now, its just hurting my brain and ill come back to it later

.close

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[reef lynx]

thanks for the help

[cedar kiln]

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[willow island]

it's physics but how can they just do the power of -1 and add up the denominators

[sacred stone]

$\frac{x}{\varepsilon_{0} A}+\frac{d-x-\ell}{\varepsilon_{0} A} = \frac{x+d-x-\ell}{\varepsilon_{0} A} = \frac{d-l}{\varepsilon_0 A}$

[wraith dagger]

秋水

[willow island]

yea but the normal formula is $\frac{\varepsilon_{0}A}{x}$

[wraith dagger]

Ruffy🎄

[willow island]

and here they

just flipped it upside down with a ^-1

to sum up the denominators

[fair geyser]

that's the physics

[willow island]

ah wait

I understand

yea it was the physics

thanks!

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[fierce python]

l

[cedar kiln]

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[thick snow]

What is the 4th root of negative 1?

[fair geyser]

,calc (-1)^(1/4)

[wraith dagger]

Result:

0.70710678118655 + 0.70710678118655i

[thick snow]

Oh

[livid hound]

there are four 4th roots, do you need all of them?

[thick snow]

How is the result the way it is?

[thick snow]

So there are 4 solutions?

[thick snow]

If by any chance you know

[fair geyser]

you can put a minus at either part or both

[livid hound]

have you started the complex numbers topic yet?

[thick snow]

I'm turning 10th grade after the summer break

[thick snow]

I did look up what it is, but not very strong at it

This question just popped up in my brain and when I press the calculator it shows an error

[sage forge]

Because there is obviously no real number 4th root of -1

[thick snow]

Oh, okay

[sage forge]

But there are imaginary roots as Ramanov pointed out

[thick snow]

Will that be taught in higher grades?

like for questions like this

[sage forge]

Not until a Level (I can only talk about Germany)

[thick snow]

When in Germany did you learn about this topic?

[sage forge]

Internet. I'm between university and school right now. But if you study mathematical physics you'll get to know them right at the beginning

[thick snow]

So is that at the beginning of university?

[wraith pebble]

idk about other places but in England if you choose to study further maths then you will do it in year 13 ( grade 12 )

[sage forge]

That's cool :)

[thick snow]

Oh, okay, thanks!

[wraith pebble]

actually i would assume its the same for Germany if you do a levels too

[balmy apex]

we learned about complex numbers in year 8

[thick snow]

Which part of the world do you live in?

[balmy apex]

germany

[thick snow]

That's cool

Is that when you're 13-14 years old?

[sage forge]

Hello, there

[balmy apex]

no

9th grade is when you're 13/14

and well for some also 10th

[thick snow]

Here in Canada 9th grade is 14 to 15 or 13 at the beginning of the school year

[balmy apex]

ew tobias

[balmy apex]

hm

[thick snow]

It's really cool that you get to learn that in such a young age

[balmy apex]

school math is bs here they don't teach you anything

[thick snow]

Same, I'll still be 14 as well

[balmy apex]

we took 8 weeks to learn about powers

lmao

[thick snow]

Same

That is why I started to take online courses

[balmy apex]

but on the upside, I don't even have to show up to class anymore and still get an A+

[thick snow]

That is true

[balmy apex]

anyhow

[sage forge]

Did you about them in depth or was it just like an excurs?

[balmy apex]

I held a presentation about them but no one underrstood shit lol

that reminds me about my presentation about

induktion des kleinen gaußes

"hä warum brauchen wir das denn überhaupt? können wir nicht einfach alle zahlen in den taschenrechner eingeben und zusammenrechnen?"

[sage forge]

Haha

[sage forge]

Do you still need the roots or can you/we close the channel?

[thick snow]

Oh yes, sorry, I forgot to close the channel

Well, I really appreciate you all for answering my questions

.close

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[tall dome]

so lets say i concluded angle U + angle uxy equaled angle T and angle TZY

[tall dome]

what postulate/theorem is that

essentially what would i write in a proof

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@tall dome Has your question been resolved?

[tall dome]

<@&286206848099549185>

[cedar kiln]

@tall dome Has your question been resolved?

[jaunty thunder]

either use angle sum of triangle or exterior angle of triangle.

@tall dome

[tall dome]

thank youuuu

.close

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[quartz vale]

can someone explain this?

what did they differentiate both sides, w.r.t?

[reef venture]

A

dE/dA then they transposed the dA

[quartz vale]

why doesnt the left term in RHS have a dA then?

[reef venture]

they transposed the dA

[quartz vale]

typo

[reef venture]

hmm it should tbh

[quartz vale]

also where does (-at) come from?

A^2 × derivative(exp(-at)) remains the same right?

[reef venture]

i dont even know why they used the product rule

e^(-at) is constant

[quartz vale]

t is a variable tho

time

[gaunt hamlet]

Even if they used the product rule, it doesn't explain the multiplication of (-at)

[reef venture]

yeah but wrt to A its constant

[quartz vale]

oh right

[gaunt hamlet]

If anything, they'd be multiplying by the derivative of (-at)

[reef venture]

or is it given that t is a function of A?

[quartz vale]

no

E is a function of t, is all

[gaunt hamlet]

Is there any context? Can we see anything before the image?

[quartz vale]

hmm it's a phy ques ... theres nothing before this in the sol

there is more after tho

idt thats relevant?

[gaunt hamlet]

What's the original question

[quartz vale]

The energy of a system as a function of time t is given as E(t) =A^2 exp(-at), where a=0.2 s^-1. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 sec is

[gaunt hamlet]

@quartz vale I see now

The first line is a typo

Or, third line

That's supposed to be multiplying -a dt, not -at

It's saying the differential of E is the differential w.r.t t + the differential w.r.t A

[quartz vale]

how you can you take w.r.t?

i thought they did w.r.t A?

also where does the (-adt) come from?

is (-adt) = dA? that would make sense honestly

[gaunt hamlet]

They did both. If we have f(x, y), then df = ∂f/∂x dx + ∂f/∂y dy

I know E is technically single variable, but it's effectively multivariabled in this problem with variables A and t

[quartz vale]

oh i see

i dont get the calc involved but ig i will when i learn it

thank you

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[crimson sedge]

f(x):cubic
f(2)=f(5)=0
x∈[2,inf), then f'(x)=0 has 1 root
g(x)=|f(x)f(2a-3x)| is differentiable in every x
g(9a)/f(3a+1)=?

[crimson sedge]

so f(x)=c(x-2)(x-5)(x-d)

and yes

thats it

<@&286206848099549185>

anyone that can proceed?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[haughty cloud]

what rule is applied here

[hazy minnow]

rule?

are you being asked the solutions to that equation?

@haughty cloud

[broken osprey]

@haughty cloud

[haughty cloud]

yes

what are the steps to get -x +5

from the first equation

[hazy minnow]

I don't think that is the question here.

[haughty cloud]

how do you get from this

[hazy minnow]

you need to find the solution to the equation?

[haughty cloud]

to -x +5

[jovial smelt]

you have -1-x = -(1+x)

since (1+x) appears on the numerator, it cancels out with the denominator, leaving (x-5)/-1

which simplifies to 5-x

[hazy minnow]

oh my fault.

[haughty cloud]

but the answer is -x +5

[jovial smelt]

5 - x = -x + 5

[haughty cloud]

ah okay

.close

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[crisp bough]

<@&286206848099549185> how do i crack this problem

[crisp bough]

Am i correct

[cedar kiln]

@crisp bough Has your question been resolved?

[crisp bough]

ayudame

por favor

lo necesito

[crisp bough]

WOULD HAVE BEEN A 100P ERCENT

lo l

.close

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[crisp bough]

.reopen

[cedar kiln]

✅

[crisp bough]

.close

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[versed pilot]

Hey, so i'm looking to learn this kind of propperties for functions.

I know function 1 has propperty b, and function 2 has propperties a and d, and function 3 has propperty b. However, as for the rest, i can't really tell.
I tried looking for resources on function propperties but it tends to lead to other kinds of stuff. Could anyone spare some enlightment?

[versed pilot]

i could also say function 7 also has propperty b

and 4 has a

[cedar kiln]

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[patent bone]

Three books: A,B,C together have 364 pages, book A has 25% less pages than book B, book C has 50% more pages than book B. How many pages does the book B have?

[marsh vapor]

let a, b, and c be the number of pages of books A, B, and C respectively

if in total three books have 364 pages

how can we show that by using a, b, and c?

[patent bone]

So i wrote A down as 75/100 and C as 150/100

[marsh vapor]

answer my question please

[patent bone]

A + B + C

[marsh vapor]

a+b+c=364

[patent bone]

yes

[marsh vapor]

book A has 25% less pages than book B

how can we show this relation by using a and b?

[patent bone]

A is 75/100 of B

[marsh vapor]

so

a=(3/4)b

or 4a=3b

[patent bone]

okay

[marsh vapor]

next

[patent bone]

C is 150/100

[marsh vapor]

book C has 50% more pages than book B

b and c?

[marsh vapor]

of B?

[patent bone]

yes

[marsh vapor]

c=(3/2)b or 2c=3b

so we have

a+b+c=364
4a=3b=2c

right?

[patent bone]

yeah

[marsh vapor]

since we know the relation between a, b, and c

we can do the following

4a=3b=2c=k

we’ll use this k now

a=k/4
b=k/3
c=k/2

put these in the first eq

we’re asked to find b

so

,w k=336, b=k/3

[wraith dagger]

Results provided by WolframAlpha

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

Requested by HeadShotCem#9237

[patent bone]

Yeah thats it

[marsh vapor]

👍

any questions?

[patent bone]

I think im good

.close

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[novel topaz]

if sin + sin^2 = 1, find the value of cos^12 + 3.cos^10 + 3.cos^8 + cos^6 + 2.cos^4 + 2.cos^2

[random shale]

Keep in mind with trig functions if you can find the value of sin, you can find the value of any trig function with that angle

So maybe use first equation to find value of sin, then find the value of cos using that and then ur done as u just put that in

[novel topaz]

i tried applying sin = cos^2 but i get stuck in the middle

[muted bear]

Try factoring

[novel topaz]

Ok i got it

.close

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[wary bramble]

Hello, I'm confused on how to factors this

[muted bear]

look for any patterns that you can use for factoring by grouping, the coefficients seem to follow a pattern

if you want a more helpful hint, usually try grouping the first two terms and last two terms and factor out anything in each one separately, you should get something that is the same on both parts

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[mortal copper]

How to do this with scientific notation?

[mortal copper]

so if i have 1000 gram?

i need to write it in scientific notation

[long arrow]

$$\frac{g}{cm^{3}}=\frac{\frac{1}{1000}kg}{\Big(\frac{1}{100} m\Big)^{3}}$$

[mortal copper]

7.5*21000000000=157500000000

thats the gram amount

[wraith dagger]

Modus

[mortal copper]

ok thx hmm

not sure how i would write in tho

x*10^y kg

157500000000 grams

[long arrow]

simplify expression I've sent, can you?

[mortal copper]

not sure what you have done there

[long arrow]

u know 1kg = 1000 grams, right?

[mortal copper]

ofcourse

[long arrow]

so from here (u can divide both sides by 1000) we have 1 gram = 1/1000 kg

you agree with me?

[mortal copper]

i dont really understand that equation exactly no

[long arrow]

1 kg = 1000 grams, then what's 1 gram equal to

u can use proportion if you want

and cross multiply then

[mortal copper]

should the number just be 1000 smaller?

157500000000/1000

or whatever grams u have

[long arrow]

if you want to convert grams into kilograms then yes

1 kg = 1000 grams
"x" kg = 1 gram
-> x = (1 kg * 1 gram) / 1000 grams = 1/1000 kg

I want to show u how to convert it in general

[mortal copper]

oh i think maybe i over thought it a bit lol

since i have to write in scientific notation

so my number 7.5*21000000000=157500000000 grams

i could write as...

[long arrow]

and this trick will be useful also for converting other units

[mortal copper]

1.575 × 10^7 kg

(15750000)

should be right

its the mass of the earths core

thx 🙂

[cedar kiln]

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[mortal copper]

Not sure how to answer the last questionmark, the density of solid earth?

[mortal copper]

probably just all of em together?

[jaunty thunder]

density of Earth = total mass of Earth/total vol. of Earth

@mortal copper

[mortal copper]

ok

thx'

the thing is i dont have the total mass of earth @jaunty thunder

but guess its no secret huh 😛

[jaunty thunder]

You have density and volume of each layer, so you can calculate the mass of each individual layer.

[mortal copper]

oh right lol

thought wrong about it i think

thx

192260000000 / 1713400000000 = 0.11

not sure that is right tho

@jaunty thunder

density should be 5.5 g/cmi think average

[jaunty thunder]

Could u list the steps for me to see, thx.

[mortal copper]

i read that is the averege at least

yes

21000000000+170000000000+380000000+880000000 |

150000000000+560000000000+1100000000+2300000000+1000000000000

192260000000 / 1713400000000 = 0.11

😛

not sure other is right tho but i think so

oh i made a answer before on solid earth not sure that is right tho, its not from this calculation

i just used the avarage 5.5 cm/g i found online

[cedar kiln]

@mortal copper Has your question been resolved?

[mortal copper]

<@&286206848099549185>

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@mortal copper Has your question been resolved?

[mortal copper]

.close

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[mortal copper]

how to approach this?

[cedar kiln]

@mortal copper Has your question been resolved?

[mortal copper]

<@&286206848099549185>

[vagrant pewter]

well, say T is the total mass of the earth in grams, then lets do iron for example, we see that iron comprises 35% of the earths crust, so the mass of iron is T*0.35 g, now the number of moles of iron is simply the mass of iron in the crust divided by the molar mass

look at the units here is key, you get $\frac{g}{\frac{g}{moles}}=moles$

[wraith dagger]

llspacebarll

[cedar kiln]

@mortal copper Has your question been resolved?

[mortal copper]

hmm ok

thx

ill try

[cedar kiln]

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[mortal copper]

@vagrant pewter what does g mean?

[vagrant pewter]

grams

[mortal copper]

ok so

[vagrant pewter]

its the masss

[mortal copper]

92300000000/24.3

f.ex.

[vagrant pewter]

is that first number the mass of the earth times 0.13?

seems a bit big

[mortal copper]

hmm

maybe i missed a step

[vagrant pewter]

yeah you need to determine the mass of magnesium first

which is T*0.13

where T is your number for mass of earth

[mortal copper]

seems it is

in grams

[vagrant pewter]

ok

[mortal copper]

according to my math at least

[vagrant pewter]

then its probably fine

[mortal copper]

ok 🙂

also thought it looked big and of

well lets see what teachers says 😛

thanks!

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[hybrid light]

can someone explain this

[vagrant pewter]

you know what it means for a transformation to be "linear"?

[hybrid light]

a function that passes from one plane to another?

[vagrant pewter]

well i was thinking the more algebraic definition, a transformation $T:\mathbb{R}\to \mathbb{R}$ is linear if and only if $T(x)+T(y)=T(x+y)$ and $T(ax)=aT(x)$ for all $x,y\in \mathbb{R}$ and $a$ a scalar in $\mathbb{R}$.

[wraith dagger]

llspacebarll

[vagrant pewter]

you can think of $T$ as just a function from $\mathbb{R}\to \mathbb{R}$ and hence it corresponds to a graph in the cartesian plane

[wraith dagger]

llspacebarll

[hybrid light]

i see, so would i just say that there are two linear transformations given the circumstances that T(x)+T(y)=T(x+y) and T(ax)=aT(x)?

[vagrant pewter]

well there are actually infinitely , many functions that satisfy that

they are all the functions whose graphsa re lines

so all the functions $f(x)=mx+b$

[wraith dagger]

llspacebarll

[vagrant pewter]

then y=f(x) is a line, and these are the only such functions

because any higher polynomial will introduce cross-terms

and any rational function will not satisfy the second requirement

then you can easily check that exponential, logarithms and trig functions dont satisfy it either

and thats basically all the elementary functions from R to R

[hybrid light]

So all linear transformations would be infinite because all the functions f(x)=mx+b and they all look linear and pass through the origin?

Would that be an okay answer for the question

[vagrant pewter]

no, my answer would be that all linear transformations from R to R have graphs that are non-vertical, non-horizontal lines, because they are the only functions that satisfy the two axioms of linearity

and think about why its called a "LINEar transformation" haha

they generalize how lines map R to itself and thats how they got the name

[hybrid light]

i see!

omg tysm sorry for the complications!!!

[vagrant pewter]

nah bro you're cool

hope i helped you understand

[hybrid light]

yes you did ty!!

[cedar kiln]

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[reef lynx]

This question has a lot of holes for me and Im not sure where to start

[reef lynx]

any suggestions?

[crystal raptor]

Maybe consider the derivative of $f(x)\cdot f(x)$

[wraith dagger]

ΣAC

[crystal raptor]

Dot being multiplication

[reef lynx]

yes, but im a bit confused what f(x) even is

[crimson delta]

some function which satisfies those two properties

we don't know more

[reef lynx]

neither do I

<@&286206848099549185>

[wraith pebble]

thats the point, you dont need to know the exact function in order to solve the problem

[reef lynx]

so how do i get the derivative of fx

without knowing what fx is

[wraith pebble]

you dont need to, anywhere that you need to refer to the derivative just write it as f'(x)

[crimson delta]

do you know the chain rule?

or I guess product rule also works here

[wanton sail]

Try using u-substitution

I think that's the most direct method

[crimson delta]

or that

[reef lynx]

I wasnt taught in english so I dont know what those are, I might know if you give me an example but just by terms I mostly dont.

Ive heard of them but I tend to forget

[crimson delta]

product rule: (uv)'=u'v+uv'

[reef lynx]

how would I apply that

[crimson delta]

u=v=f

[wanton sail]

(u-substitution is when you change the variable of integration)

[wraith pebble]

$$\frac{d}{dx} \left( f(g(x)) \right) = g'(x) \cdot f'(g(x))$$

[wraith dagger]

Nathan_

[wraith pebble]

^^for chain rule

[reef lynx]

Ive never seen a chain rule before so this is new

or at least one like that

[crimson delta]

have you seen the product rule before?

[reef lynx]

yes I have

[crimson delta]

ok then use that

what is the derivative of f*f

using the product rule

[reef lynx]

u'v?

[crimson delta]

no

[reef lynx]

f^2?

[crimson delta]

no. we want the derivative of f^2=f*f

[reef lynx]

so 1/3*f^3?

if not then im lost

[crimson delta]

from the product rule: $(f(x)\cdot f(x))' = f(x)\cdot f'(x) + f'(x)\cdot f(x) = 2f(x)f'(x)$

[wraith dagger]

Denascite

[azure horizon]

this is really dumb

[reef lynx]

I

[azure horizon]

you want to integrate f * f' right

i'm just gonna say straight up: integral of f(x)f'(x) dx is 0.5f(x)^2 + C

[crimson delta]

well yes we are working towards that

[crystal raptor]

That's literally what they're working to

[azure horizon]

you were going off on a wild tangent

[crimson delta]

but it's not obvious if you don't know stuff like the chain rule or product rule to be able to just differentiate f(x)^2

[azure horizon]

??

if they don't know the chain rule this is literally impossible

[crimson delta]

its not because the product rule does the same job here

[azure horizon]

oh my god

[reef lynx]

[crimson delta]

back to the point

[crimson delta]

this shows that the derivative of f(x)^2 is 2f(x)f'(x)

and so the derivative of 1/2 f(x)^2 is f(x)f'(x)

but this is exactly what we want to integrate

[reef lynx]

how come f'(x)+f'(x) is just stored as one f'(x) like where you gave 2f(x)f'(x) and not 2f(x)2f'(x)

[reef lynx]

i see that part

[crimson delta]

is $5\cdot 6 + 6\cdot 5$ equal to $2\cdot (5\cdot 6)$ or $2\cdot 5 \cdot 2\cdot 6$

[wraith dagger]

Denascite

[reef lynx]

the first one

[crimson delta]

good

and with f(x)f'(x) + f'(x)f(x) =2f(x)f'(x) it's the same

[reef lynx]

so then i was supposed to read it like 2(f(x)f'(x))

[crimson delta]

well I put the brackets for emphasis

multiplication is associative so the brackets don't matter

[reef lynx]

oky

[crimson delta]

ok. so now using the fundamental theorem of calculus we know that $\int f(x)f'(x) dx = \frac{1}{2} f(x)^2 +c$

[wraith dagger]

Denascite

[reef lynx]

yep

and that =10 according to the question

[crimson delta]

so in our case $10 = \int_a^b f(x)f'(x) dx = \frac{1}{2} f(x)^2 \Big|_a^b = \frac{1}{2} (f(b)^2-f(a)^2)$

[reef lynx]

but theres a b to a thingy, not sure what its called

[wraith dagger]

Denascite

[reef lynx]

oh i see

let me try

I must be missing a -

[crimson delta]

you missed the brackets around (f(b)^2+4f(b)+4)

[reef lynx]

revised

[crimson delta]

yup

[reef lynx]

wow

thank you so much

[crimson delta]

you're welcome 🙂

[reef lynx]

beat that kaisheng

.close

[cedar kiln]

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[delicate dagger]

how do I find the intervals where f is increasing and where f is decreasing?

[runic garnet]

@delicate dagger

[delicate dagger]

yeah

[runic garnet]

What don’t u understand abt this? Like what part is confusing u

[delicate dagger]

can you explain when I use ] and )

and I cant exactly tell how to get the points for the intervals

[runic garnet]

Look at the graph from left to right. If the graph goes from a smaller y value in one spot to a greater y value to the right of it, f is increasing there. The opposite is true for decreasing

[delicate dagger]

can you like give an example for part of the graph?

[runic garnet]

Sure

So we know from -5 to 0 that f(x) is increasing

Why?

[delicate dagger]

oh I see

[runic garnet]

Well it’s because the y value goes from a smaller to bigger value as we go from left to right

[delicate dagger]

so would I put (-5, 0) or [-5, 0) or what?

[runic garnet]

I would put the second option

[delicate dagger]

but why?

oh wait nvm I see

so is (-4, 0) decreasing?

for this graph

[runic garnet]

At -5 the slope is positive, at 0 there is a corner/undefined slope

Is this calculus?

[delicate dagger]

its algebra 2

[runic garnet]

Ah ok

Cuz u do some of this in calc 1

[delicate dagger]

ah ok

[runic garnet]

No

-4 to 0 is increasing

[delicate dagger]

yeah this makes sense

I can finish this now

thans for the help

[runic garnet]

Np

[delicate dagger]

.close

[cedar kiln]

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[hot rivet]

Not sure how to do this

[sick ruin]

What have you come up with so far

[hot rivet]

nothing

[sick ruin]

Do you understand the plane equation

What is this, multivariable calc?

[hot rivet]

Vector

[sick ruin]

?

[hot rivet]

no

[sick ruin]

Do you notice
$$\begin{bmatrix}
2 & 1 & -1
\end{bmatrix} \cdot \begin{bmatrix}
x\
y\
z\
\end{bmatrix} = 2$$ is the same as the plane equation

[wraith dagger]

a.b.s._.0.

[sick ruin]

?

[hot rivet]

yeah

im lost

<@&286206848099549185>

[long arrow]

this one?

[hot rivet]

Yeah

[long arrow]

notice that normal vector of a plane is a directional vector of a line

[hot rivet]

ok

[long arrow]

State that vector and tell me what you get

[hot rivet]

2, 1, -1

[long arrow]

ok

know just use formula for the line passing trough the point and parallel to the vector

[hot rivet]

whats the formula

[long arrow]

We can use parametric form

[hot rivet]

I see

[long arrow]

where point is (x0, y0, z0) and the vector is <a,b,c>

[hot rivet]

hhmm

that looks confusing lol

[sick ruin]

isn’t that just one big Y = MX + B

[hot rivet]

How do use y = mx + B with 3d vector

[sick ruin]

Instead of y,x,m being numbers, consider them as vectors

[sick ruin]

This is what that is

[hot rivet]

So I have vector (2,1,_1)

[sick ruin]

In a way

[long arrow]

yes, u can use vector form also

[hot rivet]

I can say x = 2, y = 1, b = -1

[sick ruin]

No no that’s not what I mean

[sick ruin]

This is what I mean

Imagine the first matrix is “m” and the second matrix is “x”

[hot rivet]

So I can plug the other numbers into there

For x , y ,z

[sick ruin]

the stuff you’re plugging in goes into the second matrix, just like how in y=mx+b the input goes into x

[hot rivet]

So plug point (1,0,3) into that equation

Is that what u mean

[long arrow]

in fact vector form is similar to the parametric

[sick ruin]

No I’m not telling you to do anything in particular

[sick ruin]

I’m showing you the connection between y = mx + b and that vector equation

It’s all interconnected

[hot rivet]

I see but how can I solve the problem lol

[sick ruin]

Probably use that connection to figure it out

Idk

I think it’s better to avoid using the formula

[sick ruin]

But if you just want an answer quickly use this thing

[hot rivet]

This seems confusing

[long arrow]

u can also use symmetric form

[hot rivet]

Im not understanding the formula

[long arrow]

$$\frac{x-x_{0}}{a}=\frac{y-y_{0}}{b}=\frac{z-z_{0}}{c}$$

[wraith dagger]

Modus

[sick ruin]

kunalch it depends how you want to do this

Do you just want to do the problem and get done with it

[hot rivet]

What does X, X0, and A represent

[sick ruin]

Or do you want to understand

[hot rivet]

yeah

Please

[sick ruin]

Ok

[long arrow]

Are you familiar with any formula of the line in R3?

[hot rivet]

No

[sick ruin]

There is your formula

[long arrow]

Mhm, it's hard to use formula you haven't seen before :v

Maybe let's find them out, then try to solve

[sick ruin]

wdym

[long arrow]

He doesn't know formulas for the line and how they work, I guess it's better to learn about them firstly

[hot rivet]

Im just confused why are finding the distance between the points

[long arrow]

because question says they want to?

and did you get your line?

[hot rivet]

It does not say distance

[sick ruin]

This question

Is distance

[hot rivet]

I meant part B

[sick ruin]

Oh

So you’re good with part A then

[hot rivet]

Yeah simply use the distance formula

[long arrow]

In part b) u don't need to find it, you have your directional vector and the point, use any formula to get the line (since question hasn't specified the form)

[hot rivet]

So i can do (x2-x1, y2-y1, z2-z1)

[long arrow]

what is it?, this is formula for finding vector with given points (x1, y1, z1) and (x2, y2, z2) ?

[hot rivet]

Its asking for a equation

Can I do something like this

<@&286206848099549185>

[dire geode]

Show the whole context and ask your entire question so you don't waste people's time like above

[hot rivet]

This is the question

[hot rivet]

Given this info

[long arrow]

this is the equation of the plane, not the line

[hot rivet]

It says line L right, so wouldn't that mean an equation of a line

Like what were trying to find

We are given a plane and a point

[long arrow]

you've all you need, only thing you should do is use any formula for the line and that's all

[hot rivet]

hmm

Ok got it

Im doing it rn

[dire geode]

There are no instructions here

[hot rivet]

I mean use the information from the first screenshot to answer part B (second screnshot) of the multiple part question

[cedar kiln]

@hot rivet Has your question been resolved?

[hot rivet]

Is that correct for part B?

[dire geode]

,rotate

[hot rivet]

Is this good or do I need to simplify more

<@&286206848099549185>

[long arrow]

your vector is <2,1,-1> and you did <2,1,3>

except this is OK, you don't need to right [...] = t using symmetric form

[shadow flicker]

wait lol this is so british core

[long arrow]

u mean c) now?

[hot rivet]

C and D

[long arrow]

what is it

then I'll be able to check

[hot rivet]

2

[long arrow]

wait, your answer is (2, 1/2, 5/2) ?

[hot rivet]

yeah

[long arrow]

ok it's correct

on D), why u did (2+1)^2 ?

[hot rivet]

Ok

my bad

So final answer is

SQRT(3/2)

[long arrow]

now it's ok

gj

[hot rivet]

Thank you

I really appreciate your patience

.close

[cedar kiln]

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[dire tiger]

I need example for a One Sample T-Test 😄

[cedar kiln]

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[storm junco]

hey i recently learned that for an equation like L = (100/m)+4x if you want to get m to the left side you have to multiplt both 100 and 4x by m
makes sense to me now but no im curious on an equation like this
2x-ay=-6
when subracting 2x from the left side onto the right side, why would you not subract -ay by 2x, leaving -ay-2x=-6-2x
i understand this will never solve the equation but im curious on why subtraction would be different

[storm junco]

if u need me to rephrase lmk but that should be good enough

[dire geode]

Your equations are different

[storm junco]

huh

[dire geode]

2x-ay=-ay +2x

[storm junco]

wait

no i think i explained that

ye for the 2x-ay=-6 turns into -ay-2x=-6-2x

because if you subracted 2x from everything on the left side

u would have an infinite loop of -ay-2x=-6-2x

[dire geode]

2x - ay -2x = -ay

[storm junco]

even though that logic is clearly wrong so im asking y

[dire geode]

Not -ay-2x

[dire geode]

No it doesn't

[storm junco]

yep it does not in real math

so im asking why

[dire geode]

What's fake math

[storm junco]

multiplication is different

fake math is bad math

incorrect math

[dire geode]

You're asking y is fake math wrong?

[storm junco]

nooo

[dire geode]

By definition

[storm junco]

why is my example wrong when you do the exact same thing but just a different way with multiplication

[dire geode]

There's no multiplication here

[storm junco]

yep there is not, in my initial explination there should be

[storm junco]

getting m to the left side

you have to do 100/m *m and 4x * m

so why is that different from subtracting 100/m from the right side for another example similar to my very first but not the same

if you would like a different explination please let me know but my current question is in the first block of text

[dire geode]

There's only certain rules in algebra you have to follow. Everything else is a combination of these rules

[dire geode]

This is subtraction used incorrectly

[storm junco]

could you show me to the rule that relates to this?

ik its on that forum

but which one exactly

im looking and throughout all those examples i dont see one that relates

[cedar kiln]

@storm junco Has your question been resolved?

[cedar kiln]

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[cold briar]

decay

yes

no?

np

[cedar kiln]

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[dusky pewter]

Hello!
Can someone explain to me what happened here? I’m solving a derivative and I’m not entirely sure what to do with this fraction with a square root. Did they multiply it on each side or?

[crimson sedge]

6/sqrt(x)=3
3sqrt(x)=6
sqrt(x)=2

[livid hound]

algebra is not something you should have an issue with by the time you're doing calculus

if you are struggling with solving these types of equations, its recommended that you go back and review

[cedar kiln]

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[crimson sedge]

Hello

[crimson sedge]

Why is this equal to 120.1

[livid hound]

its not quite 120.1 exactly.
it's only approximately 120.1

that's what you'll get when you evaluate it

[crimson sedge]

Yeah someone told me the answer but I don’t know how to get it

[livid hound]

plug into calculator

[soft cloak]

Yeah

[crimson sedge]

Okay

I don’t know what I’m doing wrong

I just don’t get that

Maybe I’m making a mistake because the problem is long

I have a question for this one what comes up?

Btw it’s to the power of 12*4

[cedar kiln]

@crimson sedge Has your question been resolved?

[violet flume]

this question isnt clear

[livid hound]

are you using a hand-held scientific calculuator?

[crimson sedge]

No I’m not

[crimson sedge]

I meant what’s the answer for this one

[violet flume]

I'd recommend using a computer calculator like symbolab or something, that gives you all the steps

then if you see a specific step you dont understand, investigate that or ask here

but its not clear if you mean you don't know how to approach the problem, or youre just accumulating small mistakes

[livid hound]

what calc are you using

[crimson sedge]

I was just using my phones calculator

Haha

[livid hound]

bad idea

get a proper one

[crimson sedge]

Okay thanks a lot

Okay that’s probably why there’s lots of mistakes

I’ll use symbolab cause I need the answer to continue my work

Thanks

[violet flume]

there are some on phones like

calculator++

but there are a lot

that are "proper"

still better to use symbolab while learning though

[crimson sedge]

Ohhh okay I understand

[livid hound]

too much paywall for some things

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[hot pivot]

how do I calculate time it takes to move from one location to another with linear velocity,angular velocity and distance?

[dire geode]

Show the original question and equations

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[cedar kiln]

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[dim tiger]

hii

[dim tiger]

i have a small problem in this question

the answer i got is -16cm/m

while the correct answer is -1.6cm/min

i just want to know where did i miss the x10^-1

[meager swift]

may I see your working

[dim tiger]

yes sure

i differentiated both sides with respect to t

and got 2 = ((dh/dt)b + (db/dt)h)

where h is the altitude and b is the base

then replaced dh/dt by its value which is 1

and i got the value of b by the area of triangle = (hxb)/2

which gave me b = 20 cm

so the equation became 2 = (20+10(db/dt))/2

[meager swift]

and

4 = 20 + 10(db/dt)

[dim tiger]

ohh waitt

i forgot to put the value of h=10 while solving

but i payed attention to it now

[meager swift]

ah

[meager swift]

also you forgot the 1/2 on the right here but i wanted to wait until you finished typing

[dim tiger]

now subtract 20 and divide by 10

to get -1.6

[meager swift]

yep and you'll get -1.6

[dim tiger]

which is the desired answer

[dim tiger]

yea i just forgot to type it but i considered it XDD

anyways ty for ur time and sorry if i annoyed you

[meager swift]

yeah you fixed it later on over here

[dim tiger]

i am stupid man i just annoyed you for a small mistake which i payed attention to after focusing a bit more

[meager swift]

no worries lmao you didn't annoy me

[dim tiger]

.close

[cedar kiln]

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[crimson sedge]

Confused a bit on how I could turn this into two standard forms

[crimson sedge]

It’s for a circle.

[rugged palm]

Complete the squares

you will get the standard form with translations