help-28

[eager obsidian]

Well, consider two numbers with a common divisor of 2024

they would have 2 as a common divisor too then

so 2024 cant be "minimum"

[vague panther]

I mean all lcm(a, b)= 2024

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[tardy elk]

im being dumb asking chem but can anyone answer this ?

[tardy elk]

@full forum

[nimble crane]

<@&268886789983436800>

[tardy elk]

<@&268886789983436800>

<@&286206848099549185>

[limpid junco]

I would suggest maybe try asking in #old-network chemistry server

[tardy elk]

sure thanks

[nimble crane]

yeah this is a full on chemistry problem, and i havent done IUPAC naming in a year lol

[tardy elk]

lmao i mean im being dumb asking chem in maths server

[azure eagle]

Won't it just be pentan-2-on and 2,2-dimethylopropan

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[fluid prawn]

Is this measuring the length or width?

[brave crater]

width, if its the shorter one

[fluid prawn]

Ok so r length and height the same thing

[brave crater]

well length denotes how long it is, height denotes how tall it is, breadth denotes how broad it is

[fluid prawn]

So in here they’re both the same thing?

[brave crater]

look, it depends how you place the object. say you have placed the book (or whatever it is) like you have in the image you shared. then your breadth is what you asked, length is the longer one and height is basically the thickness of the book (here)

[fluid prawn]

I thought thickness was width

Well thickness is like 1 cm??

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@fluid prawn Has your question been resolved?

[deep mauve]

Actually there is no difference between them it depends on what you say

And maybe how the object stands is important

But i don't think it makes any mathematical sense

They are just any of the 3 dimensions

But it is natural that they have names such as height and thickness to make it easier to understand

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[vestal night]

again, can someone show me how to find the solutions in this interval?

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[vestal night]

again, can someone show me how to find the solutions in this interval?

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[hidden terrace]

can someone calculate this for me? its just a definite integral but i cant find anything that can do it pls help

[viral jasper]

!xy

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

[hidden terrace]

its not a problem

i just need to know the answer to that integral

its a surface area of a solid of revolution formula

[viral jasper]

https://xyproblem.info

[hidden terrace]

if u cant help just say so lol

[wise wyvern]

I don't think many people would want to help you without knowing the context.

Or with that attitude of yours.

[hidden terrace]

i didnt mean to sound rude

i just didnt want him to waste time on me which he could help others with

[viral jasper]

I'm trying to help by saying that what you are asking for sounds ridiculous and without context I doubt anyone is willing to help. I predict solving that integral is a waste of time unless we understand how you got to it in the first place

[viral jasper]

I do actually recommend you read this

[hidden terrace]

Its a surface area of a solid of revolution and im doing it for an egg
this is the original function for the egg:

https://nyjp07.com/index_egg_E.html i got the original function from this website

[viral jasper]

Oh were those your estimates of an egg surface?

[hidden terrace]

yes

I tried using calculators online and my gdc but i cant get either to work

I was hoping someone knew a software i didnt

[minor crater]

insane lmao

i mean you can use wolfram alpha

just good luck trying to retype that correctly

[viral jasper]

It might exceed computation time tho

[minor crater]

or desmos

[hidden terrace]

desmos didnt work ill try wolfram

[minor crater]

eh, maybe. but computers are pretty damn fast at numerical computation

[hidden terrace]

yes lmao i tried doing it on a gdc and i got it stuck

[minor crater]

i don't think they want a precise result lol

[nova sigil]

Use python + mpmath + trapezium rule

[viral jasper]

Yeah but wolfram is pretty damn finicky about how much computation time it gives out for free

[hidden terrace]

alright thanks ill try those and sorry if i came of as rude

one last question

can wolfram be wrong?

[nova sigil]

Of course

Numerical procedures break down all the time

[minor crater]

are you getting something weird?

[hidden terrace]

well im gonna look at the value and see if it sounds plausable

[minor crater]

oh wait

[hidden terrace]

Yeah but im reintering it

[nova sigil]

I research numerical methods for solving non linear ODEs and answers blow up all the time. I doubt a simple integral would cause Wolfram to break tho

[hidden terrace]

that would make things simpler but for the sake of my report thing i have to show every step

Anyway i think that would be all

thanks

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[summer carbon]

how can you find the center of mass of a 1d line?

[summer carbon]

if you have a density function

[summer echo]

You take the weighted average of all positions, this is an integral. Do you have a specific question?

[summer carbon]

yup

[wise wyvern]

How'd you get that?

(also note, the dimension doesn't match)

[summer echo]

That's the average density, not the center of mass

*multiplied by the length

[summer carbon]

should it be to the first power?

[summer echo]

You would want $$\int_0^L \rho(x)\cdot x \dd x$$

[glossy valve]

Jelle

[wise wyvern]

no

[summer carbon]

I tried that

it's incorrect

[wise wyvern]

$\f{\int_0^L \rho(x)\cdot x \dd x}{\int_0^L \rho(x) \dd x}$

There.

[summer echo]

Oh, yes you're right

divide by the mass

[wise wyvern]

Of course.

[glossy valve]

! What the hell am I doing here?

[wise wyvern]

It's $\f{\int \dd m x}{\int \dd m}$ in general

[glossy valve]

! What the hell am I doing here?

[summer carbon]

why tho

[wise wyvern]

Centre of mass is meant to be a point about which the moment of mass is zero.
If it's a point, it cannot really be something like mass * x. (it needs to be just x)

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[desert cypress]

how do i start 14

[desert cypress]

like ik c will be zero

bec f(0)

but a and b

i duno how to figure out

[versed wagon]

yo

https://i.imgur.com/UM4AnJc.png

does anyone know why its like that

the primitive

[desert cypress]

bruuh go to ur own help slot thing

😭

[devout valley]

!occupied, but do a substitution for sin(x)

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[versed wagon]

how :(

[devout valley]

As for here, you're aware that polynomials/quadratics are continuous, right?

[desert cypress]

yes

[devout valley]

take #help-44｜stanley-🌲-v2-dans quickly before it goes!

[devout valley]

Anyways, can you use the fact $\lim_{x\to 1} f(x) = 5$ and $\lim_{x\to -2} f(x) = 8$ to write an equation?

[glossy valve]

@devout valley

[desert cypress]

how

[devout valley]

(do you know what continuity implies about those limits?)

[desert cypress]

no

[devout valley]

Hmmm, what do you know about continuity? Do you know how it's defined?

[desert cypress]

didnt take it yet

toms lesson

[devout valley]

I see, anyways, a tl;dr is that a function is continuous at a point, say $a$, if $\lim_{x\to a} f(x) = f(a)$ (that is the limit exists, and is equal to the function value at that point)

[glossy valve]

@devout valley

[devout valley]

Having been given that, can you then maybe rewrite the fact that $\lim_{x\to 1} f(x) = 5$ and $\lim_{x\to -2} f(x) = 8$, knowing that $f$ is continuous?

[glossy valve]

@devout valley

[desert cypress]

help

ngl

i dont get this

[devout valley]

continuity is basically saying "get rid of the limit sign, and you can then replace x in the function with the numbers you're going to"

[desert cypress]

yea

[devout valley]

Do you know how to take limits?

[desert cypress]

sub x

for z

x

[devout valley]

Welllll, I'll take that...

Can you do that with $\lim_{x\to 1} ax^2 + bx$ for me? You concluded correctly that $c=0$

[glossy valve]

@devout valley

[desert cypress]

a(1)^2+b(1)=5

[devout valley]

Cool, and now, that is equal to 5

Can you do similar for the limit $\lim_{x\to -2} ax^2 + bx$, and simplify what you get?

[glossy valve]

@devout valley

[desert cypress]

a+b=5

[devout valley]

a + b, the 1 is the only term squared

[desert cypress]

a(2)^2+b(2)=8

oops

4a-2b=8

[devout valley]

Perfect

You have a + b = 5 and 4a - 2b = 8, can you solve those?

[desert cypress]

wait its -2

[devout valley]

Yea fixed

[devout valley]

(may be worth noting the second equation you could write as 2a - b = 4...)

[desert cypress]

yes

[devout valley]

Yes as in you're happy to solve those for a and b?

[desert cypress]

wait

for the second one

u just divide

?

can i leave it as is

or

what

[devout valley]

You can divide by 2, if you find
a + b = 5
2a - b = 4
easier to solve

[desert cypress]

okay

a=3

b=2

c=0

elimination

[devout valley]

There you go, looking good

[desert cypress]

yayay tysmmm

ur so smart

gimmie ur brains

🧠

[devout valley]

Heheh, if only that were possible

[desert cypress]

tyy

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[rare plover]

Help

[rare plover]

Can someone check my work

Did I interrupt this question right

[stiff musk]

looks fine

[rare plover]

Thank you

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[vapid mango]

Need help with how to approach this. Tried integration by parts but got way too messy fast.

[fossil stump]

What if you try a substitution?

[vapid mango]

Thanks, did u-sub and it worked out nicely

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[river wave]

Just small question

When taking the limit

-ln|b+3| goes to negative infinity

And ln|b+2| goes to positive

And they cancel right

To give an answer of ln(2)

[pearl trout]

You can't take the limits separately

but you can simplify -ln(b+3)+ln(b+2)

[river wave]

Oh

But they cancel out right

[pearl trout]

The limit of -ln(b+3)+ln(b+2) as b approaches infinity is not zero if that's what you're asking

wait nevermind it is zero

[river wave]

Yeah

[pearl trout]

but you should carefully justify why that is

using the continuity of the natural logarithm

[rapid rain]

It is 0, but to prove it you cant be like "inf - inf"

[river wave]

What is the answe then

After taking the limit

[rapid rain]

Use log properties

Before taking the lim

[river wave]

Ln(ab

Right product

[rapid rain]

you have smthg of the form ln(x) - ln(y)

So almost product

[river wave]

Oh

Quotient

If you rearrange

Yeah

[rapid rain]

Ye so -ln(b+3)+ln(b+2) =

[river wave]

Ln(b+2/b+3)

Bottom goes to infinity faster

Right

[rapid rain]

No

[river wave]

Oh

[rapid rain]

Think about what the thing inside the log should be so that ln(that) = 0

[river wave]

-2

[rapid rain]

Uh

[river wave]

Wait

Nvm

Uh

Has to be ln(1)

Wait

Infinity over infinity

Ln(1) = 0

Is that correct

[rapid rain]

Again, inf/inf is not satisfying

b²/b is infinity/infinity and yet it goes to infinity

[river wave]

Ok

Uh

[rapid rain]

We need a better justification for why b+2/b+3 goes to 1

[river wave]

Idk

Not sure

[rapid rain]

Can you try to get rid of the b in the numerator?

[river wave]

Lhoptial

?

[rapid rain]

(Ie doing division of b+2 by b+3)

[river wave]

Oh

[rapid rain]

Possible, but really unneeded

[river wave]

Is that polynomial long division

[rapid rain]

Yeah

b+2 = C(b+3) + D

Should be quite easy...

[river wave]

1-(1/b+3)

[rapid rain]

Exactly

Now it should be straightforward

[river wave]

So it’s ln(1)+ln(2)

Once limit taken

So ln(2)

[rapid rain]

ln2 - ln1 but yes

[river wave]

Thanks

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[void portal]

i put this as my answer and it was marked wrong

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@void portal Has your question been resolved?

[void portal]

<@&286206848099549185>

[void portal]

<@&286206848099549185>

[polar valve]

real numbers? pi workers?

[void portal]

huh

these are all the options for the thing at the end

and for all the answers under it u can choose makes sense or doesnt make sense

[polar valve]

i would choose positive integers for the last point.

[void portal]

is that all i need to change

i cant get it wrong anymore

or i have to do 2 questions instead of just one

[polar valve]

f(5.5) does not make sense for me. or do you know 5.5 fulltime workers?

but you decide what to change/not to change.

[void portal]

well i mean it could be 5 workers and one worker only does half the job

[polar valve]

then he is not full time.

[void portal]

so would that not make the thing be does NOT make sense

[polar valve]

and you cant add or taken off someone.

[void portal]

right so this would be my final answer

[polar valve]

thats what i said: f(5.5) does not make sense for me. o

[void portal]

yeah i was just trying to make 100% sure

it was correct

thank you bro

i still have 2 questions that i might need help on can i lyk

ok im pretty sure this is right but im not sure if i made a mistake.

@polar valve

[polar valve]

you can buy -5 gallons of paint? you can buy pi gallons of paint?

[void portal]

wdym

theres no -5

and where is there pi

ohh are u refering to because i put all real numbers

[polar valve]

youre last answer ist "all real numbers". -5 is a real number. pi is a real number. so can you buy -5 gallons paint? can you buy pi gallons of paint?

[void portal]

yeah that makes sense

so what should it be? non negitive real numbers?

[polar valve]

pi is non negative

[void portal]

hm

positve integers?

i honestly dont know

i was absent the whole unit when we learned this so ive just been using common snese

sense*

[polar valve]

i dont know what you can buy in your country. can you buy one half gallon? maybe. then integer would be wrong., but i am pretty sure, you cant buy pi gallons. no one would be able to measure exact pi.

[void portal]

huh

Which one of these would be correct

[polar valve]

in "my world" none of them. i would choose maybe positive integers or - if you can buy a half gallon - non negative real numbers. but it doesnt feel right for me.

[void portal]

it was non negitve real numbers

i think ur just over compliacting it, Its alegbra 1, we havent done anything with pie yet

[polar valve]

then try to buy sqrt(2) gallons. but anyway.

[void portal]

ok so last one, Just answered this confidently but i got it wrong, So i only have one try left

@polar valve

[polar valve]

how do you get f(-20)=-1.6? and again sqrt(2) stairs?

but i am sure, i am overcomplicating.

you should ask someone else.

[void portal]

is that sarcaism or r u fr?

i did 1/100(5(-20)+3(-20)

and got -1.6

[polar valve]

its (5|-20|+3(-20))/100 which gives 0,4 for me.

[void portal]

oh okay i must have done that wrong.

if its not too much trouble could you double check the other ones too?

thanks for the help btw fr

[polar valve]

the other two values look ok for me.

[void portal]

ok so everything here is good?

@polar valve

??

<@&286206848099549185>

[full forum]

@void portal Has your question been resolved?

[void portal]

<@&286206848099549185>

[void portal]

@torn jolt yo i saw u helpin someone else u think u can help me on one problem rq

[torn jolt]

sure

[void portal]

okay so i was asking this other dude and he helped me but im not sure if this is still right

cause if i miss this i have to do 2 questions instead of one

u can put this for the last answer

and then for the other 3 u just put makes sense or does NOT make sense

[torn jolt]

it looks right to me

oh wait

for 42.5

it doesn't make sense

@void portal

[void portal]

ok

how tho

[torn jolt]

you can't run up half a step

because that would mean stopping mid air

[torn jolt]

and for this one, it's only integers

[void portal]

but its .4 at the end for all of them

[void portal]

ok

[torn jolt]

burning a decimal amount of calories does make sense

but you can't take like one half of a step

it's either you take a step, or you don't

[void portal]

ohh

okay

so this is right?

[torn jolt]

yes

[void portal]

dang

it was incorrect

[torn jolt]

really?

that's weird

what part was wrong?

[void portal]

oohhh

crap it was

but

look i forgot to put a context on the second answer

cause it reset everything and i re put in everything

[torn jolt]

oh

okay

because i was confused about what i did wrong because everything should be right

[void portal]

gotta do 2 questions now 😭

[torn jolt]

rip 😭

[void portal]

yeah u did everything right just i made a mistake

alr so i think i got all three answers right but im not sure for the last thing

@torn jolt

[torn jolt]

uhhh since it is an exponential equation

it should have all real numbers as its domain

the only restriction it has is on the range

[void portal]

wdym

like this

[torn jolt]

what are your choices?

[void portal]

no choices for the 2 things after the first

just type in the boxes

but for the first its still the same

[torn jolt]

it's just all real numbers

[void portal]

thanks it was correct

one more

i dont think i did this one right

@torn jolt

[torn jolt]

everything is right except the last part

[void portal]

what should the last one be?

[torn jolt]

you can't sell part of a t-shirt

so it can't be all real numbers

[void portal]

ok

so what should it be

@torn jolt

[torn jolt]

does it make sense to sell negative t-shirts?

[void portal]

no

bro can u just tell me the answer i gotta wake up super early tmrw and im tryna get some sleep 😭

@torn jolt

[torn jolt]

it's just whole numbers

[void portal]

something wrong

[torn jolt]

weird

actually

it's either positive integers or integers in a≤x≤b

[void portal]

yeah idk

which one would it be?

@torn jolt

[torn jolt]

how many attempts do you get here

[void portal]

2

already used one

so if i get the next one wrong i gotta do 2 again

[torn jolt]

technically it's positive integers, but i feel like it's integers in a≤x≤b

[void portal]

ok

[torn jolt]

because there are some amount of t-shirts that wouldn't produce a profit

but then it wouldn't make sense for them to sell like 109,983 shirts

[void portal]

alr

i dont even understand what ur talkin about imma be honest

which ever one u think is right i will put

u figure it out?? @torn jolt

[torn jolt]

Sorry I’m busy doing my own work

[void portal]

ur good

[lean venture]

can anyone explain to me what’s wrong.

[void portal]

make ur own thing

#❓how-to-get-help

[lean venture]

mb idk how to do that can i just dm u rq

[void portal]

nah i need help with my own stuff

this is my help thing u can make ur own at #❓how-to-get-help

[turbid jacinth]

@void portal Notice that whatever you choose for "does NOT make sense in this context" should be outside the domain

you put that f(2) does not make sense, so that would imply that 2 is not in the domain

2 is in all of the domains except either the real numbers or integers a<x<b

I think f(17.5) would rule out 'real numbers a<x<b' so you're left with one option

however, in my opinion, f(2) does make sense in this context

a negative profit is just a loss

and it makes sense (to me) that if you don't sell enough shirts you aren't profitable

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[void hearth]

Can anyone solve this? The issue is that i dont know how to approach the summation

you could first do the left side, transferring n = 8 to the right

you could do them simultaneously

or you could say that n = 3

<@&286206848099549185>

[hollow wyvern]

No idea what any of this means

But the one on the right doesn't have an i in it, are you sure that's right?

[void hearth]

yes

[void hearth]

ok basically

u could increment through the 1st summation

and n ends up being 8 at the end

and if u know how to code u can think of it as a variable

and then u put that "variable" into the next summation

or you could do the summations simultaneously

so when n = 4 on the left for example, you do the 1st summation and on the next one you would go from i=1-->4

[pulsar carbon]

What is the context of this expression?

[hollow wyvern]

Addition is commutative, does it matter?

Anyways, the left thing is just 3(3+4+5+6+7+8) and the right thing is -10(n+n+n+..... N times)
So the whole thing is 99-10n²

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[wind ibex]

help with bayes' theorem/conditional probability?

[wind ibex]

this is the question

this is my work so far

i found an answer as 5.8% but that seems really low, and i think i may have taken some liberties with the math

can you see anything wrong?

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[ripe prism]

If you flip 8 fair coins, what is the probability that you will get: A) Exactly 5 heads?

I did C(8,5)/2^8 = 56/256 is this the correct answer? I need someone to back me up. I can show the work done using LaTeX if needed

[ripe prism]

All good just delete

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[ripe prism]

??

[granite torrent]

yes

[ripe prism]

What about if I wanted at least 3 heads? What would I do in that case, find the probability of exactly 3, then 4, then 5, then 6, etc. That seems too lengthy?

[granite torrent]

1 minus the probability of 0, then 1, then 2

[ripe prism]

Oh thats smart actually

[granite torrent]

complementary counting is often useful in combinatorial exercises

[ripe prism]

Yup

Thanks

[granite torrent]

welcome

[ripe prism]

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!msgdel

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[serene hazel]

its already closed

[ripe prism]

<@&268886789983436800> The channel seems to be bugged. It says closed but remains here in the occupied list.

[grim skiff]

Give it a few minutes

[ripe prism]

I've been talking in it forever

[grim skiff]

Just don't type in it, or the bot thinks it's still active

[ripe prism]

Ah well I'm not sure why it closed like that in the first place

[grim skiff]

.

[ripe prism]

I didn't delete my original at all

Pinky promise!

[serene hazel]

oh right yea

bot buggy

[ripe prism]

Welp I hope I didn't disturb the mods too much ❤️

[calm nacelle]

Yeah it's alright, it'll disappear eventually

The bot has some limits with how often it can move channels

[ripe prism]

Thanks, sorry to bother 😅

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[glad whale]

I took an approach with this

sadly i have no answer key

So i just did 0.20 x 76

got 15.20

added 15.20+76

is that bad approac??

answer $91.20

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[keen marsh]

let 100% = x
let 80% = 76

(x/100)* 80 = 76/80
x/100 * 100 = (76/80)*100
x = (76/80)*100

x = 95

[keen marsh]

because you are dealing with percentage 20% of 76 is inconsistent, I dont know how to explain it

so just know that when you divide any number by 100, the result is 1% of your original and thats how i set up my equation

so when you do x/100 thats 1% of original and we know that 80% of original is equal to 76$
so we have to multiply that by 80
so we get (x/100)* 80 (this is equal to 80% of our original) = $76
now you just use algebra

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[noble sleet]

Calculus 2:
Question 8. I have tried multiple times but I am not getting it.

[noble sleet]

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[noble sleet]

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✅

[noble sleet]

Here are updated photos

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[tawdry grove]

why is this false

[empty sapphire]

chain rule in the derivative.

(ln|f(x)| + C)'
= (ln|f(x)|)' * (f(x))' + (C)'
= f'(x)/f(x)

[tawdry grove]

but isnt 1/(a variable) = to ln(that variable)

[empty sapphire]

what if f(x) = x^2 + 2? Just as a practical example

f(x) is not a variable, it's a function

[tawdry grove]

so it must be x in the denominator

[empty sapphire]

for that to make sense, yes.

You may not realize this but the chain rule is always being applied.
For example, say if f(x) = x, then
ln|f(x)| + C, then the derivative will be:

(ln|x| + C)'
= (ln|x|)' * (x)' + (C)'
= (1/x) * (1)
= (1/x)

[tawdry grove]

thanks

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[mellow hazel]

can someone help me please

on 27

[brisk obsidian]

Because it is an isosceles triangle, the right-angled segment splits the base in half.

[mellow hazel]

y=60?

[brisk obsidian]

Correct.

[mellow hazel]

thank you

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[pulsar token]

position or distance is the integral of velocity

[torn jolt]

you know, 1- the initial velocity, 2- the acceleration, 3- the time

[tawny nest]

so like the little squiggle with 3 and 7 as a bound and then -9.8t + 16 dt?

and evaluate the intergral?

[pulsar token]

yes pretty much yeah

[torn jolt]

you dont have to integrate

[pulsar token]

i think

[torn jolt]

btw

[tawny nest]

when i did that i got it wrong

I evaluate the intergral or I find the derivative or antiderivative?

wait nvm i got it

can you help me with this one?

is it the antiderivative of the equation?

[pulsar token]

the answer should be 260 when you integrate

wait

i lied

-132*

[tawny nest]

yes i got -132

idk what i did

wrong

first

[pulsar token]

is -132 right?

[tawny nest]

yes yes

[pulsar token]

ok pefect

mb i didn't read the message

[tawny nest]

nono youre all good 🙂

[pulsar token]

so it's the same thing kinda for this equation

you'd take the integral because distance is the integral of velocity

[tawny nest]

i got the first answer through evaluation

so the intergral of 512/3?

[pulsar token]

i mean i would do the integral from -3 to -1 of the velocity equation

[tawny nest]

so like

t^3 + 29t^2 - 30t

[pulsar token]

yes the integral of that

from -1 to 3

actually what you might need to do is 0 to 3

and -1 to 0

[tawny nest]

wait what

[pulsar token]

because the -1 might make be negative area

and that wouldn't be the "total" distance

[tawny nest]

do I add those or smth

[pulsar token]

yes you would

[tawny nest]

0 to 3 is 585/4

293/12

[pulsar token]

wait i might be wrong ab this

i think actually

what you would do

is t^3 + 29t^2 - 30t = 0

and you would get t = 0, 1, and -30

so you would do the (integral from -1 to 0 ) + (integral from 0 to 1) + (integral from 1 to 3)

and then you woudl get the right answer

and I'd just use my calculator to do all that

[tawny nest]

what do i even put in my calculator sorry im lost hahaha

[pulsar token]

its all good

i'll write it out on a notecard and send

[tawny nest]

tysm

[pulsar token]

and v(t) = t^3 + 29t^2 - 30t

[tawny nest]

tysm

OHHHH

okay

yes

let me add it

i got 512/3

[pulsar token]

is that right 😭

[tawny nest]

man oh man

[pulsar token]

its over

💀

[tawny nest]

ahhhhwejfmaeiflkjef

[pulsar token]

idk then srry

[tawny nest]

its okkk dw

[pulsar token]

i rlly thought that was the answer

[tawny nest]

tysm tho

is it like

the antiderivative

idk

[pulsar token]

actually try to do what the hint says

integral from -1 to 3 of absolute value of v(t)

[tawny nest]

im ngl idk what that means

i thought i did that

[tawny nest]

We are so up

Can I ask one more question and I will leave it alone.

you dont even need to help me i just dont know what its even asking

[pulsar token]

its all good

i have nothing better to do

[tawny nest]

none of ur own calc hw?

[pulsar token]

im on my last problem and I don't understand it at all 💀

[tawny nest]

what calc are you taking

[pulsar token]

i'm doing Calc BC or Calc 2

depends on what you call it

[tawny nest]

same

[pulsar token]

what grade are you in

[tawny nest]

college

college grade

[pulsar token]

👍

[tawny nest]

ur ahead of the game

[pulsar token]

you would take the integral

[pulsar token]

yeah lol im a junior in highschool 💀

so the integral would cancel out the d/dx

[tawny nest]

omg wow ur going to harvard

[pulsar token]

no chance

anyways finish your problem

take the integral of the equation

by hand without a calculator

[tawny nest]

aw man

howo

are there anu bounds?

[pulsar token]

using power rule for integration

no bounds

just of the equation

[tawny nest]

where do i put the y = 4?

[pulsar token]

dw ab that for now

ykw ill write it out rq

[tawny nest]

hooray

[pulsar token]

hol on this is kinda long

gimme a sec

the thing in the box should be the final answer

make sure you understand the process

you got it?

@tawny nest

[tawny nest]

Uhh

wait

sorry

How did u go from step 2 to 3

[pulsar token]

you take the integrals

using power rule

and other rules which you should've learned

😭

[tawny nest]

LOL

its okay

ill figure it out

thank you so so so much though!!

[pulsar token]

here

[tawny nest]

oh

LOL

[tawny nest]

yes

i get it now

im mathed out

[pulsar token]

then you just combine

[pulsar token]

legit how i feel

is that it

or anything else

[tawny nest]

that is it

thank you!!!!!!!!!!

[pulsar token]

yeah np

[tawny nest]

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[gilded silo]

is this correct?

ping me when replying

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[gilded silo]

Anyone?

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[gilded silo]

<@&286206848099549185>

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@gilded silo Has your question been resolved?

[gilded silo]

Anyone

Pls help tell

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[coral shoal]

How would I solve this question?

[vast fossil]

Have you tried simplifying the left hand side?

[coral shoal]

Yeah, this is what I got up to

But I feel like I've reached a dead end because idk what to do from here

Like, if I try to get rid of the Ln on the right, it'll make the left have everything raised to the e which is just as bad to deal with

[vast fossil]

The way you combined those logarithms seems wrong

lna - ln(2a) should result in ln(a/(2a)) which is ln(1/2)

Looks like you forgot about the negative sign in front of ln(2a)

[coral shoal]

I see now

I got the correct answer now
Thanks for the help!

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[prime locust]

So I have a hyperbola y=4/x and point A that is NOT located in the hyperbola. I need to find the tangent of the hyperbola that passes trough point A.
im so stuck i get how it is possible but how to find it on paper in writing i dont

[prime locust]

<@&286206848099549185>

[narrow ermine]

Hmm

Let's say we call the point on the parabola $P = (x_0, y_0) = (x_0, \frac{4}{x_0})$ and the other point $A = (x_1, y_1)$.

[glossy valve]

Azyrashacorki

[narrow ermine]

Now we want the slope of the line going between those two points to be exactly the slope of the tangent at $x_0$.

[glossy valve]

Azyrashacorki

[narrow ermine]

We know how to compute the slope of a line between two points, and we also know how to compute the slope of the tangent at $x_0$ using the derivative.

[glossy valve]

Azyrashacorki

[narrow ermine]

Try and set those equal to find the $x_0$ you need for the right slope, then it's a matter of solving for the right constant b in $y= mx+b$.

[glossy valve]

Azyrashacorki

[prime locust]

this is how the teacher solved it

i still dont get it

[narrow ermine]

That's what the teacher is doing. Notice on the left bit, they set $y-y_0 = k(x-x_0)$.

[glossy valve]

Azyrashacorki

[narrow ermine]

That's really the equation for the slope $k$ between (x,y) and $(x_0, y_0)$.

[glossy valve]

Azyrashacorki

[narrow ermine]

And then they set $k = \frac{-4}{x^2}$, which is the derivative of $\frac{4}{x}$

[glossy valve]

Azyrashacorki

[narrow ermine]

The rest is just algebraic manipulation to solve for x, they're changing the variable to u to avoid confusion

[prime locust]

Ye i dont get why it is why she replaced the y and x in the line equation not x0 and y0

[narrow ermine]

It just depends which point you call what

I decided to put indices 0 on the parabola

But their indices 0 are for the point A

It doesn't really matter.

[prime locust]

i will just go put the math book under my pillow see if it helps me in my exams

thanks for trying

[narrow ermine]

Hahaha

Ok

[prime locust]

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[torn jolt]

If a limit is equal to 2 can I do limit - 2 is equal to 0?

[torn jolt]

,, \lim_{x\to a}\m fx = 2 \Implies \lim_{x\to -2}\m fx = 0

[torn jolt]

is this what you are asking?

[vast fossil]

That's not what they meant

[torn jolt]

well im trying to verify because i dont understand myself lol

[vast fossil]

$\lim_{x\to a}f(x) = 2 \implies \lim_{x\to a}f(x) - 2 = 0$

[glossy valve]

孤独な豆

[torn jolt]

ok i see

[vast fossil]

@torn jolt This is true, does that answer your question?

[torn jolt]

i mean i don't see why not at face-value. You are still maintaining the equality

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[snow niche]

how do i do this

[thick hedge]

,rotate

[thick hedge]

what's the question?

[snow niche]

I have the answer sheet and

as you can see

[thick hedge]

,rotate

[snow niche]

the have turning points for each line

I don't know how to find it

and I don't know in what instance would I need this because generally I wouldn't think to find it

for a question like this

[silver pasture]

negative rizz 😭

wdym how to do this?

think of what would happen to various points

if u cant

just put them into the function and take some points as guides

there's no algorithm here

[snow niche]

I trying to find the tp

<@&286206848099549185>

[silver pasture]

w/o differentiation?

[snow niche]

what's that mean

[silver pasture]

calculus

[snow niche]

I'm not sure

[silver pasture]

u want a solution without using calculus?

have u studied calculus?

[snow niche]

no

only just started functions

[silver pasture]

sad luck

have u been told to do this?

[snow niche]

yes

[silver pasture]

or just practicing on ur own?

[snow niche]

homework

[silver pasture]

maybe ur teach made a mistake?

or maybe ur supposeed to use graphing software

w/o calc is too diff for me to even try sorry mate

[snow niche]

no she is just a bad teacher

she teaches only easy stuff

and she wants us to suddenly know the hard stuff

[silver pasture]

well keep checking khan acad on the side if thats true

else it will be too late

cya

[snow niche]

okay

[torn jolt]

Yes

Thanks

[cunning vessel]

What kind of things you learned for functions?

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[snow niche]

how to graph every function

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[fleet storm]

is b+a-c in the right spot? or should it be from the tail of a to the tip of -c

[spice knot]

yea it should be from the tail of a to the tip of -c

[fleet storm]

thanks 🤩

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[spice ridge]

I received a task from a book, to show how we get the actual solution of a linear non homogeneous difference equation. I'm stuck at 2.7.19 conditions and 2.7 final solution if we choose Y(0) = 1 and Y(1) = 2. Thanks for help ❤️

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@spice ridge Has your question been resolved?

[spice ridge]

<@&286206848099549185>

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[proven mango]

alright so what is another way of saying slope

[willow trail]

function?

i think

[proven mango]

well not exactly

slope is the change in y over the change in x yes

yet we want the instantaneous slope here

which would be dy/dx or the first derivative

[willow trail]

yes

[proven mango]

so do you know how to take the derivative of that equation?

[willow trail]

yeah i think so give me a sec

wait so can i transform it all on one side and then just do x and y prime seperatly?

[willow trail]

btw i though so

[proven mango]

like move all the x and y terms?

[willow trail]

yeah

or at least remove them from brackets

[proven mango]

you can

[proven mango]

yeah that’d help

[willow trail]

but be honest pls does it make any sens

ah okok

let me reduce it first

btw i send so you dont feel like you are waisting your time with me

so i just prime for example only Y?

[proven mango]

well you’re differentiating with respect to x

and since y is a function of x

we have to remember to multiply it by the chain rule

so for example if we take y^2 and differentiate it with respect to x we would get 2y * y’

[proven mango]

i’m still not sure if that expansion is right tho

i got something different

[willow trail]

yeah nvm i honestly forgot to multiply 2 things

[proven mango]

alright

expanding it here honestly kinda makes it worse too

since there are product rules you have to use here

but it does reduce the chance of making a mistake

[willow trail]

so just everyhting on the 1 site?

[proven mango]

yeah just expand out the brackets

no need to move the terms around

[willow trail]

ah ok i understand

[proven mango]

you’re missing a y^4

on the left

[willow trail]

yes

oopsie

[proven mango]

all good

[willow trail]

this is my final product so far

and now i derrerative

[proven mango]

yep

[willow trail]

sorry for wasting your time. my friend is willing to explaing it to me with talking and all. thank you very much

you have a patience of an angel

[proven mango]

it’s okay

[willow trail]

.close

[proven mango]

you’re welcome

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[torn jolt]

i got 7pi/6

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[torn jolt]

So lost on these

[stiff musk]

you could do both of these geometrically

[torn jolt]

Well what is throwing me off is the a's for the range

[stiff musk]

try drawing a picture

[torn jolt]

Can I just plug in any point?

[torn jolt]

I wouldn't know what the shift is though

[stiff musk]

what shift

[balmy rose]

yeah drawing it helps

[torn jolt]

a-

a

[stiff musk]

take -|x| and shift it upward by a (assuming a > 0)

if it helps, for the moment just give a some value like 5

to get the idea how it works

later generalize to arbitrary a

[balmy rose]

starting from this, you could look at the positive side, so the function becomes a-x. and then you can graph it. the shape will be a known one.

[torn jolt]

Oh ok

[stiff musk]

yea

[torn jolt]

But how would I get the area of that

[stiff musk]

and you know how to find the area of a triangle probably?