help-0

[ruby current]

umm

[delicate widget]

, (167/570) * 100

[ruby current]

might be leaving something out in the question

maybe ticking the yes box isnt the same as what it's asking

[delicate widget]

this is the full page

[ruby current]

ohhhh

didnt realize those questions were connected

my bad

[delicate widget]

ok

how do we do it then

[ruby current]

one sixth of the time the question is marked as yes, regardless of what the person would actually answer and five sixths of the time it's up to the person. so we expect 570/6=95 of the results to be 6 by default. for the actual proportion we know that 167-95=72 people put yes out of 570-95=475 cases where it was up to them. so 72/475 * 100 is the answer

[delicate widget]

wait lemme read this

[delicate widget]

how is it 1/6th of the time ppl tick yes

167*6 would be 1002

[delicate widget]

ooo

i didnt read that

mb

ok thank u so much @ruby current i understand now

u basically have to minus 1/6th from each of the numbers and use the formulae

[ruby current]

yep

my bad i didnt see that the question was referring to the survey you posted

this

[delicate widget]

np my bad

[alpine sable]

$\frac{167-95}{570}\cdot{100}$

[ocean seal]

IDrinkWine

[ruby current]

,w evaluate (167-95)/570 * 100

[ocean seal]

Results provided by WolframAlpha

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

Requested by tushar#1234

[ruby current]

looks to be 15.2% not 12.6%

[light coyote]

how to get laplace inverse of 1/(s-2)^2

[cursive sky]

use a laplace table

[light coyote]

it doesn't have this property directly

[oblique gate]

It's a mix of two transforms from the table

the 1/(something)^2 implies a t

and the s-2, implies an e^2t

so t*(e^2t)

@light coyote

[light coyote]

Yup just going through these messages

[cursive sky]

te^(2t)

use this one

[light coyote]

Ah ok, thank u guys @oblique gate and @cursive sky

[cursive sky]

np

[oblique gate]

np

[alpine sable]

What is the radius of this? Ty :))

[wary stream]

Set that in standard circle form

$$(x-h)^2+(y-k)^2 = r^2$$

[ocean seal]

dldh06

[alpine sable]

Alr

[wary stream]

Apply completing the square method

[alpine sable]

Ty 🥰

[wary stream]

No one will help if you spam in every channel

[gloomy canopy]

👍

[slender girder]

Hello

Is this in use?

[wary stream]

I think it is open

[slender girder]

Okay

a) Find a vector equation and parametric equations for the line '
that • passes through the points (5,1, 3) and is parallel
to the vector i + 4J -2K

[merry iris]

i-hat j-hat k-hat

[slender girder]

?

[tropic sail]

i, j, k?

you working with quaternuions?

[merry iris]

i-hat j-hat k-hat are normally the unit vectors in 3D, and i think they mean i-hat j-hat k-hat

[wary stream]

Pretty sure it's i, j, k vectors. Hard to denote them using plain text

[merry iris]

$$\hat{\imath}, \hat{\jmath}, \hat{k}$$

[ocean seal]

[Cursors]

[tropic sail]

hmm, i think the imaginaries are with serif and the unit vectors are not

[merry iris]

yep

[wary stream]

That's using latex, not everyone knows how to use the bot

[merry iris]

ik im just displaying them

i + 4j - 2k = the vector (1, 4, -2)?

so we have to find a line that passes through (5, 1, 3) that is parallel to that vector

[slender girder]

yeah please help

[merry iris]

add the vector to the point

now you have two points that define a line that is parallel to the vector

does this not work how i imagine it to be?

[winter hull]

still hvnt gotten answer to it, anyone found a solution

[wary stream]

Someone did tell you the answer in a different channel

[winter hull]

where?

[wary stream]

Whichever other channel you posted in

[merry iris]

:/ effects of crossposting: dont know when you get an answer

[merry iris]

tbf they didnt get the thought process and actual method to GET the answer

you've got the roots already tho

[vocal panther]

could someone help with this?! a bit stuck

[vocal panther]

yea but we have to find abcd

d is 2 obv

[merry iris]

i thought you could just expand $$(x + 1)(x - 2)(x - 3)$$

[wary stream]

It is this

[ocean seal]

[Cursors]

[vocal panther]

huh?

[wary stream]

But you shouldn't have said this

[vocal panther]

ohhh

ok

ok thanks

yea understood

[wary stream]

The person should have figured it out themselves

[merry iris]

nooo sorry

ok well i'll try to explain

[wary stream]

There's probably no point, that person will just expand what you said to get the answer

[merry iris]

[vocal panther]

I understood broski

[twilit cedar]

Is the gradient to a surface always the surface normal at that point?

Then how would one find the direction to move on a surface such that function has a maximum change?

Is the difference f(x,y,z) = 0 being the equation of a surface vs. f(x,y,z) being a function defined on each point of a surface?

[cloud frost]

hello

i need help in math

im doing a math epw abt parabolas and i dont understand it lmao

[alpine sable]

is it c

[wary stream]

Don't think so

[alpine sable]

oh then a

[wary stream]

Do you know why it would be a?

[alpine sable]

its either a or c

bc it says shifted to the left 2 units so it has to be (-x+2)

[wary stream]

Yes

And what's the difference between A and C?

[alpine sable]

the negative

[slow acorn]

can someone dumb down the GOOGOL:1 thing for me

[alpine sable]

i thought reflected in the y axis means its negative

[wary stream]

Look it up

[slow acorn]

i have

im a year 10 and im autistic so it aint easy for me to understand

[wary stream]

There's both a negative at the beginning and and inside the parenthese

[slow acorn]

thanks for the help

[alpine sable]

i meant -1/2

[alpine sable]

so the answer is a

[merry iris]

is that a ratio?

[wary stream]

Do you know why though?

[slow acorn]

idk

[merry iris]

:/

[wary stream]

It's a number

[slow acorn]

thats why i came to you lol

[wary stream]

,w googol

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

A number with 100 zeros

[slow acorn]

what is that

really

[merry iris]

GOOGOL => "1" + 100 zeros

[slow acorn]

wow

thx

[alpine sable]

no

[slow acorn]

and before i go

[merry iris]

100 ... 96 more zeros ... 00

[alpine sable]

bc there isnt a negative reflection in the y axis

?

[slow acorn]

is the possibility of infinity real or is this an estamate we can't yet back up with math and science

[merry iris]

:/ infinity isnt a number

[slow acorn]

ik but is there anything that is truely infinite

[wary stream]

Yes

[merry iris]

numbers

there are an infinite amount of numbers

[slow acorn]

i mean in a physical form

[merry iris]

you cant prove infinity

[wary stream]

Actually it's the x axis

[merry iris]

if there is an infinite amount of anything how do you amass all of it

[slow acorn]

so then why do we call it infinite

[alpine sable]

oh

[slow acorn]

if we can't proove it

[alpine sable]

what

[wary stream]

There's no reflection across the x axis

[slow acorn]

or is the word infinite actually mean anything

[merry iris]

usually:

1. language exaggeration
2. a mathematical idea, countable infinity, uncountable infinity
3. 3rd graders using the term wrong thinking they're big brain

[slow acorn]

is it just a word?

[merry iris]

its a word that represents something

:/ you can find more on your own

[slow acorn]

but wait

is a thing a thing or is it a noun

[wary stream]

It's a concept

[fringe spindle]

well, because we can't verify it by literally summing to infinity, but we can experimentally observe what happens, and note results, like for example numbers which have infinite decimal expansion, like 1/3 or 1/6, or for example in philosophical problems such as Zeno's Paradox of Achilles and the Tortoise

[slow acorn]

ok ill be back tomorrow cuz my head hurts

cya

[fringe spindle]

ok good luck!

[slow acorn]

thx you too

[fringe spindle]

np

ty also

[coral frigate]

This channel free?

I need help with de moivres theorem lol

[fringe spindle]

seems to be

oh i can do that

[coral frigate]

Umm, if I have 2 complex numbers

a + bi

And

a - bi

Is one's argument (pi - theta) where theta is the argument of the other? If that makes sense

Im trying to do the Q right above the challenge and I cant seem to find the way

[merry iris]

well if the result is real that means the i's cancel out right?

[coral frigate]

Yeah

[merry iris]

prove that the expansion will cancel out the i's

[coral frigate]

If I take sin(theta) and add it to sin(pi - theta), do they cancel out?

[merry iris]

you're working with radians?

[coral frigate]

Ya argand diagrams are doing my head in

[merry iris]

im pretty sure that equals 0

i cant remember the trig identity

[coral frigate]

AHHh that makes sense then

[fringe spindle]

ok so, basically i think what they want you to use, is the fact that cos is an even function, whereas sin is an odd function

[coral frigate]

Tysm :)

[coral frigate]

I wish i could type what Im doing

But theres so many powers, thetas and sines that it would take forever

But I think I got it

[slow acorn]

back

couldn't sleep

teach me algebra

please

[wary stream]

If you have a specific question that you need help with

Algebra is a big branch of math

[slow acorn]

ik

[fringe spindle]

r(cos(θ) + isin(θ))^n = r^n(cos(nθ) + isin(nθ))
r(cos(θ) - isin(θ))^n = r^n(cos(nθ) - isin(nθ))

r^n(cos(θ) + isin(θ))^n + r(cos(θ) - isin(θ))^n = 2r^ncos(nθ), which is defined as the real part of a complex number, therefore real.

[slow acorn]

what

[wary stream]

That was for someone else

If you look, it was a reply to someone else

[slow acorn]

ik but it looks very complex

[coral frigate]

You do r^n too right?

[wary stream]

Because it is complex

[coral frigate]

Its irrelevant here just asking

Yeah

[slow acorn]

math scares me sometimes

[fringe spindle]

yes i messed that up, sorry, thank you for pointing that out

[wary stream]

i is a complex number

[coral frigate]

Could you post a message with just theta in it so I can copy it pls

[wary stream]

$$i = \sqrt{-1}$$

[ocean seal]

dldh06

[slow acorn]

than what is the power of -1

[fringe spindle]

θ

like that?

i don't know latex, i abandoned it after i graduated and really can't be bothered to learn it again, because, well, i went through the wars with it i'm sorry 😭

[coral frigate]

Basically I end up getting:
i(sin(nθ) + sin(n(180 - θ)))
Does this equate to 0?

[fringe spindle]

i studied all this before we descended into all this online stuff

[coral frigate]

I know the trig identity:
sin(θ) = sin(180-θ)

But idk if it applies here because there are variables

i( sin(nθ) + sin(n(180 - θ)) )

Its just this 1 line here, I need to know if it cancels out

[fringe spindle]

i don't think you need to use this. just the fact that the sum of any complex number and its conjugate are real. and using deMoivre, you can simplify (the same) powers of a complex number and its conjugate so that they re always conjugate, as they can be written in terms of sin and cos of the same angle basically

[coral frigate]

Yeah Ive just realised ive done this the long way haha

I have a habit of that

Thanks alot though, really useful :)

Im self teaching this subject and I dont know anyone else doing it

[fringe spindle]

no problem, i remember that happened to me a lot when i was studying complex numbers, the more you familiarise yourself with them, you'll get better at how to manipulate expressions involving them etc.

[alpine sable]

Can anyone help me with this: Calculate without calculator sin 2a, cos 2a, tan 2a if:

[tropic sail]

Could you translate please

[alpine sable]

Sin a=4/5 and a belongs to the 1st quadrant

[wary stream]

Do you know what thie sin ratio is?

[alpine sable]

Nopee

[slender girder]

Hello

Find parametric equations and symmetric equations of the line that passes through the points A(2,4,-3) and B(3,-1,1)

[west vine]

use this to find the parametric equation

https://cdn.discordapp.com/attachments/870251341795176478/875715927885357056/unknown.png

r0 is the first point

and r1 is the second point

then symmetric equations using this

https://cdn.discordapp.com/attachments/870251341795176478/870980147292024862/symmetric.PNG

[slender girder]

What is r1 in this case?

[west vine]

.

https://cdn.discordapp.com/attachments/870251341795176478/875723666434957352/unknown.png

[slender girder]

You using an iPad?

[west vine]

a drawing board

[dense cape]

I've taken derivatives of both functions & substituted 0 in

I get 1 for f'(x) and 0 for g'(x)

This is my work currently

So the dot product between the two should be 0, no?

This is the identity I'm using

The answer ends up being 0.758, but arcoos(0) gives me 1.57

[modern crystal]

anyone know business calculus?

[slender girder]

Wow good luck

[mighty shadow]

Yo I know the first question is right but I got the 2nd one wrong

Can someone explain where I went wrong

[merry iris]

text is too small i cant read the subscript

[mighty shadow]

One sec

[mighty shadow]

Is that better?

[merry iris]

did you compute D and have it somewhere

im too lazy to compute D myself

[mighty shadow]

Ok one sec lemme fix my handwriting

[merry iris]

or if you know latex send it here

[mighty shadow]

Idk what latex is lmao

[merry iris]

ok

[mighty shadow]

I hope this is good enough

[merry iris]

so

[ocean seal]

[Cursors]

[merry iris]

um thats not supposed to h-

oh well

[mighty shadow]

No worries I understand

One sec

[merry iris]

a31

typo

[mighty shadow]

Oh 31 gotcha

[wary stream]

Did you ever do -(9+5p)

[mighty shadow]

-7

And 7

So -7 + 7

That's 0

And then d12

I got

[merry iris]

couldnt read smol text

oh my god its so hard for me to count correctly since im a programmer (i count from 0)

[wary stream]

Don't forget $$-d_{12}$$

[ocean seal]

dldh06

[mighty shadow]

Yeah so I got -7+7-9+5p

[wary stream]

-(9+5p)

Not -9 + 5p

[merry iris]

hmm no be careful

-(9 + 5p)

[mighty shadow]

Ohhhhhhhh

So it's -9-5p

Right?

[wary stream]

Yes that

[mighty shadow]

Tysm

[merry iris]

i have massive latency damn

[mighty shadow]

I appreciate it my brain lags sometimes

Brain.exe stopped working

Tysm

[pale cloud]

i need help

is this channel free

[wary stream]

Should be now

[pale cloud]

okay i need help with this

can you explain it to me please

[wary stream]

No because I don't get it

[pale cloud]

[ionic jewel]

rectangle area is length times width

the new rectangles area is (1.1)l*(1-p)w

[alpine sable]

Ur a god

[ionic jewel]

and the new area is (1-0.12) smaller, set up a system of equations

[alpine sable]

U too, absolute god

[pale cloud]

how

[pale cloud]

how u get 1-p

how do i find p

[wary stream]

P is what you are looking for

[pale cloud]

but how do i find it

[wary stream]

Set up a system of equations, like bunny said

[pale cloud]

but i dont know what he did

[wary stream]

Channel busy

[wary stream]

Did you read what he said?

[pale cloud]

yes but "the new rectangles area is (1.1)l*(1-p)w"

why is the area this

i dont get it

1.1l times pw

i dont know where 1-p come from

[wary stream]

Because it states that the length increase and the width decreases

The width decrease by p

[merry iris]

$$0.88A = (1 + 0.10)l \cdot (1 - p)w$$

[pale cloud]

so 1.1L times (1-p)w =0.88

[merry iris]

no

0.88 * A

A being the area of the rectangle

[pale cloud]

0.88/1.1

[ocean seal]

[Cursors]

[pale cloud]

so 0.88a=(1.10L)(1w-wp)

what

[merry iris]

ok you know what

lets pretend the rectangle has an area of 100

after we transform the side lengths, it has an area of 88

if the length was increased by 10%, then by how much was the width decreased

let's say that the rectangle is actually a square (10 x 10)

then the new length is 11

if the area is 88 and the length is 11 what is the width

[pale cloud]

8

[merry iris]

right

so by how much percent did the width decrease

10 -> 8

[pale cloud]

20

[merry iris]

thats your answer

[pale cloud]

ohhhh okay ty

[subtle elbow]

can someone help me with Question 1C it confuses the hell outta me idk if it is right

<@&286206848099549185>

[wary stream]

I think it's asking for the dimension of the matrix

[merry iris]

wait 15 minutes before pinging helpers aaa

[wary stream]

Also, you have to wait at least 15 minutes before pinging helpers

[merry iris]

order = matrix dimensions
similar to
degree = polynomial's highest exponent

[subtle elbow]

i dont understand at all

[merry iris]

:/

[wary stream]

The dimension of the matrix

[merry iris]

pretend that matrix S is a rectangle and each element is a unit square

what are the dimensions of that rectangle

[wary stream]

Like 2 x 2

Or 5 x 3

Etc

[whole herald]

first number being the line

and second the column

[wary stream]

By line, another word is the row

[subtle elbow]

what would i write exactly for an answer tho

[wary stream]

The dimension of the matrix

[subtle elbow]

cause i dont got a bloody clue

[wary stream]

How many rows and columns are there?

Because a matrix dimension is written Row x Column

[subtle elbow]

ohhhhh

okkkkk

thanks

[snow nest]

i have a question

so

in probablity

can you have conditionally independent events?

[fringe spindle]

i don't think you can, because by the formula for conditional probability, if they were both independent and conditional, one of them would cancel out. using the formula for independent events, P(A∩B) = P(A) × P(B), now if we substitute this in the formula for conditional probability, P(A | B) = P(A∩B)/P(B), however now P(A∩B) = P(A) × P(B) so we can rewrite the formula as P(A | B) = [P(A) × P(B)]/P(B) = P(A) i.e. P(A | B) is just P(A) regardless of the fact B has already happened

[fringe spindle]

using laws of logarithms it's (c) x - y

log(a) - log(b) = log(a/b)

[alpine sable]

ok ty

[fringe spindle]

np

[fringe spindle]

(a)

combining all the laws of logarithms, the addition law, the subtraction law and the power law

[alpine sable]

wait what

whys it a

[fringe spindle]

sorry, please let me explain

[alpine sable]

okay

[fringe spindle]

power law: klog(n) = log(n^k) (trying to use different variables to the ones in ur exercises to avoid confusion)

so the first step i did was to rewrite (3log_a (y))/2 as log_a (y^(3/2)) which equals log_a (√y³)

then the addition law: log(pq) = log(p) + log(q) (like regardless of what base is used, i just left it out for simplicity here, which by convention usually denotes log to the base 10; these formulae all only apply to logs which have the same base)

so since now we've got log_a (x) + log_a (√y³), we can now rewrite this as log to the base a of the product of these two terms

and finally the subtraction law, which was the one i used to answer ur previous question; log(p) - log(q) = log(p/q)

so after having first rewritten 2log_a (z) as log_a (z²) by applying the power law again, since this is being subtracted from the first expression i made using repeated application of the rules, this now gets divided by, in the expression we are taking a single logarithm to the base a of

and that's the explanation

[alpine sable]

thank you

[fringe spindle]

np

[alpine sable]

can you also help me with two more

i have his one

this*

[merry iris]

dont you add the y's together? f(x) = some output g(x) = some output so f + g = some output + some output?

well thats not an answer so guess not

[remote heron]

? its an answer

over their shared domain

[merry iris]

ah wait i didnt do the addition correctly

[slender girder]

Hello is this in use?

[remote heron]

it is

[alpine sable]

im confused

[exotic sky]

@here

[fringe spindle]

sorry i didn't notice this earlier, i think the answer is d.

because you don't add the input (domain) values, but you do add the pointwise output (range) values. so every number on the right in each set of brackets. and you have to include (1, 2) because it's included in g, however it's not got anything added to it, so it just stays the same

[wary stream]

Why did you use that ping?

It doesn't work

If you needed help from helpers, you have to wait at least 15 minutes after posting your question then you can ping helpers using @Helpers

[harsh belfry]

Was wondering what I could do to fix this function.

Not sure why it is considered incorrect

[wary stream]

What was your work?

[harsh belfry]

15*5 would equal the limit of 75 right?

I factored the numerator and simplified it to just x^2+5x+25 then plugged in 5 for x @wary stream

That gave me my limit of 75

A simplifer function to arrive at the limit of 75 would be 15*5 if I'm not mistaken.

[wary stream]

Isn't x^2+5x+25 the simplier function?

[harsh belfry]

that... would be a smart way of looking at it.

I didn't consider that.

I will give it a shot

Haha thanks...

I feel like an idiot.

[wary stream]

I think the simpler function is the simplified function, after factoring and dividing terms

[harsh belfry]

^ Wasn't aware of that till just now.

[misty holly]

where do u guys find those exercises? i also want to answer math8 exercises

[harsh belfry]

Its apart of my course in college @misty holly

Theres some websites that assign you work for any subject you want

[misty holly]

can u pls name some of these websites? only if u dont mind

[wary stream]

Khan academy is a good free site. You learn and it gives practice problems

[harsh belfry]

You could try giving a look at "MyLab" through Pearson if you want to pay for one. Otherwise I'd recommend kahn academy.

The service my college uses is webassign

In the past I've used some good paid ones but I cant remember the names

[misty holly]

oh okay, thanks you two

[pearl lily]

in logic, is there a way to express "it is impossible" in terms of not, and, or, then, if and only if

[alpine sable]

contradiction comes to mind but i could be wrong

[misty holly]

"oh yeah, ofc it's possible, if and only if you are god"

[alpine sable]

$\frac{\frac{x+2}{x+3}}{\frac{x+3}{x+2}}$

[ocean seal]

jswatj

[alpine sable]

flip them

it'll just be

$\frac{(x+2)^2}{(x+3)^2}$

[ocean seal]

jswatj

[alpine sable]

thats the answer?

well,

kinda

yeah

[magic geyser]

basically f(x)/g(x)= f(x) * g^-1(x)

[alpine sable]

that could be misleading

g^-1(x) looks like the inverse function

write it as (g(x))^-1

[magic geyser]

rhqts an inverse for me

that's*

[alpine sable]

yes, but theres a difference between the inverse of a function and the reciprocal of a function

[magic geyser]

yeah

[lone igloo]

Hi guys

what should be k in order to justify the equation:
(k - 1)cos(x) = 3 - k with x belonging to the third quadrant of the cartesian plane

[magic geyser]

is cosx positive in third quadrant?

[lone igloo]

it is not

[alpine sable]

is this a trig question

[coral pagoda]

No, it does not look like it

[coral pagoda]

The third quadrant is where both x and y are negative. Since x=cos(theta), negative x values mean the cosine is negative.

[magic geyser]

RHS needs to be negative since its in 3rd quadrant and needs to be in [-1,0]

[magic geyser]

yep was asking isao

[lone igloo]

so would you solve with a system of disequalities ?

[pearl lily]

so if i was to define a symbol for "it is impossible that p occurs" could it be defined as p <-> not p, therefore contradiction and it is impossible for p.

[lone igloo]

like (3-k) / (k-1) >= -1 && (3-k) / (k-1) <= 0

with k != 1

[alpine sable]

you could just simply say P and not P too

but yeah i think that works aswell

[pearl lily]

ah yea ok i see

[cedar hearth]

<@&286206848099549185> Hello, is there anyone that can help me with this?
https://math.stackexchange.com/questions/66077/how-to-find-the-expected-number-of-boxes-with-no-balls
Can someone help me explain Andre's answer here? I can't seem to get why we don't need to account for 2 boxes being empty $(1-p_1-p_2)^{10}$ and so on.
I know what's linearity of expectations, but I don't get why it works here, and I don't get why we don't actually need independence. Also, what do we not need independence for? Whether $p_1$ is independent of $p_2$, or we don't need independence for events $X=1$ and $X=2$.

[ocean seal]

Memiya

[gleaming snow]

Is this available

[glass lichen]

that wasnt the answer box, it was the box for the sub-question

ie fill in the blank.

[gleaming snow]

I also tried pi/180 and its not right

[glass lichen]

read the question...

[gleaming snow]

Im bad at english, can you please tell me what its asking

[glass lichen]

"To convert degrees to radians, use the fact that (blank) radians = 180 degrees"

how many radians are in 180deg...?

[gleaming snow]

Oh its pi thanks

[glass lichen]

yes

[gleaming snow]

Degrees cant be negative right?

[glass lichen]

you can have negative angle measures, yes

[sharp dust]

is there any easier way to solve this than by fully expanding the squares, putting it into standard form, and using the quadratic formula? i'm looking for an exact answer, no rounding

and this is for a personal project thing, so external applications and stuff are fine, i've tried wolframalpha but it only gives a decimal approximation

[glass lichen]

let u= (x-170.75)^2 then you have u+(thing)^2=121

so you'll get u=something, to which you can easily solve for x

@sharp dust

[sharp dust]

so you're saying make it like this

$u^{2}+\left(\frac{52.125u}{\frac{\sqrt{134247}}{8}-\frac{\sqrt{7215}}{4}}\right)^{2}=121$

[ocean seal]

Dankxiety

[sharp dust]

solve for u, then substitute x-170.75 for u and solve for x?

i'll try that, thanks

[glass lichen]

that isnt what I said

[sharp dust]

oh

[glass lichen]

$u+cu=121$ where c is just the fuck ugly fraction squared

[ocean seal]

Mosh

[glass lichen]

where $u:=(x-170.75)^2$

[ocean seal]

Mosh

[sharp dust]

i'm illiterate

$u+u\left(\frac{52.125}{\frac{\sqrt{134247}}{8}-\frac{\sqrt{7215}}{4}}\right)^{2}=121$

[ocean seal]

Dankxiety

[sharp dust]

like this?

[glass lichen]

yes

[sharp dust]

gotcha

thank you

[glass lichen]

$u=\frac{121}{1+c}$ then it's just more number crunching

[ocean seal]

Mosh

[sharp dust]

worked perfectly, tysm

[glass lichen]

yeah should be $x=170.75\pm\frac{11}{\sqrt{1+c}}$

[ocean seal]

Mosh

[alpine sable]

Okay am I dumb or is the domain of f(x)=x not (-inf,inf)

[glass lichen]

Domain of x is R

which is also (-inf,inf)

[alpine sable]

Okay thanks it needed to be in interval notation so I’ll email my prof about it

Also, $y=sqrt{x^2+2x}$

[jade birch]

\sqrt

[alpine sable]

Also, $y=\sqrt{x^2+2x}$

[ocean seal]

Klaw

[alpine sable]

Okay it asks for the inverse ik you would switch y and x and then solve for y but I’m stuck after squaring both sides

[jade birch]

What do you get after that

Type it out, I'll give you a hint

[alpine sable]

Oh $x^2=y{y+2}$

[ocean seal]

.itsjustnai

[alpine sable]

Yea

[jade birch]

Try completing the square for y

[alpine sable]

Lmfao

Thx

[jade birch]

np

[alpine sable]

does anyone know what this symbol means?

[calm burrow]

Paragraph?

[alpine sable]

it's for math though

like this

[gleaming snow]

Paragraph 2

[alpine sable]

what does paragraph mean?

[calm burrow]

https://en.wikipedia.org/wiki/Pilcrow

[gleaming snow]

It consists of atleast 3 sentences

Can anyone help me, i cant figure out how to get this answer

[alpine sable]

i mean like why is it used in maths?

[gleaming snow]

Give us context

Full picture of where you got it.

[alpine sable]

Apply formula:- theta/360 × 2πr

[alpine sable]

find the perimiter of the whole cirlce

[alpine sable]

yeah thats what i meant

so do 260/360 x 2πr

[alpine sable]

ohh so was it like a typo or something?

[gleaming snow]

And the answer shouldve been -40pi/9

Which was my previous anwer.

[alpine sable]

100/360 × 2pi. R

[gleaming snow]

?

[alpine sable]

Yep

Even, why have you put the -ve sign?

[gleaming snow]

Then im right

[ember token]

hello

i need help on something

[gray kiln]

go ahead

i will try

[ember token]

conditional probability

In connection with the roll of a single fair die.

a. State by extension the events

E: the roll is even
T: the roll is 2
O: the roll is 1

b. Determine
i. The probability that the roll is even.
ii. The probability that the roll is even, given that it is not a two.
iii. The probability that the roll is even, given that it is not a one.

[placid zinc]

Any thoughts on the problem that's got you stuck?

[frigid hatch]

lol

[light coyote]

For this laplace transform formula -When n=0, does it become F(s) or 1 ?

[restive hill]

Hi GoodMorning can anyone help me to my group activity?

[gray kiln]

this question could be solved with a trivial approach

u must be knowing that a square is always positive or 0

so just try putting different values of x and find out which value yields minimum value for y

@restive hill does it makes sense

[restive hill]

Yes thankyou So much!

[light coyote]

bump up 👆

[vale wigeon]

F(s)

the zeroth derivative of a function is that function itself

[slender girder]

hello

[light coyote]

right thanks, I was confused if it was derivative or power.

[modest jackal]

I am a student in class 9 could somebody tell me which is the best reference book for Maths?

@everyone

[vale wigeon]

@modest jackal don't ping everyone. it's disabled but it's still massively rude to do it in such a big server

[alpine sable]

Why is 52 the largest? I put 12423 = 10x + 7y on desmos and there was no solution to it.

Sorry I forgot

there is a solution

[bronze stump]

hello, i wanna help understand this
Context: i'm looking into the physics of 3d collisions for simulation purposes
Question: What does vnx/vny/vnz mean?

link: https://atmos.illinois.edu/courses/atmos100/userdocs/3Dcollisions.html

[placid cargo]

Can some one help me how to find 25^1/2

[modest jackal]

sorry

[placid cargo]

@bronze stump ?

[last obsidian]

what? no

25^1/2 is sqr root of 25

[placid cargo]

oh

Ok thank you.

[bronze stump]

right i confused with negative exponents

[last obsidian]

Yeah welcome

[last obsidian]

yeah thats common 😂

[red wadi]

why is it z/r?

i dont get this either

[alpine sable]

how to solve this?

[bronze stump]

is vnx the velocity of both spheres in the x axis summed or multiplied?

[alpine sable]

<@&286206848099549185>

[kindred warren]

i think you have to transpose the first equation to make y the subject

then find dy/dx

[alpine sable]

i found the 1st derivative

it is y/x

idk how to proceed for the 2nd derivative

just use u/v ?

[eternal spindle]

just differentiate both sides with respect to x

the derivative of the derivative is the second derivative

and the derivative of y/x is... nice

do it

[alpine sable]

ik the derivative of y/x

the problem is it will be in terms of y'

y dash

[eternal spindle]

dont worry just do it first and see if it cancels out

[alpine sable]

it dosnt

[eternal spindle]

r u sure?

try again

[alpine sable]

ya

it is (xy' - y)/x^2

[eternal spindle]

so im not supposed to spoil the answer to u

but ur wrong

it does cancel out to 0

[alpine sable]

how?

[eternal spindle]

dy/dx= y/x

d2y/dx2 = 1/x*dy/dx - y/x^2

= 1/x*y/x - y/x^2

= y/x^2 - y/x^2

also u knew that y' is y/x

[alpine sable]

how do i b?

(this is a practice test)

[alpine sable]

my bad, ya

i could just substitute

thanks a ton mate

[eternal spindle]

u r currently taking the test @alpine sable ?

[alpine sable]

no

[eternal spindle]

@alpine sable 👍

[alpine sable]

its a practice test

[eternal spindle]

ok

just multiply the price of each with the quantity sold

and write it

in a matrix i guess

[alpine sable]

?

[eternal spindle]

the number of each of the things the stores sold and the price of each, just multiply them

[alpine sable]

ohh

i misread the question

ty

its a column matrix?

[eternal spindle]

bro idk wht the question is referring to i only know the rank 2 tensor kind of matrices lol

[alpine sable]

lmao

[wary stream]

It's asking for the total amount that each store made, selling those products with that given price

[alpine sable]

yea ik now

[plain sundial]

Express theequation: √5 = 3y in standard form indicating the values of a, b and c

[alpine sable]

its also a column matrix? (for b) is that right? @wary stream

[wary stream]

It's not asking for a matrix

[alpine sable]

oh

thank you lmao

[plain sundial]

Express theequation: √5 = 3y in standard form indicating the values of a, b and c

I cant get this

[wary stream]

Don't ping me

[plain sundial]

hmm he god kicked

[quaint narwhal]

valorant?

[plain sundial]

#events

[wary stream]

Ask in #chill

[wary stream]

Wrong channel

[plain sundial]

hmm

[alpine sable]

difference between interpolation and extrapolation for linear relatioons

what are they

[karmic dew]

anyone use magic hexagon or find it beneficial?

[harsh belfry]

Been working on this for awhile

Once I realized that I couldn't square 6 I didnt know what to do

Any ideas?

[vale wigeon]

it's 9/(2sqrt(6)), first of all. not 9/sqrt(6)

also... wait

hold on

no you made more mistakes than that

[harsh belfry]

I bet I made plenty of mistakes...

Im terrible at this.

[vale wigeon]

$(\sqrt{6+x}-\sqrt{6})(\sqrt{6+x}+\sqrt{6})$ simplifies to $(6+x)-6$, not $(6+x)+6$ as you wrote.

[ocean seal]

Ann

[vale wigeon]

you know, because of the difference of squares identity that you should be familiar with

and you would need to simplify (6+x)-6 into just x before you could cancel it out in the num and denom

(not to mention that 6+6 isn't even 9 so you made an arithmetic mistake in your already erroneous working)

[harsh belfry]

Thanks for pointing that out

I will work on it.

[vale wigeon]

you're going to redo the problem now? ok.

[harsh belfry]

Of course I'm going to re-do it.

Not gonna give up on it lol.

[vale wigeon]

i suppose you can ping me once you're done if you want me to check your new work

[harsh belfry]

I appreciate that Ann.

[trail elm]

What does X=x mean in simple terms?

this is for probability and statistics

[vale wigeon]

it means the random variable called X returns the value called x

you probably saw it as in P(X=x)

[trail elm]

yos

wdum by returns the value called x

is it like the varible = x?

[vale wigeon]

if you insist on saying it that way

[trail elm]

oh oki

so like rolling a dice and getting a 2

would be P(X=2)?

[vale wigeon]

the probability of getting a 2 would be P(X=2) yes

(assuming X represents the roll of your die)

[trail elm]

Oh oki

i think i got it

ty ty 😄

[harsh belfry]

Would I multiply by the conjugate to get

[vale wigeon]

you screwed up your simplification

[harsh belfry]

Is it possible to cancel out the

with

?

Can you point out what I messed up on?

[harsh belfry]

Would I instead multiply the numerator and denominator by the conjugate a little earlier in this step?

I don't know what to do...

[fringe ember]

hey there people

[placid zinc]

That crossing out looks good, but you left an x after

[fringe ember]

how y'al doin

[harsh belfry]

@placid zinc Ah thanks! I missed that.

What do I do with my remaining radicals?

[placid zinc]

You can now plug x = 0.

[vale wigeon]

you will have 1/(sqrt(6+x)+sqrt(6)) after which it's possible to substitute x=0

[harsh belfry]

Thanks

If I'm not mistaken I should be left with

after simplifying

[light coyote]

is this channel free?

[harsh belfry]

Yep. Go ahead and grab it.

👍

[light coyote]

kk thx

How do I calculate the laplace inverse of that

[fringe ember]

First try getting the partial fraction form of the denominator

i mean, decompose this into partial fractions

[light coyote]

But what should I make it?

[fringe ember]

$\frac{1}{( s-2)^{2}( s-3)}$

[ocean seal]

the.dorkest.knight

[fringe ember]

decompose this onto partial fractions

Try to use the fact that

[light coyote]

I'm not sure what I should make it 😕

[fringe ember]

and

where u(t-a) is diirac's function

these should be enough for you to complete the solution

[light coyote]

is it the heaviside function?... cz I haven't heard of diirac

[fringe ember]

yes, the heaviside function, sorry i forgot the correct name

[light coyote]

Ah ok... I'm not very confident with heaviside function but lemme try

wait what should I do with the e^-s?

[fringe ember]

use the rule provided

[fringe ember]

this

[light coyote]

ah ok

hmm ok I haven't understood how to use it.

[light coyote]

I dont understand what happens to the e^-s

[light coyote]

<@&286206848099549185> This is the original question. Could u help me understand how to solve this.

[stuck jolt]

Make a partial fraction

Oh wait, that was already said lol

[light coyote]

Yes, but what do I do with the e ?

Should I just take the rest of the fraction?

[stuck jolt]

Apply it to the partial fraction and isolate it

[fringe ember]

use the rule directly man

[stuck jolt]

^

[light coyote]

lemme try again 😕

[fringe ember]

what's "a" in your expression?

[light coyote]

I'm not sure

[fringe ember]

are you able to isolate F(s) and $e^{-as}$

[ocean seal]

the.dorkest.knight

[fringe ember]

in your expression?

[light coyote]

I'm trying to find the partial fraction first as suggested

[lusty pewter]

hi can i have some help

[fringe ember]

you may

[fringe ember]

do that, and then come back

[lusty pewter]

should i got another channel

[fringe ember]

no, i think this is fne

[lusty pewter]

ok

one sec

how do i solve question one, and also how do i find the equation for the parabola in question 2

[fringe ember]

for the second one, just try to find a line of symmetry for the parabola

[lusty pewter]

ok

x =-0.5

[fringe ember]

i guess you can do it visually

[lusty pewter]

i can probably just google question 2 i wont waste your time

can i have some help with question 1?

[fringe ember]

widest graph=graph that has largest absolute coefficient of x^2

do you want a proof for this too?

[lusty pewter]

yeah

[fringe ember]

oh no

just try to visualise this - the larger the absolute value of the coefficient of x^2, the wider the graph

try plotting some parabolas on desmos and check it out

[lusty pewter]

ok

do negative coefficient make it wide aswell?

[fringe ember]

yes

but the direction of the graph will be reversed

[lusty pewter]

ok\

so is it d

i think its the smaller the coefficient the wider

[light coyote]

This is what I'm getting

[lusty pewter]

because 0 would mean no gradient

[lusty pewter]

which is infinitely wide

[lusty pewter]

@fringe ember ?

[fringe ember]

your reasoning is plausible

[fringe ember]

oh yes sorry

[fringe ember]

you forgot a coefficient for 1/(s-2)

[alpine sable]

in the blank(s) i just put 0

and my calculator is saying error

[light coyote]

I took it in the quadratic form 🤔

[fringe ember]

no i mean there should be an additional term for 1/(s-2)

[light coyote]

umm where is that coming from? Should I split (s-2)^2 into 2 instead?

[fringe ember]

wait

$\frac{1}{( s-2)^{2}( s-3)} =\frac{a}{( s-2)^{2}} +\frac{b}{s-2} +\frac{c}{s-3}$

[ocean seal]

the.dorkest.knight

[fringe ember]

decompose it as this

[light coyote]

oh ok

lemme do it again

[fringe ember]

a function is always a function my man

you mean when is a relation not a function

https://www.sparknotes.com/math/algebra2/functions/section1/#:~:text=A function is a relation,%3D 1 and x %3D 2.

why doesnt anyone on this sub know how to google

yes

[fringe ember]

yes

[fringe ember]

and NO

[light coyote]

😕

[fringe ember]

remove the e^-s from the numerator

and try again

[light coyote]

What where does that go then?

What am I supposed to do?

Wait u said the first image is fine 🤔 ... that has the e^-s

o well lemme just do it without the e^-s

@fringe ember

[urban lily]

hello is the room in use?

So, I tried proving and came across this last step...dont know how can sec^4(x)=y^2(3y^2-2)

[tropic sail]

How would I turn a matrix like this: $\begin{bmatrix}
a & b & c\
d & e & f
\end{bmatrix}$ into a formula?

[ocean seal]

mchw

[placid zinc]

You mean something like:
ax + by = c
dx + ey = f?

You'll want to be clear that such a thing is a block matrix

[tropic sail]

yeah well im doing some programming and matricies arent very efficient and i was once told that they could be worked with in formulas.

[urban lily]

<@&286206848099549185>

[placid zinc]

Matricies are crazy efficient if you're doing something that is matrix intensive

But if you don't need them, don't use them haha

[tropic sail]

homogeneus transformations

[haughty moth]

how to put an equation in a rectangle and then find the area?

bulletin board

[little walrus]

hi

can someone help with an exercise

?

[placid zinc]

What's C?

[little walrus]

where C is the area between 2 circles which have the same center with radious 1 and 2

[placid zinc]

Odd to see two disconnected paths for one integral

Both circles going the same way?

[little walrus]

yes

[placid zinc]

I mean Green's is a fair way to handle this and then you don't need to worry about all that haha

Just convert to an area integral, and do that instead

That would be
∫∫ -3x² - 3y² dxdy

Are you supposed to know Green's theorem yet?

[little walrus]

no

i have never heard it

[placid zinc]

But we can just do this regular too. For the larger circle:
r = (2cos(t), 2sin(t))
x = 2cos(t), dx = -2sin(t) dt
y = 2sin(t), dy = 2cos(t) dt

[little walrus]

thank you

[placid zinc]

Want any more help with it?

[little walrus]

if i will have an other question i will be back

[urban lily]

or can the question be wrong in the first place? XD.

[gleaming warren]

<@&286206848099549185>

i have so far xy+yz+zx-3xyz = x^2+y^2+z^2 - (x^3+y^3+z^3)
x^2+y^2+z^2 > xy+yz+zx
thus
x^3+y^3+z^3 > 3xyz

Anyone e

<@&286206848099549185>

Hellooooo

[alpine sable]

rule 4: if your question has not been answered for at least 15 mins, you may tag Helpers role once

https://tenor.com/view/mr-potato-cat-nataon-dimden-gif-22528109

how do i do b?

i have done T^2 x S0 and it just showed up as error

do i just remove purchase again?

[lusty pewter]

hi can i have some help?

how do i do question 8?

[alpine sable]

im waiting for help...

[lusty pewter]

can someone help with question 8

[valid pier]

pls

ans

i need it fast

[lusty pewter]

?tutor

[vale wigeon]

[valid pier]

pls

elp

help]

[sly mantle]

@valid pier what's the rush?

[lusty pewter]

surely help me i asked first

[valid pier]

this is my hw and class is starting soon

[valid pier]

if Anybody can help pls

[lusty pewter]

@sly mantle

can i have some help

im dumb

[sly mantle]

pls don't ping individuals for help

if 15min pass w/o reply you can ping helpers

[lusty pewter]

ok

[alpine sable]

please help

for A

i put everything in the matrix

[sly mantle]

@alpine sable use an unoccupied channel

[lusty pewter]

@sly mantle it has been 15 mins

[alpine sable]

i posted this first scroll up then vik used it

but got no help

[lusty pewter]

can i have some help with question 8 pls??????????????

???????????????????

[sly mantle]

@alpine sable how about you move to #help-9

[alpine sable]

i moved to 4

[sly mantle]

@lusty pewter it'd help to include what you tried & where you're stuck. as i said before you may ping helpers if you get no answer after 15min

[lusty pewter]

im stuck with everything

like x intercepts and stuff

and y intercepts

????????

[alpine sable]

did you try pythagorean theorem

[valid pier]

yea

i got the ans '

help me with this one

[lusty pewter]

8

@valid pier

[valid pier]

sure

?

[lusty pewter]

it is

[valid pier]

thannks

[reef urchin]

dont j give the ans, ure not helping them learn or how to get to that soln that way

[lusty pewter]

ok

[reef urchin]

do u wanna explain how u got the ans to them then ?

[lusty pewter]

not really

[alpine sable]

LMAO

[lusty pewter]

surely someone helps with 8a

i know the answer is 200meters i just wanna know if there is an easier way than trial and error to get to it

this is parabola

<@&286206848099549185>

<@&268886789983436800>

<@&681258879522177051>

[vale ginkgo]

thats not analysis

dont ping mods

[jade canyon]

…

[lusty pewter]

ok

can i have some help

sorry

[tough hatch]

did you just raise a death flag?

[lusty pewter]

lmao

[jovial breach]

why did i get pinged

[lusty pewter]

hope not

[lethal spoke]

he pinged analysis

[lusty pewter]

oh everyone is here

sorry guys

[alpine sable]

lmao

[crisp grove]

[lean fox]

lol

[crisp grove]

lmao indeed