help-23

[sterile vault]

here

vc me

[tardy lark]

I had those

[sterile vault]

I'll even show you

[tardy lark]

anyways

[sterile vault]

it's literally

[tardy lark]

I trust you

[sterile vault]

Right angle triangle hw

[tardy lark]

dont care tbh

[sterile vault]

well review*

LOL

alr

:3

ok so for b

I know A angle is 69.8

and I know my C

so Cos69.9=b/23.6

ye?

[tardy lark]

Yes

[sterile vault]

alr

[tardy lark]

69.8*

[sterile vault]

you right mb

[sterile vault]

ye

I got that

so that's my b?

[tardy lark]

Yes

[sterile vault]

alr

21.1, 8.150

ye?

[tardy lark]

3 figures

Not 4

8.15*

you should practice significant figures

[sterile vault]

A = 30º, cosA = 0.86
A = 30.0º, cosA = 0.866
A = 30.00º, cosA = 0.8660

is this right?

some guy just sent me this

21.1, 8.15*

ye?

[tardy lark]

Yes

[sterile vault]

pythag first

a2+b2=c2

12.6173

=3.552083895

oops I mixed up my abc lol

lemme fix

a2=c2-b2

2.371391996

so now I know all my sides how do I find the angle?

<@&286206848099549185>

[tardy lark]

Use trigonometry

[sterile vault]

bet

[tardy lark]

Cos(A)=b/c

cos^-1(b/c)=A

Or arccos(b/c)=A

[sterile vault]

done it lol

I went to search how to do it

I'm on the next question now

[tardy lark]

B is the same thing

and a is like we did previously

[sterile vault]

alr grasias

this 1

A=39.80557109 B=50.19442891

Ay yo

ndam

help me wit this 1 X_X

I got

7.810249682

<@&286206848099549185>

<@&286206848099549185>

This 1

how come I got that wrong

it should be 50.2

unless I rounded it wrong?

I did 6/5. tan-1 (1.2)

<@&286206848099549185>

[inland ivy]

soh cah tOA

[sterile vault]

hi papa 😄

so

O/A = 6/5

then I did tan-1 (1.2)

which gave me 50.19442891

but it says I'm wrong X_X

[inland ivy]

Recheck sides

[worthy hemlock]

Because it is wrong

[inland ivy]

Id assume a isnt where you think it is

[sterile vault]

hmm

oh fr?

dam

Soh cah toa

omfg

I was solving for b X_X

lol

said I got it wrong again

I got 56.4

nvm I got it

39.8

ez

this 1

I did tan-1 (15.1/31.9)

why did I get it wrong?

<@&286206848099549185>

.close

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[true jetty]

hello

[true jetty]

ok helper

I got a question

https://cdn.discordapp.com/attachments/938479969821134848/938480544231067678/unknown.png

I've done part a and b

how do I do part c

<@&286206848099549185>

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[lean otter]

help

[lean otter]

Can someone please explain this to me

im ery lost

help ;_;

<@&286206848099549185>

ee eim so lost

[final loom]

which one?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

all of them

bruh im very lost

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

someone help me ;:-;-;

[final loom]

1. State as many facts as you can about an isosceles triangle LUV with base UV. (lol)

How do we help you with that!? It's just a revision question lol, consult google

or ur textbook

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[signal herald]

if i were to draw a triangle would the -3 be the perpendicular side or the hypotenuse

[signal herald]

or the height wtv

[final loom]

[polar shadow]

Distance is a scaler

[final loom]

$\cos \theta$ is negative and $\theta$ in third quadrant

[flat frigate]

Ansh

[final loom]

what do you think are the signs of sine and tan ?

[slender flax]

+ve for tan and -ve for sin

[signal herald]

huh

[slender flax]

@signal herald If I'm not wrong, the sides should be 2 and 3, the negative sign is just an indication for it not being in the 4th quadrant (cuz cos is +ve in the 4th quadrant)

and yes 3 would be the hypotenuse

[final loom]

height² = hypotenuse² - base² [ pythagoras theorem ]

[safe radish]

@signal herald Has your question been resolved?

[signal herald]

so i would be solving for the height?

[slender flax]

yup

also keep in mind; sin is -ve in 3rd quadrant and tan is +ve, so put the signs before the actual value accordingly

[signal herald]

what is ve

[final loom]

negative ( -ve )and positive ( +ve )

[slender flax]

^

[signal herald]

what

ok then

[slender flax]

once you find the height

sin(theta) = opposite/hypotenuse

so 2/(hypothenuse, which you'll find through pythogorean identity)

but it's going to be negative since it's in 3rd quadrant

and similarly find for tan(theta)

[signal herald]

is tan

sin/cos

or cos/sin

[slender flax]

sin/cos

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[sage idol]

I've got this integral: $$\int_{0}^{1} \int_{0}^{1-x^2} \int_{0}^{1-x} f(x,y,z) dy dz dx$$

[flat frigate]

Sechmo

[sage idol]

I'm trying to reorder the limits of integration

but I got lost trying get $y$ or $z$ to the exterior-most integral

[flat frigate]

Sechmo

[sage idol]

I tried equating z=1-x^2 to get the limits of x in terms of z, I got x=Sqrt(1-z), yet I don't know how I should change y limits

Oh I guess I should'nt change them, but I'd like to know, is there anyway I could leave both y and x limits in terms of z?

it can only be expressed as $$\int_{0}^{1} \int_{0}^{\sqrt{1-z}} \int_{0}^{1-x} f(x,y,z) dydxdz$$ or is there a way $y$ limits could expressed in terms of $z$?

[flat frigate]

Sechmo

[safe radish]

@sage idol Has your question been resolved?

[sage idol]

Hmmm actually I'm lost about how could I express the integral in order dxdydz

Maybe splitting the integral somehow

<@&286206848099549185> Help, I offer you a 🍪

[tawny prairie]

Hello

What is this question

[sage idol]

You have the numeric values of x and y, just replace them into the expressions and calculate them

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@sage idol Has your question been resolved?

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@sage idol Has your question been resolved?

[sage idol]

.close

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[livid blaze]

Does anyone know what this question is actually asking?
Sicherman dice are like ordinary dice, except that they have different numbers of pips on their faces. One has 1,3,4,5,6,8 on its six faces, the other has 1,2,2,3,3,4. A pair is thrown. Find the probabilities of rolling the numbers one through 12 with these two dice. Compare with the usual probabilities

[livid blaze]

Is this just asking me to find the probability that the two dice sum to 12 when added?

and compare with 2 normal die

[merry swift]

it wants you to calculate the probability of getting every number from 1 to 12

like whats the probability of getting 1, of getting 2, of getting 3 etc

[livid blaze]

but it's not possible since the max face is 8

for numbers greater than 9

unless it means the sum

[merry swift]

It means the sum, the main special property of these dice has to do with the distribution of the sum of a pair

[livid blaze]

ok thanks lol that was a dumb question

[flat frigate]

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

[livid blaze]

2nd question: Show that if f is a borel function on R and A $\in B$, that ${x: f(x)\in A}\in B}$. Conclude that if X is a r.v. and f is a borel function, that f(x) is also a r.v.

[flat frigate]

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

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[paper creek]

.close

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[sharp void]

I am doing volume of solids for calc 2(disk/washer method) I have these 2 equations bounded by [0,3]. If I rotate it around the y axis my radius function is 3^2-(y^2)^2 however if I rotate it around x=3, my radius function is (3-y^2)^2

[sharp void]

Can someone explain why?

[ancient escarp]

which one don't you get

both of em?

or does one make sense and the other not

[sharp void]

I kinda dont understand how you can tell which one is which

[ancient escarp]

well you want to get your radius based off of where your axis of rotation is

so for example

for rotating about x=3

you'd want to use (3-y^2) as your radius

since that's the distance from your axis of rotation to your function

[sharp void]

what about rotating across the y axis?

[ancient escarp]

gotta try to visualize the shape

i'm a horrid 3d artist so it's gonna be 2d from me lol

still on the x axis one here

that's if i were to actually revolve it around that axis

the orange line being the radius

[sharp void]

I think I understand that one

[ancient escarp]

hmm the y axis one is a little harder to comprehend without someone who can't draw

it's an outside radius - inside radius type deal

let me see if i can find one online

[sharp void]

is this incorrect?

[ancient escarp]

that's a graph of x^2

or one similar

sqrtx's slope decreases as it goes on

[sharp void]

yeah oops

but the gist is the volume is above the line right

or is it still below?

[ancient escarp]

it's below

[sharp void]

oh

[ancient escarp]

,rotate

[ancient escarp]

like this lol

so it's got an outer radius and an inner radius

and with washers, formula is (outer radius)^2 - (inner radius)^2

man i need to invest in knowing how to draw

[sharp void]

uh where is the midline

[ancient escarp]

that's not the exact graph rotated about the y axis

i found it on google and rotated it via the texit bot

[sharp void]

I dont understand where the empty part comes from?

[ancient escarp]

blue stuff is solid

and it's revolved 360 degrees

empty stuff is above the graph

[sharp void]

Can I visualize it like this

so I have my area and the blue line is x=3

now if I rotate it

I rotate the x=3 as well

then I have two lines, so I kinda just go I need to apply washers here

would that process work?

[ancient escarp]

that works

[sharp void]

@ancient escarp

how about this

would this whole be the blue part?

[ancient escarp]

i'm not quite sure what that is lol

[sharp void]

uh what the volume would look like

[ancient escarp]

what exactly does "would this whole be the blue part" mean

[safe radish]

@sharp void Has your question been resolved?

[sharp void]

oh is it the empty part?

[ancient escarp]

oh

yeah

[sharp void]

got it, ty

.close

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[late wagon]

Guys i'm trying to solve this question but i can't find solution for this system

[late wagon]

and there's no option for no solution

[next kayak]

the system does not have a solution

in fact if you add the 2nd and 3rd equation you get 0=-2

[quasi bison]

@late wagon to solve a system means to find its solution set. and the solution set can be, and in this case is, empty

[next kayak]

that's in fact a very good observation

[late wagon]

can you explain more ?

[quasi bison]

is there something in what i said that you don't understand?

or do you understand what i said and want me to keep going with my explanation

[late wagon]

keep going with your explanation

[quasi bison]

consider that cramer's rule and the inverse matrix method only work when your system is known to have a unique solution

which your system is known not to have

gaussian elimination, however, can be applied to any system whatsoever

[late wagon]

so it's only gaussian elimination? since det==0 so it can't be cramer's rule , inverse

[quasi bison]

that... yes, in essence that's it

[late wagon]

thank you !!

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[tawny dome]

is this a typo? because for n>=4, the differential of x^3 is 0

[plucky elk]

Derivative*

[tawny dome]

yh my bad

[merry swift]

you're right that the >=4th derivative of x^3 is 0 but its not a typo.

[tawny dome]

wait whaaa

[merry swift]

I don't really see how the the >=4th derivative of x^3 being 0 means the nth derivative of x^3lnx couldn't be that so its hard to correct your misunderstanding without you explaining why it would do

[tawny dome]

oh

wait is the derivative the same after 4

because no new terms are added

thats why they said it

[merry swift]

no the derivative isn't always the same after the 4th one, as written it depends on n.

[tawny dome]

i meant like

you wont be getting any new terms

yh ur right the coefficents change

.clsoe

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[cosmic bloom]

I've been trying for hours to work out the answer to this question, and haven't got anywhere

[cosmic bloom]

I procrastinated by making a desmos newton method iterator https://www.desmos.com/calculator/lnthuic5n3

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[cosmic bloom]

.close

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[sharp void]

(disk/washer method from calc 2) I am trying to find the volume of the solid generated by the region bounded by y = 3x2
y = 0
x = 3

[sharp void]

The axis of rotation is y=27

can someone help me with the equation? I think it is this

[broken yew]

I don't understand where this comes from

If you're using disk, then surely you're integrating dy

If you're using shell, then dx

Draw a picture to avoid confusion . . .

Oh wait, you never said what the axis of rotation is. I was assuming y-axis

[sharp void]

the axis of rotation is y=27

[safe radish]

@sharp void Has your question been resolved?

[broken yew]

@sharp void was afk

no no, thinking

[sharp void]

Uh well the answer sheet said I was correct. Ngl it is kinda jank and I couldn't believe I got it right

[broken yew]

yh ok, this seems fine

well you just have to have the correct image on paper

(or in your head)

[sharp void]

Just to clear something up, the radius is the distance from the axis of rotation to the curve right?

[broken yew]

uh

The center is the axis of rotation

Depends which radius you're talking about

But yes, basically ig

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[sharp void]

.reopen

[safe radish]

✅

[sharp void]

if blue lines is my region, and red is my axis of rotation

[broken yew]

that's the radius of the hole you marked

[sharp void]

yeah

and the outer radius is the red line to y=0 right

[broken yew]

yes

[sharp void]

alright ty

.close

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[hybrid void]

is this a good start or no?

[fair dagger]

Are you looking for the length of x?

[hybrid void]

yes

[fair dagger]

What was your thought process so far?

[hybrid void]

i thought we had to do a proportion

[fair dagger]

I don't think that is a good start.

You should apply some statements relating the sidelengths of a triangle with a 90° angle.

[hybrid void]

what do you mean by that?

[fair dagger]

Pythagorean theorem

also inverse Pythagorean theorem maybe be helpful if you know it

[hybrid void]

yeah i haven’t learned about inverse pythagorean theorem before i think

[fair dagger]

In that case the only solution I am seeing atm is to make a system of equations using the Pythogorean theorem twice and solve for x.

You can apply the Pythogorean theorem both to the left and the right triangle.

[hybrid void]

do we divide the 12 like 12 divided by 2 to get the two sides?

[fair dagger]

We don't know the correct fraction so no.

We can only say that the upper left bit has a length of 12 - x.

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@hybrid void Has your question been resolved?

[safe radish]

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[blazing rune]

They substituted x = a tan y .... my question is how can they change the value of function x to any value?

[blazing rune]

i mean to say how can we just assign any value to x?What if we put x = a sin y ...will the integral be the same?

[snow robin]

Can you explain what you mean

No if we assign x = a sin y

y being the keyboard equivalent to theta in this case

If we do that the dx = a cos y dy

Which is different

They used this substitution that they did because it works out nice

Tan^2 + 1 = sec^2 if im not mistaken

[blazing rune]

i mean to say, that we have assigned x = a tan y...my question is .... how can we just assign x to anything since x itself is a variable and assuming it's value to be a tan y would make whole function to change

[snow robin]

We substitute it in such a way that x doesnt change

X is a variable

And in this case it can be anything because its an indefinite integral

But imagine it wasnt

Imagine x is between 3 and 6

Then we substitute x with tan y in such a way that tan y goes between 3 and 6

[blazing rune]

oh yes you got my point and i think i understood...Thank you 😀

.close

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[jagged cargo]

how do u verify this trig identity?

cosec 2θ - cot 2θ = tan θ

[jagged cargo]

i turned cosec 2θ into (1-cos 2θ)/(sin 2θ), and cot 2θ into cos 2θ/sin 2θ....and im stuck there

[safe radish]

@jagged cargo Has your question been resolved?

[plucky elk]

Use double angle formula

[jagged cargo]

now im left with (2sin^2θ)/(2sinθ cosθ)

[plucky elk]

Do you know how to simplify that?

[jagged cargo]

nope, thats where im stuck

[plucky elk]

treat sin(t) like its own variable

sin^2(t) = (sin(t))^2

Also cancel the 2 from numerator and denominator

[jagged cargo]

so u cancel both the 2s and the square?

if i do that, then it will be verified, but thats if i do it

[plucky elk]

You cancel common terms

x/x = 1, right?

[jagged cargo]

right

[plucky elk]

Look in your algebra book for algebra rules

[jagged cargo]

ah i get it

u seperated the 2 from the sin

???

ok i think i got it

thx🙏 @plucky elk

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[true marsh]

I think I'm supposed to find how many ways I can split 5, 6, 7, 8, and 9 into four groups (a, b, c, d) and add them together, but I'm not sure how to use combinatorics/permutations to do that.

[karmic cipher]

let z=a+b+c+d
4<z<10
z=5,6,7,8,9
result=no of ways of picking a,b,c,d such that they sum up to 5+no of ways of picking a,b,c,d such that they sum up to 6.....9

5->1,1,1,2
combinations of taking 4 numbers in four places but 3 repetetion

6->1,1,1,3 or 1,1,2,2
=combinations of taking 4 numbers in four places but with 3 and 2,2 repetetions

find for all numbers from 5...9 and add the total combinations

[true marsh]

How would you calculate that without having to count everything, though? D:

[karmic cipher]

its just 5 numbers so do it manually

[true marsh]

I feel like that would still take up a lot of time. I'm practicing for a timed test that will be 30 questions in 30 minutes, so I don't think I'd have time to count each one.

[karmic cipher]

i dont think there is a formula for this but maybe try to figure it out and let me know if you find

[true marsh]

Ah, okay.

[final loom]

Isn't it called stars n bars

You can directly conclude the answer :o

[safe radish]

@true marsh Has your question been resolved?

[true marsh]

:o I'll search that up. Thanks.

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[tired whale]

hey a friend of mine wanted some help with this..

[tired whale]

would be great if someone could help

thanks!

[wet sluice]

Can somebody explain this to me

[tired whale]

@timber valve this dude ;-;

[timber valve]

@wet sluice please read the #❓how-to-get-help channel

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[tired whale]

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[fathom sky]

how do you do this question without a calculator

[light shoal]

$9=3^2$ and $27=3^3$, so the equation can be rewritten as $3^{x+1} = 3^{-3}$. Now take log base 3 of both sides.

[flat frigate]

OurBelovedBungo

[fathom sky]

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[fathom sky]

thank you for your help!

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[modest cloak]

can someone explain how to solve this one? i have no idea

or walk me through it

[steel stag]

you have to think of what can go wrong on the top and bottom of the fraction

sqrt() goes wrong when the inside is negative

and the bottom can go wrong if you divide by 0, so you'll have to factor the bottom to find out where that is

[safe radish]

@modest cloak Has your question been resolved?

[modest cloak]

im still lost

[lean otter]

there can never be a negative number inside a square root because when you square a number it can’t end up negative

so take what is inside the square root and make a rule that it has to be equal or greater than zero

that’s the first condition

[modest cloak]

ok

whats next

[lean otter]

because the function is a fraction, the denominators in fractions can never be zero because you can’t divide by zero

so take whatever is in the denominator and make a second condition that it cannot equal to zero

now you have two conditions, just have to find the common values in those two conditions

[modest cloak]

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[lone crane]

How do we solve this simultaneous equation

[shy barn]

A lot of ways

Solve for n or m, ur choice, then substitute into the other, then backsubstitute to the original

[lone crane]

The thing is i dont know howw too..

[shy barn]

2m+4n = 9
m=4.5-2n

-3m+5n=14
-3(4.5-2n)+5n=14
Solve for n and then u can find m

[lone crane]

Any steps that i can follow?

[shy barn]

Like in general?

[lone crane]

Yesss

For solving simulatenous equations

[shy barn]

Isolate a variable and then substitute into the other eq

Or set up a 2x2 matrix augmented with the constants and row reducs

[lone crane]

I dont know how to do matrix soo nvm boutt itt

Pretty complicated

[lone crane]

Ill try my best tysm

[shy barn]

$\begin{bmatrix} x_1 & y_1\ x_2 & y_2 \end{bmatrix}$

[flat frigate]

MattDog_222

[shy barn]

I cant remember how to augment on tex rn but the constants go on the right and then u have a formulaic way

[lone crane]

Yessir

Tyssmmmm i really appreciate it

[shy barn]

Havent watched the vid but this might help https://www.youtube.com/watch?v=2INfJs5WaFo

[lone crane]

THANKKKSSSS MAN I REALLY APPREICATE IT

Take careeee

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[flat frigate]

Kepe

Kepe

[prime prawn]

An hour

He needs to wait an hour

Uhh

Btw B(x) is 18 I think

But idk

Wait

Nvm

Uhh

I can help you simplify this

This one

[flat frigate]

Kepe

Kepe

[prime prawn]

Wait

X = (-b+5.5)/0.25b

That’s the answer

X is -b+5.5 divided by 0.25b

Does that answer you wuestion

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[tropic wharf]

If a=2b, if a and b are complex
Then would arg(a/2) = arg(b)

?

[safe radish]

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[tropic wharf]

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[alpine crest]

hi can anyone help with 4b and 4c? i got the correct answer to 4a but i think my diagram might be missing something?

[safe radish]

@alpine crest Has your question been resolved?

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[crisp lodge]

hey everyone

[crisp lodge]

it is to be solved with spherical coordinates
however I think im not substituting it correctly in my denominator which is why it turns ugly

what I get from the region is that my set of bounds is 0-1 for r
0->2pi for phi and 0-pi for theta
but how to I sub my coords in the intergrand?

I see it's an offset sphere
but I dont know how to use that to my advantage

[broken yew]

whats the jacobian

[crisp lodge]

r^2 sin theta

[broken yew]

that will be multiplied right?

[crisp lodge]

aye

[broken yew]

so u get that thing times dr dtheta dphi

[crisp lodge]

yea

[broken yew]

uhhh interesting

[crisp lodge]

answer's 2pi/3 btw
verified with wolfie too

[broken yew]

r^2 - 4z +4
You have this under the root

If u substitute spherical at origin

[crisp lodge]

-4z ?

[broken yew]

What does z become?

[crisp lodge]

-4rcos(theta) would be better

[broken yew]

alright so cant u integrate this wrt r first

[crisp lodge]

umm this ?

[broken yew]

complete the square under the root?

[crisp lodge]

I mean

[broken yew]

theta is just constant

[crisp lodge]

I tried

the integral for that.. is not so nice

[broken yew]

i wont know the difficulties until i try then ig

but im kinda sure this is the way ur meant to

[crisp lodge]

I tried inputting that sort of integral in a caluclator
the result was..

not exactly nice

10 terms with imaginary numbers type of not nice

[final loom]

Is this called multivariable integration?

[crisp lodge]

so it really makes me think there's a nicer sub I could do but im not sure what it is

[crisp lodge]

umm I guess?

goes by triple integral here simply

[final loom]

Ah got you

[safe radish]

@crisp lodge Has your question been resolved?

[final loom]

Did you get: $\int_0^{\pi} \int_0^{2\pi} \int_0^1 r^2 \sin^2 \phi \cdot \frac{\dd{r}\dd{\theta}\dd{\phi}}{\sqrt{r^2 \sin^2 \phi + (r\cos \phi - 2)^2}}$

[flat frigate]

Ansh

[final loom]

hmm?

[crisp lodge]

yea

actually not quite that

[final loom]

then? I did the $x^2 + y^2 = r^2 \sin^2 \phi$ thing before writing

[crisp lodge]

r^2sin^2(phi)sin^2(theta)=y^2

[flat frigate]

Ansh

[crisp lodge]

ohh okay

right

yea

same thing

except it should be theta instead of phi
but that's not that big a deal lol

so yea yea

we're on the same page

[crisp lodge]

wait
its sin(phi) on the numerator, not squared .. ?

the jacobian is r^2sin(theta)

[final loom]

I wrote squared

$\int_0^{\pi} \int_0^{2\pi} \int_0^1 r^2 \sin \phi \cdot \frac{\dd{r}\dd{\theta}\dd{\phi}}{\sqrt{r^2 \sin^2 \phi + (r\cos \phi - 2)^2}}$

[flat frigate]

Ansh

[final loom]

Oh right..

[crisp lodge]

yea that's it

[final loom]

Yep.. Is it fine now?

[crisp lodge]

looks fine

[final loom]

that's why I was wondering why it looks so tough lmao

Now it's easy

$= \int_0^{\pi} \int_0^{2\pi} \int_0^1 r^2 \sin \phi \cdot \frac{\dd{r}\dd{\theta}\dd{\phi}}{\sqrt{r^2 -4r\cos \phi +4}}$

[crisp lodge]

-4*

[final loom]

hmm?

howw

[crisp lodge]

-4rcos(phi)

[flat frigate]

Ansh

[final loom]

Aaaaaaaaaaaaaaaaaaaaa why am I so bad at math

hmm looks fine now!

[crisp lodge]

you really are aren't you /bigsarc

[crisp lodge]

aye !

[final loom]

we can first integrate with respect to phi, can't we?

[crisp lodge]

w

can

we

yse

we can ?

[final loom]

we can't-

Idkkkk

okay nvm! let's just do it with "r" first

[crisp lodge]

it's def an option.. I haven't considered that
idk if it's gonna be easier tho

actually no wait that can work

numerator is denominator's derivative

[final loom]

$= \int_0^{\pi} \int_0^{2\pi} \int_0^1 r^2 \sin \phi \cdot \frac{\dd{r}\dd{\theta}\dd{\phi}}{\sqrt{(r-2\cos \phi)^2 + 4\sin^2 \phi}}$

[flat frigate]

Ansh

[broken yew]

lovely

how the heck do we do these

[final loom]

we dance around XD

[broken yew]

the thing on top is bad :D

[proud hazel]

What in the world is this

[final loom]

Actually shuri

Is it okay?

[broken yew]

huh? is what ok

thats what i said to do earlier

[final loom]

to integrate w.r.t. other variable first?

[crisp lodge]

so far it fits waht I got

[broken yew]

u can switch the order of the integrals

[final loom]

Ooo yayyyy

$\int_0^{\pi} \int_0^{2\pi} \int_0^1 r^2 \sin \phi \cdot \frac{\dd{r}\dd{\theta}\dd{\phi}}{\sqrt{r^2 -4r\cos \phi +4}}$

[flat frigate]

Ansh

[crisp lodge]

wait so now that will be
2r^2/4r (sqrt(-4rcos(phi)+r^2+4))

if we integrate wrt to phi first

does that look right ?

[final loom]

waito

$= 2\pi \int_0^{\pi}\int_0^1 r^2 \sin \phi \cdot \frac{\dd{r}\dd{\phi}}{\sqrt{r^2 -4r\cos \phi +4}}$

[flat frigate]

Ansh

[broken yew]

=.=

yh try phi first

[final loom]

$= \pi \int_0^1 r \qty[\sqrt{r^2 -4r\cos \phi +4}]_0^{\pi} \dd{r}$

$= \pi \int_0^1 r [(r+2) - (r - 2)] \dd{r}$

[flat frigate]

Ansh

Ansh

[final loom]

$=2\pi$

[flat frigate]

Ansh

[final loom]

@crisp lodge tell me that's not the answer

[broken yew]

omg u guys did it?

[crisp lodge]

1/3 is missing

[final loom]

Lmfao

[broken yew]

.

[final loom]

hmmmmm

[broken yew]

ansh

whats the integral of r^2

[final loom]

r^3/3 👀

[broken yew]

or wait

where the heck is the issue then

D:

[crisp lodge]

wait

how did you get rid of the squared term?

[final loom]

which squared term?

[crisp lodge]

shouldn't you be getting r [sqrt(r^2+8)-r]?

and integrate that ?

[final loom]

the bounds for phi ._.

[final loom]

whaa?

[crisp lodge]

that should be the result after applying bounds

cos(pi)=-1?

[final loom]

which step

I know lmao

[crisp lodge]

lol

[final loom]

Which step?

[crisp lodge]

right after here

when applying the bounds

[final loom]

Is this step right?

[crisp lodge]

the integrand seems fine

[final loom]

Okay so now we apply bounds:

$\qty[\sqrt{r^2 -4r\cos \phi +4}]_0^{\pi} =\sqrt{r^2 +4r +4} - \sqrt{r^2 -4r +4}$

[flat frigate]

Ansh

[final loom]

No?

[broken yew]

careful for sign

[final loom]

=_=

[broken yew]

the root of one of those u bodged

[crisp lodge]

and then
r*[sqrt(r^2+4r+4)-(r-2)^2] ?

[broken yew]

heheheh

[broken yew]

wut

[final loom]

hmm? why squared lmao

both are under roots

[crisp lodge]

oh yea

the second root is just (r-2)^2

[broken yew]

wut

[final loom]

(@_@;) what about them.. r belong to (0,1 ) ... ohhhhhhhhhhhhhhhh

SHuri you're genius

[broken yew]

pay attention to sign

no u did work i watch

[final loom]

Deus this wrong asf smh

Because $\sqrt{r^2 - 4r + 4} = \abs{r - 2} = 2 - r$

[crisp lodge]

ah

yes

[broken yew]

2r^2

2pi/3

[flat frigate]

Ansh

[broken yew]

heheh

[final loom]

shuri matches answers

coughs

[broken yew]

i knew it was r^2

[crisp lodge]

wh

it's what I was trying to say tho !

failing at it but still !

[broken yew]

before we even hunted

hehe

[final loom]

$= \pi \int_0^1 r \qty[\sqrt{r^2 -4r\cos \phi +4}]_0^{\pi} \dd{r}$

[flat frigate]

Ansh

[final loom]

$= \pi \int_0^1 2r^2 \dd{r}$

[flat frigate]

Ansh

[broken yew]

wow nice step

[final loom]

$=\frac{2\pi}{3}$

[flat frigate]

Ansh

[crisp lodge]

oh right

[final loom]

Yay!! I solved my first triple integral lmao

[crisp lodge]

the second was also a square

[broken yew]

help-2 your next integral awaits @final loom

[final loom]

i-

[crisp lodge]

Okay
looks good lol

thanks Ansh

.close

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[lofty holly]

how would i do this

[safe radish]

Please don't occupy multiple help channels.

[lofty holly]

ive worked out n is 14

What does the second part mean

[weak dirge]

This is calculus?

[lofty holly]

dont know

[split ether]

Rewrite (2n + 47)/(n + 1) as 2 + 45/(n + 1) if you're not familiar with limits

[lofty holly]

how?

[lofty holly]

is it 2 <@&286206848099549185>

.close

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[alpine crest]

hi can anyone help with 4b and 4c? i got the correct answer to 4a but i think my diagram might be missing something?

[safe radish]

@alpine crest Has your question been resolved?

[alpine crest]

<@&286206848099549185>

[safe radish]

@alpine crest Has your question been resolved?

[safe radish]

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[hollow berry]

So I don’t know how to do said problem

[hollow berry]

2(x+y)squared -9(x+y)+4

[formal citrus]

hm

tried a system?

[hollow berry]

Number 3

[formal citrus]

is that expression equal to what?

[hollow berry]

If that helps

Factor

Is what’s happening

[formal citrus]

hm

[hollow berry]

$2(x+y)^ -9(x+y)+4

[formal citrus]

Sorry I'm afraid I can't help. I thought it was something else

[hollow berry]

Oh.

It’s alright

[lyric ingot]

(x+y)^2 = x^2 + 2xy + y^2

[hollow berry]

wait

[formal citrus]

yes I did that

but I think that's not what he pretends right

[lyric ingot]

I don't know how to simplify this into something actually nice looking

[hollow berry]

It’s factoring

[lyric ingot]

Oh

Well then thats pretty easy

Or is it??

...

[hollow berry]

I’m very much dumbfounded

so

uh

anyone there?

[lyric ingot]

Have you simplified the (x+y)^2

[hollow berry]

Uh

Let me see

[lyric ingot]

i got 2x^2 + 4xy + 2y^2 -9x -9y -5

[hollow berry]

The thing is i don’t know what do put what into

$2(x+y)^2 -9(x+y)+4$

[flat frigate]

Absolute_5C

[lyric ingot]

Yes 2x^2 + 4xy + 2y^2 -9x -9y -5 was the furthest I was able to simplify

Probably some factoring needed to be done here

[hollow berry]

It’s factor lol

[lyric ingot]

Name leak

Ah ok

You can't really factor 2x^2 + 4xy + 2y^2 -9x -9y -5 though lol

[hollow berry]

WHAT????

i don’t know what kind of problems they be giving me

<@&286206848099549185>

[plucky elk]

Write u=x+y

And then use quadratic formula for u

Oh there's probably a simpler way

(u + a)(2u+b) = 2u^2+2au+bu +ab

[hollow berry]

Uh

could you explain further how to use the formula in this problem?

[plucky elk]

(2a+b) = ? And ab = ?

[hollow berry]

^

Oh

Alr

[plucky elk]

Solve this system of equations for your constants

[hollow berry]

Thanks!

.close

[safe radish]

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[lean otter]

can someone run me thru this question

[lean otter]

i forgot how u answer stuff like this with modulus function

all i know is that modulus ( the : | | ) means that everything inside is positive

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

<@&286206848099549185>

[lyric ingot]

How are we supposed to help you sketch?

What do you need help with?

It should look like two diagonals from the first and second quadrant approaching wherever a is

If a = 10 the y intercept is 10

And the x intercept should be 2x + 10 = 0 which comes out to -5

[lean otter]

how would u know if its an upside v

or other way

V or /\

[lyric ingot]

Well everything has to be positive

Because of the | |

So like a V

[lean otter]

oh so a modulus functions never /\

?

[lyric ingot]

They shouldnt

Then something is very wrong

XD

[lean otter]

lol

r u american

fu

🤦🏽

🤦🏽

🤦🏽

.close

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[lean otter]

how can i show that the largest area of a square inscribed in an unit cube is 9/8?

[inland ivy]

Is this for a calculus based class

[lean otter]

no calculus

i'd love to see both methods though

[inland ivy]

It might come out to a parabola or something

[lean otter]

what if we used analytical geometry?

[inland ivy]

Wait specify inscribed

[lean otter]

by inscribed i mean that all of the 4 corners of the square are contained within or on the unit cube

[inland ivy]

I guess the maximum would be like

Across the diagonal?

Im still not sure how youd prove that even if that is the case

[lean otter]

it is easy to see the area is bigger than 1 and smaller than 2

because the diagonal of a cube's face is sqrt(2), and if the side of the square passes through that diagonal, it will have to go through the height of the cube, wihch is 1, therefore it's not a square

and it's bigger than 1 because that'd be just on the cube's face

[inland ivy]

Oh thats true

Hmm

Yeah Im not sure the best way

The best way I could think of is brute force

[lean otter]

analytical geometry could work, but you'd have 12 variables, no? 3 for each point and there are 4 points

[inland ivy]

Yeah

[lean otter]

and that's too annoying to deal with

[inland ivy]

I mean maybe you could simplify it to less variables

But theyd likely be harder to deal with variables than position

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

i'll just drop it, maybe it is too much for me

[safe radish]

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[modest cloak]

im so confused with these, watched couple vids and still lost

[pulsar condor]

how did you get f(a)=4?

[modest cloak]

ignore that

idk why thats there

[pulsar condor]

ok, well if I asked you for f(3), what would you do?

[modest cloak]

i wouldnt know

im confused on where to plug the numbers in

can u elaborate

[pulsar condor]

f(3) means evaluate f(x) at x=3.

what would f(3) be?

[modest cloak]

not sure

[pulsar condor]

Put some effort in

try to tell me what f(3) is.

[lyric ingot]

But f(x) = 6x^2 + 4

🙂

[pulsar condor]

.

[modest cloak]

58

[lyric ingot]

Pretty sure thats correct 👍

[pulsar condor]

yes, and what about f(0)?

[modest cloak]

4

[pulsar condor]

yes

so, without overthinking it, what's f(a)?

Hint: It won't be a number, cause a isn't a number

[modest cloak]

6a^2+4

?

[pulsar condor]

yep

now do f(a+h)

[modest cloak]

tahts the answer for the first one?

[pulsar condor]

f(a)=6a^2+4, yes

[modest cloak]

2nd question is 6 (a+h)^2 + 4?

[pulsar condor]

check for typos

[modest cloak]

2nd question is 6 (a+h)^2 + 4?

[pulsar condor]

yes

[modest cloak]

how would u solve this? 6(a+h)^2

do i multiply 6 to a and h then square both?

[pulsar condor]

no

BEDMAS

you do powers first

[modest cloak]

how would that look

i be confusing myself too much

[pulsar condor]

can you expand (a+h)^2?

Recall FOIL

[modest cloak]

.close

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[clever sorrel]

If the momentum of a quantum particle is it's mass times its rate of change of average position, why is the momentum of this particle nonzero, it's wave function amplitude is the same at all points

PS, If you answer this question please ping me

[pulsar condor]

#old-network for physics server

[clever sorrel]

I understand this is a physics problem but the physics discord is a lot slower at answering

[pulsar condor]

Quantum doesn't use p=mv though

it uses the De Broglie Relations

[clever sorrel]

In griffiths, they say the momentum p=mdx/dt where x is the average position

and then they derive the momentum operator

[plucky elk]

what step are you lost at in the image

explain it in math terms

[clever sorrel]

This problem can't be solved with just math i think

[plucky elk]

https://giphy.com/gifs/the-simpsons-scared-homer-simpson-jUwpNzg9IcyrK

[clever sorrel]

It could be if i linked the derivation from griffiths

I can try that

[plucky elk]

you should understand the physics involved then ask your question again in math terms

[plucky elk]

and also look this up if you haven't

[clever sorrel]

Okay, I can try rephrasing it as a maths question

later

.close

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[cedar crystal]

Not really sure how to solve.

<@&286206848099549185>

[crisp lodge]

DevFire, ping helpers at least 15 mins after your question was asked

as the rules state

[cedar crystal]

Oh

Sorry sir

[crisp lodge]

hmm

have you tried constructing an equation ?

[cedar crystal]

i tried

@crisp lodge

but im not sure

to be honest

i dont know how to make the system in this case

i mean I know that its going to be 60d

d represeting the days

but like i just cant build off of that

[crisp lodge]

maybe, try to define the amount of pages in total of the book

[cedar crystal]

yea

so i think its

60d

for the days

but for the pages i dont know

[crisp lodge]

the pages and days come together

[cedar crystal]

cause i think d + 4 would be like the last 4 days

hmm

[crisp lodge]

if it's expected to read a certain number of pages, such that it would take 60 pages per day to read

then if we call x- the number of days required to read

60x= pages in total