help-19

[light zodiac]

Wth is this😭

Is it C

[mystic saffron]

yes

[light zodiac]

Woo

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[mystic saffron]

.reopen

[junior ether]

is 0'th root always undefined

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[humble light]

Can someone help me with problem 49

I have to sketch at least one cycle of the graph

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@humble light Has your question been resolved?

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[mystic saffron]

im confused how to solve this

what consitiutes it being zero?

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@mystic saffron Has your question been resolved?

[mystic saffron]

nvm I did it and there were no "zero" answers even though it was a choice

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[obtuse rivet]

For these two problems I need to find f(g(x)) and g(f(x)). Can someone walk me through it?

[main creek]

what is x equal to in f(g(x))?

[obtuse rivet]

3sqrt(x+1/x^3)

[main creek]

yup

use brackets

$\sqrt[3]{\frac{x+1}{x^{3}}}$

[clever fjord]

saad

[obtuse rivet]

Is that the final answer?

@main creek

[main creek]

yeah

thats f(g(x))

[obtuse rivet]

Oh ok I thought there would be more to it

[obtuse rivet]

And this is g(f(x)) right?

[main creek]

yes

please use brackets

[obtuse rivet]

What do you mean?

[main creek]

i mean you could simplify it a bit

but they probably dont want you to do that

[main creek]

$\frac {\sqrt[3]{x} + 1}{(\sqrt[3]{x})^{3}}$

[clever fjord]

saad

[obtuse rivet]

Oh I’m not sure how to do that bot

[main creek]

no no, im just saying that you should use brackets

even on paper

[obtuse rivet]

Oh

[odd edge]

@obtuse rivet Has your question been resolved?

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[livid briar]

It's not that much, but I've read a little bit of combinatorics (got to permutations and combinations) and as I read some abstract algebra, I had to deal with associativity of a set of two elements, and I got 8 different outcomes, but I can't imagine atm the possible number of elements/lengths to get 8 cases

[livid briar]

Because I've got
a a a
a a b
a b a
b a a
a b b
b b a
b a b
b b b

for possible cases

For permutations I know:
P_r^n = n!/(n-r)!

and for combinations:
C_r^n = n!/(r!(n-r)!)

I think

I'm just unsure how to get 8 cases from what I've read, or if there's something else that I'm unaware of

After thinking of it, I see it's probably because of 2 elements and three spaces, so 2^3.
And thinking of length 2, I get
a,a
a,b
b,a
b,b

Which is 2^2

Is it that simple for a set of two elements? 2^n, where n is the length needed

Or, n^r, where n = number of elements in a set and r = the length of the result?

[static totem]

i don't understand the question

uh yes

n^r

[livid briar]

I'm sorry, I'm just asking for clarification on why I get eight cases when I have two elements in a set

[static totem]

cases of what

[livid briar]

For associativity on a set of two elements

[static totem]

i don't understand what it means

if your outcomes are sets, you use stars and bars

then it's not 8

[static totem]

if you;re sure it's 8, then you do n^r

[livid briar]

In the set of {a, b} where I have to prove * is associative

I was being a bit dumb and wondering why it's 8 cases, but I think talking about it helped me understand lol

[livid briar]

wdym by this?

I realized it's 3am and I'm trying to find reasonings, it might be best to sleep on it for now to see if I have questions later lol

ty!

Forgot to close mb

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[shy agate]

determine the acceleration, I got 0.25ms^-2

can somebody check if correct

nvm I found it

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[mystic saffron]

can someone help me with this problem

[light burrow]

assume an integer a has two representations of that form, subtract them and try to find a contradiction

[mystic saffron]

ah ok

can i just use comparison of terms

[crisp wadi]

Prove existence before that though

[mystic saffron]

there was a proof above alr

this one

[crisp wadi]

That's not a proof, they simply stated that to be true

[mystic saffron]

the proof of the above

[odd edge]

@mystic saffron Has your question been resolved?

[weary pelican]

find a way to link this back to your basis representation theorem

[odd edge]

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[normal mauve]

Hi. I am new to trig integrals, could someone please check my work?

[clever fjord]

themathboi #2137

[upbeat drum]

yup

[normal mauve]

thanks : )

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[karmic bloom]

Pretty easy problem, but I am not sure if I am right. So I have the set A = {a, b, c}, and I must find the number of subsets. I did the sum of all the aranjements [A of 3 taken by 1 + A of 3 taken by 2 + A of 3 taken by 3], and I got 15. This should be the correct answer, since it doesn't ask me for a specific type of subset, ordered or unordered, right?

[karmic bloom]

Like, isn't {a, b} different from {b, a}? Their order is different, thus making them different subsets.

I know the formula says 2^n, where n is the number of elements the set has, but I just can't wrap my head around it.

[zenith jasper]

not different

sets are irrespective of order

just the elements they contain

[karmic bloom]

Oh, alright, gotchu.

Thanks.

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[vapid flint]

Can someone help with the graph

[vapid flint]

I dont know if it should be > or < since its y intercept is b

[long tinsel]

Can you get the equation of the line

[vapid flint]

sure

[long tinsel]

What would it be?

[vapid flint]

y (?) 3/4x

idk the inequality

[long tinsel]

That's fine we need the line for now

So you can put an = sign in there

rewrite it like y - 3x/4 = 0

Now all you need to do is test a point above and below the line

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@vapid flint Has your question been resolved?

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[dense zenith]

Help me i don't understand which one is the missing one in this picture

[upbeat drum]

remember that everything is enlarged by x3

[dense zenith]

ik

[upbeat drum]

so the position of the vertex will be also x3

[dense zenith]

ok

[wicked nest]

take the left bottom corner, how much do you need to "walk" up and right to get to the middle corner?

[dense zenith]

where exactly

can you show pls

thre no middle in the shape

do you mean point d?

[wicked nest]

wait lemme try to mark everything

[dense zenith]

k

[dense zenith]

thats point D

1 up 1 right

[wicked nest]

ok, so in a 3 times enlarged picture, how much would you need to walk?

[dense zenith]

enlarged would be 3 up 3 right

[wicked nest]

so do it and you'll get the answer

[dense zenith]

D

from bottom left corner?

[wicked nest]

👍

yes

well that's the answer then

any other questions?

[dense zenith]

i still don't get why point D tho

[wicked nest]

cuz you go 3 up and 3 right from the left bottom corner

[dense zenith]

why the bottom left corner?

[wicked nest]

cuz in the little diagram you walked 1 and 1 from the bottom left corner

[dense zenith]

also how do you know you need to go vertex D

hmm

would 3 up and 2 right work?

in the little one

[wicked nest]

3 up and 2 right won't work, since it would get you to a different corner

[dense zenith]

yeh lemm see if the answer is correct

it worked

so i always start from bottom left?

[wicked nest]

not neccescarely

[dense zenith]

ok

[wicked nest]

you can start from wherever you want

[dense zenith]

ok

mhm

[wicked nest]

but no matter where you start, you need to check how much you need to go from each corner

[dense zenith]

oh ok

ty

[wicked nest]

let's say you started from the upper right corner

[dense zenith]

that makes sense

[wicked nest]

how much would you need to go to get to the mid corner?

[dense zenith]

hmm

3 up 3 right

[wicked nest]

nope

[dense zenith]

heh

[wicked nest]

this time we started from a different corner

the upper right

[dense zenith]

Oooh

1 left 2 down

3 left 6 down

[wicked nest]

yes

[dense zenith]

to point d

ok ty sm

sir

[wicked nest]

yay im glad i helped

bye

[dense zenith]

bye

.close

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[dense zenith]

Hello

[dense zenith]

I don't get this question

idk where the "cross" is

[tall veldt]

the red cross in the bottom right?

[dense zenith]

yeh

idk what to do tho

[tall veldt]

why did you say "idk where the cross is"

[dense zenith]

cuz im stupid

help me pls

[dense zenith]

smart man

[tall veldt]

look in your notes for what happens to point under enlargements

https://www.bbc.co.uk/bitesize/guides/z9jpv9q/revision/6

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@dense zenith Has your question been resolved?

[dense zenith]

.close

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[hoary pendant]

Hi, I have a constrained optimisation question

[hoary pendant]

Basically, a frustum is connected to a cylinder of radius R = 4.14cm. With this in mind, how do I minimise surface area for a constant frustum volume?

I’m not sure how to solve it, but I did a few partial derivatives as I assumed those would be helpful

<@&286206848099549185>

@jolly lantern

@rancid moat Sorry I’m not sure how this works so apologies if you’re not part of this channel

.close

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[keen lodge]

a is a real number and I=[-a,a] . prove that all fonctions f: I -> R can be written as a sum of an even fonction and an odd fonction

[low locust]

lets say f(x)=g(x)+h(x) where g is odd and h is even

what can you say about f(-x)

[upbeat drum]

f(-x)=-g(x)+h(x)

probably neither?

[low locust]

what happens if you now add the two equations you have

[upbeat drum]

oh i stumbled thinking this was the actual question sorry

[keen lodge]

f(-x)=g(-x)+h(-x)

[low locust]

and now use that g is odd and h is even

[keen lodge]

h(x)-g(x)

=f(-x)

[low locust]

.

[keen lodge]

we get f(x)+f(-x)=2g(x)

[odd edge]

@keen lodge Has your question been resolved?

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[neon shuttle]

Hi

[brisk fulcrum]

Wassup

[toxic rose]

.close

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[eternal cave]

Help me simplify A and calculate P

[void yew]

What a ni e looking problem

[upbeat drum]

$A=\frac{x^2+y^2}{\sqrt{x^2-y^2}}(\frac{\sqrt{x-y}(\sqrt{x+y}-\sqrt{x-y})}{x+y-(x-y)}+\frac{\sqrt{x-y}\sqrt{x-y}}{\sqrt{x-y}(\sqrt{x+y}-\sqrt{x-y})})$

i'm going to kill a family of 5

[clever fjord]

chlamydia

[upbeat drum]

this is literally your fault'

[void yew]

my family has 5 people

[upbeat drum]

$\frac{x^2+y^2}{\sqrt{x+y}}(\frac{\sqrt{x+y}-\sqrt{x-y}}{2y}+\frac1{\sqrt{x+y}-\sqrt{x-y}}})$

bruh

[clever fjord]

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

[upbeat drum]

$\frac{x^2+y^2}{2y\sqrt{x+y}}(\frac{x+y-(x-y)+2y}{\sqrt{x+y}-\sqrt{x-y}})$

[clever fjord]

chlamydia

[upbeat drum]

$\frac{2(x^2+y^2)}{x+y-\sqrt{x^2-y^2}}$

probably wrong

[clever fjord]

chlamydia

[upbeat drum]

and Q2 implies each term=0 separately

fknlmao

[eternal cave]

I've just had a mistake with my latex

[upbeat drum]

by the way, have you even tried doing these questions

!status

[odd edge]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[upbeat drum]

it just seems like tedious algebra

[eternal cave]

2

now what?

[tall iris]

gl

[eternal cave]

?

[tall iris]

(good luck)

[eternal cave]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185> ?

.close

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[vivid tide]

part i() i got 7sin(theta+51.8) noit sure how this would help for part b

[vivid tide]

ive noticed they changed the beta and the angle is there something i can use from part i to helpm with part b?

[dusty breach]

hello, I need help, I need at least 30 answers to the question "what is your favorite color" (chart), please click on your favorite color

[tight crescent]

Please vanish

[dusty breach]

why

[vivid tide]

frrr im here looking for help and this guy wants to know my favourite color

[dusty breach]

I'VE GOT A HOMEWORK FOR A MATH!

[odd edge]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[dusty breach]

ok bot

[mystic saffron]

you could help me 😉 im in channel 41

[lavish osprey]

wtf is up with people infiltrating these channels?!?

[odd edge]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, and no one person can be prioritized over other people, so please patiently wait. Anyone who chooses to help you is a volunteer who is doing so out of their own kindness.

[mystic saffron]

appologies

[odd edge]

@vivid tide Has your question been resolved?

[vivid tide]

<@&286206848099549185>

[odd edge]

@vivid tide Has your question been resolved?

[odd edge]

@vivid tide Has your question been resolved?

[odd edge]

@vivid tide Has your question been resolved?

[vivid tide]

<@&286206848099549185>

[limpid plume]

it looks like they want you to convert a sin to a cos or something like that

[vivid tide]

thats what ive been trying to do

i just cant see it

[limpid plume]

wait I completely misread the question LMAO

[vivid tide]

oh

LMao

[limpid plume]

oh wait

did you try expanding using the cos addition formulas?

[vivid tide]

yep

let me write it out

(5cos1/3bcos(-40)-5sin1/3bsin(-40))+(3cos1/3bcos(20)-3sin1/3bsin(20))

now if i try using an identity like sinx=cos(90-x) it dosent get me anywher

[limpid plume]

wait lemme see

hmm

there has to be a trick somewhere

[vivid tide]

yr

ye ik

i just cant see it

part a the anser is 7sin(x+51.8)

[storm fiber]

Notice that the difference between both the angles is 60 degree

[vivid tide]

ye i see where you going at

how does that help

[storm fiber]

If you write the first angle as a new variable x, i.e. b/3 - 40 = x then you can write the equation as
5cos(x) + 3 cos(x+60) = 3

Now try to proceed from here, like you did earlier

[vivid tide]

i tried doing that from the beging

but just didnt look right

oh

[storm fiber]

Did you try to solve this specifically

[vivid tide]

ina i tried doing 7sinx+51.8= b/3-40.
thats where i went wrong i see where your going let me try work it out now

[vivid tide]

using addition formula?

[storm fiber]

Yeah expand the second angle

I mean expand the second term using cos(A+B) YEAH

[vivid tide]

5cosx +3cosx+3cos60 or
5cosx+3cosxcos60-3sinxsin60=3

lol

[storm fiber]

Do you know the formula for cos(A+B) ?

Do you think it's the first or latter

[vivid tide]

ye cos CosACosB+-SinAsinB?

[storm fiber]

cos(A+B) = CosACosB-SinAsinB yeah

[vivid tide]

ye? so 5cosx+3cosxcos60-3sinxsin60=3?

[storm fiber]

Yep 🙂

[vivid tide]

now what lol

cos 60 =1/2

sin 60 = root3/2

[storm fiber]

So how does the simplified equation look now?

[vivid tide]

13/2cos(x)-3root3/2sinx=3?

[storm fiber]

Yess

Now got any idea how to proceed from here?

[vivid tide]

now im thinking make tan x but that dont work

urmm hmm

[storm fiber]

Hint: you've already done the part i)

[vivid tide]

wait what

it canb be 7sin(x+51.8)=3?

ohj

OH

OMG

[storm fiber]

HAHAHA

[vivid tide]

put it into r(theta

right?

[storm fiber]

That OH

XD

[vivid tide]

BERO

IVE BEEN DOPINF THIS QUYESTION

FORE 2 HOURS

and u just come here liek WELL ACTUALLY

[storm fiber]

Ok so if you assume b/3+20 = x then b/3-40 becomes x-60

[vivid tide]

wait forgot about that tbh Lmao

do i do r theta thing then just sub it in

[storm fiber]

It's basically 5cos(X-60) + 3cosX = 3

And since you already transformed 5cos(X-60) + 3cosX to 7sin(x+51.8) in first part

So you can just substitute it and find the value of X and then from there, find beta

[vivid tide]

wait wait u lost me

so im i turning 13/2cos(x)-3root3/2sinx=3? back into r theta form then subbing in x

[storm fiber]

Ok so

[storm fiber]

Forget about it for now

[vivid tide]

ok

[storm fiber]

Let's go back to the original equation and substitute the second angle as X

earlier i told you to assume first angle as X

But it would be better if you did that for the second

Cos then

the first angle becomes X-60

[vivid tide]

5cosx+3cosxcos60-3sinxsin60=3?

this equation?

[storm fiber]

And it becomes 5cos(X-60) + 3cosX = 3

The one printed in your ss

[vivid tide]

oh yes

5cos(theta-60) + 3cos theta

[storm fiber]

I'm talking about the original one in ur ss

Yeah you could assume theta = beta / 3 + 20

[storm fiber]

And arrive at this

[vivid tide]

5cos(b/3-60)+3cos1/3b-40

[storm fiber]

Now you should know how to simplify this expression to a simpler trigonometric function (because you alr did the exact same thing in part i) )

[storm fiber]

So if you assume b/3+20 = theta

Second term becomes 3costheta

And the first term = 5cos(b/3-40) = 5cos(b/3+20 -60) = 5cos(theta - 60)

Just look at the original equation printed in your ss

I'm referring to that

[vivid tide]

whats the point of this? 13/2cos(x)-3root3/2sinx=3? why cant i use this

[storm fiber]

You can

[storm fiber]

But if you use this one then it's easier since you already solved it earlier

[vivid tide]

i suppose but tbh probs perfer method 1 dont mind it taking an extra 2 min then looking for short cuts

[storm fiber]

Because you can then say that the left hand side of the equation = 7sin(theta+51.8)

[storm fiber]

Yeah whatever works

But the question's earlier parts are suggesting and encouraging you to transform it into the 5cos(x-60) + 3cosx form

But you can technically use any method, I think

It is correct

[vivid tide]

why we assuming 1/3b +20 = theta

i see what u mean now

thank you so much bttw

[odd edge]

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[hollow hearth]

Is it a system or something else?

[tepid yacht]

What on earth does this even mean?

[zinc glacier]

Is this a pattern recognition question?

[hollow hearth]

That’s what I’m trying to figure out

[tepid yacht]

Can you post the original question?

[zinc glacier]

Oh

[hollow hearth]

So it’s like a function?

[tepid yacht]

Tbh, just excel or some other application that does function approximation

[zinc glacier]

I dont think that will work since its angles vs distance

Im blanking on how to do this

[dry scarab]

ballistic trajectory go brrr

can you draw a diagram with distances to dot and tank?

and if there is friction

[tepid yacht]

.close

[odd edge]

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[tepid yacht]

Btw this

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[frozen bear]

All of the answers are wrong wtf?

[odd edge]

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[mystic saffron]

I need help with this problem please

So I think I have to use chain rule

And maybe product rule

This is what I got so far

I found the inside and outside functions

And their derivative

[bronze cradle]

How many functions do you see in there?

[mystic saffron]

2

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[rotund garnet]

can someone teach me how to simplify numbers with a negative fraction exponent? for example

-2/5 x^-4/5 +12x^2

how would I simplify that?

[dry scarab]

,tex .exp rules

[clever fjord]

ils

[dry scarab]

usually the term with fractional exponent should be at the numerator

[rotund garnet]

may you provide me with an example?

[dry scarab]

1/sqrt(x) should be sqrt(x)/x

[odd edge]

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[mystic saffron]

Let m/n be a fraction, where m and n are positive integers. Consider the operation defined by replacing m/n by (m+1)/(n+1) and then writing the result in lowest terms. For example, applying this operation to 5/14 would give 2/5. How many times must this operation be repeatedly applied to 1/2005 before we obtain 2004/2005?

[mystic saffron]

I don't know where to start

[void yew]

it ends up reducing to solving a linear equation

sooo you can let k be the number of steps

Then what is m/n after k steps in terms of m, n, and k?

[odd edge]

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[soft compass]

Hi i need help

[soft compass]

I need to isolate for PMT

This is beyond my abilities

😭

[merry finch]

I just see $a = Xb + Xc$

[clever fjord]

Frosst

[merry finch]

a b c are constants

[soft compass]

formula without numbers :

[merry finch]

X is what you want to solve for

[merry finch]

How do you make X the subject here?

[soft compass]

yeah but they are divided and liftet up in the power of t

[merry finch]

Literally makes no sifference to me

[soft compass]

i say 2xbc

no?

[merry finch]

You can’t just add them what

[soft compass]

idk

idk how i got into uni

[merry finch]

14 = 6 + 8 = 2*3 + 2*4 ≠ 2*2*3*4 = 48

How do you make $x$ the subject in $2x + 3x = 1$

[clever fjord]

Frosst

[soft compass]

5x/5=1/5

riiiight?

[merry finch]

That is not correct notation

[merry finch]

Ok what if I have

$ax+2x = 5$

[clever fjord]

Frosst

[soft compass]

3x=5+a?

[merry finch]

How did you do that

[soft compass]

you said this bro

so i said ax+2x=5

a* x + 2* x

[merry finch]

I said it’s not equal to

[soft compass]

riight

[merry finch]

I was giving an example which would otherwise show that 14 = 48

Which is clearly not true

[soft compass]

you are right

i have to make a the subject

right

so i transfer 2x to the other side

ax = 5-2x

then i need to get rid of x

so i say ax/x = 5-2x/x

right

[merry finch]

You are not trying to get rid of x

You are trying to make x the subject

Do you know what it means to make x the subject?

[soft compass]

no

or wait

[merry finch]

It means you have x = something

[soft compass]

yeah okay

i take the ax the other side

2x = 5 - ax

2x/2= 5 - ax/2

x= 2.5 - 0.5ax

🤨

[merry finch]

You still have x on both sides

This is elementary algebra, you should go back and revise the topics of algebra again

But for now, have you heard of factorisation?

[soft compass]

i am on my 2nd year at the top uni in my country 😭

[merry finch]

That doesn’t matter you can always go back and revise earlier topics

[soft compass]

yeah i used to be good at this stuff

[merry finch]

That’s okay, just get back into the rhythm

[merry finch]

Anyhow, this?

[soft compass]

im not an english speaker so let me search it up

[merry finch]

$ax+bx = (a+b)x$

[clever fjord]

Frosst

[soft compass]

yeah

[merry finch]

Try using this here

[merry finch]

Btw do you know where this comes from

[soft compass]

greece

[merry finch]

Lol

[soft compass]

lol

[merry finch]

No it comes from the actual definition of + and *

[soft compass]

(a+2)x

[merry finch]

The definition of + and * tells us this is possible

[merry finch]

And then?

[soft compass]

we take the (a+2) to the other side

and because it is * x

it needs to be divded

so

[merry finch]

Where is the other side

[soft compass]

x = 5/(a+2)

[merry finch]

Ok good

[merry finch]

All the numbers

They are just constants

They are just some number on the real line

It really doesn’t matter what number they are precisely

[merry finch]

Do you see how this adequately represents the formula

The a, b and c’s don’t depend on X (or PMT in your case)

[soft compass]

hmm

so you are saying

i have to put everything in ()*PMT

[merry finch]

Yep

If the part doesn’t have PMT in it then it’s a constant in the eyes of PMT

It turns into and a, b, c sort of thing

Also the capital X doesn’t mean anything I just capitalised it to emphasise that is what we want to isolate

[soft compass]

but here we have

2 pmts with different values in the equation

[merry finch]

They have the same value

[soft compass]

i mean the numbers that it is multiplying

((1+0,05885)^9-1)/0,05885

and ((1+0,018399)^2-1)/(0,018399)

you are saying they are just constants

[merry finch]

These are just some numbers

I can just put them into a calculator and get 1 number out of them

[soft compass]

so i can just say

[merry finch]

They are the same as 5PMT + 4PMT

Woah

[soft compass]

like this?

[merry finch]

What happened to the end

[merry finch]

Look

[soft compass]

yes?

[soft compass]

(a b c)pmt

[merry finch]

Where’s the end bit

[soft compass]

ye?

[merry finch]

You’re missing the last bracket

Look at the green part

[soft compass]

oh right

so like this?

[merry finch]

Yes

[merry finch]

Yes

I’m not looking exactly but that’s the idea

[soft compass]

so it gives the same now

[merry finch]

Yep

[soft compass]

when i insert the PMT we found into the formula

it gives us the number infront of the = in the start

which means this is the correct PMT

we isolated it CORRECTLY!

[merry finch]

Yep

Why is it a bit different to the given number though?

[soft compass]

this one gives almost the same

only with ,1 difference

[merry finch]

Yeah but it’s not exact

Why isn’t it exact?

[soft compass]

because i rounded up and down some things i believe

let me try with the exact settinghs

[merry finch]

Where

[soft compass]

let me look

the original number was ,02

i cant quite see why

it became ,1

[merry finch]

It’s just rounding error

That’s all I wanted you to also be aware of

[soft compass]

Okay thank you, i will just remove the ,1 and hope the professor doesnt realize lool

https://tenor.com/view/funny-laugh-gif-25603013

But thank you so much, you dont know how much it means to me 🙏

[merry finch]

👍

[soft compass]

https://tenor.com/view/thanks-thank-you-thank-you-very-much-thanks-a-lot-crypto-gif-27338631

i hope u have a good life bro

good future

good family

more money more life your way

[merry finch]

All the best to you too! c:

[soft compass]

thanks

[odd edge]

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[mystic saffron]

Many income tax systems are calculated using a tiered method. Under
a certain tax law, the first $100 000 of earnings are subject to a 35%
tax; earnings greater than $100 000 and up to $500 000 are subject to
a 45% tax. Any earnings greater than $500 000 are taxed at 55%.
Write a piecewise function that models this situation.

[odd edge]

Please don't occupy multiple help channels.

[mystic saffron]

ok

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

no

hello?

[mystic saffron]

.close

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[sinful radish]

Abt the squeeze theorem, why does it have to be limits, why isn't it just: for g(x) smaller or = f(x) smaller or = h(x) , if g(a) = L & h(a) = L then f(a) = L

[gleaming turtle]

!help

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[gleaming turtle]

That's also true, it's just not the squeeze theorem

Open a new channel

[odd edge]

@sinful radish Has your question been resolved?

[reef sandal]

I mean it's not limited to only limits if you think about it

Pun intended

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[spark yarrow]

I've figured out the numerator using the constant, power, and identity rule but when I use the power rule on the denominator it tells me I'm wrong.. not sure what to do to solve it

[fossil cedar]

No bro

You use the quotient rule

[copper quarry]

illegal

[spark yarrow]

Lol what

[copper quarry]

you can’t do that

[fossil cedar]

💀

[spark yarrow]

Oh ahaha

[fossil cedar]

Yeah u can't

[copper quarry]

you can’t separately differentiate whatever part of the fraction you like

[fossil cedar]

Yeah you have to use quotient rule

Which is u'(x) * v(x) -u(x)*v'(x)/v(x)^2

[copper quarry]

Or you can use product and chain if you really wanted to

[spark yarrow]

Is there another way other than quotient rule, my professor doesnt want us using it, or the product or chain rules....

[fossil cedar]

Hmm???

[spark yarrow]

He taught us power, id, constant, logarithm, sum & difference rules but he wont give credit for work with those three rules

[copper quarry]

i mean

You can use first principles 💀

But you’re not going to have a fun time

[fossil cedar]

Hell nah bruh

Ye XD

[spark yarrow]

oh no XD

Yeah this whole hw assignment is a pain

[copper quarry]

honestly just take the no extra credit man ain’t no way anyone be first principling that

[spark yarrow]

we'll see

i have a 42 right now so i dont know if its the best idea lol

[fossil cedar]

YE

[copper quarry]

Maybe do it then

[fossil cedar]

UR alg has to be exceptionally good to be using first principle too

Cos so easy to make mistake

[spark yarrow]

nah i got this

so i gotta start over then right

[fossil cedar]

Gl

[spark yarrow]

thanks

ill be back if i die

.close

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[void yew]

Er did u mean to write z-pi instead of z-z

hmm nvm z - pi wouldn't help

yeah

yeah

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[tidal harbor]

Suppose that f : [−3, ∞) → [−8, ∞)

Here what does the arrow mean?

Or the arrow here?

[gleaming turtle]

The syntax here means "f is a function from the set A to the set R"

[tidal harbor]

: means such that right?

[gleaming turtle]

It can mean such that. I suppose you can read the second : in the screenshot as such that

[wooden python]

not here no

: and -> are just part of the same notation

the function signature

<function name> : <domain> → <codomain>

[tidal harbor]

What about the : after the codomain?

[wooden python]

that might just be a plain-english colon?

can you uncrop your image

[tidal harbor]

Here

[gleaming turtle]

I don't think that second colon is standard notation, it just seems to be used as a generic separator here.

"such that" wouldn't be a terrible way of reading it tbh
"the function f from A to R such that x maps to sin x"

[odd edge]

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[limber comet]

This is the answer i got to this question

But the answer given is 1/2 of this and I don't understand why

[noble forge]

are you given with the bounds?

[limber comet]

no

its indefinite

[noble forge]

,w indefinite integral of 1/sqrt(1+4x^2)dx

[limber comet]

what

thats completely wrong

[clever fjord]

Results provided by WolframAlpha

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

Requested by beard420

[limber comet]

bruh

[noble forge]

well, there are alternate forms

[limber comet]

wdym

but its the answer given everywhere online as well

i just directly applied the formula

they expanded it in weird ways

when there's no need to

[lean willow]

Lucky you

[limber comet]

why do we need the 1/2 😭

[reef sandal]

Show me your entire work

[limber comet]

that is my entire work

[limber comet]

.

[reef sandal]

Well I mean it doesn't show much intermediate work

What did you set 2x to

[limber comet]

theres no need of intermeidate work bro

[reef sandal]

Or a to

a = 2x?

[limber comet]

yes

no

x = 2x

[reef sandal]

Oh no I see you used an identity

[limber comet]

a = 1

yeah

i did

[reef sandal]

You need the one half because of chain rule

The derivative of 2x is 2

But clearly you don't want that 2

[limber comet]

this identity

[reef sandal]

1/2 will just "neutralize" the effect of the chain rule

Because let's assume you let u = 2x

Do a u-sub here

Then 1/2 du = dx

$\frac12 \int\frac{1}{\sqrt{1 + u^2}} \dd u$

[clever fjord]

Umbraleviathan

[limber comet]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

because if you take 1/2 outside you only have x^2 left inside

and then you dont need chain rule

got it bro thanks

[reef sandal]

Yeah

And then if you were confused about the arcsinh(2x) thing wolfram kicked out

$\ln(\sqrt{1 + x^2} + x) = \text{arcsinh}(x)$

Bruh

Dumbass bit

[clever fjord]

Umbraleviathan

[reef sandal]

There

So it's going the short route with the identity

[limber comet]

i see

so whenever we have questions like this

we just ensure the coeff of x^2 should always be one

and then complete the square accordingly

thanks man

[reef sandal]

Np

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[hollow warren]

can someone help me solve the one i got wrong pls

[hollow warren]

oh wait i think i put the q without realizing

nvm i deleted it and it says im submitting the same answer

[uncut remnant]

34i/29 isnt a + bi maybe?

(34/29)i is

[hollow warren]

o

[uncut remnant]

or to be pedantic

0 + (34/29)i

[grizzled tide]

it's asking for b specifically

[uncut remnant]

oh right yeah, better answer, didnt see.

[grizzled tide]

,w simplify (7+4i)/(5-2i)

[hollow warren]

so would i only put 34i?

[clever fjord]

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[grizzled tide]

ok ur answer is right ur software just sucks

[uncut remnant]

no it isnt?

ur right they put the wrong thing in

a+bi form

a and b are real numbers

if u enter a non-real number into the field, thats wrong.

[grizzled tide]

oh of course

yeah that's right

[hollow warren]

so then how would i write it, im still a bit lost haha

[grizzled tide]

remove the i

b is real

[uncut remnant]

write for us your answer in a+bi form

like the entire thing

then identify what a and b must be

[hollow warren]

like you want to see my work?

[hollow warren]

oh, I thought the i was needed in the answer

[uncut remnant]

what is your final answer

a+bi

[grizzled tide]

ok to be fair while the answer they put in is wrong, they did clearly understand the math they were intended to be doing, so while the software is correctly saying the answer is wrong Id still argue it's poorly designed

[hollow warren]

i ended with 27 + 34i/ 29 + 0i

then simplified it to

a= 27/29
b= 34i/29

[uncut remnant]

,,\frac{27+34i}{29}

[uncut remnant]

is that correct?

[hollow warren]

yeah

[uncut remnant]

then you need to simplify further

so separate the real and imaginary parts

what can you do?

[uncut remnant]

like whats the next step on this

[hollow warren]

uh, im not sure, for this step i just turned it into

27/29 and 34i/29

[uncut remnant]

youre distributing division over addition

,,\frac{27+34i}{29}= \frac{27}{29}+\frac{34i}{29}

[uncut remnant]

but thats still not a + bi form

(ci)/d = (c/d)i

focus on what ive said, does it make sense?

,,\frac{27+34i}{29}= \frac{27}{29}+\frac{34i}{29}=\frac{27}{29}+\frac{34}{29}i

[uncut remnant]

first distribute the division.
Then observe the order of multiplication and division doesnt matter

now the final thing on the right is in a + bi form

and you can tell me what a and b are.

yes

a + bi form means u wanna get it to look like ??? + ???i where the ??? are real numbers

[odd edge]

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[high isle]

Hi

[wooden python]

hello, do you have a question to ask?

[high isle]

Yes

[wooden python]

ok then you should ask it, not just say hi.

[high isle]

I am trying to translate it

[wooden python]

!original

[odd edge]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[high isle]

Okey

Show that 30℅ of the flag is yellow

[wooden python]

ok

progress?

[high isle]

I dont understand how to get the answer i want to know if anyone know how to do it

[wooden python]

do you know generally how to find the area of a rectangle?

[high isle]

Yes

[wooden python]

ok

can you find the area of the whole flag?

[high isle]

8a * 5a = 40a

@wooden python

[wooden python]

not 40a

40a^2

[high isle]

How did it become ^2

[wooden python]

ok now find the yellow area. you can do it either as two rectangles minus a square, or five rectangles.

[high isle]

8a *a

[wooden python]

a * a = a^2

[high isle]

8a^2

[wooden python]

this is not the yellow area

you didn't count it all

[high isle]

.close

[odd edge]

Channel closed

Closed by @high isle

Use .reopen if this was a mistake.

[high isle]

Thx for the help got the answer

.close

[odd edge]

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[nocturne basin]

I have to determine whether this series diverges or converges by using the divergence test (I think), but I'm not sure on how to start. I think I need to use L'hopitals

[uncut remnant]

inf/inf form in limit is indeterminate

u have not determined anything about that limit

[nocturne basin]

I can use l'hopitals rule to differentiate it, though

[uncut remnant]

then do so.

[nocturne basin]

I had the feeling that differentiating the bottom term would be incorrect because it would be very long

is l'hopitals really the correct way to do it

this is how pearson suggested to do it, but I'm really confused on how the denominator divided in the second step

[reef plover]

u remember that trick with limits where you divide the entire thing by the highest degree term?

that's basically what you're doing here, to get rid of the variables that are causing the limit to be indetermindate

[nocturne basin]

I understand it mathematically probably

I just don't get how the denominator turned out like that

[reef plover]

because the square root of k^8 is k^4

[nocturne basin]

this is what I have right now

[reef plover]

they're rewriting it in a way that it fits under the radical

[nocturne basin]

wait that's crazy

[reef plover]

yeah idk why they always use these shortcuts without explaining

[nocturne basin]

I hope that they can get like AI integration when it gets good enough to reliably explain calc

to explain stuff

still trying to wrap my hea daround it

[reef plover]

lemme see if i can draw an example to show whats happening

[nocturne basin]

sorry it's sideways lol

an illustration would be appreciated thank you a lot

yahoo
(I accidentally wrote the wrong problem up there btw but they are functionally equivalent so any explanation that you provide is still valid)

I just feel like the problem was saying that logic like this is true, when it doesn't seem true at all, so I'm confused on how they were allowed to do that division under the sqroot

[reef plover]

the logic is weird because its not traditional algebra. its one of those weird limit tricks

you basically deduct the highest degree term from every variable which should leave you with only constants (only for limits going to zero)

[nocturne basin]

but I see all of this as one variable so it's weird to me how you can treat them as separate things

[reef plover]

i keep erasing my thingy but ill have it in a sec lol

ill rephrase that it is real algebra, it just takes a bit to recognize what exactly they did to get there sometimes haha im ngl I had to rewrite that quite a few times

[reef plover]

lim should be to infinity not 0! yeesh i should go to bed soon

its not that bad 😂

[nocturne basin]

ohhh it makes sense now

https://tenor.com/view/patrick-bateman-silly-me-oh-silly-me-patrick-bateman-gif-25589956

[reef plover]

got it okay? dontcha love it when they skip over the most important steps

[nocturne basin]

yeah
thank you pearson 😩

and thank you stripbubbles

🥂

[reef plover]

haha np, been there before

[nocturne basin]

have a good rest

.close

[odd edge]

Channel closed

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[odd edge]

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Send your question here to claim the channel.

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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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• Be polite and have a nice day!

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[heavy birch]

I need help wtih this math problem

[upbeat drum]

!status

[odd edge]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[heavy birch]

4

basically we have to determine if it is a function or not. For that, we had to first simplify the problem. I got the answer but there is that part where i had to multiply both sides.

And I want to know why you multiply both sides instead of cross multiplying?

By the way my final answer is, it is a function

[uncut remnant]

cross multiplying isnt a thing

a/b = c/d -> ad = bc
is the act of multiplying both sides by bd

[heavy birch]

oh

well when we derive formulas, dont we cross multiply? Or was I just misconcepted

[uncut remnant]

read what I wrote carefully

[heavy birch]

so there's no such thing as cross multiplication? instead that concept is actually just multiplying both sides with bd?

[uncut remnant]

correct.

[uncut remnant]

or more like - just forget about "cross multiplication" as a thing, remember its just this.

one less thing to remember, and it tells u exactly why it works

[heavy birch]

i see

one more thing

[uncut remnant]

what the fuck is thissssss

its absolutely awful

using x as a multiplication symbol

[heavy birch]

why did it use (x+1)(2-x)(x+2)

[heavy birch]

haha i know right

[uncut remnant]

thats the lcm of the denominators

if these were numbers

denominators were 6 and 9 for example

you only need to multiply by 18

not 54

[heavy birch]

hmm but why did it only use (x+2) once?

[uncut remnant]

yh i explained

you can use it twice

[heavy birch]

aren't there 2 (x+2)?

[uncut remnant]

but its not necessary

,,\frac16 - \frac19

[uncut remnant]

how would u compute this?

u could make the common denom 54

[heavy birch]

so the lcd is 18 right

[uncut remnant]

or you could just make it 18

gcd

greatest common divisor

oh sht ur right

lcm is what we want mb

lowest common multiple, ive missaid everything above

so lcm of 6 and 9 is 18

and we can just focus on 18 instead of doing 54

[uncut remnant]

similarly, this is the lcm

[heavy birch]

what if i put the lcm like this: (x+1)(2-x)(x+2)(x+2)