help-27

[tranquil flower]

these arent in the same denominator right?

[cursive skiff]

No

[tranquil flower]

so thats why we want to have 3wholes as a fraction of 7

hence

21/7

[cursive skiff]

Okay

Now what

[tranquil flower]

now we can continue

2/7 * 21/7

since we have common denominator we can say

(2*21)/7

right?

[cursive skiff]

Wait what

We still have the 2/7

I thought it turned into 21/7

[tranquil flower]

no

the 3 did

[cursive skiff]

Oh

How does just the 3

I don’t get it

[tranquil flower]

ok

so say we have 1/2 + 1/3

to make them the same denominator what do we have to do

[cursive skiff]

3 * 2 and 2 * 3

[tranquil flower]

yes

so for

2/7 * 3/1

whats the common denominator

[cursive skiff]

Ohh 21

[tranquil flower]

not quite

[cursive skiff]

What

[tranquil flower]

2/7 * 3/1

7 and 1

whats the common denominator

[cursive skiff]

7

[tranquil flower]

yes

so what do we do to the 3

[cursive skiff]

Times it by 7

[tranquil flower]

nice

[cursive skiff]

Ohh ok

[tranquil flower]

thats how we end up at 2/7 * 21/7

right?

[cursive skiff]

Ok ok I get it now

[tranquil flower]

nice

so now that we have -3 = -21/7

we can multiply right?

(2*-21)/7

[cursive skiff]

Wait what

I have 5 = 2/7 * 21/7 + b

[tranquil flower]

well we still have the negtive

we cant just delete it

[tranquil flower]

5 = 2/7 * -21/7 + b

[cursive skiff]

Ok

[tranquil flower]

ok

so now how do we cancel out the 2/7

[cursive skiff]

-2/7

[tranquil flower]

actually wait

lets not do it that way

[cursive skiff]

Why

[tranquil flower]

it can be done easier

[cursive skiff]

Ok

[tranquil flower]

5 = 2/7 * -21/7 + b

so do the multiplication

[cursive skiff]

42/49?

-42^

[tranquil flower]

wait

im tripping

yo forget everyhting i said about the multiplication part for fractions

[cursive skiff]

Okay hahaha

[tranquil flower]

LMFAO

but you have to do that for addition and subtraction

[cursive skiff]

Okay

[tranquil flower]

for 2/7 * 3

think of it as

2/7 x 3/1

[cursive skiff]

Alright

[tranquil flower]

just multiply the nonimators by each other

and the denominators by eachother

[cursive skiff]

Like do that now?

[tranquil flower]

yeah

[cursive skiff]

So 6/7?

[tranquil flower]

nice

5 = 6/7 + b

right

so how do we get rid of 6/7

[cursive skiff]

-6/7

[tranquil flower]

to both sides

now we have?

[cursive skiff]

Wait is it supposed to be -6/7 to start with

Cuz u said we don’t get rid of the negative

[tranquil flower]

yes

good job remembering that

[cursive skiff]

But I can still do -6/7 to get rid of it or do I have to do +6/7

[tranquil flower]

you would do +6/7 for this case

[cursive skiff]

Ok

To the 5 as well?

[tranquil flower]

yep

what will you have

[cursive skiff]

How would I do that

[tranquil flower]

5 + 6/7

[cursive skiff]

Wait

I know

11/8

[tranquil flower]

can you show me how you got thar?

that*

[cursive skiff]

5/1 +6/7

6+5

[tranquil flower]

not quite

[cursive skiff]

I thought u said that’s what I’m supposed to do

[tranquil flower]

were working with addition now

not multiplication

[cursive skiff]

Yea I added them

[tranquil flower]

but remember what we have to do for addition and subtraction?

[cursive skiff]

No

[tranquil flower]

when using fractions

[cursive skiff]

Common denominator?

[tranquil flower]

bingo

[cursive skiff]

So 35/7?

Or no

[tranquil flower]

nice

35/7 + 6/7

we can rewrite this as

(35+6)/7 because we have common denominators

which gives us?

[cursive skiff]

41/7?

[tranquil flower]

nice

41/7 is our b value now

[cursive skiff]

Ok now how do I put it in general form

[tranquil flower]

so take the equation

whats our new equation now that we found b

[cursive skiff]

Idk

[tranquil flower]

sub b into the y = mx + b equation

[cursive skiff]

5= 2/7 + 41/7

[tranquil flower]

leave x and y as is

so y = 2/7x + 41/7

[cursive skiff]

Okay

[tranquil flower]

now

to turn y=mx + b into -> Ax + By + C = 0

[cursive skiff]

Yea

[tranquil flower]

lets move everything to the right side

so remember how to move stuff?

[cursive skiff]

I do not

[tranquil flower]

remember this?

[cursive skiff]

So fake away 2/7

[tranquil flower]

we cant leave x there though

[cursive skiff]

Take away 2/7x

[tranquil flower]

nice

that gives us?

[cursive skiff]

Y= 39

[tranquil flower]

not quite

[cursive skiff]

39x

[tranquil flower]

let me write it out

[cursive skiff]

Ok

[tranquil flower]

do you understand this?

@cursive skiff

[cursive skiff]

No but is that the answer on the bottom

[tranquil flower]

no

[cursive skiff]

Oh

[tranquil flower]

the green highlight is the opperation that i performed to the equation

to move 2/7x to the left

[cursive skiff]

Ohh ok

[tranquil flower]

now we dont have 0 by itself

so we have to move the other term over

can you do that

[cursive skiff]

-41/7

This question is taking way too long why am I so dumb

Can u quickly do 19 for me after

[tranquil flower]

ur not dumb

but we're also not done

because you cant leave the fractions ther

there*

[cursive skiff]

The answer is y = 2/7x + 41/7

[tranquil flower]

this isnt in the general form tough

though*

[cursive skiff]

Oh

[tranquil flower]

y = mx + b is the slope intercept form

[cursive skiff]

So what is it in general form

[tranquil flower]

thats what were doing right now

[cursive skiff]

Okay

[tranquil flower]

look at your sheet

[cursive skiff]

When we get this one done can u pls just do the other one for me I don’t have time to do it for so long

[tranquil flower]

you said that the general form is Ax + By + C = 0

[cursive skiff]

Yes

[tranquil flower]

so we're now changing y=mx+b to Ax + By + C = 0

[cursive skiff]

Okay how

[tranquil flower]

thats what i was just explaining

[cursive skiff]

Ok

[tranquil flower]

the green highlight is the opperation that i performed to the equation
to move 2/7x to the left

[cursive skiff]

Yes

[tranquil flower]

you said that to move 41/7 to the left we have to do this

continue from here

[cursive skiff]

Dude idk I just need the answer I’m stressing out I have somewhere to be

[tranquil flower]

well i cant just give you the answers

[cursive skiff]

Well idk how to do it

This question has taken an hour

[tranquil flower]

im trying to help you understand how to do it

so that you know how to do it in the future

[cursive skiff]

Ok can u explain then bc idk man

[tranquil flower]

i have been explaining it

start from here

and move everything to where y is

[cursive skiff]

Idk how

[tranquil flower]

it says how to do it right there in the picture

and you've been giving the right response when i ask you how

i mean if you want i can give you how to get to the answer

here

To convert from slope intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction.

example

y=1/2x + 5 ----translates to--> −x + 2y − 10=0

[cursive skiff]

So what’s the answer

[tranquil flower]

i mean i gave you the recipe to get to it

[cursive skiff]

Can u just give me it Pleasee🙏🙏😂😂

[tranquil flower]

that wont help you bc you still wouldnt know how to do it

[cursive skiff]

Okay I’ll figure it out later but I need the answer rn

I’m begging u😭😭😂

[tranquil flower]

i mean you can ask someone else for the answers

but i gave you everything you need to find it

gl

[cursive skiff]

Broooo

[devout snow]

@cursive skiff Has your question been resolved?

[devout snow]

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[inland mantle]

Hello. I'm stuck. Wouldn't I just have to look up the z score?

[drifting pewter]

yeah do u hv access to the tables

[inland mantle]

Yeah

[drifting pewter]

find the 2 z-scores yk its in between

and then u might hv to use linear interpolation to find the exact z-score

[inland mantle]

Interpowhat?

[drifting pewter]

😭 ill explain

find the approximate z-score first

[oblique jay]

hi hello i greet ya'll

[inland mantle]

Are you a helper?

[devout snow]

@inland mantle Has your question been resolved?

[inland mantle]

<@&286206848099549185>

[chilly quartz]

Sqrt(pi)/2-0,29

[chilly quartz]

Gausse integrell

[dire forge]

Please don't post in help channels unless you're helping

Can you show me the table where you got this number from?

You might be reading the table the wrong way, but I just want to check what the table looks like

[devout snow]

@inland mantle Has your question been resolved?

[inland mantle]

I forgot how I got it 😅

[dire forge]

😭

Can you try looking at the table again?

And trying to look up what z-score corresponds to an area of 0.29?

[devout snow]

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[lilac crescent]

i dont know how to find the primitive of this function:
$f(x) = \frac{x^2 + x -2}{x^2}$

[woven radish]

rajel

[undone belfry]

are you looking for the integral of this function?

@lilac crescent

[eager nova]

Split

[undone belfry]

$\int \frac{x^2 + x -2}{x^2} dx$

[woven radish]

xtra

[devout snow]

@lilac crescent Has your question been resolved?

[lilac crescent]

yeah i was looking for the integration

[lilac crescent]

thx i found the solution

any advice to get good with primitives

any book, doc ?

[tight onyx]

Are u seriously talking about math???

Man y’all are some real losers

[devout snow]

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[primal gyro]

To find theta 1 i used tan^-1(x/z)

but when I find theta2 it is incorrect. I'm using tan^-1(y, x)

oh but also the point could be anywhere between x and z

I'm not sure what the equation to do this is

Like this, I'm not sure how to find the angle of that

Oh yeah x and z are not always equal when trying to find theta

so far I tried:
theta = tan^-1(y, z) and
theta = tan^-1(y, x)

wait i think im correct my program is just being weird maybe?

.close

[devout snow]

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[restive river]

I'm lost I know the equation needed but I don't know where to plug in everything

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[rugged crater]

oh is this like optimization or something like that

[restive river]

volume of shells

[rugged crater]

this isn’t calc?

[restive river]

cal 2

[rugged crater]

hmm

isn’t it like integral of pi f(x)-g(x) to the power of 2

or pi is on the outside i think

[restive river]

my notes say integral of pi(length of shell)(radius)

[rugged crater]

i thjnk you can also just do integral of f(x) - integral of f(x) and since it’s bound by 3 i think you can do (0,3)

i’m not sure

[restive river]

.close

[devout snow]

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[solid osprey]

hey, how do i make a function thats a circle with some radius r where it passes trough 2 points (x1,y1) (x2,y2)

[solid osprey]

assuming we use the circle thats closer to 0,0

so like, (x-a)^2+(y-b)^2=r^2 would be the base function, but we need to find a and b in terms of x1,y1,x2,y2

[urban harbor]

two points aren't enough to determine a circle, there are an infinite number of circles that can pass through 2 points

[solid osprey]

but the radius is defined

[urban harbor]

oh, sorry

[solid osprey]

there would be 2 then right? i want to take the one closer to (0,0)

[urban harbor]

yeah, gotcha

so something like this

if you are given the two red points, connect them with a segment (blue), find the midpoint of that, then along perpendicular bisector (green), find the 2 points that are a distance R from the original 2 points. now pick the one closer to (0, 0)

[solid osprey]

dunno

[urban harbor]

dunno what?

[solid osprey]

i had no idea what your diagram meant lol but ok lemme try and think about it

[urban harbor]

it isn't that bad

[solid osprey]

hm yea

lemme try

[urban harbor]

the midpoint of the blue will just be the average of the two points: ( (x1+x2)/2, (y1+y2)/2

then to get the slope of the blue it's just perpendicular to the green

green slope is (y2 - y1) / (x2 - x1) so to get the slope of perpendicular its opposite reciprocal: ((-x2-x1)/(y2-y1) etc

[solid osprey]

hm yeah

[urban harbor]

does this answer your question enough, not sure what you meant by "make a function", like you need something to spit out an immediate solution?

[solid osprey]

like i just want some equation where if i plug in x1 y1 x2 y2 r it would create a circle

[urban harbor]

how would an equation decide between the two options

[solid osprey]

fuck good point

[urban harbor]

well i guess you can make a quadratic where they will be the 2 solutions

[solid osprey]

having both circles wouldnt be too bad

hm why am i kinda confused on what to do next

like i can find the distance from the midpoint ti the center but idk what to do with that

[urban harbor]

btw can we guarantee that the points arent uh vertical (same x coordinates) cause that'll lead to problems kinda if we write a function in terms of x

[urban harbor]

so we can write an equation for the line just using point slope form and what we wrote above

point: ( (x1+x2)/2, (y1+y2)/2
slope: ((-x2-x1)/(y2-y1)

[solid osprey]

yeah that would give the equation

[urban harbor]

so it's gonna start being a bit ugly but basically our green line is:
y - (y1+y2)/2 = ((-x2-x1)/(y2-y1))(x - (x1+x2)/2)

just plugging those things into classic point slope equation

and if we write the line equation by isolating y on one side:
y = ((-x2-x1)/(y2-y1))(x - (x1+x2)/2) + (y1+y2)/2

so we have a function for y on the line in terms of just x on the right side (y1 and y2 are just constants)

now we could write an equation for distance between (x1 and x2) and an arbitrary point on the line:

d = (x1 - x)^2 + (y - (the whole right side of that equation))^2

[solid osprey]

wtf uh gimme a sec

[urban harbor]

and if we plug in R for d:
R = (x1 - x)^2 + (y - (whole right side of that equation))^2 and now you basically have a single unknown of x you could solve for and i think that should be a quadratic, but this becomes extremely ugly

whats the motivation for wanting to do this with "plug in numbers and you get the circles" like that in a single step lol?

[solid osprey]

i thought it would be cool

[urban harbor]

well it will become a bit of a fugly equation but probably itll simply somewhat when everything is squared, like things added and whatnot

i dont think there will be anything like a simple elegant finale though

[solid osprey]

idrc tbh as long as it looks cool

[solid osprey]

btw im lost at this, how did you get that?

[urban harbor]

so if we think of our line equation, which again is this:
y = ((-x2-x1)/(y2-y1))(x - (x1+x2)/2) + (y1+y2)/2

[urban harbor]

as y = f(x) right? just f(x) is quite ugly

[solid osprey]

my progress

uh sure ig

[urban harbor]

then a point on the line is (x, f(x))

so the distance between x1, y1 and a point on the line is just distance formula between x1, y1 and x, f(x)

and sorry it should be d^2, i forgot to square the hypotenuse since i didnt put in a square root

so just pythagorean theorem:
d^2 = (x - x1)^2 + (y1 - f(x))^2

and the distance we want is R so
R^2 = same thing

[solid osprey]

wouldnt it be
d^2 = (x - x1)^2 + (f(x) - y1)^2?

huh ok

[urban harbor]

yes, i was just editing to change y to y1

[solid osprey]

the same

[urban harbor]

order we subtract coordinates from doesnt matter cause its getting squared anyway but yeah 🤷‍♂️

so that equation has a single unknown (x) and a bunch of constants: R, x1, y1, as well as y2 and x2 somewhere in the f(x)

and you could rewrite so you have x isolated on one side presumably (i think it would be a quadratic?)

then the two solutions of the quadratic should give you at least the x coordinate of the circle's center you'd still have to plug that into f(x) to get the y coordinate of the center

[solid osprey]

hm

so what happens when i isolate x

[urban harbor]

i just said that

[solid osprey]

oh

[urban harbor]

anyhow i've gotta go, i'll let you explore it more from here : )

[solid osprey]

didnt read

alright thanks

.close

[devout snow]

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[full ferry]

Help

[full ferry]

I know how to do this question but I don’t know how to use synthetic division

Can someone please show me how to did this question using synthetic division

[solid osprey]

how do you do it if you were given this question?

[full ferry]

I just simplify

Let the x out

So it will be something like (x-5)

(X-3)

And (x+1)

But I just don’t know how to do this question by using synthetic division

<@&286206848099549185>

[stable storm]

you would need to guess a zero if you want to use synthetic division

[regal mulch]

Yep try to see a factor that works

Coz you need something like x-5 (js an example) to be your divisor

[stable storm]

-1 seems to work

[full ferry]

Guys

Look

[frozen stump]

have you used it before?

[full ferry]

Is it how this work?

[frozen stump]

yea

[full ferry]

Ok, thank you

[regal mulch]

Yep

[full ferry]

Ty

.close

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[inner ibex]

idk where to satret

[inner ibex]

start

how do i do dis one

[stable cloak]

The distance of the first walk will be the first term "a"

Just use an = a+(n-1)d for the last walk

Value of n will be 15 for the last walk btw

[inner ibex]

oooohh

ok thx

[smoky gyro]

bum chicken

[devout snow]

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[lethal harbor]

dy/dx = y^2 + (1/(x^2)) + x/y

[lethal harbor]

Can one find the function for this diff eqn given say x=1 y =1 are the conditions

[pastel pasture]

,w y' = y^2 + 1/x^2 + x/y

[woven radish]

Results provided by WolframAlpha

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

Requested by neonperseus

[pastel pasture]

yeah doesn't look like it

[devout snow]

@lethal harbor Has your question been resolved?

[devout snow]

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[solid osprey]

let $A_{n}=2^{3n}+3^{6n+2}+5^{6n+2}$ for all $n\geq 0$, find $\gcd{A_{0},A_{1},A_{2},\dots,A_{2021}}$

[woven radish]

Skill_Issue

[olive snow]

Ça doit être un trick de zinzin

[solid osprey]

the what

[olive snow]

Oh mb, the trick must be crazy

[solid osprey]

whar

[olive snow]

nvm

Try n=0 and n=1

What do you get for n=0 ?

[solid osprey]

3

[olive snow]

You sure ?

[solid osprey]

op

35

[olive snow]

Yeah

So its Either 1,5,7,35 now try n= 1

[solid osprey]

thats like 6 digits no 😭

[olive snow]

397194

Indeed

[solid osprey]

wtff

[olive snow]

But 397194 = 2*3 times 7^3

So it could be 1 or 7

So try A_n mod 7

[solid osprey]

:shrug:

[olive snow]

Common divisor with A_0 so 1 and 7

Since you look for gcd

[solid osprey]

yea

how do you mod that

oh

[olive snow]

2^3n mod 7 ?

3^6n+2 mod 7 ?

[solid osprey]

1^n+2^{3n+1}+5^{6n+2}

1+2+25^{3n+1}
3+4^{3n+1}
3+4×4^3n
3+4×1
7
0?

oh

[olive snow]

So ?

[solid osprey]

jalr then thanks

[solid osprey]

its 7?

[olive snow]

Gg wp ez

[solid osprey]

.close

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[devout snow]

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[wooden talon]

Hi, I tried writing the definition of the integral of bounded function formally. I got the definition from the book Calculus I by Tom Apostol and wanted to prove some things related to it, and I thought it would be easier if I wrote it formally and go from there. So did I do it correctly? From another book, I know that a function from set P to set Q, is a subset of A x B, the cartesian product between those two sets. So that is why I wrote that s and t are elements of the power set of R^2, because s and t are subsets of R^2. Thanks for any help.

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[wooden talon]

<@&286206848099549185>

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[clever pine]

Derivative help

[clever pine]

Q6

[covert root]

For Q6 you need to use implicit differentiation

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[reef prism]

Hello, I just want to ask. What's the real essence of "least positive residue"?

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[prisma pebble]

40+80+2(180-x)=360

Solve

[verbal loom]

The sum of internal angles in a square is 360°

[proper crow]

.close

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[hard ocean]

How to prove that limx⅓=3 as x approaches 27 while using the formula (a³-b³)=(a-b)(a²+ab+b²)

[pastel pasture]

wat

just sub 27

[thin inlet]

probably means using epsilon delta

[boreal helm]

Oh ok

let x-27=t so as X approaches 27 t tends to zero

lim t tends to 0 (t+27)^1/3

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[limber berry]

.reopen

@north roost When I try to distribute that I get a denominator with no way to pull the h out

[limber berry]

so [-10h/(5x+5h+3)(5x+3) ] / h

[devout snow]

@limber berry Has your question been resolved?

[north roost]

${\lim_{h \to 0} \frac{\frac{-10(x+h)}{(5(x+h)+3)(5x+3)}}{h}}$

[woven radish]

:D

[north roost]

expand the bottom term

and split fraction

@limber berry

Then substitution

[devout snow]

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[mellow scroll]

hi

[mellow scroll]

im meant to use the addition rule to solve this

do i used sin(180-theta)

and cos(360-theta)

[devout snow]

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[eternal marsh]

Square both side and use the fact that 2sin(x)cos(x) = sin(2x)

[devout snow]

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[mellow scroll]

thanks

[devout snow]

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[karmic vault]

6. The sum of the digits of the positive integer n is 123. The sum of the digits of 2n is 66. The
   digits of n include two 3s, six 7s, p 5s, q 6s and no other digits. What is p^2 + q^2?
   (A) 106 (B) 109 (C) 160 (D) 58 (E) 72

[karmic vault]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[karmic vault]

1

[frozen aurora]

well, you are given that
3*2 + 6*7 + p*5 + q*6 = 123

,w 32 + 67

[woven radish]

Results provided by WolframAlpha

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Requested by arte_m_etra

[karmic vault]

yes

[frozen aurora]

p*5 + q*6 = 75

[karmic vault]

yeah i did that part then got stuck

[frozen aurora]

2n is a bit trickier but doable i think

[karmic vault]

is it

???

[frozen aurora]

let me think

[karmic vault]

k np

[devout snow]

@karmic vault Has your question been resolved?

[karmic vault]

hello?

imma try it another time

😄

[devout snow]

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[devout snow]

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[zinc pewter]

in this problem, we see vector F is essentially F(r(u,v)) when put into the integral

In this problem, why is it not like that?

It's just the vector that they provide but with z put in

[faint gorge]

How would you parameterize the cone?

[zinc pewter]

probably x = u, y = v, so z = sqrt(...)

[faint gorge]

yea

that's it

now the thing is

whether you use u and v

or x and y

it's the same

[zinc pewter]

so pretty much for surface integrals with z = g(x,y) i dont really do shit besides plug in g(x,y) for z?

[faint gorge]

yes

[zinc pewter]

ok one last question

on one example

actually if you can give me a sec i want to grab something from a video i watched...

[faint gorge]

you can always parameterize in cartesian with the vector (x,y,z) and proceed from there

ok sure

[zinc pewter]

so in this example

the lady in the video takes two surface integrals.

one for S1, one for S2

[zinc pewter]

in this example, my professor only takes 1 surface integral.

me no really understand that :/

she does one for z = g(x,y) and z = 0

my professor only does z = g(x,y)

this is the drawing my professor made of his cone

looks like there are two surfaces to me

[faint gorge]

what i can think of is because it says "part of the cone" that is between z=1 and z=3

[zinc pewter]

doesnt that make 3 surfaces then?

where z = 1, the outer surface of the cone, and where z = 3

so i would think 3 integrals :/

[faint gorge]

yea you are thinking right

what i am trying to say is that maybe your professor meant only the "mantle" which wouldn't include the two upper and lower cap

[zinc pewter]

hmmm, perhaps

me tryna figure this out on an exam... 😭

wednesday will be torture

[faint gorge]

but you are right if it's meant to be a closed surface we would have 3 integrals in your professors task

[faint gorge]

can't you ask if you think it's vague

[zinc pewter]

i guess but i feel like my brain wont even register that

this entire chapter has just been awful

[faint gorge]

i had mine days ago on this lol

[zinc pewter]

😭

doesnt even feel like math

[faint gorge]

but i haven gotten my result back yet

[faint gorge]

i feel it's mathest math i learnt

[zinc pewter]

bro half of it is intuition

like parametrization

[faint gorge]

probability theory doesnt feel like math

[zinc pewter]

that is not done with math

[faint gorge]

hmm why

[zinc pewter]

that is done with "hope youve seen it before"

[faint gorge]

you are just writing something in vector form basically

expressing the same thing in other form

[zinc pewter]

yeah but you dont do that mathematically

you do it because youve seen it elsewhere before

that aint math bro 😭 aint no way

[faint gorge]

what

If you consider a surface

you know it depends on two variables

[zinc pewter]

like x^2 + y^2 + z^1 = 1

[faint gorge]

yea

[zinc pewter]

sure you can go "ahhh thats spherical coordinates with phi = 1"

[faint gorge]

You can parametrize it in 3 ways

[zinc pewter]

but thats not math bro

[faint gorge]

no

you can also stay in cartesian

[zinc pewter]

how

[faint gorge]

you solve for one variable

You can always start a parameterization $\vec{s}$ with $$\vec{s}(x,y,z) = \begin{pmatrix} x \ y \ z \end{pmatrix}$$

[zinc pewter]

bro did you have that ready for copy & paste?

[woven radish]

𝔸dωn𝓲²s

[faint gorge]

yea i wanted to write that sooner

lol

[zinc pewter]

lol

[faint gorge]

now

acshually lemme show it with desmos

[zinc pewter]

are you just suggesting like

z = sqrt(x^2 + y^2) and x = u, y = v

instead of using spherical

[faint gorge]

yea

you can also do

x = sqrt(z^2+y^2) z = u, y = v

there are many ways to say the same shit in different form

now you would just need to define u and v

in terms of interval

[zinc pewter]

wdym?

like # < u < # and stuff?

[faint gorge]

ye

[faint gorge]

oh no that's wrong

[zinc pewter]

oh yeah i mean subtract

w/e lol

[faint gorge]

,,x^2+y^2+z^2=1 \Rightarrow z = \pm \sqrt{1-x^2-y^2}

[woven radish]

𝔸dωn𝓲²s

[zinc pewter]

ye

i am going to have a brain aneurysm

ok well ty

[faint gorge]

actually cartesian is so awfull bruh

[zinc pewter]

yeah

the bounds are... rubbish

[faint gorge]

they are from 0 to 1

because of radius we know 1 is the max

[zinc pewter]

for that one yes

[faint gorge]

looking at the square root

it cannot become greate thean 1

otherwise you get negative

but the thing is one parametrization is like one of eight sphere parts

[zinc pewter]

.close

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[faint gorge]

oh wait i am dumb

you would have 2 parametrizations in cartesian at most

see thats why defining intervals is important

-1 <= u,v <=1

not from 0 lmao

then you get the upper and lower parts

and from ther you can use polar coordinates if you are not comfortable with spherical coordinates to simplify your parameterization even further

[devout snow]

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[brittle anvil]

i am new here and new in mathematics i only like maths and just now school lessons

and i want to be good in math

any help ??
i wana be good in olampyade

[violet umbra]

Just learn with some old tasks

[devout snow]

@brittle anvil Has your question been resolved?

[brittle anvil]

How do I learn to solve these problems because even the easy problems I do not have the idea of ​​a solution to?

[devout snow]

@brittle anvil Has your question been resolved?

[smoky nimbus]

Try asking in #competition-math and check out the Mathematical Olympiads server that's linked in the room topic

[devout snow]

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[lean ether]

Ann will donate up to 500 to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Ann would like the amount donated to the Educational Growth Foundation to be at least twice the amount donated to the City Youth Fund. Let x denote the amount of money (in dollars) donated to the City Youth Fund. Let y denote the amount of money (in dollars) donated to the Educational Growth Foundation. Shade the region corresponding to all values of x and y that satisfy these requirements.

[devout snow]

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@lean ether Has your question been resolved?

[devout snow]

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[brisk flax]

Alright, I'm doing calculus integrals right now, and I think it's asking me to find e^x^2? Or is it (e^x)^2? I can't tell

[brisk flax]

like is this $e^{(x^2)}$ or is it $(e^x)^2$

[woven radish]

PODEPOM

[acoustic leaf]

it means $e^{(x^2)}$, otherwise they could just write $e^{2x}$ equivalently

[woven radish]

cloud

[topaz beacon]

in general, $x^{y^z}$ is interpreted as $x^{(y^z)}$ because $(x^y)^z$ can be simplified to $x^{yz}$

[woven radish]

Underfull \hbox (badness 10000)

[topaz beacon]

sniped

[brisk flax]

I see

so, I got u = $e^x$ and du = $e^{x^{2}}2xdx$. but now my du can substitute my entire initial integral without any original u

right?

[woven radish]

PODEPOM

[brisk flax]

I need it to be the integral of u du in some way for me to do the integration, but now I have what looks like 2 integral du with no u

unless that extra 2 multiplier somehow makes another $e^x$ for me, I have a problem here, right?

[woven radish]

PODEPOM

[acoustic leaf]

not sure where you got the du from, it should be the derivative of u

[brisk flax]

yeah, du is the derivative of u

u is $e^{x^2}$

[acoustic leaf]

the derivative of e^x is itself

[woven radish]

PODEPOM

[brisk flax]

then the derivative of that would be the derivative of the e, times the derivative of the exponent of the e, which makes 2x, then the derivative of the 2, which makes dx

[acoustic leaf]

so you would end up with [ 2\int \odif u ]

[woven radish]

cloud

[brisk flax]

I think that makes sense

but now, looking at the original function, what I made it, $2\int 2xe^{x^2}dx$ can now be made to be $2\int du$ without any normal u inside it

[acoustic leaf]

the new integral is integrating the function g(u) = 1

[woven radish]

PODEPOM

[brisk flax]

I don't understand

[acoustic leaf]

,, \int \odif u = \int 1 \odif u

[woven radish]

cloud

[acoustic leaf]

it is a constant function

[brisk flax]

hold on

ok so like

we want the integral to have f(u)du in it

what we got was just du, with no f(u)

somehow

[acoustic leaf]

we omitted the 1 because it is implied

[brisk flax]

and now, we're pulling in a new f(u) where u is presumably whatever it has to be to make the function come out as 1

and that's going to be our new f(u)

so we would want to make x=0 for that, so that $e^{x^2}=1$

[woven radish]

PODEPOM

[brisk flax]

because $e^{x^2}$ is what u is equal to

[woven radish]

PODEPOM

[brisk flax]

am I on the right track with any of this at all?

[acoustic leaf]

we can say that [ 2\int \odif u = \int 2 \odif u ] so then the important part is only that we end up with a constant function

[woven radish]

cloud

[brisk flax]

Currently at the function on the far right

now there's a 4 outside of it

[acoustic leaf]

where did the 4 come from

[brisk flax]

it was there at the start of the problem

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

[woven radish]

PODEPOM

[brisk flax]

cut the 4, you get $2\int 2xe^{x^2}dx$

[woven radish]

PODEPOM

[brisk flax]

where the inside is now exactly my du

so then I get $2\int du$

[woven radish]

PODEPOM

[acoustic leaf]

can you integrate $\int du$?

[woven radish]

cloud

[brisk flax]

that's what I'm wondering

can you?

I guess you can? We have an integral of the function du, and we already know what u is

so then the integral and the d cancel out, leaving just the u, right?

[acoustic leaf]

it may be suggestive to write [ \int du = \int 1 \odif u = \int u^0 \odif u ]

[woven radish]

cloud

[acoustic leaf]

the seeming lack of a function is just notational shorthand

[brisk flax]

but wouldn't that only work if there wasn't the extra 2 outside the integral?

you're pulling the 1 in from out there

[acoustic leaf]

the 1 was there in the first place

when we write $\int dx$ or $\int du$ there is an ``implied'' 1 that we don't write for convenience

[woven radish]

cloud

[brisk flax]

I understand that part, yes

because it's techincally possible to say that it's being multiplied by 1

but now what does adding that in really do for us? Because yeah, you got that u^0 in, but it's not a variable now, right? It's a constant

[acoustic leaf]

yes, but we can still apply the power rule just as well

[brisk flax]

and get and integrated output of u^1?

[acoustic leaf]

yes

[brisk flax]

I guess that makes sense

[acoustic leaf]

if we were to differentiate u we would get 1, so we are just reversing that

[brisk flax]

ok

I think I get it

this is so confusing, man

.close

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[restive river]

help

[restive river]

If f has no local extrema then f is monotonic

sps f is not monotonic then there is some a<b<c s.t. f(a) < f(b) > f(c) or f(a) > f(b) <f(c)

but then f(b) is a local extrema

qed

correct?

[jaunty mantle]

Looks good

Not monotonic => has local extrema

Then its contrapositive statement which is what you want to prove is then also true

[restive river]

sorry this question was so easy i was doubting my proof my contradiction skills

i saw some answers on stackexchange using EVT

and thought i might've been oversimplifying it

thanks

.close

[devout snow]

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[jaunty mantle]

It does sort of depend how you define extrema and monotonicity

Is a constant function monotone?

[jaunty mantle]

It’ll change whether you need strict or not strict inequalities here

[boreal helm]

Okok

[devout snow]

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[devout snow]

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[humble gale]

.close

.close

!close

close

[boreal helm]

Okok

[humble gale]

see

so ping a mod idk

[devout snow]

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[frail osprey]

A school has 20% less students in 2011 than it did in 2010. It can be stated that the school had "k" times more students in 2010 than it did in 2011, what is the value of k?

[frail osprey]

Im bad at these percentage things

Im aware its not 1.2, because % more is not equal to % less, but idk what it is or how to solve it

[boreal helm]

Let the no of students school had at 2010 be x

So in 2011

It has x-20%of x students

That is 4x/5

So now you can compare

That no of students in 2010=k.no of students in 2011

That is x=k.(4x/5)

So we get k=5/4

That is .12

1.25

@frail osprey

Hope it helps

[safe jasper]

1.25**

[boreal helm]

Bro

He wrote 1.#

1.2

By mistake I also wrote that

[frail osprey]

ok then

so if i say that instead of 20%, its 30% less, then would my answer be 10/7?

[boreal helm]

Yes

[frail osprey]

ok thanks bro

.close

[devout snow]

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[devout snow]

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[urban palm]

Pls explain part b

[radiant hare]

Well you just plug in 0.01 for x

[urban palm]

But why

[radiant hare]

Because 1.99(1.02)^9=(2-0.01)(1+2*0.01)^9

[urban palm]

💀

What

But how does that make 0.01 the x value

OHHH

[radiant hare]

Because you get the value you want to approximate when you plug in 0.01 for x in the first term

[urban palm]

I got iy

It

Your comparing 2-x with 1.99

And (1+2x)^9 with 1.02^9

[devout snow]

@urban palm Has your question been resolved?

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[boreal helm]

This equation has 4 roots and all are irrational

Wow

Must be product of two perfect squares

[dim lantern]

How do we know that all are irrational ??

[boreal helm]

See idk

U write equation in open form

If it becomes product of two perfect squares=0

[mystic scarab]

Are you sure?

I'm not getting that

[mystic scarab]

Yeah indeed

[dim lantern]

So how to solve?

[mystic scarab]

Idk

I arrived there but don't know how to go on

[boreal helm]

Form full equation

One side should be 0

[dim lantern]

<@&286206848099549185>

[boreal helm]

And one side equation

Do this

I am helper only

[dim lantern]

Idk it will go bi quadratic then nah

[boreal helm]

See

It will have simple roots

I guarantee

Wait let me do it

And show you

[dim lantern]

Ok

[boreal helm]

,w solve (x-2)(3x-2)(3x+1)(x-1)=12

[woven radish]

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[boreal helm]

Has 2 roots

@dim lantern

Now let me explain you

[dim lantern]

What is I? Imaginary?

[boreal helm]

You will form bi quadratic

Listen

[dim lantern]

Ok

[olive snow]

it 21 chief not 12

[boreal helm]

It will become paah

Aah

Sry my bad

[mystic scarab]

Yep imaginary unit

[boreal helm]

@dim lantern

I'm sorry

I wrote 12 instead of 21

[dim lantern]

Np

[mystic scarab]

There's no need to tag every time 😅

[boreal helm]

,w solve (x-2)(x-1)(3x+1)(3x-2)=21

[woven radish]

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[boreal helm]

Aah

Lol

Now for the explaination part

We will see the biquadratic

Ok

,w expand (x-2)(x-1)(3x+1)(3x-2)-21

[woven radish]

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[boreal helm]

Fr

Now can u see ?

[dim lantern]

Ya

[boreal helm]

,w factorise 9x^4-30x^3+25x^2-25

[woven radish]

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Requested by oppailol.

[boreal helm]

Fr

Now see

Two quadratics

[dim lantern]

Ya

[boreal helm]

Now you check the discrimants of both you will understand how many irrational roots

[dim lantern]

Oh

[boreal helm]

You can now solve even to get the irrational roots and then mark the answer

Hint: D not equal to perfect square roots irrational

[dim lantern]

Was thinking the same

[boreal helm]

,w explain how to factor
9x^4-30x^3+25x^2-25

[woven radish]

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Upgrade to WolframAlpha Pro!

Requested by oppailol.

[boreal helm]

Lol

Actually idk

Wait let me think

[dim lantern]

Lmao

[boreal helm]

I knew Alberto would write

[mystic scarab]

@dim lantern

[boreal helm]

,w type W Alberto Z

[woven radish]

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Upgrade to WolframAlpha Pro!

Requested by oppailol.

[boreal helm]

What

[olive snow]

W

[dim lantern]

Lol

[boreal helm]

The

[dim lantern]

Got it

Thanks

[boreal helm]

That means Alberto Z is quantum

.close

[mystic scarab]

You're welcome 🤗

[dim lantern]

Thanks @boreal helm @mystic scarab

[boreal helm]

Welcome np

🫡

[dim lantern]

🫶

.close

[devout snow]

Channel closed

Closed by @dim lantern

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[devout snow]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[viral lynx]

I got really far but im stuck on 1 part

(x - 2)/(x^2 + 2x + 8)

(x - 2)/((x + 1)^2 + 7)

-2/((x + 1)^2 + 7) + x/((x + 1)^2 + 7)

I can solve the left fraction by making it into arctan, but im confused about the right fraction

Im not really sure how to solve x/((x + 1)^2 + 7), the x in the numerator is kinda ruining things

[winter patrol]

since the denominator isn't factorisable over real numbers, you'd want to express the integrand in the form:
$$\frac{m\cdot f'(x)}{f(x)} + \frac{n}{f(x)}$$

[woven radish]

ℝαμΩℕωⅤ

[viral lynx]

Ive never seen this formula before, what does it do?

OHHHH WAIT

I think I have

Hold up I will try something

Yeye I think I can solve this

Thank you!

❤️

.close

[devout snow]

Channel closed

Closed by @viral lynx

Use .reopen if this was a mistake.

[boreal helm]

Aah

[dim lantern]

Hi again

[viral lynx]

Just warning you this channel will close any second haha

Might want to open a new one

[dim lantern]

Ohh

[boreal helm]

Yes

[dim lantern]

Ok

[viral lynx]

All good haha just thought you might wanna know 😅

[dim lantern]

Nah ty

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vivid estuary]

Can anyone help me through this one

[vivid estuary]

Not sure what to do

I'm assuming theres gonna be three variables?

and I know I need to use integral F * dr

Im thinking the spiral stairs form a cylinder?

oh maybe

[gusty nexus]

are frictions excluded?