help-0

[dull lily]

??

[sudden hinge]

no, the exact slope at any point, not its change

[dull lily]

oops

my mistake

[sudden hinge]

now remember how you did derivatives with linear functions (straight lines)?

[dull lily]

yeah

[sudden hinge]

you drew a triangle at some point

[dull lily]

yeah rise over run right

[sudden hinge]

exactly

dy/dx represents exactly that

[dull lily]

mhm

[sudden hinge]

put for very small regions

[dull lily]

why small again?

[sudden hinge]

so that you get an accurate result for curves

you can approximate a small enough part of any curve as a line

if you zoom in enough

[dull lily]

ohhhh ok

so with that cleared up

how does that relate to this

[sudden hinge]

thats just taking the derivative of y^2

but y is a function of x, right

[dull lily]

isnt derivative of y^2

ok wait so derivative of y^2 is just 2y

but because y is a function of x

what does that make it?

[sudden hinge]

d/dy (y^2) = 2y, but d/dx (y^2) = 2yy' if y is a function of x, ie y(x)

because you need to use the chain rule there

basically you have d/dx (y(x)^2) where you have an outer function (square) and an inner function (y itself)

[dull lily]

oh ok

i understand that

so how does that tie in with my math prioblem

do I plug y into the equation

or?

[sudden hinge]

part (a)?

[dull lily]

i kinda need some sort of footing

yeah

just starting off with part a

[sudden hinge]

you want to get y' somehow into your equation

[dull lily]

so

[sudden hinge]

so a good idea would be to differentiate both sides with respect to x

[dull lily]

rn i have y = 3 rad 5x^2-7

my job is to find the derivative

of it

bychainruling it

[sudden hinge]

no you don't have y explicitly in (a)

take the equation from your picture

and just take the derivative of both sides

[dull lily]

oh

that works too

10x-3y^2

=1

[sudden hinge]

$\dv{x}\qty(5x^2 - y^3 = 7)$

[ocean seal]

Navix

[dull lily]

yeah

looks about right to me

$10x-3y^2=1$

[sudden hinge]

you didnt apply the chain rule and the right hand side is wrong

[ocean seal]

c0nc3ptsz

[dull lily]

wait

slope of any constant k is 1

right

[sudden hinge]

0

[dull lily]

0

my mistake

im tired

[sudden hinge]

slope of x is 1

[dull lily]

also

how do I find the left hand side cuz I have 2 variables

I thought I just do them seperately

no?

[sudden hinge]

y = y(x), remember

you actually only have one variable, x

y is a function of x, for example y(x) could be 3x^2 - x or sth

[dull lily]

ohhh so

then

its 5x^2-x^3?

right

[sudden hinge]

nono

you can't just say y = x

y could be anything

we just know it only includes the variable x

[dull lily]

mhm so we know that y=y(x)

can we do

[sudden hinge]

we need the chain rule here

[dull lily]

5x^2-y(x)^3

[sudden hinge]

yes

[dull lily]

im sorry

but how can we chain rule out y(x)^3

when y is still there

?

[sudden hinge]

whats the outer function here

[dull lily]

inner is x^3

outter is u(x) then?

[sudden hinge]

lets say y(x)^3 = u(v(x)), where u = z^3 and v = y(x). then the derivative is u'(v(x)) * v'(x) right?

[dull lily]

yeah so

the outter is just Uu

correct?

[sudden hinge]

outer derivative is u' = 3z^2, inner is v' = y'(x), agree?

[dull lily]

wait

isnt that inner

oh

no

nvm

im really just brain damaged

this makes sense now

wait

the outter is yu^2

for my problem

and the inner is just x

[sudden hinge]

this is for your problem

[dull lily]

then yes

I agree the outter derivative is 3z^2

and the inner works aswell

[sudden hinge]

so then what is u'(v(x)) * v'(x) if you substitute?

[dull lily]

z^3 (y'(x)) * y'(x)

[sudden hinge]

$\dv{x}\qty(y(x)^3) = u'(v(x)) * v'(x) = 3 v(x)^2 \cdot v'(x) = 3 y(x)^2 \cdot y'(x)$

[ocean seal]

Navix

[dull lily]

ok yeah I get that

cuz chain rule right

u pull out the inners and the outters

so if we look at the OG problem

y(u)^3 is the outter

and x is the inner right?

[sudden hinge]

no the structure is [y(x)]^3, the outer is just ^3, the inner is y(x)

so 3 * [y(x)]^2 * y'(x)

[dull lily]

so the outter is just u^3

[sudden hinge]

right

[dull lily]

and the inner is y(x)

that

makes a lot of sense

ok cool I got that part down so

we know that 5x^2 is just

10x

product property comes next right

after I

chain rule the inner and outter

[sudden hinge]

what do you get after differentiating once?

like the whole equation

[dull lily]

uhhh

[sudden hinge]

10x - ... = ...

[dull lily]

its just 3x^2

so

10x-3x^2

[sudden hinge]

10x - 3 * y^2 * y' = 0, no?

we discussed how to take the derivative of y^3 with respect to x earlier

[dull lily]

wait ur right

sorry

we know the inner is y(x) and the outter is u^3

which means 2u^2

[sudden hinge]

3u^2

[dull lily]

3(y'(x))^2

sry

typo

d/dx of y(x) is just y

[sudden hinge]

3u^2 * inner derivative = 3 * y(x)^2 * y'(x)

no its y'

[dull lily]

oh because f(x) = y thing

right?

[sudden hinge]

yea

[dull lily]

ok so

y'(x) is just y'

so we sub that in

[sudden hinge]

yes

[dull lily]

3(y')^2

correct?

so its 10x-3(y')^2

right

?

[sudden hinge]

no

[dull lily]

damn so close

[sudden hinge]

outer = u^3, inner = y(x)
outer derivative = 3u^2, inner derivative = y'(x)

so: outer derivative * inner derivative = 3u^2 * y'(x)

[dull lily]

yes but we have to plug in

u first so

[sudden hinge]

u = y(x)

[dull lily]

ok yeah i was just about to say that

so

3(y(x)^2)(y'x)

[sudden hinge]

yess

now write down the whole equation and try to isolate y'

thats what they mean by getting it "implicitly"

[dull lily]

uhhh

since there r still two variables

how would we actually isolate y

would I just

move 10x to the other side of the equation

and then divide out hte and call it at that?

[sudden hinge]

you want y'

not y

$10x - 3y^2 y' = 0$ isolate y'

[ocean seal]

Navix

[dull lily]

y' = 10x/3y^2

[sudden hinge]

yup

[dull lily]

so thats part a right?\

[sudden hinge]

thats part (a) yes

[dull lily]

then part be requires me to just solve what y is so I can plug it into the equation

and get y'

[sudden hinge]

++

[dull lily]

?

[sudden hinge]

part (b) is the normal procedure, yes

[dull lily]

so back to the original problem

with 2 diff variables

how do we solve it?

[sudden hinge]

solve the og equation for y

then take the derivative

[dull lily]

the oh equiation being 10x-3y^2y' = 0

right?

[sudden hinge]

no the one from the exercise

[dull lily]

oh

[sudden hinge]

they want you to do it 2 diff ways

[dull lily]

ofc

y = (5x^2-7)^1/3

derive that out

??

i got 1/3(5x^2-7)^-2/3

multiplied by 10x

is that right?

[sudden hinge]

thats correct

[dull lily]

so we chain rule thatout

right

[sudden hinge]

yes

[dull lily]

so is this step correct

when I already derived it out

?

[sudden hinge]

lemme check

you forgot a * 10x

[dull lily]

alrigh tcool

so

ok

im sorry how would we algebraicly solve thgis out

can I leave it like that

and sub

??

[sudden hinge]

$\frac{10x}{3 \sqrt[3]{(5x^2-7)^2}}$

[ocean seal]

Navix

[dull lily]

oh that works too actually huh

[sudden hinge]

same thing

just cleaner

[dull lily]

ok but I

does that mean

part 2 is complete

meaning part three I set them equal

and finish?

[sudden hinge]

part 3 means

you take the result from (a) which is $y' = \frac{10x}{3y^2}$

[ocean seal]

Navix

[sudden hinge]

and substitute the original equation for y into that

and compare it with the solution from (b)

$y = \sqrt[3]{5x^2 - 7}$

[ocean seal]

Navix

[dull lily]

its the same

up and down

[sudden hinge]

thats what you should get ;)

[dull lily]

Alright I got it!

Thanks so much for your help!

[sudden hinge]

np

[dull lily]

I really appreciate it man

Your a life saver ❤️

[sudden hinge]

glad i could help

[dull lily]

.close

[lone heart]

Channel closed

Closed by @dull lily

Use .reopen if this was a mistake.

[lone heart]

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.

[limpid lava]

yo i need help with (x-mu)^2 P(X)

[limpid lava]

i completely forgot how to solve this

[lone heart]

@limpid lava Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

Channel closed

Closed due to the original message being deleted

[rough acorn]

i thought it would be E because all the angles are 45 degrees, so you use a 45/45 triangle, therefore 6sin(45) = E (not B)

[drifting hull]

its a regular triangle, so each angle is 60°

[lone heart]

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.

[lean plover]

help, brain implosion

so x ~ number of females in each litter

so p is the probability of uh 1 female?

idk im confused

p is meant to be chance of success

but i dont really understand whats going on here

[lone heart]

@lean plover Has your question been resolved?

[noble sinew]

What they wrote makes no sense and is wrong

[lone heart]

@lean plover Has your question been resolved?

[lean plover]

uh really?

this is like a legit exam paper from the exam board

it was actually sat in 2019

lemme show mark scheme

[noble sinew]

0,1,2,…,7 is 8 groups not 7? And if its binomial each individual trial should only have 2 outputs - here that doesn’t look like the case. Surely this should be a multinomial model, (which is also what it seems like they are doing in b) and c))

[lone heart]

@lean plover Has your question been resolved?

[lean plover]

.close

[lone heart]

Channel closed

Closed by @lean plover

Use .reopen if this was a mistake.

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.

[fickle grail]

I need to find out if this is true or false

[raven rover]

Use properties of limits: you can pull constants out of limits.

[lone heart]

@fickle grail Has your question been resolved?

Channel closed

Closed by @fickle grail

Use .reopen if this was a mistake.

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.

[crude plinth]

Can someone help ??

[raven rover]

What have you tried?

If you don’t know L’Hospital’s Rule, then multiplying by the conjugate of the numerator may be helpful

[crude plinth]

Umm

Sorry to ask but, what's L'Hospital's Rule ??

[glass lichen]

You'll probably see L'H later

[raven rover]

@crude plinth ^^

[crude plinth]

oh ok..

thanks

[lone heart]

@crude plinth Has your question been resolved?

Channel closed

Closed by @crude plinth

Use .reopen if this was a mistake.

[lone heart]

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.

[arctic mortar]

#9

[arctic mortar]

im not entirely sure on how fence is setup since the question is kinda confusing

i already know the total area is 260625 but i’m not sure how to calculate it

[lone heart]

@arctic mortar Has your question been resolved?

[arctic mortar]

<@&286206848099549185>

[arctic mortar]

.close

[lone heart]

Channel closed

Closed by @arctic mortar

Use .reopen if this was a mistake.

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.

[fallen rain]

can someone check for me, if my calcualtion is correct or not please?

[bright hedge]

,w simplify x^2 + (x+1)^2 + (x+2)^2 - 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Yottachad#6969

[bright hedge]

yep but also i wouldn't say congruent to 3x

it should say congruent to 0(mod 3)

[fallen rain]

what does congrument means?

[placid zinc]

https://www.wolframalpha.com/

[bright hedge]

you were writing the congruent symbo

but you don't know what it means?

well here

[placid zinc]

The entire thing has "= 3x" for no real reason. The work would be correct if you erased those

[bright hedge]

$a \equiv b (\text{mod n}) \iff a = b + mn, \text{ for some } m \in \mbb{Z}$

[ocean seal]

Shuri 4 honorable (Yottachad)

[bright hedge]

so if b was 0 then you would obviously have a = mn and if n was 3 then you would have a = m*3 for some integer m

which is the definition of being a multiple of 3

but yeah what kaynex said

you also can't prove something by assuming its true (which you do at the top by assuming its congruent to 0 mod 3)

so you should prob just get rid of the entire LHS cuz ur RHS is correct

[lone heart]

@fallen rain Has your question been resolved?

[fallen rain]

thank you

.close

[lone heart]

Channel closed

Closed by @fallen rain

Use .reopen if this was a mistake.

[lone heart]

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.

[naive inlet]

Could you give me a name for this?

the letter n with squiggles

[dusty grove]

Aleph

It's an Arabic letter

[naive inlet]

What does it mean in sums

[dusty grove]

I probably should wait someone more qualified than me to answer
What I know about the notation Aleph_n is that it states the "nth bigger infinity"

For instance

Aleph_0 indicates the countable infinity (natural numbers)

[dusty grove]

What's strange about this question is that both real and irrational numbers are uncountable, so there should be more than 1 answer

Oh wait you can pick more answers

Nvm

[naive inlet]

real numbers was the other correct option

Im a little confused so the Aleph_0 indicates the countable infinity what does Aleph_1 mean

[dusty grove]

Yup, Aleph_1 indicates the "uncountable infinity" such as real numbers, or all the numbers in (0,1)

[naive inlet]

right

[dusty grove]

Uncountable

[naive inlet]

thank you!

[dusty grove]

No problem, but if you want more info about the generic Aleph_n notation I suggest you ask someone more qualified, I only know aleph 0 and 1

[naive inlet]

Thats fine ill do some of my own research on it thank you

[dusty grove]

You're welcome

[naive inlet]

do you know sums?

or anyone else im not sure how this works do i stick with one person?

Which formulas do i use to calculate this?

[vague coral]

$\sum (x+y) = \sum x + \sum y$

[ocean seal]

Herels

[dusty grove]

I'd just do it by hand

I mean, I don't know any other explicit formula in this case

[vague coral]

and we know that $\sum_{k=0}^n k^3 = \frac{n(n+1)(2n+1)}{6}$

[naive inlet]

How would i use the cubed sum and the starting from > 1 sum

[ocean seal]

Herels

[dusty grove]

Oh, wow
The more you know...

[naive inlet]

yea that would take a long time

[naive inlet]

So if i get this correct

You use a sum for the k > 1 as the weird E (x)

and the weird E (y) is the cubed equation

and you add them together

but i get something completely wrong

[vague coral]

what is E

[naive inlet]

sorry idk the proper term for its name

[vague coral]

$\sum_{i=32}^{40} [3+i^3] = \sum_{i=32}^{40} 3 + \sum_{i=32}^{40} i^3$

[ocean seal]

Herels

[naive inlet]

Right so i got half way there

Thank you

the last part

How would i do the sum for the cubed forumula when the counter i > 1

how would i put these together to get an answer

[vague coral]

$\sum_{i=32}^{40}$ is the same as $\sum_{i=1}^{9}$

[ocean seal]

Herels

[vague coral]

because when you sum from 32 to 40, you have 40-32+1=9 terms

[naive inlet]

Im sorry

im still having trouble understanding

If i change that in the equation for cubed i just get that

[naive inlet]

Sorry if im being a pain but im generally trying to understand i just cant get into my head how to put them together even with 9 for n and i =1 it just doesnt make sense to me on how to do this equation

[vague coral]

you are not understanding the formula, or the fact that the sum from 32 to 40 is the same as the sum from 1 to 9 ?

[naive inlet]

Im not understanding any of this

I know that you can change the equation ot this

but then i change this one

to this

and continue with the same cubed formula i showed earlier

and then do this equation

and i end up with the wrong number once i add them together

this is the correct answer and im getting nowhere near that value

[vague coral]

$\sum_{i=32}^{40} 3 = 9 \times 3 = 27$ right ?

[ocean seal]

Herels

[vague coral]

and for i^3, you apply the formula

[naive inlet]

so i would have 27 as the forumula?

like this?

[vague coral]

no no

what are you doing

you have two terms

the sum of 3 gives his result which is 27

the sum of i^3 gives an other result

you add those results

simple

[naive inlet]

this is the sum of that

[vague coral]

look closely at the formula

$\sum_{i=1}^n i^3 = (\frac{n(n+1)}{2})²$

whoops

[ocean seal]

Herels

[vague coral]

the i must starts with 1 obligatory

[naive inlet]

Right

and the n is 40

because that is what was given

or would it be 9 because it was simplified?

[vague coral]

we need to start with 1, thats why I changed the index

[naive inlet]

So its 9

[vague coral]

yes

[naive inlet]

which gives this

2025 + 27 = 2052

[vague coral]

now add this with 27

yes

[naive inlet]

which is incorrect

[vague coral]

then wrong formula

https://cdn.discordapp.com/attachments/490557019623915520/945423703213240330/411882877933060109.png

but I think we are correct

[naive inlet]

this is what was given

[naive inlet]

that is a sum of a squared counter

[vague coral]

oh wait I see why now

[naive inlet]

whats that

[vague coral]

give me one sec

$\sum_{i=32}^{40} i^3 = \sum_{i=32-31}^{40-31} (i+31)^3 = \sum_{i=1}^{9} (i+31)^3$

[ocean seal]

Herels

[vague coral]

$(i+31)^3 = i^3 + 3i² \times 31 + 3i \times 31² + 31^3 = i^3 +93i² + 2883i + 29791$

[naive inlet]

right

[ocean seal]

Herels

[naive inlet]

jeez

thats now confusing

[vague coral]

well the calculations are starting to become uglier

[naive inlet]

Surely one of the formulas do iy

That's what I'm being taught is to use calculations but I'm just confused I'll have to refer back to my videos but thanks for the help so far

[vague coral]

$\sum_{i=1}^{9} (i+31)^3 = \sum_{i=1}^{9} i^3 + 93\sum_{i=1}^{9} i^2 + 2883\sum_{i=1}^{9} i + 29791 \times 9$

[ocean seal]

Herels

[vague coral]

ok

[naive inlet]

I'll check if ur calculations work but ni bet they do cause ur amazing

Thank you so much for this all

[vague coral]

maybe I'm wrong lol

[vague coral]

no problem

[lone heart]

@naive inlet Has your question been resolved?

[tacit arch]

There's nothing wrong with this approach, but it might be simpler to just write the sum from 32 to 40 as a difference of sums: sum from 1 to 40 minus sum from 1 to 31

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[elder lark]

am I doing positive work when I compress a spring?

[elder lark]

spring
|-8888 (rest)
|-***<--- force

[manic wind]

Well reference the equation for Work and see if it is positive or negative

(for this case)

[elder lark]

the force for the spring is messing me up because it's negative right

fspring = -kx, x displacement, k coeff

[manic wind]

Well first define which direction is positive or negative

[elder lark]

I'm defining to the left of the spring negative to the right positive

[manic wind]

So compressing would be negative displacement?

[elder lark]

yes

so would that be
work = force * displacement
work = fspring * displacement
work = -kx*-x
work = kx^2? -> work = positive?

[manic wind]

Well no

You need to integrate

W = Fs cos theta assumes constant force

[elder lark]

yeah we have constant force

[manic wind]

The spring does not apply a constant force

[elder lark]

we compress it to a specific amount in the question I think

i see what you're saying

[manic wind]

Still thats not constant force

[elder lark]

however, would the overall sign be positive still?

assuming we integrated and whichever

please haha we haven't gone over integration just wondering on the end product

[manic wind]

If you want an intuitive answer, negative work means storing energy, so when you compress a spring, now it has spring potential energy. And you had to put in positive work

[manic wind]

The spring does negative work, so yes you would be doing positive work

Positive work = spending energy
Negative work = storing energy

[elder lark]

cool, thanks

[lone heart]

@elder lark Has your question been resolved?

Channel closed

Closed by @elder lark

Use .reopen if this was a mistake.

[lone heart]

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.

[spark latch]

I am confused

would an equation opposite of the integral of d(t) not work?

[placid zinc]

d(t) is the rate at which sand is removed during the hurricane.
r(p) is the rate at which sand is added during the reclamation project.

d(t) and r(p) don't relate at all, haha

[spark latch]

ohh then I have no clue what I am doing

lol

[placid zinc]

If r(p) is the rate sand is added, then
integral of r(p) dp is the amount of sand that has been added

[placid zinc]

Wait, you are correct, haha

Just, I think they want another half of that

Okay so they do relate, with some kind of integral

Finding that relation is the idea

[spark latch]

what other half?

[placid zinc]

integral of d(t) dt [from 0 to 10] is the amount of sand that was lost

That does not answer "how long was the reclamation project?"

[spark latch]

• integral[0, 10] d(t)dx = integral[0, p??] r(p)dp ????

[placid zinc]

Nailed it

But rather than use ??, put n or something

Then, if you were to solve for the number of days, you'd solve for n

(The question tells you not to do this, though)

I'm not being clear. I mean this:
-integral[0, 10] d(t)dx = integral[0, n] r(p)dp

[spark latch]

would using p instead of n not be alright?

I am not sure what using p does to the logic of the equation

because the question does say p is the number of days

[placid zinc]

p is a dummy variable to the integral

p doesn't represent "number of days to finish the project" it represents "current day of the project"

Where n is some unknown that actually represents "last day of the project"

p can change. n is a constant unknown.

Importantly, it will be used up in the integral and has to disappear after this.

[spark latch]

alright yeah that makes sense

how would I better explain how I came to this conclusion

[placid zinc]

-Amount of sand lost = Amount needed to fill

-integral[0, 10] d(t)dt = integral[0, n] r(p)dp

[spark latch]

okay yeah makes sense

the way I had thought in my head was more confusing but same thing

alr ty

.close

[lone heart]

Channel closed

Closed by @spark latch

Use .reopen if this was a mistake.

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.

[green marsh]

Hi. I am having issues with a word problem for my coding class

[green marsh]

It states that assume price is an integer variable whose value is the price in cents of an item. Assuming the item is paid for with a minimum amount of change and just single dollars, write an expression for the amount of change (in cents) that would have to be paid

So from my understanding, it’s saying that the price

Is an integer

Like 10.00

But not like 10.01 Bc it’s saying that the amount is paid in single dollars

Meaning that there is no change

I’m not sure how this makes sense

Bc then I’m guessing they want you to find the remainder

Of the price

Which is the cents

?

I just need clarification tbh

What I put was an equation to calculate the cents you get back

But apparently that’s wrong

So I’m not sure what the question is asking me to do

[hasty elk]

i think it's a price (in cents) that's an integer, for example $1 will be interpreted as the value 100

[lone heart]

@green marsh Has your question been resolved?

Channel closed

Closed by @green marsh

Use .reopen if this was a mistake.

[stoic lynx]

7198=9x−2

[lone heart]

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.

[leaden glacier]

for the first one i did the area of a triangle and then the second i took that area *2 and then took the area of the rectangle

[vague coral]

the area of the first must be sqrt(2) if im not wrong

[dense sleet]

Isnt the area from 0 to 2 0? Bc of the negative and positive area?

[leaden glacier]

it would be -2 if u did -2(2)/2

[dense sleet]

What is the question here?

Cant you just click and check answers if you think thats right?

[leaden glacier]

oh yeah 0 is right

how did you do that though?

[dense sleet]

Well it asks you area from 0 to 2

I saw triangle in negative part and triangle in positive part. So they both cancel ane you get 0

[leaden glacier]

isn't it just one big triangle?

[dense sleet]

No its 2 triangles

[leaden glacier]

how come , i thought you had to count everything within 0 and 2

[dense sleet]

Im bad at drawing

But there you go

1 triangle below x axis and 1 above

They cancel and you get 0

[dense sleet]

Umm no

[leaden glacier]

the square doesn't count?

[dense sleet]

It doesnt

Nor the red thing you draw down there

[dense sleet]

This is what you calculate with integral

[leaden glacier]

im confused

[dense sleet]

When graph is under x axis you calculate whats above line to x axis. And when its above you calculate whats below it

[leaden glacier]

so the triangle under turns into a positive?

and then the triangle above is negative?

[dense sleet]

The triangle under is negative area and triangle above is positive area

Let me give you example

,w plot x - 1 from 0 to 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pluton#6301

[dense sleet]

,w integrate x - 1 from 0 to 1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pluton#6301

[dense sleet]

,w integrate x - 1 from 1 to 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pluton#6301

[dense sleet]

They cancel and you get 0

[leaden glacier]

oh i see

but then why doesn't the square count

[dense sleet]

Which squqre

[dense sleet]

The one you draw here with blue lines

[leaden glacier]

yes

[dense sleet]

That is outside of what integral counts

That is area under the graph under x axis

,w plot -1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pluton#6301

[dense sleet]

Like here if you integrate it will calculate negative area above the graph

The area under means nothing

[leaden glacier]

oh ok

so the shape counts within the squares on the graph

[dense sleet]

Can you rephrase?

[leaden glacier]

like the line makes a shape within the box that it is in on the graph i showed

and if it is above the shape is from the line down to the x axis

[dense sleet]

Yes

[leaden glacier]

and if it's under it goes up to the x axis as well?

[dense sleet]

From any point you are integrating you should be able to draw lines to the x axis to represant what you are calculating

[leaden glacier]

oh ok

thanks a lot

[dense sleet]

In this example

Drive 2 lines 1 in point 0 that connects - 1 and x axie and at point 2 that connects 1 to x axis

And thats your shape

No more lines

[leaden glacier]

oh ok

[dense sleet]

Your x line counts as a line

[leaden glacier]

ok thank you

i understand now

.close

[lone heart]

Channel closed

Closed by @leaden glacier

Use .reopen if this was a mistake.

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.

[bleak latch]

how do i show that the limit doesnt exist

cuz if i do y=x or y=2x, itll still give e^(-1/0)

or would y=x+1 work?

.close

[lone heart]

Channel closed

Closed by @bleak latch

Use .reopen if this was a mistake.

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.

[alpine sable]

How do you find the volume of a rectangular prism( Cereal box) Using Lego Pieces

[alpine sable]

are they special pieces?

or just regular ol' Legos

you can approximate the volume by placing them consecutively layer by layer and then counting the amount needed to fill the object

but that seems too obvious

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Ok. They are Regular legos

[lone heart]

Channel closed

Closed by @subtle valve

Use .reopen if this was a mistake.

[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

i mean X

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[tough dawn]

I need help with this. I wrote down what I did and I got 30.7 which is obviously wrong.

[little drum]

find another help channel

#❓how-to-get-help

[little drum]

Do you know cosine law?

Apply what's given there smh..

[tough dawn]

Ya I have an understanding of it but I don't think I did it right

[little drum]

$c^2 = a^2 + b^2 - 2ab \cos C$

[tough dawn]

I did ;-;

[little drum]

what's the C vertex?

[tough dawn]

30?

[little drum]

Vertexxxxx

and 30° yes

what's the side "a"?

[tough dawn]

16

Here let me just show you what I wrote

[little drum]

,w 16^2 + 30^2 - 2(16)(30)(√3)/2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ansh#3502

[little drum]

....

Da heck

,calc 21630

[ocean seal]

Result:

960

[little drum]

why is cos(30°) 0.15?

[tough dawn]

That's what Google said it was

[little drum]

,calc cos(30)

[ocean seal]

Result:

0.15425144988758

[little drum]

aaaaaaaaaaaaaa they taking the 30 in radians

You're supposed to enter 30 degrees

[tough dawn]

Oh ok

So if you do the sqrt of 3 then divide that by 2 it should be 0.865

Or I guess 0.86

[little drum]

,calc sqrt(3)/2

[ocean seal]

Result:

0.86602540378444

[tough dawn]

Ok so ya 0.86

After doing the math I got 15 and that's also wrong

[little drum]

._.

,calc sqrt(324.6156)

[ocean seal]

Result:

18.017091885207

[little drum]

Is that wrong?

[tough dawn]

No that's right

I don't understand how you got 324.6156 tho

.close

[lone heart]

Channel closed

Closed by @tough dawn

Use .reopen if this was a mistake.

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.

[forest ore]

Could anyone help me to solve this two?

[tacit arch]

What have you tried so far for 3

[tacit arch]

So far so good for 3.

What's B?

[tacit arch]

Oh that's b and not a 6

[tacit arch]

Solve for B here. The numerator to (3x+2)

[lone heart]

@forest ore Has your question been resolved?

[forest ore]

Yes. Finally , I have solved it.

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[lethal sinew]

So far what I have is
Consider that n is even
i^n=i^2y

which equals (-1)^y

And for odd I'm kind of stuck

[alpine sable]

Hmm

[wanton valley]

Well

[alpine sable]

What do u think

Multiplying

By i

Does

To a point in space

[wanton valley]

Visually

[alpine sable]

No tell me

[wanton valley]

?

[alpine sable]

90 degree rotation

Multiplying by i rotates by 90 degress

[wanton valley]

I didnt ask the question

[alpine sable]

i^n = rotating the point0+1i by 90 degress n times

[alpine sable]

I am telling him ☠️

[lethal sinew]

Hi, me, yes, I asked the question lol

[wanton valley]

Owh okay sorry im tired xd

[lethal sinew]

Relatable XD

[alpine sable]

U get it @lethal sinew

[lethal sinew]

Not really 😅

[alpine sable]

Uh

Have u learned imaginary graphs

Or only the fact

[lethal sinew]

Nope

[alpine sable]

That i=sqrt(-1)

[lethal sinew]

Oh

[alpine sable]

☠️ then I don't think u solve that

Do u know what multiplying by i does geometrically?

[lethal sinew]

💀

[lethal sinew]

Multiplying what by i? 😅

[wanton valley]

Zizi

[alpine sable]

This thing

Here

[lethal sinew]

Yes?

[alpine sable]

Take a look

[lethal sinew]

Oh, ok!

[alpine sable]

Do u recognize that

Or have learned it?

[lethal sinew]

I recognize it, yeah

[alpine sable]

So i * i * i = i^3

And i * i= -1

That -1* i=-i

This is how u solve that

[lethal sinew]

Right ok

[alpine sable]

Now tell what will be i^4

What do u think

[lethal sinew]

1

[alpine sable]

Yes

And i^5

[lethal sinew]

-1

[alpine sable]

How

i^5=i^4*i

So what will it be?

[lethal sinew]

Uhm
-1?

[alpine sable]

Dude

i^4=1

so

[lethal sinew]

Aight

[alpine sable]

i^5=1 * i

So i^5=i

[lethal sinew]

i

[alpine sable]

Using that u can easily compute for higher exponents

As it will just repeat

[lethal sinew]

Ohhhh

Ok so I just look for the pattern?

[alpine sable]

Ya

[lethal sinew]

Tysm! I got it now

.close

[lone heart]

Channel closed

Closed by @lethal sinew

Use .reopen if this was a mistake.

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.

[waxen spruce]

how would you do f

[alpine sable]

I guess

U can break it down

Into a triangle

And a semi circle

And calculate those areas

The semi circle will have a negative area

[waxen spruce]

Right but how would hte + 2 part work

[alpine sable]

Wait what's hte?

I guess

U are trying to compute those integrals

The first one should be -1/4*pi *2 *2

Same as -pi

[waxen spruce]

the

[waxen spruce]

Wat

[alpine sable]

Dude

U see a semicircle

Yea?

What's it's area

Even simply

What's its radius?

[waxen spruce]

I get that

But what is the +2 part

in f

[alpine sable]

Ah now I understand

[alpine sable]

I thought f meant the function

Rather than the question XD

[waxen spruce]

LOL

but how owould you do it in question f

[alpine sable]

Ok

If I rephrase

f(x) +2

What effect does the +2 have?

What do u think?

[waxen spruce]

it shifts two up

[alpine sable]

And what will happen to the area

[waxen spruce]

it goes up

well

no

it stays

positive

*constnat

[alpine sable]

Ya

Now when it will be shifted

By 2

What will be the area

Of the semicircle

It will be shifted by 2

[waxen spruce]

da same

[alpine sable]

Which is it's radius

So all that will change

Is it becoming positive

From negative?

[waxen spruce]

Yessss

[alpine sable]

What about the triangle

5*2+previous area

Right?

[waxen spruce]

Yeah

[alpine sable]

And the right angled triangle

On the left side

What will happen to that?

[waxen spruce]

it goes up

[alpine sable]

I mean like the previous objects

What will be it's new area

[waxen spruce]

the same

[alpine sable]

Nope

It's going to become positive first thing for sure

3+|previous area|

Right?

Imagine it

Break it down

To a rectangle

And a triangle on top of it

[waxen spruce]

Yeah

[alpine sable]

Then add of these up

U have ur answer

[waxen spruce]

ah thank you

.close

[lone heart]

Channel closed

Closed by @waxen spruce

Use .reopen if this was a mistake.

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.

[half frost]

Hello, I'm working a a game project. I have a character who is walking and then on release of a key press, the character decelerates to a stop. His feet/legs are independent of the movement... meaning his feet just cycles. Even if the character is stopped the feet are still walking in place. I have the ability to control the animation of the feet so that they can slow and stop. What information would I need to be able to calculate the correct slowing curve? I have the deceleration amount, I have the distance to stop. What else would I need?

[half frost]

.close

[lone heart]

Channel closed

Closed by @half frost

Use .reopen if this was a mistake.

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.

[alpine sable]

hi! may i get help with these two questions, please?

[lone heart]

Channel closed

Closed by @wide gulch

Use .reopen if this was a mistake.

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.

[alpine sable]

how can i do this with letting u = root x?

[buoyant kayak]

do you have to do it that way?

cause if so i'm not sure

[alpine sable]

not necessarily but wouldnt it be a lot easier?

[buoyant kayak]

i'm not sure how you'd apply that

note that you have a sum of cubes within that 1/3 power

[alpine sable]

i was thinking setting u=cuberoot x n then the bottom as u^3

how could we do it without the variables?

[buoyant kayak]

i mean you're gonna wanna do a sub

just probably not any root of x

you normally look for composite functions when you do subs

[covert agate]

difference of cubes identity would be helpful

[buoyant kayak]

not yet

[alpine sable]

i dont c how id use it?

[alpine sable]

got no clue what that is

[buoyant kayak]

cause you're not on that step yet

i'll give you this: your sub is gonna be what's inside the power

you might be able to do something from there

[alpine sable]

ok

ill try that

[little drum]

Let $u = \sqrt[3]{x}$. Then what? I'll just substitute it for you and show you what you're speaking... $$\lim_{u \to 0} \frac{(343 + u^3)^{\frac{1}{3}} - 7}{u^3}$$

[little drum]

how does that help in the slightest?

[buoyant kayak]

and also, by this, when i say composite functions, i'm talking about functions within functions. f(g(x)). (343+x)^{1/3} is the function g(x)=343+x within the function f(x)=x^{1/3}

if that makes sense

[alpine sable]

well for one it would be outside the bracket but yeah it still leaves me with 0/0

[alpine sable]

i dont think we learned those

[buoyant kayak]

well it's more of an algebra thing, so if your algebra teacher missed it, they probably won't reteach it in calc/precalc

[alpine sable]

i tried

doing

u=7+cuberootx and i still get 0/0 as my final answer

[little drum]

⁉️

[buoyant kayak]

7+cbrtx is not within your power

[little drum]

shhh

[alpine sable]

cuberoot 343 is 7

[little drum]

Do you know the identity for $$a^3 - b^3$$??

[buoyant kayak]

why are you taking the cube root of 343

ansh he hasn't got the sub down he can't do that yet :(

[alpine sable]

(a-b)(a^2+ab+b^2)

[alpine sable]

cuz its in the bracket i thought that u meant to make the bracket = too some variable

[buoyant kayak]

no i mean literally make the stuff inside those parenthesis your u

[alpine sable]

so cuberoot u - 7 is the numerator

[buoyant kayak]

yes

[alpine sable]

ok then next what?

[buoyant kayak]

well you gotta change your limit and the denominator to get that in terms of u as well;

[alpine sable]

denominator is u^3-343?

[buoyant kayak]

why'd you cube u?

you set u=343+x

solve for x

[alpine sable]

u-343

[buoyant kayak]

right

and your new limit?

[alpine sable]

343?

[buoyant kayak]

u approaches 343, yes

so now you're at $\lim_{u\to 343}\frac{u^\frac13-7}{u-343}$

[ocean seal]

a disappointing son

[buoyant kayak]

now we can make another sub to get this into a friendlier form

we don't like that power there

looks gross

so sub it in

with something else

[alpine sable]

ok so say we do p then (p-7)/(p^3-343)

[buoyant kayak]

right, and compute your new limit

[alpine sable]

7?

[buoyant kayak]

p approaches 7, yup

so now you have $\lim_{p\to 7}\frac{p-7}{p^3-343}$

[ocean seal]

a disappointing son

[alpine sable]

still equals 0

[buoyant kayak]

now comes time for this

[alpine sable]

ok

so the bottom is (p-7)(p^2+7p+343)

[buoyant kayak]

looks good

[alpine sable]

so 1/441?

[buoyant kayak]

wait

not 343, sorry

[alpine sable]

o

49

[buoyant kayak]

yea

[alpine sable]

ahh i got it thxx

[buoyant kayak]

👍

[little drum]

wdym? $$\lim_{x \to 0} \frac{(343+x)^{\frac{1}{3}} - 7}{x} = \lim_{x \to 0} \frac{(343 + x) - 7^3}{x[(343+x)^{2/3} + 7(343 + x)^{1/3} + 7^2]}$$

you just use the identity as it is

[buoyant kayak]

very difficult to recognize and apply

[little drum]

:O

bleaks out lol

[buoyant kayak]

i bleak out a lot

[alpine sable]

alr guys tysm btw appreciate the time

.close

[lone heart]

Channel closed

Closed by @rose oxide

Use .reopen if this was a mistake.

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.

[sand dagger]

i did this alone, and ended up getting 3.6 Cm

the video stated 7.2 cm