help-27

[unreal thunder]

let's first square

$y'^2=\left(x^2-\frac{1}{4x^2}\right)^2$

[jaunty gazelle]

Okay.

[woven radish]

Dubleyou

[jaunty gazelle]

I know we got x^4 because x^2 *x^2

[unreal thunder]

notice, that this is just the identity (a+b)^2

[jaunty gazelle]

yes

[unreal thunder]

so we can rewrite this as,$y'^2=(x^2)^2-2x^2\frac{1}{4x^2}+(\frac{1}{4x^2})^2$

[woven radish]

Dubleyou

[unreal thunder]

all good?

[jaunty gazelle]

I understand the (x^2)^2 but how did we get -2x^21/4x^2+(1/4x^2)^2...?

[unreal thunder]

can you expand (a+b)^2 ?

what is it?

$(a+b)^2=(a+b)*(a+b) = a(a+b) +b(a+b) = a^2 + ba+ba +b^2 = a^2+2ab+b^2$

[woven radish]

Dubleyou

[jaunty gazelle]

When foiling I get this:

[unreal thunder]

when you foil, you have to use every terms

ie multiply x^2 with other twos also -1/4x^2 with other twos

it seems like you have only used x^2 with all others

my bad

looks correct

but the multiplication sign is wrong

you have put paranthesis around (-1/4x^2 * x^2)

that should be subtracted from x^4 not multiplied

[jaunty gazelle]

got it

[unreal thunder]

same for others

the other foil will be

[jaunty gazelle]

So like this

[unreal thunder]

$x^4 -\frac{1}{4x^2}x^2 -\frac{1}{4x^2}x^2 + \frac{1}{4x^2} * \frac{1}{4x^2}$

[unreal thunder]

yes, simply this

[jaunty gazelle]

I'm confused on your simplification above

oh

got it

[woven radish]

Dubleyou

[jaunty gazelle]

oh

got it

[unreal thunder]

the simplification will be $x^4 -\frac{2}{4x^2} + (\frac{1}{4x^2} )^2= x^4 -\frac{1}{2x^2} + (\frac{1}{4x^2} )^2$

[woven radish]

Dubleyou

[jaunty gazelle]

Okay hold on...let me understand.

[unreal thunder]

which is same as this step above

[jaunty gazelle]

So these x^2’s cancel out?

[unreal thunder]

no no

they get factored out

they are of same sign

think x^2 as some number and think

they are numbers when plugged in indeed

does -2 -2 gets cancels out ?

if $-23 + -26$

[jaunty gazelle]

no it gets -4

[woven radish]

Dubleyou

[unreal thunder]

can you cancel -2 ?

nope, but can you factor out -2 ?

the whole point of factoring is to make it look as multiplication

[jaunty gazelle]

Okay how are you factoring x^2 out here..I'm not seeing it.

[unreal thunder]

can you try factoring -2 from the above?

this will help you see factoring x, for sure

[jaunty gazelle]

-2*3+(-2) times 6 = 2 times 2 times 3..?

[unreal thunder]

you can factor $-23 + -26 = -2(3+6)$

[woven radish]

Dubleyou

[unreal thunder]

i'm not sure how you got that

[jaunty gazelle]

I see.

[unreal thunder]

This is know as distributive property

recall that

we usually factor out the gcf this way

[jaunty gazelle]

ok

[unreal thunder]

so notice in the other problem, when x is plugged it looks similar to one we just did

[unreal thunder]

can you try it now?

[jaunty gazelle]

I just don't see how the pair of x^2's dissapear and turn into -2/4x^2...

We leave x^4 the way it is, compute -1/4x^2-1/4x^2 and get -2/4x^2, and we combine 1/4x^2*1/4x^2 into (1/4x^2)^2...?

[unreal thunder]

let's see

we are trying to simplify the middle two terms right?

what is gcf of them or what's the common to both terms ?

[jaunty gazelle]

You're talking about these two terms, right?:

[unreal thunder]

can you instantly cancel the x^2 from numerator

[jaunty gazelle]

x^2 is common to both terms..

[unreal thunder]

what is -1/4 -1/4 ?

[jaunty gazelle]

-1/2..

[unreal thunder]

what is exactly the middle term

[jaunty gazelle]

-1/4x^2^x^2

[unreal thunder]

wait

$-\frac{1}{4x^2} x^2 =-\frac{x^2}{4x^2} =-\frac{1}{4}$

I hope this clicks

[woven radish]

Dubleyou

[unreal thunder]

this applies to both the terms in middle

which will later become -1/2

[jaunty gazelle]

we multiply the x^2 by the 1, and we get -x^2/4x^2...the x^2's in the numerator and denominator cancel out, and we get -1/4..?

[unreal thunder]

yes indeed

[jaunty gazelle]

Since this applies to both terms in the middle..we add them up and get -1/4-1/4 = -1/2..

[unreal thunder]

yes

Please find time to strengthen your algebra skills

[jaunty gazelle]

Yeah...I'm rusty.

[unreal thunder]

people usually struggle in pre-calculus in calculus class

calculus concepts are intuitive but pre-calculus takes the fun away

[jaunty gazelle]

But how do we get -1/2x^2...I get the -1/2 and how the x^2's cancel in numerator and denominator but how did the x^2 spawn randomly in the denominator?

[unreal thunder]

this step?

[jaunty gazelle]

yes

[unreal thunder]

you have to cancel it

oh that's my mistake

[jaunty gazelle]

Do both middle terms not simplify to -1/4?

[jaunty gazelle]

ok

[unreal thunder]

this is correct one

so we can rewrite this as,$y'^2=(x^2)^2-2x^2\frac{1}{4x^2}+(\frac{1}{4x^2})^2$

[woven radish]

Dubleyou

[unreal thunder]

so we can rewrite this as,$y'^2=x^4-\frac{1}{2}+(\frac{1}{4x^2})^2$

[woven radish]

Dubleyou

[jaunty gazelle]

There we go... 😃

I understand up to this part.

so y'2 = x^4-1/2+(1/4x^2)^2..

[unreal thunder]

now add 1 to it

$y'^2+1=x^4-\frac{1}{2}+(\frac{1}{4x^2})^2+1=x^4+\frac{1}{2}+(\frac{1}{4x^2})^2$

[woven radish]

Dubleyou

[jaunty gazelle]

By adding one, aren't we just distributing the 1 to each term? so x^4 * 1, -1/2 * 1, and 1/4x^2 * 1..?

[unreal thunder]

just added -1/2 +1 = 1/2

It seems like you have a lot of misconceptions

[jaunty gazelle]

Oh...I thought we were distributing, nevermind..

I thought it was 1 * (y')^2...

[unreal thunder]

when adding 1 to $23+64$ do we distribute ?

[woven radish]

Dubleyou

[jaunty gazelle]

No, we add.

My mistake.

[unreal thunder]

np

add it you get the desired step

[jaunty gazelle]

Okay, so we do x^4+1/2+(1/4x^2)^2+1...which is effectively adding 1/2 to 1 and we get x^4+3/2+1/16x^4...

[unreal thunder]

add 1 to -1/2

not 1/2

[jaunty gazelle]

Well you had that here...did you not intend to add 1/2+1 in the last expression?

you get: x^4+1/2+1/16x^4...

[unreal thunder]

I had -1/2 as middle term, adding +1 makes it 1/2

[jaunty gazelle]

Did you mean to add another 1 after that?

[unreal thunder]

after this step

[jaunty gazelle]

Did you mean to have that circled 1 there?

[unreal thunder]

$y'^2+1=x^4-\frac{1}{2}+(\frac{1}{4x^2})^2+1=x^4+\frac{1}{2}+(\frac{1}{4x^2})^2$

[woven radish]

Dubleyou

[jaunty gazelle]

okay yeah I'm following then

[unreal thunder]

My bad, I can see how bad a typo hurts

[unreal thunder]

You have to recognize this as (a+b)^2

[jaunty gazelle]

Got it

[unreal thunder]

which will get your to your disred expression

[jaunty gazelle]

So the final expression should get us to the original expression I circled above that was red?

[unreal thunder]

yes

[jaunty gazelle]

How can we tell this intuitively though?

[unreal thunder]

well, intuition in algebra comes from practice

so it requires consistent handwork

[jaunty gazelle]

Surely there's a verification step or something that you use to prove that the expression can be derived from the circled one??

[devout snow]

@jaunty gazelle Has your question been resolved?

[devout snow]

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[dreamy sky]

I don’t know if I’m doing this right and if I’m going towards the right direction

[dreamy sky]

I'm not sure how to simplify the yellow part

[vast rain]

you can't really

[dreamy sky]

Are there any steps to continue simplifying?

I entered it in but it's showing up as incorrect for me, so I'm thinking I might have gone wrong with my other steps in simplfying

[vast rain]

nah that yellow part doesn't simplify

,w differentiate (x^9 - x^(1/3))*2^x

[woven radish]

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Requested by Saccharine#3780

[devout snow]

@dreamy sky Has your question been resolved?

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[zenith stump]

a curve C is defined by the equation x^2+xy^2-y^3=1. use implicit differentiation to compute the slope of the line tangent to the curve at the point (1,0)

[devout snow]

Please don't occupy multiple help channels.

[zenith stump]

@vast rain I don't know of I'm doing this right

@tall knoll can you help

[long pasture]

!help

[devout snow]

Please read #❓how-to-get-help

[zenith stump]

but nobody came

[long pasture]

well, maybe it's because you said you dont know if you're doing right, but you didn't post anything so that none of us can check

lets see

[zenith stump]

I dont have to simplify the answer

[long pasture]

looks good, except with those (

[zenith stump]

wdym

[long pasture]

this
2x ( cos(x)

open bracket

[zenith stump]

ah, so it should be 2x[cos(x)-x^2(sin(x))]

[long pasture]

nah

it should be
2xcos(x)-x²sin(x)

without those open brackets

[zenith stump]

ahh

[long pasture]

glad that helps!

[zenith stump]

thanks man

I have a few more though

[long pasture]

like?

btw, close the other channel, we are out of channels lol

lets see

[zenith stump]

is it fine if i use f(x) to solve even though it is a d/dx problem

[long pasture]

well, if you wanna use f(x), you'll just have to define it

just write something like
f(x)="that expression"

[zenith stump]

ahh I see

like f(x)=d/dx(x^2*cosx)

[long pasture]

hmmm....

without the d/dx

yep

[zenith stump]

okay

so back to the second question

[long pasture]

ok

btw, if you just wanna check your answer (and not steps) you can just use Wolframalpha

[zenith stump]

do you have a link for that ir is it an app

[long pasture]

,w differentiate (x^5-4x^2+2)/(x^3+x)

[woven radish]

Results provided by WolframAlpha

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Requested by OldBiscuit#6122

[long pasture]

seems correct

[long pasture]

just Google Wolframalpha or
www.wolframalpha.com

[zenith stump]

so it doesnt show the steps if i got it incorrect

[long pasture]

true

so, that's mainly for answer checking

[zenith stump]

okay, next question

[long pasture]

yea?

i see, that's the one you've typed out

[zenith stump]

yeah

[long pasture]

do you know what is implicit differentiation?

[zenith stump]

does it have something to do with seperating the equation in 2 halves

[long pasture]

nah

here's an article for implicit differentiation

https://www.mathsisfun.com/calculus/implicit-differentiation.html

[zenith stump]

okay

[long pasture]

let's see if you can do it after reading it

both works imo

[zenith stump]

first denominator is a little cleaner tho

[long pasture]

well, yea, so it really depends on the situation

let's see

[zenith stump]

This is the original question I asked btw

[long pasture]

should be
2x+y²+ "2 x y dy/dx" -3y²dy/dx=0

sorry, typo

[zenith stump]

Should the dy/dx be in parentheses

[long pasture]

yea

my bad

lazy

[zenith stump]

All good

[zenith stump]

So I just have to simplify this?

[long pasture]

looks like it

but it feels weird

[zenith stump]

im just getting 2 as an answer

[long pasture]

2x+y²+2xy(dy/dx)-3y²(dy/dx)=0

2xy(dy/dx)-3y²(dy/dx)=-2x-y²

(2xy-3y²)(dy/dx)=-2x-y²

dy/dx=(-2x-y²)/(2xy-3y²)

the weird thing here is that

2xy-3y²=0 at (x,y)=(1,0)

[zenith stump]

hm

[long pasture]

looks like the slop is vertical, which is tends to infinity

[zenith stump]

oh really

how can you tell the slope is vertical from the equations

[long pasture]

recall

when you plug in (1,0)

we get
1/0

which tends to infinity

[zenith stump]

yeah

[long pasture]

and when slope tends to infinity, the slope is vertical

[zenith stump]

how are you geting a slope of 1,0

im getting -2

[long pasture]

how did you get -2?

[long pasture]

my work is here

[zenith stump]

im plugging in 1 for x and 0 for y

[long pasture]

i know. i mean do you have a photo that i can correct it?

numerator is -2, but look carefully at the denominator

[zenith stump]

is there anythign wrong with my work

[long pasture]

nothing wrong up till here

but for the last step

the denominator is 0-0 which is 0

[zenith stump]

yeah, so im getting -2/0

lol my mind is messing something up

can you show what I should do for the last step

[long pasture]

you can just state that since it's -2/0 which tends to infinity

yea

[zenith stump]

but im confused how you got 1,0 and i didnt

[long pasture]

(1,0) from the question itself

[zenith stump]

ah I see, so you also got -2/0

[zenith stump]

would it be positive or negative infinity?

[long pasture]

very good question

it's depends on which side you are measuring

so, just infinity will do

[zenith stump]

ah

[long pasture]

yea... that's why i say it's weird

[zenith stump]

alright, I have 2 more questions

question is: suppose T(h) is the temperatire in degrees fahrenheit "h" hours after midnight on july 1, 2023.

what are the units if T'(h)?

I got degrees fahrenheit per hour

part b is where they are asking is T'(8) likeley greater or less than 0?

[long pasture]

hmmm T(h) is not given, right?

[zenith stump]

nope, but part c asks if T(8) is greater or less than 0

[long pasture]

it looks like a geography question lol

[zenith stump]

yeah lol

[long pasture]

i guess I can't help with that

it really depends on the general knowledge of the place you are living in

[zenith stump]

okay, i got a different question

Man this is a long homework packet lol

@long pasture

[long pasture]

good

all done well

[zenith stump]

alright, i have a question about d/dt

is it the same as d/dx

[long pasture]

good question

like if you have

f(x)=x²

then df(x)/dx=2x

you can change it to t

like

f(t)=t²

and df(t)/dt=2t

it really depends on which variable you are differentiating with respect to

[zenith stump]

like for example, how would I find the derivative of this one since it has d/dt

[long pasture]

you can't

[zenith stump]

what

[long pasture]

if you don't know if x and t have relationship

[zenith stump]

ahh, so its a no solution?

[long pasture]

let's say if you know x(t) = t²+t+1 something like that, you can find it

but if you don't, you can't tell anything from that

and usually, it's just a typo

[zenith stump]

oh

[long pasture]

teachers do have typos lol

[zenith stump]

you mean i should solve it with d/dx in case its a typo

[long pasture]

yep

that's the best way i guess, or you can just report the question the your teacher

[zenith stump]

yeah

[long pasture]

and usually your teacher will just say, yea it's a typo and you'll have to calculate it

[devout snow]

@zenith stump Has your question been resolved?

[zenith stump]

thanks man, I really appreciate the help!

[devout snow]

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[restive river]

wait would BE and BC be equla

[rare mantle]

show the full problem

[restive river]

@rare mantle

[rare mantle]

I actually don't know, sry

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[devout snow]

Please don't occupy multiple help channels.

[young hill]

since PQ is always required, so let it equal one speak called U, so find how many ways you can permute 4 speakers

[restive river]

but

[young hill]

4!

[restive river]

cant it

also be

p r q

like

would that

still count

[young hill]

oh

[restive river]

it dont say

[young hill]

very true

[restive river]

it gotta be beside it

ik how to do it

[wooden wraith]

yeah I don't think it means P is immediately before Q

[restive river]

if its beside it

but all it states

[young hill]

that would be too simple

[restive river]

is that its in front of it

but it dont have to be just 1 in front

[young hill]

P(4!) + 3P(3!) would be the first two terms

[buoyant coyote]

so for each possibility either p goes before q or q goes before p

you can derive something from that

[young hill]

oh, like 5! divided by 2

[buoyant coyote]

yeah

[young hill]

P(4!) + 3P(3!) + Permute(3,2)P(2!) + Permute(3,3)P(1!)

[wooden wraith]

what is P?

[young hill]

where Permute(n,k) = n!/(n-k)!

[young hill]

it's just the P speaker

4! + 3(3!) + (3!)(2!) + (3!)

24 + 18 + 12 + 6 = 60

which equals 5!/2

[young hill]

yeah that's the right answer

[young hill]

i was just enumerating the 4 possible positions the P speaker could be

[wooden wraith]

I gotcha now

[devout snow]

@restive river Has your question been resolved?

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[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[zenith mist]

Start by factoring by the (1/5) and after that you will have 10*(1/5), which is equal to 2

Maybe I misunderstood something, sorry but I can't help you

[devout snow]

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[devout snow]

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[frigid hatch]

Will z limit start from 0?

[devout snow]

@frigid hatch Has your question been resolved?

[devout snow]

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[frank dew]

can somebody explain the math here?

[regal torrent]

It's completing the square method

[frank dew]

i understand completing the square

but what did they do between line 2 and 3

[regal torrent]

Took 1/4 out

Common

[frank dew]

??

[lusty sapphire]

They factored a 1/2 out the square root

[frank dew]

wait how

[regal torrent]

Do lcm

[frank dew]

elaborate

[regal torrent]

(2x-1)/2

[frank dew]

you're not spelling it out

i don't understand..

[regal torrent]

Bro

U see the bracket

[frank dew]

mhm

[regal torrent]

Which is squared

[frank dew]

mhm

[regal torrent]

Take lcm

Of stuff inside bracket

[regal torrent]

Nd u get this

@frank dew u know cross mutiolication ryt

[frank dew]

dear lord the spelling

yes

[regal torrent]

Lol

Do it

[frank dew]

no, i'm writing

[regal torrent]

This is it

[frank dew]

ofc you gave me answer

i'm trying to arrive there via paper

[regal torrent]

U square it and u have four in denominator

U don't need paper

[frank dew]

its not making sense on text lmfao

thats why i'm writing it out

its like 4am

[regal torrent]

Oh damn

Pain in brain eh

Sleep sir

[frank dew]

nope, i have to do this now

[regal torrent]

Ok then did u write

[frank dew]

this exponent is confusing me

[regal torrent]

It squares 1/2

[frank dew]

doesn't it expand x-1/2??

[regal torrent]

The two of the denominator

[regal torrent]

Do cross multiplication first then square

Step by step

[frank dew]

isn't (x-1/2)^2 the same as (x-1/2)(x-1/2)?

[regal torrent]

Don't do that

It's more painful

Let the exponent wait

[frank dew]

i can't see the cross multiplication with this fraction

[regal torrent]

Deal with the bracket first!

Ok tell me... What's inside the bracket!?

[frank dew]

x-1/2

i'm trying to change that

[regal torrent]

Ok what's an odder way of writing THIS

How do u subtract simple fraction s

[frank dew]

if i knew, i'd write it out by now 😔

oh

[regal torrent]

What's 1-0.5

[radiant dune]

I wonder what school makes people learn calculus before making them learn fractions

[frank dew]

yeah the communication was just not clicking for me

[frank dew]

years of forgetting basic math does that

[regal torrent]

Answer!!!

[frank dew]

i got the answer

2x-1

1/(1/2) = 2

[regal torrent]

There's 2 in denominator

[frank dew]

x-1/2 = (2x-1)/2

double it and divide

[regal torrent]

Yess

[frank dew]

🧌

i just undid what i multiplied lmfao

dont think i did what you asked but it works

[regal torrent]

WHAT

[frank dew]

multiply the whole expression by 2

and divide it

[regal torrent]

WHY

[frank dew]

because that made more sense to me in that moment

[regal torrent]

Dude look

[regal torrent]

Everything is good here OK?

[frank dew]

mhm

[regal torrent]

NOW SQUARE THE FRIKIN FRACTION

isn't that what the bloody exponent is supposed to do

Teh ' ^2'

@frank dew

[regal torrent]

Simplify

Square

Sqyare eet

1/4 times (2x-1)^2

[frank dew]

i factored out a 1/4

why not 1/2?

[regal torrent]

Good

[frank dew]

oh wait

they applied the sqrt to 1/2

to get 1/4

[regal torrent]

Now theres another ROoT

[radiant dune]

There's a riot

Lmao

[regal torrent]

Quite the opposite

[regal torrent]

Lololol the jonas aden track was good tho

[regal torrent]

All good

[frank dew]

sqrt of 1/4 is 1/2

[regal torrent]

Yeassir!

[frank dew]

so that can be moved to the outside of the integral

oh i flopped the numbers

[regal torrent]

Mission accomplished

[frank dew]

i blame it almost being 5am

ok done

.close

[devout snow]

Channel closed

Closed by @frank dew

Use .reopen if this was a mistake.

[frank dew]

ty for bearing w me btw

[regal torrent]

No sir apparently I'm a differently abled person in my education system

[frank dew]

damn

[devout snow]

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[fathom thicket]

that graph doesnt even make sense, how does x^2 + y^2 = 1 have a coordinate at (0,2)

[frigid hatch]

Yea im confused as well,need to convert it into polar coordinates,or was that just a printing mistake and we should just ignore the two?

[analog trellis]

Could be a typo. If the book has a new edition check that online or think of something which seems reasonable in the context to fix the typo.

Maybe it was meant to be x^2 + y^2 = 4.

[devout snow]

@frigid hatch Has your question been resolved?

[devout snow]

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[scenic frost]

I can't seem to understand what I'm doing wrong for this question

[scenic frost]

I have my mean, and with the same data I am attempting to calculate s.d. , but it doesn't seem to be the right answer. could someone help please, thanks.

btw I know all the formulas etc. but I can't understand why I'm getting this wrong

.close

[devout snow]

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[devout snow]

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[winter bloom]

yo i need help classifying angles

[short shore]

adjacent angles mean they're beside each other, sharing a common side and a vertex. While vertical angles, are usually opposite each other

while still sharing a vertex but not a side, because they are the result of two lines crossing each other

[winter bloom]

wait so number 2 would be M and L?

[short shore]

you usually name angles using the three letters

[winter bloom]

oh

[short shore]

with the middle letter being the vertex

[winter bloom]

so M, L, P

[short shore]

an example of an angle would be MPL

since the vertex is P

[winter bloom]

ohhhh

that makes more sense

[short shore]

and for 11 -14

acute angles are angles under 90 degrees

obtuse angles are those over 90 but less than 180

right angles are 90 degrees and obviously straight angles are 180

[devout snow]

@winter bloom Has your question been resolved?

[devout snow]

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[edgy sparrow]

Linear algebra

length of vector u = 2, length of vector v = sqrt(3)
We know that the dot product dot(u,v) = 1
What is the length of the vector 2u-v?

[edgy sparrow]

I got this far but I'm not sure how to proceed

[mellow panther]

use the formula for ||a+b||^2

[edgy sparrow]

how do i calculate dot([2u-v],[2u-v], I don't think I have it in my material

[devout snow]

@edgy sparrow Has your question been resolved?

[edgy sparrow]

Is this the correct answer?

[stone stump]

yes

[edgy sparrow]

OK, thanks bro

.close

[devout snow]

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Closed by @edgy sparrow

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[devout snow]

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[devout snow]

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[umbral heath]

Can someone check my work?

[umbral heath]

“Find Exact Values”

[hybrid snow]

It's ,rotate

[umbral heath]

ok thx

[ancient furnace]

Looks right

[ancient furnace]

I think you should try to not convert into degrees though, try to think abt it only in radians. It can be kinda tough at first but overall makes it easier once you get it down. Not really a big deal but just something that helped me

[umbral heath]

Ok

[hybrid snow]

I tend to turn them into degrees. Nothing wrong with that, since I just memorize 30-60-90 and 45-45-90 theorems

[warped relic]

Mood

Degrees are easier than radians when it comes to triangles

But it's all preference

[warped relic]

However, when adding angles to numbers algebraically, you need to convert to radians

[warped relic]

#❓how-to-get-help

[ancient furnace]

Yea nothing wrong with it I just find it easier to stay in rad rather than make mistakes when converting from degrees to rad

[warped relic]

Well getting used to the conversion is super simple

Just needs practice

[ancient furnace]

I go back and forth too but I think when first learning it, you kinda limiting yourself if you can only understand rad if you convert to degrees

[umbral heath]

I’m stuck

did I do the picture wrong ?

[ancient furnace]

Looks right

[umbral heath]

ok

WAIT NO

that’s wrong

would they be negative ?

like that picture ?

or positive

the long 1 is not negative

I think

yes

I think right

but which one do I pick for the opposite

-1 or 1

how do I know what to pick

Final answer

[devout snow]

@umbral heath Has your question been resolved?

[warped relic]

Okay react to the bot first

[umbral heath]

Ok

I did

now answe me

I have a next question after u confirm that’s right

[warped relic]

Which?

[umbral heath]

This one

[warped relic]

Okay

So like

7pi/4 is 315°

[umbral heath]

ok

[warped relic]

So it's a 45° triangle

[fathom thicket]

its best to just get used to radians

when you use trig in calculus

you can only use radians

[umbral heath]

yep

[warped relic]

You drew it well

[umbral heath]

Ok

and then the math part ?

[warped relic]

Correct

[umbral heath]

ok

[umbral heath]

ok but I did the radian and degree

?

what do u mean by radian

Show

[fathom thicket]

i mean, its best if you can get to the point where you can completely think in radians

[warped relic]

Radian is in terms of pi and not degrees

Like you work only with radians

[fathom thicket]

and not have to rely on degrees

[warped relic]

No conversions

Like you draw a 45° triangle and label every angle as π/4

[umbral heath]

the top half is in radians right ??? Or am I not doing radian I’m comfused

[warped relic]

The angle inside the tan is in radians

[umbral heath]

yes

[warped relic]

What doctor means is that you write the 30° as π/6 and the 60° as π/3

And not ever depend on degrees

[umbral heath]

oh

like don’t do the

[warped relic]

But that depends on your preference of course

[umbral heath]

306090

454590

?

Don’t do that

[warped relic]

Yeah you do them as (π/6)(π/3)(π/2) and (π/4)(π/4)(π/2)

[umbral heath]

ok yea we’re not there yet

this is just the beginning of trigonometry

ok so netx question

,rotate

[umbral heath]

so bottom

so

what does it mean when

the b is raise to the 0 power

b^0 = 1?

[warped relic]

Yep

Btw the algebra seems kinda weird

[umbral heath]

how come?

I also agree lol

[warped relic]

163 = ab^0 +13 is good

[umbral heath]

my friend from North Carolina came to wisocnsin and was like wtf is this sh

NO

[warped relic]

Then the next step everything died

[umbral heath]

do t look at the rest

I was just organizing my

thing

[warped relic]

Hmm

[umbral heath]

I’ll show u when I’m done

[warped relic]

No like the 149 is not correct

[umbral heath]

I KNOW

[warped relic]

Okay

[umbral heath]

,rotate

[umbral heath]

so far so good ?

[warped relic]

Yeah

[umbral heath]

And then that’s A

[warped relic]

Wait you got b = 0.8?

[warped relic]

Yeah

[umbral heath]

yes

[warped relic]

Hmm...

,w calculate cube root (0.51)

[umbral heath]

LOOK

It’s my calculator not me

[woven radish]

Results provided by WolframAlpha

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

Requested by VulcanOne#5806

[umbral heath]

SEE

[warped relic]

Ok yeah I missed the 3

You good

[umbral heath]

Ok

now the hard part

OF THE WOrksheet

[warped relic]

Sketching?

[umbral heath]

ya

[warped relic]

Okay

[umbral heath]

I gona. Do on my own first

also I changed it a little bit

[warped relic]

Oki

[umbral heath]

P is for period

[warped relic]

Okay

[umbral heath]

,rotate

[umbral heath]

IDK how to scale

but that’s my road

I have to go pick up my brother I’ll be back in 10-15 min

[warped relic]

Okay sure

[umbral heath]

Are u kiddi mg me

all these mom and dads come here 30 min early

and I can’t get a spot

[warped relic]

Worst feeling ever

[devout snow]

@umbral heath Has your question been resolved?

[umbral heath]

ok

I’m back

[warped relic]

Bot please or else channel will be lost

Btw welcome back

[umbral heath]

what should I scale by?

thank u

idrk how the scaling works

[warped relic]

Your y-axis scale works just fine

[umbral heath]

my X axis tho

idk

bcuz we need pi/4 right

or somethign

[warped relic]

Well considering how repeated the angles will be, you will need to expand it a bit

[umbral heath]

WAIT I GOT IT

so

it would be

pi/4

3pi/4

5pi/4

right ??

and then 7pi/4

bcuz if we can do pi/2, pi, 3pi/2, 2pi we can do same with that one

[warped relic]

Hmm

I suggest doing π/8

2π/8

3π/8

4π/8

And so on

[umbral heath]

awh

why*

Bcuz

isn’t my starting point pi/4

btw I’m not arguing with u I just want to understand

[warped relic]

I can feel that don't worry

Okay so you know how the period works right?

[umbral heath]

no idk

[warped relic]

Okay

[umbral heath]

Yes

I know

but I forgot

it’s where like one length

idk

[warped relic]

2π = period * number of times in one period

Or 2π = p*b

[umbral heath]

what do that get u

[warped relic]

First you identified b right?

[umbral heath]

ya it’s

4

[warped relic]

Yep

[umbral heath]

ISNT TO FIND THE PERIOD 2pi/4 which would be pi/2

[warped relic]

Yep

[umbral heath]

then

[warped relic]

An entire period goes through 4 stages though.

[umbral heath]

oh ok

[warped relic]

So to get each stage, you need to have the angle for it

So in this case you will divide π/2 by 4

Which gives π/8

[umbral heath]

ohh

and that is the

what to score by ?

Scale

[warped relic]

Yeah

You will capture the peaks and troughs more easily with this scale

[umbral heath]

and u divided by 4 bcuz it go thru 4 stages?

[warped relic]

Yep

[umbral heath]

ok thx

scaling done

now

my teacher say

to find the starting point and the ending point

[warped relic]

Mhm yep

Also keep in mind that your wave will be negative so ye

[umbral heath]

how do I find the starting point tho bcuz pi/4 isn’t in the thing u know

[warped relic]

Well

If your x = π/4, what does the y value equal to?

[umbral heath]

Idk

[warped relic]

Plug in?

[umbral heath]

plug in what

[warped relic]

x as π/4

Into your function

Hint: you get -2(sin(0)) + 1

[umbral heath]

where did the 4 go

-2sin(4(0))+1

[warped relic]

Well 4*0 equals 0 in the end

[umbral heath]

ok

now what

[warped relic]

You got 1 right?

[umbral heath]

no I got

-2sin+1

[warped relic]

sin of what?

Should be sin(0)

[umbral heath]

0

yes

[warped relic]

Yep

[umbral heath]

OMG THIS IS SO CONFUSING

now what to do after

[warped relic]

You got sin(0), which should equal 0

[umbral heath]

yes then

-1

[warped relic]

-2*0 + 1

= 1

Right?

[umbral heath]

-2sin(0)+ 1
-2+0+1

bcuz

sin0

=0

[warped relic]

Wait wait

The -2 is multiplied by the sin(0)

And sin(0) is the same as 0

So -2 multiplied by 0

[umbral heath]

=0

[warped relic]

So like

At x=π/4, y = 1

Which is your dashed line

[umbral heath]

1

WE WERE

FINDING THE DADJ LINE THIS WHO TIME

WHOLE

[warped relic]

Nooooo I didn't mean it to be disappointing

Problem was because of the sin(0) thingy

Anyways we found the starting point of your graph

[umbral heath]

NONWE DIDNT

[warped relic]

Put a point at x=π/4 and y=1

[umbral heath]

I can’t

bcuz

we don’t have pi/4

[warped relic]

Wait what?

π/4 = 2π/8

If that's what you mean by no π/4

[umbral heath]

Omfg I’m gonna kill u

now the end point

[warped relic]

Hmm

[umbral heath]

U KNOWNwr didn’t even have to find the mid line

bcuz it’s alredy given

[warped relic]

So like here's where I don't understand the "endpoint"

[umbral heath]

one cycles

so

it would prob be at

[warped relic]

Okay we found the period

As add π/2 to π/4

[umbral heath]

what

2pi/6

?

[warped relic]

1/2 + 1/4 = 2/4 + 1/4 = 3/4

So like 6π/8

[umbral heath]

ok

is that the end point

[warped relic]

Yea

Then do the stages in between

[umbral heath]

K

,rotate

[warped relic]

Yepp

[umbral heath]

that was so confusing

[warped relic]

Can I tell you some corrections to make or are you aware of them?

[umbral heath]

what is it

[warped relic]

Mood. Me with my first sine wave graphing exercise.

[warped relic]

Okay so that 4 under the 2π. You can keep it as 4 by erasing the 2 next to π or you change the 4 to an 8

Also I think you know that the lines should behave more like waves

[umbral heath]

so basically pi/2

[warped relic]

No it's π/4

You can keep the 4 by just erasing the 2

Or you change it to 8 without erasing the 2

Also I think it will be easier for you rn to check with a graphing calculator

[umbral heath]

k

well thanks

Bye.

.close

[devout snow]

Channel closed

Closed by @umbral heath

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[devout snow]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[inner sedge]

having a hard time with this question

[winter patrol]

where did you get stuck?

[inner sedge]

I've substituted u in and taken 2 out of the integral leaving 2 /int_{1}^{2} 1/u^2 dx

but I don't think that's right

and I'm not sure what is

[winter patrol]

can you take a pic of what you did?

[inner sedge]

Not at the moment, my roommate is sleeping. But I can type it lol

<@&286206848099549185>

[devout snow]

@inner sedge Has your question been resolved?

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[devout snow]

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[tepid maple]

How would I solve this?

[gentle mantle]

look up disks and shells by organic chemistry teacher

[tepid maple]

Well I have some work done but I'm getting the wrong answer.

[gentle mantle]

idk how to do it myself, I just know thats how youre supposed to do it

you gotta wait 15 min to ping helpers, so not on here no

[devout snow]

@tepid maple Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[hidden charm]

angle SVT = angle TWU

yknow why?

@woven raft

@woven raft

i am going to close this forum

[woven raft]

why

sorry was in a class

[hidden charm]

ahh i understand

r u out of class now

[woven raft]

yes

[hidden charm]

ok i hope u r sitting down

without distractions

i will begin when u confirm

[woven raft]

I am

[hidden charm]

@woven raft

[woven raft]

I am siting down

[hidden charm]

angle svt = angle vtw because of alternate angles

Usually i ask for a photo

but i will take ur word for it

and angle vtw = angle twu because of alternate angles again!

r u following?

please confirm

[woven raft]

yea

not relly

SV
∥
TW
. Prove that △STV≅△TUW.

thats what it wants not sure how this proves it

[hidden charm]

OK

so you have an angle!

[woven raft]

yea

[hidden charm]

we need more stuff to be equal!

vst = wtu by correpsonding angles

thats two angles!

[woven raft]

ahh ok

[hidden charm]

VS = WT

so we have two angles

AAS

im going next

hope this solves it!

sorry

does that symbol

that u hv there

mean similarity or congruency

if its simialrity we are done

cos we have two angles and its equiangular

@woven raft

[devout snow]

@woven raft Has your question been resolved?

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[odd elbow]

Hi

[odd elbow]

I'm given a triangular based pyramid Smth like this:

Is it possible to find all three slant height of the pyramid

[devout snow]

@odd elbow Has your question been resolved?

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[west salmon]

I have been recently pondering about probability.

Let's consider a toy example of a gacha game where you want to get a particular roll. I always thought that the probability of getting what you want in the next three rolls does not depend on the past. Lets assume that you stop rolling as soon as you get the "item".

Going over my probability notes I was thinking about the case where we want to calculate the proability of a machine to break down in the next time instant, given that it has already lived for a time t.

P(t < X < t+ dt | X >t) = P(t < X <t+ dt and x >t)/P(x>t) = P(t < X <t+ dt)/P(x>t).

Wouldn't it be possible to consider the gacha game where X is, instead of the life expectancy, the number of rolls needed to get the item? And would the calculation be different from the above and why?

[west salmon]

I believe the core of the issue is when we say that P(t < X <t+ dt and x >t) = P(t < X <t+ dt).

but even so, why wouldn't this hold for the toy example of the gacha game?

TL DR, if X is an independent variable why is P(y < X < z and X > y) = P(y < X < z)P(X > y) and not simply = P(y<X<z)?

<@&286206848099549185>

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[glass tusk]

okay you got a bet with these rules:

[glass tusk]

50/50 chance to win, double money on win

if you got 2000€ and you bet 1000€ does that give you more than 50% chance to success? if you lose you can retry to win with another 1000€

[hybrid snow]

Still 50/50

The money you gain or lose has nothing to do with the chances

[glass tusk]

My friend argued that since you basically got two tries it has to be more than 50% chance

[glass tusk]

Okay thanks

[hybrid snow]

Each try is 50/50

Your friend fell for the gambler's trap

[glass tusk]

Thanks for helping

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[edgy sparrow]

Linear algebra

I have to prove that polarization identity exists for all {u, v = R}

[edgy sparrow]

I'm not really sure if I follow, isn't this proof enough?

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[stone stump]

yes that is enough

[edgy sparrow]

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[ashen ledge]

Hey! Can anyone help me with this problem?

let f(x) = 1/2ln((1+x)/(1-x)) for every xE(-1,1). Find a,bER such that f(a^2 + b^2) + f(a-b+1/2) = 0