help-13

[frigid cloud]

Pi * r?

Instead of squared

Since you’re here, you can help me.

[pearl night]

Area of a half-circle:

\text{Area} = \frac{1}{2} \pi r^2

Circumference of a half-circle (excluding the flat edge):

\text{Circumference} = \pi r

If you want the total perimeter (which includes both the curved edge and the flat edge), it would be:

\text{Perimeter} = \pi r + 2r

[frigid cloud]

Latex didn’t work

[pearl night]

What you mean It didn't work

Can you clarify

[frigid cloud]

$\text{Area} = \frac{1}{2} \pi r^2$

[wraith dagger]

Bettany

[frigid cloud]

Why don’t we just ignore the square ?

@pearl night

.close

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[sinful mist]

how do you do this?

[hard wolf]

you replace y with 4 and z with 3 and solve

[sinful mist]

is it adding fractions

[hard wolf]

when an variable (y, z etc) is placed right beside a number it means multiplication

[sinful mist]

I SEE

okay

so u divide the fraction looking thing then times the answer by the letter

[hard wolf]

what do you mean divide

its just an equation.
(3/2)*4 is equal to 6
and continue from there

fractions are numbers as well

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[waxen geyser]

I need to understand the Summation form of the Tayor series of f(x) = cos(x) for when a = pi/3

[waxen geyser]

before we begin let me post some things

firstly, if possible, I would love to voice-chat with someone

it would make life so much easier

secondly:

[dusk goblet]

secondly

[waxen geyser]

hold on

[opaque root]

Do not use these channels to ask in voice chat, these channels are for specific questions that must be answered in the own channel

[waxen geyser]

ah okay

alright so, my main issues are

1. why does 2n denote evens and 2n+1 denote odds

[dusk goblet]

definition of even number

odd number = not even number

2n+1 is not even

remainder is 1 not 0

even if 2 divides the number

[waxen geyser]

another thing, the summation above should've given me the results for when n = even. does 0 count as even for that?

[copper cove]

0 is even, yes

[waxen geyser]

alright so my main question is why does the summation with the 2n alternate as (-1)^n instead of (-1)^(n-1) since n = 0 gives me a positive.

and why do the odd terms alternate as (-1)^(n-1) when n = 1 start as a negative?

here is the full f(x)

[waxen geyser]

<@&286206848099549185>

[eternal gale]

that looks right

[eternal gale]

this

[waxen geyser]

?

[eternal gale]

just saying thats right, sorry im helping someone else rn

[waxen geyser]

ah

[eternal gale]

anyways it would be 2n if youre skipping a power

or to keep the negative only

depends on where you use it

if you use it on a number or variable its to skip and power on -1 its to keep the negative

by keeping an odd power

[waxen geyser]

okay so assuming I'm skipping a power, the alternating begins with n=2 for the even terms which means f''x = -1/2 and that would be correct for (-1)^n

so then would the second summation begin its alternation at n=3 which would be (sqrt3)/2 which is positive?

what i'm currently thinking

is that

[eternal gale]

yes that allows it to switch powers

[waxen geyser]

I input n=1 on the (x-pi/3)^(2n+1) giving me a 3, then I use that 3 for (-1)^n-1 giving me a positive 1

[eternal gale]

no

the n stayes the same throught the whoel equation

its jsut a number youre plugging in

[waxen geyser]

oh wait a second

so say I'm plugging in n=1 for the second summation

i'm given:

[eternal gale]

yes

[waxen geyser]

so when n = 1, f`(x) = -(sqrt3)/2 but since i'm skipping a term, I immediately go to where n=3 is and thats where I have pos (sqrt3)/2

[eternal gale]

youre not skipping a term

it goes from n = 1 to n= 2 you use the 2n in the equation to keep it a postive or negative power so like

[waxen geyser]

the other summation determines whether it is positive or negative?

[eternal gale]

the first will be -1 because the power is odd and the second would be 1 because the power is even so if we do n = 2 then the first is -1 because its an odd power and the second is 1 because its an even power and it will keep an odd or even power depend on which you use 2n or 2n +1

[eternal gale]

wait a sec

"(-1)^2n or (-1)^2n +1"

these

[waxen geyser]

[eternal gale]

Understand?

[waxen geyser]

gimme a moment im going it over in my mind

lemme ping you again when i get stuck

[eternal gale]

ok

[waxen geyser]

Is this a good visual representation?

(Black and green markers)

[eternal gale]

no i dont think so, we are talking about keepinfg an even or odd power whcih maintains the neg or positive value you want when youre forming the summation

[waxen geyser]

🤔

gimme a second

[cedar kiln]

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[sage lance]

what is 1+1 I have been trying to solve this problem all night

[digital cliff]

.close

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[trail dune]

Is this graph correct? -2cos3pix

[trail dune]

When I drew it I started at the -2

This wat I did

Why does the cos (orange), start at 2, but sin (green) starts at 0? They have the same function of 2\cos x3\pi

[dull oxide]

What?

[dull oxide]

No

[trail dune]

Look where they start getting drawn

One is at 0, origin, and one starts at the amplitude

.solved

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[tight epoch]

@eternal gale hey assuming we have the carrying capacity formula how do I find K and what is K?

[dire geode]

!noping

[cedar kiln]

Please do not ping individual helpers unprompted.

@tight epoch Has your question been resolved?

[tight epoch]

no

so let's say I have the carrying capacity formula dP/dT =kP(1-P/L) what is k and how do I find it?

that's what I'm trying to figure otu

out

within this proble: In 1992 the moose population was measured to be 3790 by 1996 the population was measured to be 3870 Find a new formula for P in terms of t the years since 1990 what does your model predict the moose population to be in 2009

Is K just a constant for a model represented by P?

<@&286206848099549185>

[eternal gale]

i did none of the sort

[empty spear]

!noping

[cedar kiln]

Please do not ping individual helpers unprompted.

[eternal gale]

i helped before?

[eternal gale]

!noping

[cedar kiln]

Please do not ping individual helpers unprompted.

[tight epoch]

wait did I do something? Yeah she helped so that's why I pinged but I wouldn't have done so otherwise.

[eternal gale]

theyre just being annoying dont worry about it

[tight epoch]

oh okay

but yeah basically am I solving for K or within the context of a problem how do I derive K?

I guess the math is all okay it's just problem statements that stump me lol

[eternal gale]

i dont think you do i think you leave it as dk/dt

[tight epoch]

oh okay

and just solve for it

so dP is the change in P and dT is the change in T right?

or am I getting it wrong?

huh

[eternal gale]

dp is the change in p in terms of t

thats why its dP/dt

[tight epoch]

I'm still confused

hold on

any ideas?

[tight epoch]

<@&286206848099549185> If I have a carrying capacity formula problem what is K supposed to represent?

[eternal gale]

do you have the foermula i gave you?

[tight epoch]

yep

dP/dT=kP(1-P/L)

so I know that k is the contant of proportionality but how do I find it though? I can find everything else but not K

so okI have Dp but not Dt which is change in time since it wants me to find the years after 1990 do I just use 1991-1990?

um

wait I got it

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[atomic forum]

This question is unusually easy and here’s my solution and I highly suspect there’s a trap since my teacher is notoriously strict and likes to give extremely hard questions

At one point I am just copy paste my answer for (a) for both (b) and (c) thus I am definitely doing something wrong it can’t be this easy

<@&286206848099549185>

<@&286206848099549185>

Big big brothers onii chan help me with math

[cedar kiln]

@atomic forum Has your question been resolved?

[atomic forum]

<@&286206848099549185> Onii chan help me with verifying my solution please please

The point is whether the solution is valid, or I have to isolate every variable to find explicit expression rather than an abstract definition, however for the subquestion (a) and (b) the construction is very easy but it goes significantly more challenging if it shifts to subquestion(c) the isolation of y is algebraically intricate involving carden formula and necessity of introducing new parameters.. but the current method I use is way too easy as if it’s a word game

And think my teacher is quite strict (almost at a notorious level ) I seriously felt like if there is trap

Onii Chan

[atomic forum]

😭😭😭

<@&286206848099549185>

[steep badge]

If you don't get help here

check early university category

[atomic forum]

I will definitely try that one because the question are too weird too easy or too hard

<@&286206848099549185>

[cedar kiln]

@atomic forum Has your question been resolved?

[eternal gale]

youre not going to get an answer very fast, not many people know how to do that math, it might take a few hours or days i recommend finding a video

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@atomic forum Has your question been resolved?

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[ruby path]

How can I determine the domain and range of any quadratic function?

[plucky jacinth]

the domain of a quadratic function is all the real numbers

cause you can plug in any number and it'll work

the range is all the numbers you can get out

these are any y values above/below the maximum/minimum

[ruby path]

the domain here is all the real numbers
and the range is y=> 3?

[proper mortar]

check the sign of the x² term, if it's positive, then the range goes from minimum to infinity

[plucky jacinth]

yes exactly!

[ruby path]

alr tysm

[plucky jacinth]

because the squared term must be positive

np!

i'm glad i could help 😄

.close

hm

[ruby path]

.close

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[upbeat cipher]

PLS HELP CURVE LENGTH

[slender ginkgo]

Set up integral

[pastel vault]

$\int_{-2.95}^{2.95} \sqrt{1 + (dy/dx)^2}\ dx$

[upbeat cipher]

u sure?

[wraith dagger]

south

[pastel vault]

why do you ask

yeah that thing you deleted is completely unrelated

[upbeat cipher]

i mean this one

[slender ginkgo]

Literally this equation

[pastel vault]

this one, yes

[upbeat cipher]

so i just have to insert everything like that

wait let me try

like that right?

@pastel vault

[pastel vault]

yeah

[upbeat cipher]

I also got another question

[pastel vault]

ok

[upbeat cipher]

.

how do i do that?

[pastel vault]

just integrate from -2.95 to 2.95

[upbeat cipher]

with this one?

[pastel vault]

then subtract the area of the rectangle

[pastel vault]

yes

[upbeat cipher]

1.8*2=3.6?

A-3.6=answer?

let me try

@pastel vault

like that?

is that correct

[pastel vault]

yes that's correct

[upbeat cipher]

Thank you so much

i think i got one more question

let me check

The questions are in danish let me translate little quiq

I made the 1. one

but i am missing the second

let me send pic of what i did

1. one

but i miss the second question

@pastel vault

[pastel vault]

ah so you just need to minimise $|3(t^2 + 2t) + 4(t^2 - 2t) + 2|$

you can forget the absolute value for now, so just differentiate the quadratic inside the absolute value to find the turning point

after you find the minimum value of this

don't forget to divide your answer by sqrt(3^2 + 4^2)

[upbeat cipher]

let me try

[pastel vault]

wait I mistyped

corrected

[wraith dagger]

south

[upbeat cipher]

why we dont put x(t) on them both, and y(t) on them both

or something like that?

I am getting this

xD

[pastel vault]

yeah

you're stuck here right, well just simplify

you get a quadratic and you can ignore the absolute value actually

[cedar kiln]

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[frozen relic]

can someone tell me about the big o notation in terms of an analogy

[frozen relic]

it sounds like a limit but i dont get it

[cedar kiln]

@frozen relic Has your question been resolved?

[proper prism]

big o notation is just a way to determine how fast/big a function is growing

[frozen relic]

ohh, why is it called that way

[proper prism]

the creator of it, just proposed it ig, but honestly there is nothing wrong with it no?

[frozen relic]

like is there any particular reasoning as such. like a limit tells us the 'limit' of something

[proper prism]

aah honestly i dont know, i just use it , i never questioned why its named like that because it was never relevant to me

[frozen relic]

ahhh gotcha

so its basically just a notation for the general form of the function?

[proper prism]

it just describes the limiting behavior of a function when the argument tends towards a particular value or infinity

[frozen relic]

so how the graph tends to look near a particular value?

[proper prism]

the way the function's behavior tells it to? hahaha

how is the graph of happiness in your day looks like near a particular time of the day?

[frozen relic]

depends

[proper prism]

its function-dependent, not for u or me to decide hahah

[frozen relic]

yeahh

[proper prism]

exactly so for example f(x) = x² + x + 1

f(x) is in O(x²)

because when x -> infty

[frozen relic]

yes

[proper prism]

the function behaves like a x² function

[frozen relic]

ahh

makes sense now

tysm

[proper prism]

no worries

[frozen relic]

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[cedar kiln]

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[glossy light]

a) proof that this sequence is increasing
b) find the limit of the sequence
c) proof that S(2014)<2014 and find the limit of S(n)

[glossy light]

idk how to solve any of them, can someone help

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[pine ridge]

solve ii please from permutations and combinations

[sacred salmon]

do you know about "!" ?

[pine ridge]

yes factorial

[sacred salmon]

so here you can process the math book as one since it as to be keep together

try to solve it with this hint

[pine ridge]

.-.

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[wheat herald]

how do we justifiy lim x=>-1 ln(x+1)

[idle tusk]

wdym justify

[cedar kiln]

@wheat herald Has your question been resolved?

[wheat herald]

calculate

i know its -inf but i dont think its enough the write it like this

[idle tusk]

let u=x+1

$\lim_{x\to -1} \ln(1+x) = \lim_{u\to 0} \ln(u)$

[wraith dagger]

artemetra

[wheat herald]

how do you get the reflex to know when to make a composed function ?

[wanton sail]

because ln(1+x) is ln composed with 1+x

so if you can simplify the problem by "getting rid" of the inner 1+x, sometimes it helps you see the answer

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[elfin summit]

Suppose I have this histogram

Would we say this is normally distributed or left-skewed?

[cedar kiln]

@elfin summit Has your question been resolved?

[sonic helm]

left skewed or (negatively skewed) yes

[elfin summit]

its slightly left skewed right?

not too much

not too obvious* rather

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[sonic helm]

Yes slightly
the tail on the left side is longer but the skewness is not extreme as the majority of the data clusters near the cente

Center

[cedar kiln]

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[mint python]

Hi how do I integrate the -3e-x part

[quiet plover]

Do you know that $\frac{d}{dx} e^{-x} = -e^{-x}$? (using chain rule)

[mint python]

No

[quiet plover]

or just $\frac{d}{dx} e^x = e^x$?

[mint python]

No we haven't covered the chain rule yet

So u just use that ??

[oak yarrow]

Typo, no - sign

[mint python]

So it's 3e-x ??

[fresh quarry]

Yes

[mint python]

Ok thanks

[fresh quarry]

And plus C

😁

[mint python]

Yup 👍

[quiet plover]

with a minus

[mint python]

.close

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[quiet plover]

oh

yeah

just 3e^-x

[crimson sedge]

@everyone
"All days I work hard but the night I play even harder" 🗣️

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[main marlin]

how do i get the angels on teh triangle wer

i only need d e and f

[crimson sedge]

What is the value of <WRP

[main marlin]

-27.5

[crimson sedge]

What ?!

Negative?

[main marlin]

WAIT SORRY

27.5

noo

not 27.5

90

its 90 @crimson sedge

[crimson sedge]

angle PWR would be 90

[main marlin]

oh its 27.5 then

[main marlin]

27.5 then

.clsoe

.close

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[crude veldt]

Im confused on how to get what x equals from a square root

[crude veldt]

My best idea is to do 2 + 3x ≥ 0

[cedar kiln]

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[still smelt]

Hello. I have a question about Lagrange Multipliers. Can they be variable? e.g. lambda=3x?

[earnest socket]

lambda, no

should be a real number

[still smelt]

Oh, that's weird

I had this equation, and got to the right answer

12x^2=λ(4x)

2y=λ(2y)

Considering the point where y=0, λ varies depending on x

Oh nvm, this is only valid for the points where y=0, so lambda WILL be a constant there

Ty!

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[honest cliff]

How to solve it?

[cedar kiln]

Please don't occupy multiple help channels.

[vague sparrow]

hard to read, what are you solving for?

[honest cliff]

find domains

Find natural domains of functions:

arctg

ln

[dusk goblet]

180p

[honest cliff]

f(x)

yeah sorry about that

[dusk goblet]

$f(x) = \arctan(x+2) - \ln(-x)$

[wraith dagger]

knief

[honest cliff]

oh wow

[dusk goblet]

what’s the domain of ln(-x)

[honest cliff]

domain of ln function is all real numbers maybe

[dusk goblet]

🤔

try again

don’t guess

[honest cliff]

ln is a logarithmic function, and it is opposite of exponential function.

I know that

[dusk goblet]

inverse

you can think of it that way if you’d like

if D is the domain of ln(x), then what’s the range of e^x

[honest cliff]

all positive

numbers

[dusk goblet]

are you sure

can e^x = -10

for some x

[honest cliff]

no

[dusk goblet]

well then it’s not all real numbers is it

[honest cliff]

all real numbers can go into x but result must always be positive

[dusk goblet]

great so the range of e^x is

can you write it out

what does always be positive mean

mathematically

[honest cliff]

X element of <0,+inf>

[dusk goblet]

or just y > 0

note that we do not include 0

[honest cliff]

x is the domain and y is codomain?

in this case?

[dusk goblet]

yes for e^x

[honest cliff]

x is what goes in, y is what goes out

y>0

alright

so the opposite of that would be

y = all real numbers

[dusk goblet]

what is the relationship between the domain of ln x and the range of e^x

[honest cliff]

x > 0

they're inverse

so the opposite rules apply

x can be only higher than 0

but y can be all real numbers

going by logic I was taught on friday by some guy in school

university I mean

[dusk goblet]

are you saying the domain of ln(x) is x > 0 btw

you’re all over the place

[honest cliff]

domain is the entrance

[dusk goblet]

🤔

[honest cliff]

codomain is the exit values

isn't that how it works

domain of exponential function is

[dusk goblet]

sir

[honest cliff]

okay

[dusk goblet]

^

[honest cliff]

yes

[dusk goblet]

ok great

now what’s the domain of ln(-x)

[honest cliff]

x has to be negative

[dusk goblet]

-x > 0 -> x < 0

now that we’ve finished that part

what’s the domain of arctan(x)

[honest cliff]

tangential function: it is a function that looks like a curve going from up to down

[dusk goblet]

🤔

how about

what’s the range of tan(x)

[honest cliff]

one moment

all real numbers

[dusk goblet]

yep

so what’s the domain of the entire function

[honest cliff]

[-pi/2, pi/2]

[dusk goblet]

what

[honest cliff]

from -pi/2 to pi/2

So codomain can be equal to all real numbers but domain can only be from -pi/2 to pi/2

[dusk goblet]

the function was arctan(x+2)

[honest cliff]

right

arctan from what I've been told means when we take only 1 of these three curves

[dusk goblet]

domain of arctan(x) is all real numbers

[dusk goblet]

yes we restrict the range to be between -pi/2 and pi/2

[honest cliff]

we have $arctan(x+2)

[dusk goblet]

doesn’t matter

that’s just shifted left 2

still the same domain

[honest cliff]

okay, so if it's shifted that means x will be pi/2 -2pi

[dusk goblet]

what

we only care about the domain sir

[honest cliff]

domain should always be between -pi/2 and pi/2

to make this one fall into that range
we must put x to be

some number<x<some number

it's 1 AM

I should sleep I guess

then tomorrow I come back

close this please

[cedar kiln]

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[tender wing]

this is what i've got so far on this

[blazing zephyr]

i mean you know 2x^2 is the side of the triangle which you can find

[tender wing]

umm

wym

i'm like super new to this

i'm solving for x with this equation

and x is my answer to the problem no ?

i just don't know how to solve this equation bc of the x * squareroot(5) squared

pemdas

i just don't know how to distribute that exponent

would it be x5?

that doesn't make sense to me bc i thought it's supposed to be 5x

i've been doing this for a LONG time now so i'm sorry if i'm sounding dumb

i alr tried to put this equation into an online calculator but it won't even let me

i'm so lost 😭

[tender wing]

bro

i'm an idiot

they gave me the parameter

mb

sorry

.close

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[tribal echo]

help guys

i would like some help

first of all, im not sure what they mean by points, and things like BD

however i still got the equation right

however, im not sure how they get the coordinates of B, and C

[twilit bison]

a point has an x-coordinate and a y-coordinate

it's a point on the cartesian plane

BD means the line that passes through those two points

[tribal echo]

how do we get point c then, knowing that point b is (1,5)

[twilit bison]

use AB=BC

that means the distance from A to B is the same as the distance from B to C

[tribal echo]

wouldnt ab = bc mean

that ab = bc

a * b = b * c

or does that also say the same thing

[tribal echo]

thank you

[twilit bison]

no you can't multiply points together

[tribal echo]

whats the logic behind this then?

well yeah do you know what the logic behind this is

[twilit bison]

this is a kind of notation that is used in geometry

usually with a line over the letters

[tribal echo]

ah yeah i understand now

thank you 🙏 ❤️

[twilit bison]

you're welcome

[cedar kiln]

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[oblique glacier]

There is a company selling watches. If they sell each watch for $400, they sell 3000 watches. For every one dollar they decrease the price by, they sell 20 more watches. For every one dollar they increase the price by, they sell 20 less watches. What's the optimal sale price?

x=#s decreased/increased y=total revenue

y=(400-x)(3000+20x)

y=(400+x)(3000-20x)

idrk where to go from here

[oblique glacier]

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[cedar kiln]

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[true oasis]

am I correct? where did I go wrong?

[neon jolt]

c and d are where your mistakes are

[true oasis]

phew. thank goodness

thats bad, but at least half as bad

[neon jolt]

look at the end behaviors of each side of the graph

notice how they both go down

[true oasis]

I see. when +inf on the ends its positive and -inf its negative?

[neon jolt]

not fully

[true oasis]

okay. could you help explain d?

[neon jolt]

do you know how even degree functions behave vs odd

[true oasis]

yes. an even degree is the highest exponent of x being even

my fault I read that wrong

[neon jolt]

well in terms of end behaviors

even functions have the same end behavior (both up or both down)

odd functions have opposite

[true oasis]

ahh

[neon jolt]

so from the end behaviors on the graph

you can tell if the degree is even or odd

[true oasis]

its even then correct?

since they both go down

[neon jolt]

yep

[true oasis]

okay. so how do I approach this?

[neon jolt]

so for d

[true oasis]

yes sir

[neon jolt]

it can be any even degree

[true oasis]

why is that so?

[neon jolt]

that is greater than the number of "turning points"

(in this case 3)

[true oasis]

local extrema?

the listed points on the graph

[neon jolt]

yes

[true oasis]

okay. so if it were say 4. what would it be then? 6 and 8?

[neon jolt]

because of the end behaviors

we don't know the exact degree

[true oasis]

I see I see

[neon jolt]

but can see the end behaviors of the graph and determine if it's even or odd

[true oasis]

so due to the ends being even and there only being 3 extrema, we can deduce that 4, 6, and 8 are the only possibilities?

[neon jolt]

indeed

[true oasis]

thanks the most!

[neon jolt]

for c just look at the direction of the end behaviors

[true oasis]

is it the same rule?

[neon jolt]

the sign of the leading coefficient defines the overall direction of the end behaviors

think about x^2 vs -x^2

[true oasis]

ahh

[neon jolt]

and the end behaviors

same rule applies

[true oasis]

so to clarify, the leading as in the left side of the parabola?

the left side of the line

the function*

[neon jolt]

wait

[neon jolt]

yes

the highest power

within the expression

is the leading coefficient

well, the leading term

[true oasis]

how would I determine that without knowing the co?

in this I dont believe it shows it

[neon jolt]

the coefficient?

[true oasis]

yes

[neon jolt]

no matter the coefficient number, it'll be the same shape right? (if the same sign)

it just stretches/shrinks the graph vertically

the sign is what flips it

[true oasis]

Im just asking that if I were looking at this graph, how could I tell what the leading co was

Sorry, Im terrible at math

[neon jolt]

that would be pretty difficult

but it's never something you would have to determine from a graph

only the sign

[neon jolt]

(at your current level)

[true oasis]

well thank you very much for your help brother

how do I close the chat?

how late do yall usually help with this kind of stuff btw?

[neon jolt]

just say .close

[neon jolt]

uh im pretty sure theres people 24/7

just a community

[true oasis]

.close

[cedar kiln]

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[true oasis]

ty

[tribal kite]

DOLPHIN? (didnt expect to see u here lmao)

[neon jolt]

math is cool fr

[tribal kite]

fr

[cedar kiln]

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[odd veldt]

Hi

[odd veldt]

Can someone help me with this question plz

My physics teacher said it was wrong and said that there are only 2 ways to do this and I genuinely do not know how to solve this

Lmk if u are lacking info

[nova totem]

not enough info

[odd veldt]

What info do you need to solve it

[nova totem]

it seems the whole sum is part of some experiment?

[odd veldt]

Yes but I just don’t how what to do or how to set up the equation to solve it

The only thing I know is that the givens for water will be used

.close

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[wispy grotto]

can someone help me with ap physics 2

[scenic heron]

you should probably ask the question first considering this is a math server

[scenic heron]

bros taking a quiz

[wispy grotto]

it’s just review

😭

[scenic heron]

what are you confused about

[wispy grotto]

everything

that wire screws everything up for me

[scenic heron]

im ngl i would help but i had my e&m final on friday and i really wanna stop thinking about physics

someone will prob help u tho assuming its not actually a quiz

its pretty basic

[wispy grotto]

lol youre good

physics sucks

i suck at it

[cedar kiln]

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[quasi venture]

How are they getting Rsin(theta)

Like to me

[dire geode]

If R is the hypotenuse of a right triangle where one of the angles is theta, what's the side lengths

[quasi venture]

but theta isn't located there

Theta is located to inside the left triangle

that is my confusion

[dire geode]

I don't think you have the right theta

Your theta doesn't match the width of the strip

[quasi venture]

the width of the stripe id R*dtheta

[dire geode]

Yes. That theta is the one connecting to m

[dire geode]

I assume it's also explained in the resource you got the notes from

[quasi venture]

this is how I see the whole thing

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html

I don't see it

I just don't see how it is is that same theta

[dire geode]

Oh yes you're right

[quasi venture]

not sure what went wrong though

[dire geode]

Your angles don't add up to 180 in your red triangle

[dire geode]

This one

[quasi venture]

okay sure but like that still doesn't resolve for me that I dont see it being theta

ill just have to call it something other than theta

or is it maybe just a trig thing

thing

ohh

it is

sin(pi-x) = sin(x), right?

i guess that resolves it

thanks for the help @dire geode

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[wooden vortex]

i got 0 for this but clearly the answer isn't zero what did i do wrong

[dire geode]

Show your work

[wooden vortex]

integrate from 0 to pi/2 right with the equation being 19sinx-19cos which = 0

[lean lotus]

try finding the intersection of the two curves first

and the integrate from 0 to intersection point + intersection point to pi/2

[wooden vortex]

ok

[dire geode]

Your integrand will be different for each integral

[dire geode]

Neither of which is the one you have

[wooden vortex]

is the answer 38(sqrt2-1)

[dire geode]

Show work

[cedar kiln]

@wooden vortex Has your question been resolved?

[dire geode]

No

I don't see why you keep subtracting the two functions

That difference isn't the height of any rectangle for your area

The height is either the blue curve or the red curve

Can you write an integral (don't evaluate) for just this shaded region? For x in [pi/4, pi/2]

[wooden vortex]

pi/4-pi/2(19cosx)?

[cedar kiln]

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[soft egret]

for b I found strongman A is exerting more force in the direction of motion

so I thought for C that answer is just strongman A because he contributes more force

however the answer key says No because Strongman A is closer to the train

how exactly does the distance determine which one is contributing to the movement?

from the answer key it seems they think the closer you are to the train the less movement you contribute?

[flint plinth]

i think what it is pointing out is that B is exerting more force total

but A is exerting more force in the direction of motion

[soft egret]

but it says closer?

[flint plinth]

well that's a touchy feely answer

[soft egret]

nvm i think ur right

[flint plinth]

a more precise answer would be, the component of A's force in the direction of motion is larger than the component of B's force in the direction of motion

but (as you showed in part a) B exerts more force total

[hollow trail]

i think it's trying to explain why A exerts more force in the direction of the train than B despite B exerting a larger force (without mentioning that's what it's explaining)

[soft egret]

thanks I was confused by the wording of the answer

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[stuck thorn]

help

[gritty heath]

Do you understand how these two are the same picture? She moves from E to E'

[cedar kiln]

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[fast lotus]

By parts

[cedar kiln]

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[plucky seal]

I don't understand why
n = 1 + 2m

I understand n is odd and odd numbers are
even number +1

but why was 2m used here?

[sonic thicket]

2m is always even where m is a natural number

[clear ember]

an odd number is such that it always leaves a remainder 1 when divided by 2

thus you express it as odd number = 2k + 1

for some integer k

[plucky seal]

ahhhh

okay, now I get it. thanks 😊👍

.closed

[woeful isle]

.close

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[grand oxide]

can anyone teach me logarithm

[blazing zephyr]

do you know what logarithm means?

[cedar kiln]

@grand oxide Has your question been resolved?

[cedar kiln]

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[cold mulch]

the answer is C, which I understand that it is true. However, why A is not true?

[cold mulch]

Isn't intermediate value theorem implying this?

or i misunderstood it, [a,b] means interval of x, while IVT is referring to interval of f(x)

[autumn glade]

[a, b] is the input interval. When you say f assumes some set of values, you're talking about the outputs.

For example f(x) = 1 is continuous on R, but it only assumes the value of 1, nothing else.

[cold mulch]

yup i think it is the reason

cuz it can be undefined at one point but still continuous right?

as long as limit exists

[autumn glade]

A continuous function must be defined at every point of a given interval.

[cold mulch]

okay, i will try to figure that out

.close

[cedar kiln]

Channel closed

Closed by @cold mulch

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[slim tulip]

Ok so

Is this a square

My friend said they need confirmation from math server
Since they dont believe me

[crimson sedge]

wat

[cedar kiln]

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[gilded tangle]

Im back

this looks even worse than before

nvm ill ask later im sleeping

.close

[cedar kiln]

Channel closed

Closed by @gilded tangle

Use .reopen if this was a mistake.

[trail tulip]

wait no come back

come back this is really easy @gilded tangle

takes 5 seconds to solve

[gilded tangle]

.reopen

[cedar kiln]

✅

[gilded tangle]

alrighty

[trail tulip]

okay, since the right side is variable, what do we have to do to find the answer?

[gilded tangle]

uh

pythagorean theorem?

[trail tulip]

hmm, close. Yes, you do use the pythagorean theorem, but with any given equation, if you want to find the variable, you have to...isolate it, right? So, what should we do to get rid of the power of two on the h?

[gilded tangle]

i actually do not remember

i havent done exponents in ages

i assume

uh

subtract it

[trail tulip]

that's okay. we all start from somewhere. Let's start off with an the easier side, which is the left side. All you have to do is add 8^2 and 21^2 together.

[gilded tangle]

29^2

[trail tulip]

no

[gilded tangle]

🗿

oh

29^4

?

[trail tulip]

do you know what raising something to the power of 2 does?

[gilded tangle]

you multiply it against itself

[trail tulip]

that's correct, so, following pemdas, you would?

[gilded tangle]

multiply

[trail tulip]

correct! so, knowing that, what does (8^2) + (21^2) give us?

[gilded tangle]

64+441

[trail tulip]

awesome! which equals?

[gilded tangle]

1005

wait

[trail tulip]

come on now

[gilded tangle]

misclikg

😭

[trail tulip]

okay 😂

[gilded tangle]

505

[trail tulip]

good job, so...do you know what the opposite of raising something to the power of 2 is?

[gilded tangle]

square rooting it

or does that fall under division

[trail tulip]

yay! So, looking back on the right side, of h^2, what do you think we're going to do next?

[gilded tangle]

oh

uh square root 505

[trail tulip]

yay!! you got it!

[ruby blade]

That’s easy? You use Pythagoras

[gilded tangle]

yo fr

[ruby blade]

,w sqrt(8^2+21^2)

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by elisabethrae

[gilded tangle]

22.47?

oh

[ruby blade]

h = 22,47

[trail tulip]

yes, but i was teaching him how to do it without a calculator

nope, because there's a sqrt after h, you can just put 505 in that box. It's simplified for you

[gilded tangle]

sick

[wraith dagger]

elizabethrae

[ruby blade]

@gilded tangle

[ruby blade]

You sqrt 505 wym

[ruby blade]

You can’t do it without a calculator

[ruby blade]

Otherwise u have to guess

[ruby blade]

Use Pythagoras again

That’s easy af

[gilded tangle]

ill try

lets see here

[ruby blade]

You’re finding b now

[trail tulip]

in this case, you can, because it's not asking you for the decimal answer

[ruby blade]

It’s just algebra

Use this @gilded tangle

You have a and c

Find it yourself

It’s very easy

You just put numbers in

And you have equation

And you’d have to do next step to find b

!close

.close

[gilded tangle]

sheesh kicked out already 😓

.close

[cedar kiln]

Channel closed

Closed by @gilded tangle

Use .reopen if this was a mistake.

[ruby blade]

It’s pointless to ask question of Pythagoras

[gilded tangle]

what i tried to do was

do the exponents

[trail tulip]

it kinda is, but it's good to ask for help every now and then. I'm sure you can solve this one on your own now

[gilded tangle]

so i had 324+x^2=729

then tried to subtract 729-324

[ruby blade]

Well done

Last step?

You have x^2

You have to have x

[gilded tangle]

so do i square root it

[ruby blade]

Yes

Good job

Well done

You use your brain cells

👏

[gilded tangle]

looks fishy

[ruby blade]

Yes

Round it and you have the answer

[gilded tangle]

20.1

[ruby blade]

Yes.

Yes.

[gilded tangle]

how do i fill this in tho

[ruby blade]

It’s actually

[wraith dagger]

elizabethrae

[gilded tangle]

what

why

[ruby blade]

Full answer

[gilded tangle]

where did those numbers apepar from

[ruby blade]

,w sqrt(5)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by elisabethrae

[ruby blade]

2,24*9

= 20,16

Here’s your answer

[gilded tangle]

lies wont be told

i have no idea what youre saying to me right now

[ruby blade]

That is just more formal answer

Cuz what u give is just rounded up

Just write down that

[gilded tangle]

but like 9 from where

and 5 from where

[ruby blade]

https://youtu.be/B4zejSI8zho?feature=shared

You have to do this

[gilded tangle]

whats this exactly

[pastel vault]

they mean that $x = \sqrt{27^2 - 18^2}$ (length has to be positive so discard the negative square root)

but that means $x = \sqrt{9^2} \sqrt{3^2 - 2^2}$

[wraith dagger]

south

[pastel vault]

we used $\sqrt{ab} = \sqrt{a} \sqrt{b}$ when $a, b \ge 0$

[wraith dagger]

south

[ruby blade]

I’m helping them, quiet. @pastel vault

[pastel vault]

bruh

your explanation wasn't very useful

[gilded tangle]

to be frank

[ruby blade]

@gilded tangle

[gilded tangle]

whats up

[ruby blade]

You can divide 405 with 5

It’s gonna be 81

Square that

You get 9

And 5 remains in the square root

[gilded tangle]

why 5

[ruby blade]

Because it’s highest number it can be divided to.

[gilded tangle]

is that its square root

ah

[ruby blade]

You need to simplify a square root.

I told you, that answer is more formal than 20,01.

[pastel vault]

yes you need an exact answer

that exact answer must have a square root

[ruby blade]

^^^

It it was sqrt(25) it’ll be just 5

However this isn’t a complete square root

You have to do that way

Cause you can’t square it

[pastel vault]

yeah I mean we know it's not an integer from calculating it

that's why we know there's a square root

[ruby blade]

Exactly

[cedar kiln]

Available help channel!

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[honest cliff]

How to solve this? We must find the domain of the function.

[coral jewel]

i can count the pixels

[honest cliff]

I took a picture of my coleague's notebook

[coral jewel]

well whats the arctan domain?

[honest cliff]

from -pi/2 to pi/2

[coral jewel]

wrong, thats range

[honest cliff]

All real numbers then

[coral jewel]

good

what about ln(x)?

[honest cliff]

it's domain is opposite of exponential function's so that means all positive numbers

[coral jewel]

good, so x > 0

now what about ln(-x)?

[honest cliff]

x<0