help-26

[ivory cradle]

6600(0.825)^0-1, so -1, 0.825^-1=1.21

[pastel oracle]

just use a calculator...

[ivory cradle]

?

[pastel oracle]

,w calc 6600 / 0.825

[thorny flame]

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[ivory cradle]

yes i got that ..

so what is the annual rate of depreciation as a percentage

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[ivory cradle]

ghost ping

oh just now it loaded wack

yea I give up

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[gilded needle]

can someone just double check my work for this one?

i got
1/2((ln2)^2-(ln4)^2

[gilded needle]

i used u sub and made u f(x)

[acoustic tangle]

Seems right

[floral bison]

It’s good

You have to use double substitution

[acoustic tangle]

Or just one sub (u = ln(f(x)))

[floral bison]

Works as well

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[unique lintel]

Why is this proof, that the product of 2 numbers = 0, wrong ?

[cursive thorn]

2 * 0 = 3 * 0, so 2 = 3

[unique lintel]

at which line ?

[cursive thorn]

5 to 6, ab - c = 0, so you can't cancel it

[unique lintel]

so I would divide by 0 ?

why is ab-c = 0 ?

aah

because a*b = c = 0 ?

[cursive thorn]

ab = c, so ab - c = 0, what you wrote is incorrect since c isn't 0

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[balmy quartz]

Did I do this right? Cause I feel like I missed up

[bold nebula]

,w normal line to y = 8/x - x + 3x^2 at x = 1

[thorny flame]

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[bold nebula]

I don't think so

[balmy quartz]

I didn’t think so either 😭

[bold nebula]

normal line equation is y = m(x-x1) + y1

where m is slope given by -1/f'(x1)

[balmy quartz]

Yeah and I got the gradient from the tangent equation and flipped it

[bold nebula]

yeah

but

it doesn't have to be perpendicular to the given tangent

it's another point

if it was (2,14) then it would work

[balmy quartz]

So how do I get it?

[bold nebula]

-1/f'(x1)

[balmy quartz]

What’s x1

[bold nebula]

(x1, y1) is the point of tangency

here (x1, y1) = (1,10)

so x1 = 1

[balmy quartz]

And I plug this into the the equation of the tangent?

[bold nebula]

no, you need slope of the normal line

which is given by -1/f'(x1), start from finding derivative of the given function

[balmy quartz]

Which function tho the one to the curve or the one for the tangent

[bold nebula]

of the curve y

[balmy quartz]

When we find the derivative for the function and plug in x1 we find the gradient for the tangent right?

Then we flip it to get the normal

[bold nebula]

for the normal* (if we plug into -1/f'(x1))

ah ye

you can do it that way

[balmy quartz]

I just like to understand what am calculating lol

[bold nebula]

as you can see -1/f'(x1) comes from "flipping" f'(x1)

just general case

[balmy quartz]

What is the function in a curve tho what does that mean Ik what the tangent is I don’t understand the curve part

[bold nebula]

curve is given as y = 8/x - x + 3x^2

we want to calculate slope of the normal (we can firstly find slope of the tangent line then flip np., doesn't matter at all)

this is why we calculate the derivative

of the curve

[balmy quartz]

Yeah yeah I got that am asking what is the curve like in general

[bold nebula]

curve represents a function here, function for which we are supposed to find tangent/normal at some its point

[balmy quartz]

So I found the derivative of the function which is 6x-8x^2

I plugged in 1 which gives me -2

[bold nebula]

Check this out.

Should be -8/x^2 - 1 + 6x

[balmy quartz]

I see what I did wrong

That’s so frustrating but thank you so much 🙏🙏🙏

[bold nebula]

thank yourself, np

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[neon iron]

need help... i tried but the correct solution is
a^(9/5)

mine is a^3 (as you can see)

Where did I make a mistake?

[odd pagoda]

remember that $\sqrt{x}$ means $\sqrt[2]{x}$

[thorny flame]

Denascite

[odd pagoda]

which I assume was your mistake. otherwise not sure where the 60 comes from

[neon iron]

oh... exactly. I must be careful with that!
Thank you @odd pagoda

[odd pagoda]

something is still off tho

[neon iron]

hmm.. but still I get a different solution..

yeah

[odd pagoda]

who says it is a^9/5 ?

[neon iron]

A book, but i am not sure if they are correct (wouldn't be the first time they're wrong).

[odd pagoda]

theyre not

[neon iron]

not correct.. or not wrong.. 👀

[odd pagoda]

not correct

[neon iron]

i think so too

[odd pagoda]

what did you get now?

[neon iron]

a^(1/2)

[odd pagoda]

yes

[neon iron]

there're two similar (a bit harder) examples, I'll try to do them. If I do them correctly I'll assume that this one is solved and they wrote wrong solution. (Or maybe later I'll try to use one of those apps where you take a photo of a math problem).
Thanks again for pointing out square root!

[odd pagoda]

you could also just type it into wolframalpha to check it

[neon iron]

I am on the phone currently, it's pain to type this.
I did use microsoft math photo solver, and the result i get is
sqrt(a)
which is a^(1/2)

so,yeah, pretty confident we have done it correctly.

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[burnt hare]

I don' t realy understand this one

if s and t are smaller then 0 and u take x1 and x2 as 0 it still is smaller then 1

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[burnt hare]

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[odd pagoda]

well sure you could take them as 0

but you could also take them as 1000 or whatever

[burnt hare]

but if u take tehm as 0 there is always a feasible solution ?

because 0 + 0 is always less then 1

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[burnt hare]

this question is realy vague maybe I am seeing it wrong

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[burnt hare]

can I ask a different question

[granite hull]

yes

[burnt hare]

what is the reason for this substiution

nvm I see it it's because x1 can be negative but I don't understand why it's not allowed to be negative

I guess it's just a rule part of a linear program problem\

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[burnt pumice]

Hi, could someone explain algebraically how the numerator simplifies to that?

[keen raptor]

First you have to expand the binomial

Then use the distributive property

then combine like terms

[burnt pumice]

ah, that makes more sense i was forgetting the expand the binomial

thank you!

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[last marsh]

A 40-ft chain with mass density 3 lb/ft is initially coiled on the ground. Find the amount of work required to lift the chain so that it is fully extended with one end touching the ground. Include appropriate units in your answer.

[gusty bane]

what have you tried

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[exotic light]

Can anyone help me understand where I'm going wrong with my answer?

[sour bloom]

why does your line not contain k

i.e. why is it in the xy plane?

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[exotic light]

I don't know. I'm not completely sure what I'm supposed to be doing here. I'm just following a formula I saw online.

[sour bloom]

the line needs to use i, j, k

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[exotic light]

@sour bloom Okay, but in what way?

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[modest agate]

Can i suppose here that n equals different things when dividing the inequality?

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<@&286206848099549185>

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[sour bloom]

which step are you describing

your m and n look very similar?

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[tender fulcrum]

Not sure how to find the lim x -> 0 cos^x-1 / x^2

[dapper lantern]

$\frac{cos(x-1)}{x^2}$

[thorny flame]

Rub05

[dapper lantern]

This one?

[tender fulcrum]

woops sorry

that ones a bit hard to reaad

[dapper lantern]

L'Hopital

[whole slate]

L’hopital?

[tender fulcrum]

aaaa i see now ty

i forgot

after differentiating it goes to -sinxcosx/x right?

so it should be -sinx/x * cosx which is -1 * 1 = -1

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[tender fulcrum]

ty

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[half rune]

For the sequence {nln(1 +7/n)}, the limit I found was 0 but my teacher did L'Hopital once and found the limit to be = 7, why is that right?

[half rune]

$nln(1+\frac{7}{n})$

[thorny flame]

c0urier

[lucid pond]

Well I got 7 aswell I don't think L'hopital can be used here cuz this limit doesn't have an indeterminate form

[half rune]

Ill send a screenshot

[lucid pond]

ok

[half rune]

Really?

But like 7/inf that's 0 and you end up with inf•ln1 which is 0 no?

[lucid pond]

Oh yeah sorry I meant that it can be used in the case of 0/0 or infinity/infinity

Not this case

[half rune]

I still dont get why 0 is wrong

[lucid pond]

Because as I said L'hopital isnt reliable in this case so you're going to get a wrong answer

Using any other way you'll still get 7

[half rune]

But I didn't use L'Hopital

[lucid pond]

Oh what did you use

[half rune]

Well I straight up wrote 0 after plugging inf saying that
inf•ln(1 + 7/inf) = inf•ln1 = 0

[lucid pond]

Well inf*0 is an indeterminate form

It isnt 0

I just saw what your teacher wrote and he's correct

[half rune]

Ohhhhhh

Ah damn alright

Can you show me how did you get to 7?

[lucid pond]

Well Idk how to explain it

I guessed its gonna be 7

[half rune]

Lol all good

Thanks fam

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[lucid pond]

Np

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[versed trellis]

With the half angle identity, does your answer take the sign of the angle? Or the sign of half the angle?

[versed trellis]

For example tan(112.5), would you take the sign of tan(112.5) or of tan(225)?

<@&286206848099549185>

[lost sphinx]

you just need to follow the formula and that will take care of the sign on its own

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[versed trellis]

??

[lost sphinx]

which double angle formula are you using?

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[neon iron]

How do I approximately find what is sqrt(13)?

[neon iron]

condition: x < 2

and one of the solutions is

(1+ sqrt(13)) / 2

[long stirrup]

it's between 3 and 4

[neon iron]

that makes sense

yeah

[long stirrup]

so that's def more than 2

[neon iron]

got it

@long stirrup thanks

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[neon iron]

hm... now I got a tricky one.

condition: x < 2/5

x = (-5 +sqrt(41)) / 4

What I did:
sqrt(41) is between 6 and 7
it's 6.a (a is the decimal part)

So, we have:
(-5 + 6.a) / 4 = 0.b / 4 (b is a new decimal)

Ok, now we compare 2/5 and 0.b / 4

Let's give them the same denominator:

2/5 = 8/20
0.b/4 = (0.b)*5 / 20

0.b * 5 is never going to be greater than or equal to 5, therefore it won't be greater than or equal to 8 either.

So, our 0.b*5/20 is less than 8/20, so the solution satisfies the condition.

Anyway, I answered my own question...

[neon iron]

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[undone flicker]

Any short method to solve this equation

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[mental hatch]

How to find the antiderivative of 5/x ?

[sweet shard]

,tex .int rules

[thorny flame]

riemann

[sweet shard]

use constant multiple to factor out 5

then you have to use the fact that the integral of 1/x is log(x)

[mental hatch]

Isnt integral of 1/x ln|x| ?

[sweet shard]

yes it is

,w \int 1/x dx

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[sweet shard]

• C

[mental hatch]

Wait, then what is log(x)?

ln|x| = log_e(|x|)

log(x) = log_10(x)

[sweet shard]

not in math

probably in your calculator

[mental hatch]

What?

[sweet shard]

log(x) = natural log in math

[sweet shard]

this is what calculators use

[mental hatch]

I was told that lg(b) = log(b) = log_10(b)

[sweet shard]

good for you?

[sweet shard]

log = natural log here

[mental hatch]

Can I just write it like ln(x)?

[sweet shard]

write whatever you want

[mental hatch]

So, what's int of 5/x ?

Is it like 5 * x^-1 = 5 * x^0 / 0 ?

but x^0 = 1; 1/0 = undefined

So, what's it?

[sweet shard]

.

[sweet shard]

.

[sweet shard]

.

[sweet shard]

.

[mental hatch]

Is it 5*lnx ?

[sweet shard]

yes

[mental hatch]

Thank you

[sweet shard]

,w int 5/x

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[sweet shard]

• C

[mental hatch]

I'm just wondering, I have to solve integral, but I don't know If I'm correct

int (1) ^ (3) ([4/x] - x) dx = 4lnx - (x^2 / 2) | (1) ^ (3)

It's (4ln(3) - (9/2)) - (4ln(1) - (1/2)) = ((8ln(3) - 9)/2) + 1/2 = (8ln(3) - 8) / 2 = 4ln(3) - 4

Is it correct?

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[neon iron]

The water consumption of a machine is approximately normally distributed with the expected value of 60 liters, but the standard deviation is unknown. This machine uses more than 65 liters for 10% of the wash cycles.
Determine the unknown standard deviation.

[neon iron]

i tried finding the z value of 10% and find the standard deviation but it didnt work

[neon iron]

all i found is a negative standard deviation which doesnt really make sense

or does it?

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[neon iron]

I have a feeling I see how this could come about... Can you show your work?

yeah sure

10% corresponds to z(-1.28)

Okay yeah my intuition was correct

The problem is... Which 10%?

must be the lower bound since sd is negative

[cunning kestrel]

well if the expected value is 60 liters, and 65 is greater than 60, wouldn't it have to be the upper bound?

[neon iron]

but since its symmetrical does it really matter?

[cunning kestrel]

yes

well...

i'm not 100% sure but i would still definitely go with the upper

i'm still trying to figure out how to solve though

[neon iron]

yes the solution also says 3.9

[neon iron]

Yes, the question is talking about the portion right of the z-value

Which is why the actual value you found, using a z-score table (or whatever you were using) which instead uses the left portion, didn't match up

[neon iron]

i calculated it by myself with the phi formular

i only have a z table for postive values

thats why i did it by myslef

[neon iron]

kinda scuffed

[neon iron]

Yeah that'd do

The Gaussian distribution is symmetric

So when you flip the z-value you also flip the uh... The... Oh screw it I'm no statistician I don't have the terms

You get what I mean

[neon iron]

i know this feeling too well xD

[neon iron]

so you can also take the positive z value?

Yeah, if you want the z-value for 10% you can just take the only for 90% and flip the sign

but id have to subtract it with 1 right?

But in that case you don't need to

nvm im confusing myself

Wait is the z-value the percent thing or the other thing

Ah frick I put a sticker

🤣

Okay okay I did some Googling

Pretend I didn't ask that question

[neon iron]

percent are the values in the table

and theres no 0.1

So anyways as I was saying

The question says "more than 65 liters"

Hence on a number line this would mean everything right of 65

However the z-value table and the formula use the area left of the z-value

Which is why instead of 10% you have to use 90%

[neon iron]

ahhh

If it said "less than 65 liters" you wouldn't have to do this switcheroo because it already matches

Like think of "more than 65 liters 10% of the time" as "less than 65 liters 90% of the time", and then it becomes blatantly obvious

1.28

Exactly

lol its the same

Yeah but just flipped

Because the Gaussian distribution is symmetric

So if you flip the percentage around you also just flip the z-value

And vice-versa

that seems plausible

alr thanks 👌

@neon iron Don't forget to .close

.close

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[tacit sundial]

why does this equal to that

[tacit sundial]

the sec2x-1 = tan2 2x

[noble laurel]

$\sin^{2}(x)+\cos^{2}(x)=1$

[thorny flame]

AustinU

[noble laurel]

are you familiar with this identity?

@tacit sundial

[topaz sinew]

@tacit sundial Has your question been resolved?

[noble laurel]

When you see this, divide all terms of the equation by cos^2(x). You will see that after a few rearrangments and replacing x with 2x you will get the desired identity.

[topaz sinew]

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[tacit sundial]

.reopen

[topaz sinew]

✅

[tacit sundial]

@noble laurel

sorry for ping

what about this one

How did they do 2(2sinx cosx)

= (1+2cosx)

nvm factored

i just realised

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[near condor]

if 5x:8y is equal to 4:3 compute the ratio of 9x:10y

[near condor]

I’m having trouble understanding what you need to do in order to be able to get the right answer, like if there is a formula

<@&286206848099549185>

[smoky slate]

can someone help me

[topaz sinew]

Please read #❓how-to-get-help

[neon iron]

@near condor hello

[near condor]

hello

[neon iron]

so 5x = 8y right

[near condor]

I’m pretty sure

[neon iron]

and 5x = 4

and 8y = 3

what is x?

what is y?

what is 9x?

what is 10y?

[near condor]

8?

[near condor]

5?

[summer canyon]

i think 9:15/32

[summer canyon]

bro it is 5y not y=5

[near condor]

where is 5y?

[summer canyon]

i meant 8

[neon iron]

Ignore nikemike

[neon iron]

so if you read the question

5x:8y is equal to 4:3

it is saying that

[summer canyon]

9x4/5:(10x3/8)

[neon iron]

5x = 4

and 8y = 3

they are equl ratios

so the terms on either side would also have to be equal

[summer canyon]

calculate this

[neon iron]

if you know 5x = 4

how would you figure out what x is?

[near condor]

divide

[summer canyon]

x=4/5

[neon iron]

bro are you the person who asked the question?

[summer canyon]

and then multiply

[near condor]

so x is 0.8?

[summer canyon]

how u figure

yeah

[neon iron]

Correct

second part of the question says

compute the ratio of 9x:10y

what is 9x?

[summer canyon]

9x4/5:(10x3/8)

do this the ratio

[neon iron]

Bro what are you doing

no body can read that

[summer canyon]

36/5:30/8

[neon iron]

<@&268886789983436800> derailing

[summer canyon]

?

[near condor]

7.2

[summer canyon]

bro 9x4=36

[neon iron]

Correct

So you figured out the 9x part of the ratio

all you have to do is figure out the 10y part now

[summer canyon]

10x3=30

[neon iron]

its the exact same process

[near condor]

then just do the same thing basically

[near condor]

yea

[summer canyon]

yes

[near condor]

so the answer is 7.2:3.75

[summer canyon]

yeah then mulitply by 100 and simplify

it will be 720:375

[neon iron]

Yse that is the answer. you do not have to muliply by 100

[near condor]

ok thanks guys

that was easier then I thought

.close

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[undone flicker]

I tried this but very long

[junior pumice]

<@&268886789983436800> spammer

[undone flicker]

Wtf??

I see. Thanks

[topaz sinew]

@undone flicker Has your question been resolved?

[fathom loom]

Wait this seems fun let me give it a try

[sweet shard]

Show the full question with instructions

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[fringe atlas]

quick question! I know I'm supposed to be using the geometric series on this somehow to decide if it converges/diverges but I'm not sure how to take care of the +1

[wispy bobcat]

Use exponent properties to rewrite the exponent term into the product of two exponential terms.

[fringe atlas]

so I have (2/3)^n * (2/3)

[wispy bobcat]

yep

[fringe atlas]

and I can just ignore the 2/3?

[wispy bobcat]

you only need to look at the ratio to figure out if it converges/diverges

since you're not actually trying to find the sum of an infinite geometric series

but the 2/3 is important if you want to find that sum

[fringe atlas]

Can I ignore all values like that in a problem if I just want to know if its converging or diverging

[wispy bobcat]

yep, cuz you only care about the absolute value of the multiplier

if you get stuck, try just plugging in n=0 or n=1 (depending on where you start) to see what the first few terms look like

you'll get the first term automatically, and it shouldn't be hard to see what the multiplier is

[fringe atlas]

I see! thank you so much

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[proud hinge]

how do i solve this

[frosty garden]

Hint: Try establish the integration region first. You may want to begin with some simple curve sketching. 🙂

[proud hinge]

i have an idea of a circle right

how do I even find the bounds for this integral?

@frosty garden

can someone help me find the bounds for this integral

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[mighty shell]

what type of graph sketch thingy do I need here?

like does anyone have an image i can print to do these questions or smth

or is it constructable using a pencil and stuff?

[novel echo]

you can use geogebra maybe

https://www.geogebra.org/

[mighty shell]

oki

lemme try

but uh should i just draw this on a page with pencil

[novel echo]

No, you can plot the points by defining coordinates

[mighty shell]

yeah but i think my practice will be better doing on paper

no?

[keen matrix]

do you have graph paper?

[mighty shell]

nope

normal paper

[keen matrix]

can you print any graph paper?

[mighty shell]

yep

I can

but do you have any image i can print?

is this fine?

probably like could get the y-axis longer here

but this good?

[keen matrix]

I'd probably print a 20x20

so go from -10 to 10 on the x-axis

and -10 to 10 on the y-axis

[mighty shell]

oh ok

[keen matrix]

just ping me when you've done that and I'll be back to help you!

[keen matrix]

you wanted to do it on paper... just like put it on a doc or smthn and print it

unless you want to do it on Desmos

[mighty shell]

tysm

[mighty shell]

ok i will print it

i was just confirming if that is fine for printing

[keen matrix]

ohhh

yeas that is fine

[mighty shell]

icic

ty

[mighty shell]

this looks fine

the lines in the block aren't visible in the image as they are like not thick enough

[keen matrix]

that looks solid

ok so you know how to plot points?

[mighty shell]

yee

ill try the questions now

[keen matrix]

cool

ping me when you plotted points

[mighty shell]

answer should be 56.3

[keen matrix]

Point A is (5,0) not (0,0)

[mighty shell]

oh 💀

im so dumb

sorry

for this CD line

they are asking angle between y-axis

which one is it

@keen matrix

[keen matrix]

"the angle is makes with the x-axis"

oh shit

nvm

that's actually a damn good question

idk I'd do green

[mighty shell]

i see

[mighty shell]

that gives the right answer

[keen matrix]

In theory

[mighty shell]

i think with red, a right-angled triangle cannot be made or smth?

[mighty shell]

?

[keen matrix]

ig that's a good point

[mighty shell]

ic

tysm

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[rigid pier]

how could you prove that these 2 triangles are congruent? sorry for my bad drawing but they are squares and the triangle is right-angled

[icy sky]

Theyre not

Think a triangle with a really big hypotenuse and a really small leg

[rigid pier]

i got told to prove they are congruent

apparently you can use SAS?

[icy sky]

Is it a specific triangle?

[rigid pier]

triangle A and B

[icy sky]

Can you show the original problem

[rigid ivy]

They will not always be congruent in the general case

[rigid pier]

ahh i see i may have gotten the problem wrong ill double check thank you

[rigid ivy]

These two triangles I believe are always congruent

[rigid pier]

how could i prove their congruency?

[rigid ivy]

SAS maybe

[rigid pier]

i'm confused on the side bit i'm not sure how to prove they are the same

[rigid ivy]

side bit?

[topaz sinew]

@rigid pier Has your question been resolved?

[rigid pier]

yeah

also I discovered i had to prove these 2

for the angle I could prove it by saying 90 + the small angle between them is shared so they have the same angle right?

[rigid ivy]

Yes

[rigid pier]

and then to prove SAS i would need to prove the sides are the same but I'm not sure how to go about that

[rigid ivy]

They're on squares

[rigid pier]

oh so if the squares are the same length then theyre congruent

but what ab pythagoras i thought hypotenuse had to be longer

[rigid ivy]

Doesn't matter.

You just need the corresponding sides of the triangles to be equal

[rigid pier]

ah i see thank you :)

[topaz sinew]

@rigid pier Has your question been resolved?

[topaz sinew]

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[neon iron]

Someone help

[neon iron]

I just had this integral on my exam

And I couldn’t solve it

this was in my calc 1 exam

[distant lantern]

ight

[neon iron]

Integral from 0 to 1 integral of 4xe^x^2

[vernal vale]

[neon venture]

reverse chain rule

[neon iron]

I did

Theres another integral

[rigid ivy]

!show

[topaz sinew]

Show your work, and if possible, explain where you are stuck.

[neon iron]

I have to integrate 2e^x^2 from 0 to 1

How tf do you do that

[rigid ivy]

Show us your work

[distant lantern]

☠️

[vernal vale]

wrong and dont give them answers

[rigid ivy]

du/zx?

[distant lantern]

☠️

[neon iron]

?

[vernal vale]

if you mean $\int 4e^{x^2}\dd x$ youre gonna have a hard time

[thorny flame]

jan Niku

[distant lantern]

bruh i'm dumb I put a 4 instead of a 2

[neon iron]

You have to integrate twice

[vernal vale]

but we could link videos

[neon iron]

No I mean

[vernal vale]

this is not a calc i integral

calc iii maybe

[neon iron]

$\int$ $\int 4xe^{x^2}\dd x$

[thorny flame]

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

[neon iron]

Remove the $

[vernal vale]

oh theres an x

swr reacting me

[neon iron]

It was a double integral

THERES TWO INTEGRALS

[vernal vale]

paradox can you take some time to determine what the question youre asking is supposed to be

[noble laurel]

try u-sub u=x^2

[neon iron]

I did

Integral from 0 to 1 integral 4xe^x^2 dx

[vernal vale]

how is that 2 integrals

[neon iron]

It’s two integrals

An indefinite and definite

[noble laurel]

$\int_{0}^{1} {\int 4xe^{x^{2}} dx}dx$

[neon iron]

no the other way

Definite integral first

I dont think it matters thoufh

[thorny flame]

AustinU

[neon iron]

Yes

[noble laurel]

that is the question you got?

[neon iron]

Yes

[noble laurel]

how odd

[rigid ivy]

[neon iron]

This was on my calc 1

[rigid ivy]

[vernal vale]

what a weird question

[neon iron]

I finished my calc 2 ap bc exam

And it wasn’t as hard as this one

[noble laurel]

It "was" on, so you are telling us this question from memory?

[neon iron]

Yes

[rigid ivy]

doubt

[noble laurel]

I think this isn't the original question then

[neon iron]

I remember because I spent lots of time doing it

I swear on my life

On everything

That was the integral

[rigid ivy]

AP exam?

[neon iron]

No normal class exam

[noble laurel]

okay, what is your issue with it then

you said you tried u=x^2

[neon iron]

I did not know how to do it

[noble laurel]

what went wrong

[neon iron]

I cant integrate 2e^x^2

I don’t know how

[vernal vale]

its not easy

[rigid ivy]

You can't by normal means

[noble laurel]

that isn't what it left after performing the substitution

[neon iron]

Yes it is

[noble laurel]

what is left is 2e^u

[vernal vale]

no its not

[neon iron]

2e^u then I plug u back in

[vernal vale]

too many helpers

[rigid ivy]

bingo square

[noble laurel]

I'll leave ☮️

[vernal vale]

me too

ping if u wanna switch

[neon iron]

I didn’t know what to do so I just did e^2x

I think my teacher made a mistake

[rigid ivy]

I agree

[noble laurel]

$e^{(x^{2})} \neq e^{2x}$

[thorny flame]

AustinU

[rigid ivy]

,w integral 4xe^(x^2)

[noble laurel]

I didn't leave

[neon iron]

I didnt know what to so

I had no choice

Wtf is erfi

[thorny flame]

Results provided by WolframAlpha

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

Requested by SWR#8588

[neon iron]

I’m learning calc 3

Im on partial diff

[rigid ivy]

,w integral 2e^(x^2)

[thorny flame]

Results provided by WolframAlpha

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

Requested by SWR#8588

[neon iron]

?????

How am I supposed to know that

[noble laurel]

basic integral tbh

[rigid ivy]

Something is mega sus then.

[neon iron]

Im not in calc 3

Im self learning

Im not even in a calc 1 class

I self taught everything

[rigid ivy]

then how did you take a test?

[neon iron]

He let me do it for cresit

[rigid ivy]

Then there's a mistake somewhere

[neon iron]

Should I go have a talk with him?

[rigid ivy]

yes

[neon iron]

Dude

What the hell

Calc 3 question in calc 1 exam

[rigid ivy]

This isn't calc 3 either

[distant lantern]

☠️

wtf is going on

[neon iron]

What is erfi

My bad it’s calc 4

[rigid ivy]

bruh calc 4 isn't real

[neon iron]

It’s imaginary

[noble laurel]

it is real to me

calc4 is what some unis call multivariable calc actually though all jokes aside

[rigid ivy]

https://en.wikipedia.org/wiki/Error_function

[neon iron]

Thanks

[noble laurel]

some combine 3/4 into just calc3, some have a multivariable calc class, and it seems a small minority have calc 4 instead of "multivariable"

[rigid ivy]

weird

[neon iron]

Calc 4 is no variable

[rigid ivy]

wow calc 4 is a real thing

[neon iron]

I sent my teacher an email

[rigid ivy]

good luck

I'm dying to know where the mistake was.

All I know for sure is that there is no way to solve the problem you gave (by standard integration techniques)

[neon iron]

So it said solve the following definite integrals

And then that integral was there

[rigid ivy]

[neon iron]

Maybe the indefinite integral was there by mistake

[rigid ivy]

doesn't matter

[neon iron]

But I did not think it was

[rigid ivy]

two integrals creates the same erfi issue

[neon iron]

No I mean it’s supposed to be only the definite integral

[rigid ivy]

Oh

yes

likely that

If it's one integral, then you're fine

[neon iron]

And he added the indefinite integral by mistake

He should give me bonus marks

Because he made a mistke

[rigid ivy]

And if you're in calc 1, I most believe that it was just 1 integral

[noble laurel]

agreed

[neon iron]

Ive done all calc except calc 3 I’m learning it rn

[rigid ivy]

that problem would not show up in calc 3

[neon iron]

Where would it show up

[rigid ivy]

statistics, physics, or perhaps real analysis

[noble laurel]

nowhere really, classes don't really test students on non-elementary integrals

it would show up if you were studying integration techniques

[neon iron]

So if I tried to solve it it’s not my fault that I got it wrong

[noble laurel]

I think if anything actually complex analysis

[neon iron]

Thanks everyone

I appreciate it

.close

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[urban heath]

Hello, I need some help with my data management homework. It's regarding probability distributions.

[urban heath]

I'll type out the question.

Determine the probability distribution for the sum rolled with two dice.

So I get the sums which are just going to be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, & 12 - but I don't understand the actual probability part

shouldn't it be a uniform distribution with the probability being 2/6 for each sum?

because for ex. you have a 1/6 chance of rolling a one with one dice, and a 1/6 chance of rolling a two with another dice

so the combined probability would be 2/6

actually sorry it'd be out of 36

[barren turret]

,calc 2/6 * 11

[hasty cosmos]

is there a document that you could send, that could be better

[thorny flame]

Result:

3.6666666666667

[barren turret]

You have a 367% total probability?

[urban heath]

no sorry

[pastel oracle]

you multiply...

[urban heath]

I forgot it was with two dice

so it'd be 2/36

multiplied by 11 is 61.1 percent

[barren turret]

That's still not it

[urban heath]

That's what made sense to me but it's not the answer.

[barren turret]

Do you have 2 dice

Try rolling them and counting

[urban heath]

unfortunately not

[barren turret]

It's almost impossible to give you hints

Read notes about independence or something

[urban heath]

The question itself isn’t hard, I’m just trying to figure out how the text book got the probabilities listed

[pastel oracle]

why would you multiply by 11?

[urban heath]

there's 11 sums

and probabilities should add up to 100

my answer got me 61

[pastel oracle]

you have to calculate for each outcome, not all outcomes have equal probability

[urban heath]

right

but how would that work

if there's a 1/6 chance for rolling a 1

and there's a 1/6 chance for rolling a 2

the sum would be 3 and the prob would be 2/36

but how does that change for any other number on the die? it's all 1/6 for any one number

[barren turret]

Do an example of 2-faced die with numbers 1 and 2

Sum 2 of the 2-faced die

[urban heath]

1 & 1?

[barren turret]

I'm trying to get you to see you have an error in calculation

Just do the probabilities

Literally only 4 possibilities

Tabulate the possibilities

[urban heath]

idk how to explain this but would it be the combinations of the numbers on the die that can make the sum?

[barren turret]

There is nothing to explain

[urban heath]

since sum 2 is 1/36, there's only one 1 on each dice

[barren turret]

11 12 21 22

Do an example of 2-faced die with numbers 1 and 2

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[cinder oxide]

Is the inverse of any matrix 1/determinant?

[cinder oxide]

or only 2x2 matrices

[merry mason]

You can only find inverse of non singular matrices. And it's not 1/determinant because inverse of an matrix(if exists) is a matrix only. And its of the same order as of the matrix whose inverse you're finding.

1/determinant is a scalar value, not a matrix. So it can't be a inverse.

[pastel oracle]

the det of A^{-1} is 1/det(A), if that's what you're asking

[cinder oxide]

oh

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[rigid ivy]

6 minutes. Nice

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[fleet thicket]

um I know this is stupid but I need help on mean and median (I am in sixth grade) Help?

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[rigid ivy]

stick to original channel

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[coarse tusk]

,rcw

[coarse tusk]

which question

[hazy cypress]

the bottem one

would scale factor be ratio of sa???

[coarse tusk]

no

scale factor is the square root of ratio of surface area or the cube root of the ratio of volumes

[hazy cypress]

so just square root 28/63

[coarse tusk]

correct

[hazy cypress]

what about the pi

[coarse tusk]

actually it should be 63/28

[coarse tusk]

well it cancels out

[hazy cypress]

oh 👍

thx

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[cursive thorn]

omg, just literally look at potd-discussion

I bet someone wrote down some hints already or maybe even a full solution

nvm, nobody wrote down much of a hint, but you could ask for it

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[neon iron]

when you do u sub do you alwyas need to change the limits of integration

[wintry phoenix]

Can you elaborate and put an example if possible?

[neon iron]

i was watching a video about surface area of revolution and when the dude did a u sub he recalculated the limits of integration by plugging the x values into u

i remeber doing that for derivatives but not for intergrals which is why i was confused

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[stoic dawn]

\

[stoic dawn]

i don't know how to apply the formula here. it doesn't seem to be an exact translation from the table of integrals.

not sure how to manipulate u to make it fit the formula

[topaz sinew]

@stoic dawn Has your question been resolved?

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@stoic dawn Has your question been resolved?

[stoic dawn]

I don't understand this question at all. I can't follow the steps. I'm completely lost

<@&286206848099549185>

[high mulch]

Do you understand how to get the answers that have been filled in so far?

[stoic dawn]

yes

by completing the square

and substitution

but afterwards i don't follow

[high mulch]

Ok

So after you substitute, you can't integrate that thing easily so you simplify (u-9)sqrt(u^2+7) by distributing thr square root

[stoic dawn]

distributing the square root?

[high mulch]

So one term is $u\sqrt{u^2+7}$ and thr other is $-9\sqrt{u^2+7}$

[thorny flame]

catGPT

[stoic dawn]

not sure i follow the first part

how did they get du - 9?

[high mulch]

Do you see why $(u-9)\sqrt{u^2+7} = u\sqrt{u^2+7} - 9\sqrt{u^2+7}$

[thorny flame]

catGPT

[stoic dawn]

it seems they split it but i don't understand why

[high mulch]

Because it becomes easier to integrate if you split it

There's probably nothing in the table of integrals that looks specifically like that ,so you split it

[stoic dawn]

ok. i've seen all the techniques of integration in the last three weeks and i'm completely overwhelmed now

i have an exam next week

[stoic dawn]

ok

[high mulch]

And now you have 2 integrals which do look like something from the table

[stoic dawn]

ok

[high mulch]

Now they do the first one with substitution, do you see why they did that

[stoic dawn]

not sure why u-9 is easier to work with as opposed to x+9

but i suppose we are looking for a similar structure to our integral table

[high mulch]

Yes. The integral cannot be done directly so you do some algebra and try to make it look like something in you table or something that you can solve with a technique you know (in this case substitution)

[stoic dawn]

ok

[high mulch]

So the first integral looks like $\sqrt{stuff} \textd{stuff}$ which means you can use substitution

[thorny flame]

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

[high mulch]

Horrible latex sorry, but anyways

[stoic dawn]

yea sometimes the bot doesn't compile properly

[high mulch]

Do you need help understanding how to the substitution on the first integral or are you good with that

[stoic dawn]

let me check

one sec

i don't follow the second blank i filled in now

not sure why

[high mulch]

The u-9?

[stoic dawn]

yes

[high mulch]

Well our first substitution was u=x+9, so x=u-9

[stoic dawn]

ok why are we filling in x there?

the x sits outside the integral originally

[high mulch]

Because there is an x outside the root in the original problem

Yes

[stoic dawn]

ah ok

i see that now

what abou the next blank

where did du-9 come from?

[high mulch]

They want you to do this

[stoic dawn]

ok they want me to split it

let me take a look now

du-u?

[high mulch]

Yes, the first blank on that line w9uld be $u\sqrt{u^2+7}$

[stoic dawn]

usqrtu^2+7?

[thorny flame]

catGPT

[high mulch]

?

Not du - u

[stoic dawn]

because of the t sub?

ah ok

[high mulch]

Just fr9m distributing

[stoic dawn]

but why do we have the u outside the sqrt?

[high mulch]

Cause of this

[stoic dawn]

ah yes

that's how we split it

i didn't see that at first glance

now the next blank we just sub t

correct? it's just asking for the substitution

[high mulch]

Yeah

[stoic dawn]

ok. i don't see the next blank at all

[high mulch]

After substituting and integrating, you have a function of t. But you want a function of u, so you need to substitute back

[stoic dawn]

oh that straightforward?

so u back in for t?

[high mulch]

Yep

[stoic dawn]

the expression looks completely different like they've manipulated it

[high mulch]

Show me awhat you put in

[stoic dawn]

ok

one sec

it wants an exact number though

[high mulch]

Not like that

Just replace the t in the line above with whatever t is equal to

[stoic dawn]

ok

[high mulch]

They've partially do e it for you

Done*

T=u^2+7

[high mulch]

Yes!

[stoic dawn]

ln = 1/x

in this case how do we apply this?

[high mulch]

This doesn't make sense. All you're doing is using the table of integrals for $\sqrt{u^2+\sqrt{7}^2}$

[thorny flame]

catGPT

[high mulch]

Well in you table it should look like $\sqrt{x^2+a^2}$ so all you gotta do is take its integral and replace all the x's with u and the a's with $\sqrt{7}$

[thorny flame]

catGPT

[high mulch]

And simplify if possible

[stoic dawn]

it wants an exact number there

i want to put sqrt 7 there

[high mulch]

,w integrate sqrt(x^2+a^2)

[thorny flame]

Results provided by WolframAlpha

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Requested by catGPT#9757

[stoic dawn]

aw that's something that i should be able to look up in the table

is ee

[high mulch]

Yes but it's being squared so you just get 7

[stoic dawn]

x = u-9

following the table

[high mulch]

No, replace x with just u

I'll ex0lain in a bit

[high mulch]

There should be stuff in a root inside the log, no?

[stoic dawn]

true