help-27

[plush knot]

Let's plug in x = 1.5 and y = 0

$0 - 2 = \frac{k}{1.5+2}$

[woven radish]

Nonna

[plush knot]

Do you agree?

[mental spire]

Yea

-2

=k/3.5

[plush knot]

Yes, very nice

got any ideas to find k?

[mental spire]

Umm

[plush knot]

$-2 = \frac{k}{3.5}$

[mental spire]

3.5 x -2

[woven radish]

Nonna

[mental spire]

=k

[plush knot]

Yeah!

So what's k?

[mental spire]

7

-7

[plush knot]

Yup!

and we are done

our equation is

$y - 2 = -\frac{7}{x+2}$

[woven radish]

Nonna

[plush knot]

i put -7 instead of k

[mental spire]

Oh ok

So that’s the equation

[plush knot]

Yeah!

[mental spire]

Oh wow

[plush knot]

You can also write it as $y = -\frac{7}{x+2} + 2$

[woven radish]

Nonna

[mental spire]

Oh ok thanks

[plush knot]

Does your teacher require you to write it in the form $y = \frac{ax + b}{cx + d}$?

[woven radish]

Nonna

[mental spire]

Boo

Nope

[plush knot]

Ok

[mental spire]

Thanks

[plush knot]

We went for a different solution than usual

With asymptotes it would have been much easier

[mental spire]

Oh

[plush knot]

But we solved it 👍

If you don't have any questions you can close the channel @mental spire

[devout snow]

@mental spire Has your question been resolved?

[devout snow]

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[foggy wedge]

I was hoping someone could help me solve this one

basically I have to rotate this shaded region about the dotted line

but I dont know how to set it up

[devout snow]

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[devout snow]

@foggy wedge Has your question been resolved?

[devout snow]

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[bronze willow]

mostly, I need a brief explanation for each case.
fyi: I have all the results

[hybrid snow]

What are you trying to find

X and y?

Use geometric mean for all of them

$$6 = \sqrt{12n}$$

Solve for n

[woven radish]

Umbraleviathan

[bronze willow]

and letter B?

u can assist me?

[hybrid snow]

Find the altitude

Use pythag

[bronze willow]

b^2 = 12^2 + x^2

yeah, right?

[hybrid snow]

No

Use your geometric mean to find the altitude

Let $h$, $a$, and $b$ be the altitude and the two sectors of the base respectively,

$$h^2 = \sqrt{ab}$$

[woven radish]

Umbraleviathan

[bronze willow]

I added up the projections 3 and 9, and i did

12

applied pythag

EXPRESS DRAW, OK? xdd

[devout snow]

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@bronze willow Has your question been resolved?

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[devout snow]

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[nocturne zinc]

hey guys

I need help

Do I just find P

by finding torque of 500 N

500 x 2 = P x 2

P = 500 ?

ye

I am figuring it out

[gleaming socket]

what is the pivot here?

[nocturne zinc]

u tell me

I got it btw

[devout snow]

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[odd elbow]

Hi

[odd elbow]

Can anyone tell me what does this 'thick' word mean over here?

I mean

Is it length of the piece, or is it breadth or height l??

[glacial dagger]

Height

[odd elbow]

How

Can u

Explain

Me

Thickness is length

Isn't it?

[main gull]

Not necessarily, it's all based on perspective

[gleaming socket]

so if a person is thick that means they are tall?

[odd elbow]

Over here how can u say thats its a height??

[odd elbow]

Ye same

I think the same

[jaunty mantle]

thick is just a measurement of a dimension, usually width

[main gull]

If they are laying on their stomach, sure

[jaunty mantle]

well actually that depends on your view angle

[odd elbow]

How can u say that the thick word over here is height l?

[wooden veldt]

Think about the saying "walking on thin ice", that's how it's being used here

[glacial dagger]

Three are three measurements of a 3d figure: Width, length, Height/thickness

[main gull]

As mentioned, it's based on perspective

[odd elbow]

Well....

Ok

I'll consider it as a height

.close

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[sage granite]

i had no idea where to start solving this problems

[devout snow]

@sage granite Has your question been resolved?

[worn gorge]

I don't know about the mathematical procedure but one way i can think of right now is to do it manually

So you have ..

$12a+8b=68$

[woven radish]

Lelouch

[worn gorge]

Plug in and check for all values of a and b

Both are natural no s btw

[worn gorge]

For the second one ..

It's just like the first one

So no help needed i suppose

[devout snow]

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[untold anvil]

$\frac{(x\sqrt{x} - 8)(x - \sqrt{x} - 6)}{x\sqrt{x} - x - 2\sqrt{x} - 12} = 6; x = ?$

[woven radish]

Yushu

[untold anvil]

A) 6
B) 8
C) 10
D) 12
E) 16

[wooden zodiac]

what have u tried

[deft wagon]

$\frac{\tau \alpha lo}{gist}$

[woven radish]

Big xdddd

[wooden zodiac]

what

did i ask your permission to try me???!

[deft wagon]

what does that even mean

[wooden zodiac]

mean what

[untold anvil]

I tried factoring but didnt got anything

[deft wagon]

talo/gist

[wooden zodiac]

A compulsory indirecting infrange to the inahibalitus of a smoiring Dirichlet.

[deft wagon]

ive heard dirichlet before in signal theory but idk what the rest is

[wooden zodiac]

what have u tried

show us your work

[devout snow]

@untold anvil Has your question been resolved?

[untold anvil]

I don't have, I erase what didn't work

[untold anvil]

I "reduced" it to $x^2\sqrt{x} - x^2 - 12x\sqrt{x} - 2x + 20\sqrt{x} + 120 = 0$

[woven radish]

Yushu

[untold anvil]

Not sure how to solve it now

[devout snow]

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[untold anvil]

.close

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[restive river]

hey im stuck on this question

[steel sage]

Let A be the area of unit disk, so π, C be the area of small gray heart shape region, B be C+area of inside white region

Then you are looking for A-B+C

A is π

B is 2(integral rdrdθ) , θ from π to 3π,r from 0 to sin(θ/6)

C is 2(integral rdrdθ), θ from 0 to π , r from 0 to sin(θ/6)

Now calculate them I am going to sleep

[restive river]

goodnight bro

im still trying to figure out xD

[steel sage]

Sorry made a mistake

A is not area of unit disk

[restive river]

yeah the thing im struggling with is finding the limits of the things

[steel sage]

A is 2(integral rdrdθ), θ is from 2π to 3π, r from 0 to sin(θ/6)

It’s correct now

[restive river]

like how do i know where the curve winds up at pi, 2pi and 3pi

do i just have to put it in r and see what values i get?

[steel sage]

Call those curves from out to inside, on the upper half, c1,c2,c3

Call those part of curves from outside to inside, on the lower half, d1,d2,d3

Anti-clockwise:

Start from origin: c3->d2->c1->d1->c2->d3: back to origin

[restive river]

ah yeah that makes sense if you draw it like that

thanks man

i got it

[steel sage]

Np

[restive river]

what do you do btw

[steel sage]

What do you mean

[restive river]

like uni

or job

[steel sage]

Yeah graduate student

[restive river]

in maths?

[steel sage]

Yeah

[restive river]

sick

[steel sage]

😂

Easiest subject man

[restive river]

true

[steel sage]

No need of any extra information from outside, no gray area, no confusion, everything can be explained by logic , don’t need anything else, like experiments, memorization…

[restive river]

ive got another questions but we can leave it for another day haha

yeah exactly man

i hate biology

[steel sage]

Go ahead, what is it

[restive river]

because things come out of nowhere and you have to remember it

okay lemme get it

its not gonna be on my exam but im just curious whether its blindly obvious

[steel sage]

Consider z=cos(θ)+isin(θ), then those two things are Re((1+z)^n) and Im((1+z)^n)

And to calculate (1+z)^n

Rewrite 1+cos(θ)+isin(θ) as

[restive river]

where did you get Re((1+z)^n) from

[steel sage]

$\sqrt{(1+\cos(θ))^{2}+\sin(θ)^{2}}(\frac{1+\cos(θ)}{\sqrt{(1+\cos(θ))^{2}+\sin(θ)^{2}}}+i\frac{\sin(θ)}{\sqrt{(1+\cos(θ))^{2}+\sin(θ)^{2}}})$

[woven radish]

Cogwheels of the mind

[supple knot]

binomial expansion and demoivre's theorem

[steel sage]

$(1+z)^{n}=\sum \binom{n}{k}z^{k}$

[woven radish]

Cogwheels of the mind

[restive river]

okay lemme try

[steel sage]

Btw, I was dumb

[steel sage]

Forget about this, simply:

[steel sage]

1+cos(θ)+isin(θ)=2cos(θ/2)(cos(θ/2)+isin(θ/2))

[restive river]

ohhh

[steel sage]

The rest is clear

[restive river]

is that double angle?

[steel sage]

Yeah

[restive river]

oh dear

😂 😂

thanks bro

[steel sage]

Np

Thanks for interesting questions

[restive river]

its aight man my exam finishes in 3 weeks

and then hopefully no more maths xD

[steel sage]

😂

[restive river]

.close

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[outer cove]

Hello! I am wondering if someone can help me figure out what this problem is asking me. I don't need the solutions, just help understanding what I need to do.

[outer cove]

<@&286206848099549185> if I haven't provided enough info or context please let me know, I am just confused by the amount of info it is throwing at me.

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[outer cove]

.close

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[fading cobalt]

why do all finite dimentional vector spaces over R have a inner product space

[devout snow]

@fading cobalt Has your question been resolved?

[wooden veldt]

Because any finite dimensional vector space over is isomorphic to R^n for some n

And we know an inner product on R^n, for example the dot product

So you can send the vectors over to R^n via the isomorphism and compute the dot product of their images in R^n

This will give you a dot product on your vector space

[fading cobalt]

how do we know this

[wooden veldt]

It's a consequence of the fact that any finite dimensional vector space has a basis

Once you fix a basis, you can write vectors as coordinates in that basis, giving an isomorphism between your basis elements and the standard basis of R^n

[devout snow]

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[cedar kraken]

how can i find the intersection points between the first equation to the others

in exact form

thanks in advance

[devout snow]

@cedar kraken Has your question been resolved?

[supple knot]

Can you write them here

[cedar kraken]

not too sure how

3r=(1.4cos(6theta)^3)+3

|y^2|=|x| domain[-1,1] range [-1,1]

y=0.2/x domain [-0.5848, -0.342]U[0.342, 0.5848] rnage [-0.5848, -0.342]U[0.342, 0.5848]

y=-0.2/x domain[-0.5848, -0.342]U[0.342, 0.5848] rnage[-0.5848, -0.342]U[0.342, 0.5848]

@supple knot

[devout snow]

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[cedar kraken]

.reopen

[devout snow]

✅

[cedar kraken]

<@&286206848099549185>

[devout snow]

@cedar kraken Has your question been resolved?

[cedar kraken]

??

<@&286206848099549185>

[devout snow]

@cedar kraken Has your question been resolved?

[devout snow]

@cedar kraken Has your question been resolved?

[cedar kraken]

<@&286206848099549185>

[charred pebble]

you can convert the polar equation into cartesian then try to find the intersections

[vernal pivot]

also you only need to find one intersection you can reflect the rest across the x and y axis

[cedar kraken]

Ok thanks

.close

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[devout snow]

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[restive river]

So bad news

[restive river]

I failed my maths exam

and I need help

with soemthing simple

fractions

25/55 is equivalent to 5/10 as an example

[gleaming socket]

yes?

thats wrong

[restive river]

so

yeah IK

it is an exampple

[gleaming socket]

ok

[restive river]

how do u get the equivalent of a fraction

like

20/40 = 5/10

like that

[gleaming socket]

divide both the top and the bottom with the same number

[restive river]

huh?

[main gull]

https://www.youtube.com/watch?v=PcEwj5_v75g&ab_channel=TheOrganicChemistryTutor

[restive river]

not simplifying

i alr know

[gleaming socket]

20 divided by 4 is 5

[main gull]

This is simplifying

[gleaming socket]

40 divided by 4 is 10

[restive river]

I didnt ask for simplifying

[gleaming socket]

you can simply 5/10 more

divide both by 5

[restive river]

1/2

[gleaming socket]

yes

[restive river]

wait

its not taht

[main gull]

Your examples are based on simplifying

[restive river]

like 20/40 = to 50/100

like that

[main gull]

Find what you need to multiply 20 by to get to 50

[restive river]

2.5

nvm u guys arent helping

.close

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[gleaming socket]

kids need to learn patience

[restive river]

u dont understand what I am talkin bout

[main gull]

I did

I told you what to do

[restive river]

not really

[main gull]

Find what you need to multiply 20 by to get to 50

[restive river]

not that

[main gull]

Yes it's that

Because 20 * 2.5 = 50

[restive river]

no bro

i am not talking about that

it will give us like 2/4 = 50/100

wait no

2/4=

you have to get to answer

25/35=

[main gull]

If you were clearer in asking your question, people could have helped you better

[main gull]

Because this is simplifying

[restive river]

yeah

[devout snow]

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[restive river]

re.open

[main gull]

This was just finding a multiple to multiply 20/40 to make it 50/100

[restive river]

ik

but it will ask questionss like

100/200=

find it without simplified then with simplified

find the answer without simplifying

then simplify

[main gull]

1/2

Simple

[restive river]

BRUH

25/35=

70/100=

[main gull]

5/7

7/10

[restive river]

how tho

[main gull]

The way you are asking makes no sense

You just simplify

[copper flower]

that is simplifying

[restive river]

just nvm it

ill watch a video

[main gull]

Or properly ask your question

Because all of that is simplifying

[restive river]

.close

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[rapid cobalt]

Hi ive had a problem thats has been bugging me lately

[rapid cobalt]

Let F be the event of female, event M of males and I the event of getting an IBB diploma. Records show that students have been composed by 60% females and 40% males from which 75% of females get an IBB diploma. If a student is selected at random and found to have got an IBB diploma, what is the probability that the student is female?

I tried solving it like this but i was told it was wrong as we dont know the what percentage of males get a diploma

^^ Probabilities btw 🙂

[devout snow]

@rapid cobalt Has your question been resolved?

[rapid cobalt]

<@&286206848099549185> 🙂

[wooden veldt]

You want probability student is female given that they have a diploma

You want to use Bayes theorem

So that you can use prob student has diploma given they are female, which you know

[devout snow]

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[devout snow]

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[agile narwhal]

I have 50 students (distinguishable). I have 3 grades A,C and FX. In how many ways can they get grades ?

[agile narwhal]

3^50

?

[orchid sierra]

yes

[agile narwhal]

thx

[orchid sierra]

any student's grade is not dependent on any other student's grades

these are independent events

[agile narwhal]

.close

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[restive river]

For this I got D=5/7 of G and then J=5/6 of D but I dont know what to do next

[wooden veldt]

,rcww

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[restive river]

.close

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[flat mesa]

https://media.discordapp.net/attachments/975380515978891284/983420026222678037/20220606_181947.jpg?width=507&height=676

[rough beacon]

$x+3\geq 2$, thus $x\geq -1$, which is simultaneously greater than -4, so the lower boundary is -1.
$x+3<9$, thus $x<6$, but also $x\leq 2$, thus the upper boundary is 2.
x = -1/0/1/2

[woven radish]

Wa3Wa

[rough beacon]

||upper right, lower right||

explanation: ||x > -2, so any list that contain numbers less or equal to -2 are out of question. this leaves upper right and lower right as the only options, none of which exceed 4, so both are good||

[devout snow]

@flat mesa Has your question been resolved?

[flat mesa]

Way too hard for me to understand lol

.close

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[sacred raven]

Im stuck on question 13 (b) where u hv to form a formula

[sacred raven]

This is what we use to form the formula

Heres what i did, when i looked at the back my answer ws very different and i dont know where i rly went wrong

Heres the answer at the back ex8.3 Q13(b)

[gleaming socket]

Hmm I can't really understand what you tried

[gleaming socket]

I want to rotate this

Reupload this

[sacred raven]

There hope this is better

[sacred raven]

I tried forming my own formula so basically a general term. Using the formula highlighted in green.

[gleaming socket]

I literally have never heard about quadratic patterns so I don't know what these mean

[devout snow]

@sacred raven Has your question been resolved?

[long pasture]

2b+c= -4

[devout snow]

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[celest wasp]

what is the percent change from 85 and 64? (round to the nearest percent)

[celest wasp]

i think its 33

[neon folio]

,w 85-33/100 * 85

[woven radish]

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Requested by Mike Oxbig#0599

[celest wasp]

huh

[neon folio]

its not

[celest wasp]

bc 85- 64
and the relative change is (85 - 64) / 64
to get % just multply by 100%

,w 85 - 64/64 x 100

[woven radish]

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[celest wasp]

huh wait

[main gull]

Parentheses is needed

[celest wasp]

its -24.705

[celest wasp]

oh

[main gull]

,w (85 - 64)/64 x 100

[woven radish]

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Requested by dldh06#2659

[celest wasp]

oh

see

but if it was rounded

it would be 33 correct?

[main gull]

Yes

[celest wasp]

oh

ty

.close

[devout snow]

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[celest wasp]

wait in this one would u just do 200 x 6 lol

.reopen

[devout snow]

✅

[west cliff]

Hello?

.open

[celest wasp]

?

go to help 26

[celest wasp]

and post ur question

[west cliff]

Ok

[celest wasp]

.close

[devout snow]

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[celest wasp]

no put it

*now

[west cliff]

Wdym?

I did

[celest wasp]

no bc i was using this channel

post ur question again lol

[celest wasp]

ok

[west cliff]

Is it wrong is it correct? Also I don’t know what to do for the B question.

Hello?????

[west cliff]

Hello?

[main gull]

Please read #❓how-to-get-help

[west cliff]

Bro wdym

[main gull]

Bro, just wait for someone to come by

[celest wasp]

idk

[devout snow]

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[nova shore]

could it be right angled triangle

[urban harbor]

hint: the problem states they are all unit vectors

[nova shore]

yes

[urban harbor]

so what does that mean about their length? : )

[nova shore]

magnitude would be same

right

[urban harbor]

so what kind of triangle is that?

[nova shore]

equilateral

[urban harbor]

yep, so could it be option A?

[nova shore]

yes

my teacher

says its A

that's why I'm here

[urban harbor]

that makes no sense : )

[nova shore]

and what abt isosceles

[urban harbor]

well every equilateral triangle is technically isosceles so it would be B & C

definition of isosceles is at least two sides are of equal length

[nova shore]

ok

thanks @urban harbor

[urban harbor]

cheers

[nova shore]

hey wait

what abt a+b=c?

@urban harbor
T-T

I'm crying

[urban harbor]

?

[nova shore]

A+B=C

[nova shore]

.

[urban harbor]

yes, what about it?

[nova shore]

if it's equilateral

how A+B=C will fit

[devout snow]

@nova shore Has your question been resolved?

[neon folio]

it wont

only isoscles fits

[long kettle]

But it is equilateral. All 3 sides have length 1

[neon folio]

oh yeah

lol

maybe a+b=c is reffering to angles

in which case it could be right

[long kettle]

A + B = C is adding the vectors

[neon folio]

and isoscles

as the teachert said

[long kettle]

It's vector addition

[neon folio]

maybe

why else did the teacher say its a right triangle?

[long kettle]

Perhaps they just misspoke. Maybe they were mistaken

[neon folio]

perhaps

[devout snow]

@nova shore Has your question been resolved?

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[ruby abyss]

"what is the number of ways of distributing 15 identical cards on 4 persons such that everyone gets at least 2 cards"
i'm aware that since they're identical, it doesn't matter who gets what cards so 8 cards are given out to meet the requirement that each one has 2 cards, and i know that the remaining 7 can be distributed all 4 where arrangement is irrelevant but replacement is possible so i have to use (n+r-1)Cr, but i don't know whether it should be 10C4 or 10C7, and the reason for that

[fringe parrot]

10C4

or 10C6

[ruby abyss]

why 6

[fringe parrot]

nCk = nCn-k

[ruby abyss]

ah i see

wasn't familiar with that one so i didn't know where 6 came from

thanks

.close

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[devout snow]

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[agile narwhal]

C = {R, G, B, Y } and V = {7, 8, 9, 10, D, H, K, E}, C x V is set of cards where C is set of colors and V is set of values

In how many ways can 4 cards be distributed to five players? (Distribution is ordered (A, B, C, D, E), where A, B, C, D, E are mutually disjoint 4-elements subsets of CxV)

[devout snow]

@agile narwhal Has your question been resolved?

[devout snow]

@agile narwhal Has your question been resolved?

[agile narwhal]

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[weak flare]

Local Maximum of function x=0

[bold prism]

thats not a function

[weak flare]

y=x , maxima

in a way

ig

[bold prism]

?

[weak flare]

nothing , f(0)=x

[bold prism]

??

[weak flare]

Need to find the maxima of this function

[bold prism]

linear functions do not have a maxima

[restive river]

@bold prism Are you the real Swasthik?

[weak flare]

ik , but , they want the ANSWER

[bold prism]

that is the answer

[weak flare]

@bold prism Which uni do you go to ?

[bold prism]

no maxima

[weak flare]

sick

appreciate you

[bold prism]

I'm in 12th grade

not in uni yet

[weak flare]

Sameeee

lessgoo

[bold prism]

this doesn't make sense

[weak flare]

good luck for uni this september

[weak flare]

ik

i was baffled too

[bold prism]

actually next year for me 💀

[weak flare]

6th Form ?

lol

[bold prism]

in my country academic sessions are from April -> March

[weak flare]

cool cool , good luck

.close

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[devout snow]

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[lime linden]

What would the length of a tunnel from New York to San Francisco be? Give me a confidence interval.

[long kettle]

Is that the whole question?

[lime linden]

yes

[devout snow]

@lime linden Has your question been resolved?

[lime linden]

<@&286206848099549185>

[long kettle]

Really? Absolutely no other information is given anywhere else?

[lime linden]

i promise im not lying

[long kettle]

Well, you're gonna need the distance from new york to san francisco, along with the uncertainty or standard deviation or sumn

How do they expect you to find that though?

[lime linden]

idek

why cant i solve this?

what am i missing?

[long kettle]

The length from new york to san francisco along with the standard deviation, for one

Good luck finding those though, cuz I don't know how

Length is easy. Standard deviation? Not so much

[lime linden]

true it never specified if its by car, walking, train etc

[long kettle]

The distance is gonna be the same regardless of how you're travelling

[lime linden]

yeah but miles tho

how long itll take

[long kettle]

Miles is not a measure of time

[lime linden]

im trying to say each transportation has different distance

which correlates to different time to get there

but it shouldnt matter tbh

[long kettle]

If we're digging a tunnel, we just need the straight distance from one city to the other

[lime linden]

yeah

so it wouldnt matter

[long kettle]

That's easy enough to Google. Dunno how to get the SD though

Are you sure there's no information before the question?

[lime linden]

we would assume 95% confidence interval right?

[long kettle]

Prolly

[lime linden]

the pic i sent is the only info i receive

[long kettle]

Can you send a picture of the whole screen?

Chegg?

[lime linden]

yeah?

[long kettle]

Is this assigned by a teacher?

[lime linden]

no

[long kettle]

What are you trying to do then?

[lime linden]

why do you wanna know?

[long kettle]

Because it's entirely possible that's just a question from a rando who didn't think about if the question was possible to answer

[lime linden]

ive been solving qs from this list, its doable

its fine ill skip that q

lol

.close

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[small pagoda]

Hey! I'm having issues setting up the problem

I calculate the area as

Which gives me 4/3, which is then flipped to 3/4

Then I plug it into these formulas, and I got:

Any idea where I may have gone wrong?

I got xbar from

ybar from

[devout snow]

@small pagoda Has your question been resolved?

[small pagoda]

<@&286206848099549185>

[gaunt quiver]

if im not mistaken

These formulae assume a constant density of the material

where in your case, your density varies with respect to x

[small pagoda]

That’s valid actually I hadn’t thought of that

How would I adjust this for the density?

[gaunt quiver]

do you happen to have the derivations of these formulae ? it should be on there

regardless ill get back to you in a bit

@small pagoda https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/15%3A_Multiple_Integration/15.6%3A_Calculating_Centers_of_Mass_and_Moments_of_Inertia#:~:text=5%3D4427%2C-,ˉy%3DMxm%3D∬Ryρ(,4427%2C10063).&text=Calculate the mass%2C moments%2C and,0≤x≤1.

you can try and follow the examples here

essentially the idea is that mass= density * area
these would give you a double integral that you would solve to get the mass

after that you'd essentially want to integrate the sum of moments at each point of the metallic plate
and divide it by mass, leaving you with the precise coordinate you're looking for

[small pagoda]

I really appreciate you helping out, I found the proper formulas

Going to be re-writing my notes with these because this is a super easy adjustment

[gaunt quiver]

$m=\int\int\rho(x)dA=\int_{6}^{10}dx\int_{0}^y={\frac{20}{x^2}}2x^2dxdy = \int_0^6 2x^2\cdot \frac{20}{x^2}dx$

[woven radish]

Deus_Vult

[gaunt quiver]

is essentially the rigth way

[small pagoda]

Yeah I'd like to be able to derive these but we have about 1-2 chapters a day due in this accelerated course and plug/chug is the main goal

[gaunt quiver]

and from there on you can get the rest

[gaunt quiver]

the derivation is through physics actually lol

[small pagoda]

oh I know, this entire section has been breaking my kneecaps with physics problems

[gaunt quiver]

its based on the total sum of moments being 0, defining differential volume, differential moments and differential weight and etc...

[small pagoda]

This is the last physics I will have to do for calc 2

[gaunt quiver]

hehe I know that feeling, im taking a statics course thou so its aimed directly at that rather than taking that kinda thing in calc 2

[small pagoda]

I'm simultaneously really excited and scared of what they have me taking next semester

[gaunt quiver]

there are great examples here tho none the less

[small pagoda]

Stats/Probability, Linear Algebra, Cal 3, and Proofs

[gaunt quiver]

Oh

that's heavy

what major are you ?

[small pagoda]

double majoring stats/math

[gaunt quiver]

Ohh fair enough

[small pagoda]

going to drop to one or the other eventually though

As it stands I have to take 15 or so credits of almost entirely math to graduate in 3 years

[gaunt quiver]

But Cal 3 isn't too bad

compared to cal 2 at least
from my experience with it

[small pagoda]

I'm expecting a (somewhat) easier time through the rest of cal 2

I was told integral applications are the hardest part

[gaunt quiver]

in calc 3 ?

[small pagoda]

cal2

[gaunt quiver]

That's fair
it requires a more abstract type of thinking

[small pagoda]

again, I appreciate the wisdom and will check out some more of the examples after I take the quiz/exam tonight.

.close

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[signal raft]

Do you know the area formula for a rectangle?

In this case, it is x * (x+2)

isn't it?

And they have given the area right?

Equate and solve for x

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[merry stream]

one sec

[merry stream]

so

this is the graph of the bounded region

and I also included the polar equivalents

my issue is

idk how to find the integral using polar represntation

because L2 and L3 in polar coordinates give only angles

oh I can add my work as how I found my polar equivalents of the given cartesians

[wooden veldt]

Why have you graphed r=θ?

[merry stream]

its r=theta and theta=π/4 and π/3 for different equations

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@merry stream Has your question been resolved?

[devout snow]

@merry stream Has your question been resolved?

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[empty sphinx]

Hello can I have help verifying the graph of y=2sin((x/4)+(4pi/3))-1?

[empty sphinx]

So I know the amplitude is 2, the period is pi/2, and you shift the graph down 1

but for phase shift I used C/B to get that it moves left 16pi/3, but when I check that using desmos and other graphing websites its wrong

[devout snow]

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[empty sphinx]

.close

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[young hare]

we are given an example neural network, I was wondering if this would be the correct representation of the outputs with the Leibniz notation?

[devout snow]

Please don't occupy multiple help channels.

@young hare Has your question been resolved?

[devout snow]

@young hare Has your question been resolved?

[young hare]

<@&286206848099549185>

[devout snow]

@young hare Has your question been resolved?

[devout snow]

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[young hare]

.reopen

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✅

[devout snow]

@young hare Has your question been resolved?

[ocean zenith]

i am sorry i cant be of any help :)

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[mighty acorn]

How would I find the sum of this sequence: 200-199+198-197+196 ... +2-1

[topaz axle]

it breaks in two

you have 200+198+196... and you have 199+197+195... which you subtract

double the work half the fun

[mighty acorn]

u mean -199,-197,-195

[mighty acorn]

how would u find the sum tho

[topaz axle]

i didn't mean that

you would have to add if you did it that way

[winter patrol]

formula for arithmetic series

[mighty acorn]

tn=a+(n-1)d

the answers are a) 99 b) 100 c) 200 d) 101

[bright burrow]

thats for the n th term

u need the sum of n terms

[winter patrol]

I mean you could just consider grouping the terms in pairs

[topaz axle]

true

[mighty acorn]

n[2a+(n-1)d] all over 2

[winter patrol]

(200-199)+(198-197)+...(2-1)

[mighty acorn]

that would mean 1+2 ... +1

so I cant really

[winter patrol]

where's +2 coming from

[mighty acorn]

wait

how would I do it if its all one

1+1 ... +1

[winter patrol]

consider how many pairs there are

and hence the number of 1s effectively being added together

[mighty acorn]

im confused

how would I find n and then the sum

with that

[winter patrol]

consider how many pairs there are

[bright burrow]

Try seperating the two series, and then u can try finding the number of terms of each series, and then the number of pairs formed

[winter patrol]

there are numbers from 200 to 1 with alternating signs in the summation

how many numbers are there in total?

[mighty acorn]

100?

[winter patrol]

not the answer to the question I'm asking

atm

[mighty acorn]

201 numbers?

[winter patrol]

no

do not overthink this

[mighty acorn]

200?

im not

sure

[winter patrol]

yes

there are 200 integers from 1 to 200 inclusive

[mighty acorn]

ok

[winter patrol]

and considering how I grouped/paired numbers above, how many pairs are there?

[mighty acorn]

100 pairs

[winter patrol]

yes

and what's the sum of each pair?

[mighty acorn]

weach pair is 1

[winter patrol]

yes

[mighty acorn]

abnd since 100 paris

1x100

right?>

[winter patrol]

yes

[mighty acorn]

so the answer is 100

which is one of the multiple choiec answers

oh

I thought I had to find some genearl term

But this is more like logic

[devout snow]

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[vale turret]

is this proof correct for \
Show that, whenever $\sqrt{n}$ is not an integer (that is, whenever n is not a square n \in \mathbb{Z}), then
$\sqrt{n}$ is in fact irrational. \

proof:
let $ \sqrt{n} = \frac{a}{b} $ , for , $(a,, b , integers ,, b \neq 0 , n>1) , and , gcb(a,b) =1 $ \
$n = \frac{ a^2}{b^2} \implies b^{2}n=a^2 \$

case 1: \
if a is even then b or m must be even therefore $b^{2}n=a^2$ can be expressed as $b^n =(2r)^2 $ \
let $b=2s$ then $ (2s)^{2 }n=(2r)^2$ therefore we get $s^2 =r^2$ and since the division by 2 was possible this is a contradiction since we have assumed $gcb(a,b) =1$ therefore $\sqrt{n}$ is irrational in this case. \

case 2: \
if a is odd then b and m are odd therefore $n = \frac{ a^2}{b^2}$ can be expressed as
$n = \frac{ (r+1)^2}{(1+s)^2} = \frac{ (r^{2} +2r +1}{s^{2} +2s +1} =1$ which is a contradiction with $n>1$

case 3: \
let $n= m^2$ then $b^{2}m^{2} = a^{2} \implies m =\fraq{a}{b}$ which means n is rational
therefore the only case where $ \sqrt{n}$ is rational is when $n is perfect square

[woven radish]

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

[devout snow]

@vale turret Has your question been resolved?

[devout snow]

@vale turret Has your question been resolved?

[devout snow]

@vale turret Has your question been resolved?

[vale turret]

<@&286206848099549185>

[copper flower]

I already showed you a counterexample twice

[vale turret]

oh thanks. I just want to know is the text book I sent you the link today is wrong or I misinterpret what they were saying

shall I send you the link again?

also I have looked online it seems like the proof has to be about showing that the square root of a positive integer is either an integer or irrational. In this case if √n if is an integer then by definition n is n is a square number If it's not an integer then this implies that √n is irrational. I think this is what they were trying to say in that paragraph

[restive river]

How is the claim wrong? I haven't looked at their proof but the claim they are making is correct.

[devout snow]

@vale turret Has your question been resolved?

[vale turret]

he gave this as a counter example.

$\sqrt{0.25}$ is rational and $0.25 \not\in \mathbb{Z}$

[woven radish]

xzino

[vale turret]

<@&286206848099549185>

.close

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[wanton rapids]

Here we have a quantity difference where we are interested in all the elements that are in B but not in the union of A and C.

Is this correctly formulated?

[oak harness]

I am confused on what you mean by quantity difference

all the elements that are in B but not in the union of A and C.
But this part is correct.

[wanton rapids]

I don't know hoow you say it in english

But we call it mängd differens

[oak harness]

ah, set difference

Menge in German heh

The English equivalent is set

[wanton rapids]

Nice

So would we write it as B\(AUC)?

[oak harness]

$B \setminus (A \cup C)$

Yes.

[woven radish]

Remavas

[wanton rapids]

Okay thanks.

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[inner wraith]

help

[devout snow]

Please don't occupy multiple help channels.

[inner wraith]

are any helpers here?

hello?

[mild nexus]

• Pick a channel in the “Available” section and post your problem. The bot will move your channel to the “Occupied” section, and the channel will be reserved for you until your question is answered. Stick to one channel and don't post the same question in multiple channels. Don't ask for help in other channels if no one is responding in the one you have posted your question in.

you already have a channel open

[inner wraith]

I am new to discord so im kinda bad at this

[mild nexus]

and post your question

[inner wraith]

oh okay

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@inner wraith Has your question been resolved?

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[reef pilot]

,,T:\ P_{3}\to R\ where\ T\left(f\right)\left(t\right)=f\left(0\right)

[woven radish]

epiphonically

[reef pilot]

i need to show that this is a linear transformation

how do i do that with polynomials?

[mild nexus]

what would $T(f+g)(t)$ be

[woven radish]

lirmirit

[reef pilot]

f(0) + g(0)?

oh is that the same as T(f)(t) + T(g)(t)?

[mild nexus]

yes

[reef pilot]

i seeee

is the (t) apart of the linear transformation?

[mild nexus]

not sure what you mean by that

but $T(f+g)(t)$ would be a function (more specifically, a linear transformation) that takes in a real number $t$

if that's what you mean

[woven radish]

lirmirit

[reef pilot]

is it multiplynig by t?

or is it T(f(t))

[mild nexus]

T(f(t))

[reef pilot]

ohhhh

i thought it was multipling

for quite a while

huh

well thats good to know

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[wanton herald]

how do you solve the following for x?
$y=3+x+e^x$

[woven radish]

Hairo

[copper flower]

lambert w function kekw

$W(x) = f^{-1}(x), f(x)=xe^x$

[woven radish]

illuminator3

[wanton herald]

is there no other way? I am learning calc I rn with the book by stewart 😦

[supple knot]

Show the problem

You're probably not asked to find x

[wanton herald]

ohh, no

[supple knot]

Just plug in some values for x and try

[wanton herald]

really?

[supple knot]

Trial and error is great

[wanton herald]

do you think that's the intended way?

[stone stump]

here yes

[copper flower]

Yes

here yes

darn it denascite beat me to it

[stone stump]

😛

[ripe gust]

It's always a good way if it works

[copper flower]

you could also plot the function

so you don't just try completely random values

[supple knot]

Could have plugged in 10 values by now

[wanton herald]

it's 0

[stone stump]

yes

[wanton herald]

I didn't even think about solving it like that 😄

ty guys

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[quartz ice]

How would I solve (4/9) to the power of -2

[normal crater]

what does a power of -2 mean

can you tell me

[stone stump]

x^(-2)

ok so we have $\left(\frac{4}{9}\right)^{-2}$

[woven radish]

Denascite

[stone stump]

which exponent laws can we apply

[quartz ice]

Hmm

idk

I thought we could use the reciporical

but thatd be too complicated

[normal crater]

what does a negative power mean

you are on the right track

[stone stump]

reciprocal is good. what is the reciprocal of 4/9 ?

[quartz ice]

9/4 to the power of 2

[stone stump]

yes

[normal crater]

good

now apply normal squaring

so

[quartz ice]

81 to the power of 16?

81/16

my bad

[normal crater]

correct!

[quartz ice]

damn that was easy

cheers

.close

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[devout snow]

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[vestal juniper]

cos x = -5/2 gives error. Please help

[bright burrow]

cosx=-5/2 and no x for that

[vestal juniper]

wym no x?

[bright burrow]

as cosx is between [-1,1]

[bright burrow]

whatever value of x u put cosx always comes between [-1,1]

so no solution

[vestal juniper]

oh

ok makes sense

thanks

.close

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[visual spire]

how do i do this?

[long fog]

Para la funcion?

[visual spire]

for the function

calcular=solve

[long fog]

You can find the partial differentials

[visual spire]

but how?

[long fog]

Treat y independent to x and then differentiate f(x,y) wrt x

There's one more way to this

[woven radish]

fäf

[long fog]

When y²+x=0 , f(x,y)=0

[visual spire]

by definition so

[long fog]

Observe one thing that -1,1 satisfies y²+x so f(-1,1)=0

[woven radish]

fäf

[visual spire]

yeah that

[long fog]

Solve the limit problem now

[visual spire]

change f to its definition?

to solve or how

[long fog]

Substitute x=-1+h and y=1

[pine geyser]

hey so im workig on a project right now trying to relate quadratic inequalities to real life physics and i need an opinon if thats alll right

[restive river]

Go to another help

[pine geyser]

liek withc one

[long fog]

See the channel that are free at bottom of channel panel

[visual spire]

$$\frac{(h-1)^3+1}{h-1+1}$$