help-0

[frosty blaze]

into R3?

or am i going to need to do that anyway

[placid zinc]

Those colors are wacky

[frosty blaze]

sorry, they help me to better fathom what i'm reading with this jargon

[placid zinc]

Map these into R3? No, unless you specifically like to work with matrices

I'd personally avoid

[frosty blaze]

i mean i personally feel like they make things feel cleaner but also they're intimidating to look at anyway so

but you're saying we don't have to work with matrices here?

see now i'm a little confused, i thought dot product/inner product was all about matrices

well. vectors, but

i was sent this earlier in reference to this question

[frosty blaze]

am i to evaluate this integral for all three vectors in the set?

how would i tell that it's orthogonal?

i just verify that that integral = 0?

is that integral literally the definition of the inner product?

are you telling me that that integral, the one here

that this thing is literally how the dot product between two vectors would be computed?

is that true???

OMFG IT IS

BRO OKAY I THINK I UNDERSTAND HOW TO TACKLE THAT ONE, TOO

alright. last question, this one has been a doozy for me

i know that i could obviously plot these data points into excel and calculate the line of best fit

but i also know that obviously that's not what i'm asked for here

i don't really understand how i'm supposed to set up a linear system using the equation $r = c + e(r\cos{\alpha})$

[ocean seal]

Rivvnik

[frosty blaze]

c can be any constant? so i should just set it to 0???

[lone heart]

@frosty blaze Has your question been resolved?

[frosty blaze]

it has not

<@&286206848099549185>

hello???

[frosty blaze]

.close

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[gusty ginkgo]

yo

[gusty ginkgo]

I don't get this

how is it D

and how do you get 55.6 on t his

pls help

<@&286206848099549185>

[lone heart]

@gusty ginkgo Has your question been resolved?

[open folio]

The volumes of the two cones are the same, but one of them has a different height, you can make an equation to solve for radius

The diameter of the original is 48.6, radius is 24.3..
V = 1/3 * pi * r^2 * h
(pi * 24.3^2 * 15.3)/3 = (pi * r^2 * (15.3 - 3.6))/3

9034.497 * pi = 11.7r^2 * pi
9034.497 = 11.7r^2
772.179231 = r^2
r = 27.7881131

2r = 55.5762262
Rounded is 55.6

[gusty ginkgo]

so isolate r

?

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[hazy plank]

one of the standard tests should work

just assume n>1

you are testing for convergence, you dont care what the value of the series actually is

[lone heart]

@spare sierra Has your question been resolved?

[hazy plank]

I would say yes

[lone heart]

@spare sierra Has your question been resolved?

[last ether]

You have a (-1)^n

Immediately that tells me something to try out

Which test should you try out first

If that doesn't work, try ratio

Ratio proves absolute convergence

[hazy plank]

you just used a test

its the limit test

in the long run you will get 1-1-1-1-1-1-1.... which does not converge

[lone heart]

@spare sierra Has your question been resolved?

[hazy plank]

wdym

the alternating series test will also fail

try the test for divergence

which tests do you have?

do you have limit test?

well the alternating series test will work in a way that lim(a_n) = 1
which proves that the series diverges

you need the limit test in reality for this

https://mathworld.wolfram.com/LimitTest.html

but just think about it, when you let n go to infinity (n^2-1)/(n^2+1) goes to 1

so in the end you are doing +1-1+1-1+1......

which is divergent

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[wispy olive]

Can Someone Explain The solution please?

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@wispy olive Has your question been resolved?

[vale wigeon]

@wispy olive which part of the solution do you want explained?

[lone heart]

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[spare fern]

Hey

[spare fern]

For compound inequalities for an “OR” question what if the arrows on the number line do not overlap but instead go opposite directions what would I do?

[thick talon]

that means that the values within both arrows are x

since x can be either the values in the first arrow OR the values in the other arrow

[spare fern]

Here is the question

I know that for an “AND” question if the arrows are pointing opposite and there is no overlap there are no solutions however I do not know what to do if there is the same shape with an “OR” question.

[thick talon]

if it's OR then it means that the values within both arrows work

[spare fern]

So does that mean all values of x are solutions?

[thick talon]

no

it has to be within the arrows

[spare fern]

Oh well it said the answer is this

[thick talon]

yeaj

yeah

[spare fern]

But how would you find this as the answer?

[thick talon]

when it says OR it means that any values that are covered by the arrows are solutions for x

[spare fern]

Do you just take the two numbers and right “OR”?

Yes but the answer is not any value in between the two arrows?

[wispy olive]

Shall Tell After This channel help done.

[spare fern]

Well at least the one on the screen said it is the two previous numbers

For a shape like this for “OR” specifically do I just write the two numbers along with “OR”?

[thick talon]

don't remember it like that

[spare fern]

Then how should I remember it?

[thick talon]

when a question says "OR", then the solutions for x are the values covered by either arrow

[spare fern]

Yes

Then why isn’t the answer a value from in between the arrows?

[thick talon]

bc there is no arrow between the arrows

it's only for the values that make up an arrow

[spare fern]

?

You just said the values in between the arrows work

[thick talon]

i meant within the arrows

like the values that make up the arrows

[spare fern]

So -6 would fit both inequalities right?

[thick talon]

it only fits for one of the inequalities

[spare fern]

Hmm

[spare fern]

So then why is this the answer?

[thick talon]

because OR means that any values inside the arrows will be the solutions for x

[spare fern]

Oh ok

[spare fern]

But for example if I see this shape for “OR” on the number line does this indicate the answer will involve x or x for example?

[thick talon]

what do u mean by x or x

[spare fern]

I mean an answer like this

[thick talon]

yeah you would need to say it's either x or x

[spare fern]

Oh ok

[spare fern]

So that particular shape will always indicate this?

For “OR”?

[thick talon]

yes

[spare fern]

Alright thanks

[thick talon]

no problem (sorry im not that great at explaining stuff)

[spare fern]

All good

.close

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[marsh sonnet]

34, 50, 43, 47, 38, 36
any pattern on this?

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[snow mason]

.reopen

[rugged thistle]

Can I ask?

[rugged thistle]

Do u know how to solve no.2?

[limpid spade]

,w plot y=6x+x^2-x^3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Grubert#2374

[limpid spade]

basically u can do two itnegrals

from first zero value to second, then from second to third zero value

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@rugged thistle Has your question been resolved?

[limpid spade]

u can do it in one integral, but u have to use absolute value something like that, so am not sure

[lone heart]

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[alpine sable]

Hi

[alpine sable]

I understand what decay constant means

but let's say i have 2 elements

which have same units

how do i find out which decays faster?

,close

.close

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[lone heart]

@haughty oar Has your question been resolved?

[haughty oar]

<@&286206848099549185>

[haughty oar]

<@&286206848099549185>

Someone plz help

[lone heart]

@haughty oar Has your question been resolved?

[hard patio]

which question do you need help with?

@haughty oar

[haughty oar]

Number 13

Matching

@hard patio

[lone heart]

@haughty oar Has your question been resolved?

[haughty oar]

No

<@&286206848099549185>

[oblique pier]

@haughty oar you still need help?

[haughty oar]

Yes please

Thanks for responding

[oblique pier]

alr there are many to solve a quadratic problem as you know

[haughty oar]

Correct

[oblique pier]

@haughty oar what do you A match with

which one we could solve my square root both side

[haughty oar]

Capital or lowercase?

Oh A

[oblique pier]

yes

[haughty oar]

I’m not sure

[oblique pier]

just look at the equation again

which one you could solve just by isolating x using square root

[haughty oar]

I’m only good with the graphing method and quadratic equation

Idk the square root method

[oblique pier]

it's just basically square root both side :/

alr since you don't know imma give you a small tip

[haughty oar]

Ok

[oblique pier]

focus on the one that x are not alone, it is x plus or minus a number

and that chunk of x and with number are being square up

[haughty oar]

So for a that would be 7?

[oblique pier]

look at e

[haughty oar]

Yeah

[oblique pier]

you saw that square on top of that chunk that contain x?

[haughty oar]

Oh yeah yeah yeah

[oblique pier]

when you see something like that you think of square root both side

since it help you to get rid of the square thingy

[haughty oar]

Makes sense cuz it’s to the power of 2

[oblique pier]

yes

[haughty oar]

So A and e

What about the next ones

[oblique pier]

alr into factor

what do your definition of factoring @haughty oar

[haughty oar]

(X-9)(x+7)

Or something similar

@oblique pier

[oblique pier]

yea

sorry for responding late i was doing homework

[haughty oar]

No problem

[oblique pier]

@haughty oar which one has been factor out for you

check again the list of equations

[haughty oar]

Was it C?

[oblique pier]

uh it's not

[haughty oar]

Oh so I was right for that one

[oblique pier]

its said solve by factor by the equations is already been factor for you

it doesn't require you to factor

[haughty oar]

Has to be b then

Right?

[oblique pier]

yea

[haughty oar]

Ok so B b

[oblique pier]

since they already factor it all for ya

[haughty oar]

C c is correct

[oblique pier]

jezz your country got lots of way to factor

[haughty oar]

Lol

Welcome to America

[oblique pier]

c is B

since like i said

[haughty oar]

Oh crap

[oblique pier]

they already factor out for you

[oblique pier]

🤨 🍿 im from vietnam

[haughty oar]

Oh lol

Far away

[oblique pier]

yea either way lets continue

[haughty oar]

Ok

[oblique pier]

https://tenor.com/view/troll-pilled-gif-19289988

shortcut

[haughty oar]

lol

[oblique pier]

alr you know the shortcut business we usually do in solving equation?

[haughty oar]

Brb

I have class now

[oblique pier]

when ur done ping me

[haughty oar]

I’ll be back in like an hour

Ok

Thanks

[oblique pier]

i might go to sleep

it's kinda late for me

[haughty oar]

Ok no problem

I would assume

[oblique pier]

@haughty oar imma help you when i wake up

[haughty oar]

Ok

Thanks

[oblique pier]

maybe ping another helper when you're back

that will save you time

timezone man jezz

[haughty oar]

Yeah

@oblique pier

Back

<@&286206848099549185>

[lone heart]

@haughty oar Has your question been resolved?

[haughty oar]

<@&286206848099549185>

[lone heart]

@haughty oar Has your question been resolved?

[tacit arch]

.close

[lone heart]

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[lone heart]

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[austere torrent]

Hello can anyone help me with my homework

[wary stream]

Look up videos

No one has the time to help you with all that

[lone heart]

@austere torrent Has your question been resolved?

[wary stream]

Have you tried anything yet?

[gritty hinge]

,

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[sleek blade]

Anyone know how I'd go about discretizing this PDE with forward upwind scheme? The second term is throwing me off a lot.

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[vague night]

help pls

[vague night]

im lost on this question

[gray isle]

do you know what they're referring to here when they say decomposition

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[steel turret]

i was wondering how to do c?

equations are y=0.5x+2 and y=-2x+17

intersection is at 6,5

do i calculate the distance of the 2 lines?

and see which one is shorter?

[lone heart]

@steel turret Has your question been resolved?

[lone heart]

@steel turret Has your question been resolved?

[steel turret]

<@&286206848099549185>

[subtle moat]

you can use Pythagoras theorem

boat a starts at 0 in x and ends at 6 in x

so one side of the triangle is length 6

and starts at y=2 and ends at y = 5

so other side is length 3

like this

remember Pythagoras theorem

so we can square both sides

we get 36 + 9 = c^2

45 = c^2

so c is √ 45

@steel turret

you can do the same for the boat b

and the root of the smaller number will be the boat that will arrive first

@steel turret so is everything clear?

[steel turret]

Oh yes this makes it clearer, thank you

[subtle moat]

also, for last, for boat b 6-8 will give you negative, but you can turn it positive

that's everything I've gotta say

best wishes

[steel turret]

thank you

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[halcyon tree]

does anyone think they can help with the derivative?

[real solar]

Post it

[halcyon tree]

first I have to work out the distance

which I did

But next is solving for derivative, right?

I'm stuck on that part

[real solar]

You have to minimize the distance

[halcyon tree]

yes

I'm stuck on what to do after this

anyone?

[lone heart]

@halcyon tree Has your question been resolved?

[uncut sleet]

x^2 + 4x -6 = (x+2)^2-10

then you can treat (x+2)^2 as a, and minimize a+(a-10)^2

[halcyon tree]

whereis the -10 coming from?

[lone heart]

@halcyon tree Has your question been resolved?

[tribal oxide]

You would need a -10 so that the +4-10 becomes the -6 in the original term

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[rough acorn]

can someone help explain why it gets these red areas from the partial derivatives, question 1 ii

[tight locust]

d/dx (xytan(z)) = ytan(z)

Is that what you're confused on

[lone heart]

@rough acorn Has your question been resolved?

[rough acorn]

no how does pardial derivative w/x become y, partial derivative w/y become x, and partial derivative w/z become xy

[tight locust]

It's not

dw/dx = ytan(z)

It's not just y

[rough acorn]

oh

yeah how do they get that then \

[tight locust]

Can you find the derivative of 5x

[rough acorn]

5x derived is five ?

[tight locust]

Yeah

So then whats the derivative of (ytan(z))x

With respect to x

[rough acorn]

ytan(z) but idk how u got to ytan(z)*x

[tight locust]

Commutativity of multiplication

Did you know!
5×3 = 3×5

[rough acorn]

i did

[tight locust]

There you go

Glad to see you figured it out

[rough acorn]

what

[tight locust]

Oh my bad I thought you understood

So you really don't see how
w = (ytan(z))x

?

[rough acorn]

i do see it now, um but with z how do u get xytan(z), derive in terms of z and its sec^2(z), thats just a general rule isnt it

[tight locust]

Yeah the derivative of tan is sec^2

[rough acorn]

aight thanks lol

.close

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[chilly torrent]

Is it enough here to take the integral of all these combinations and show that they all are 0 to show that they are orthogonal?

[naive valley]

6 integrals total, one for each pair of functions

[chilly torrent]

but normally to proof that it's orthogonal don't we also have to show that the norm is 1?

[naive valley]

that's for proving orthonormality

[chilly torrent]

oh that's orthonormal

thank you

okay thank you so much, I mixed up the terms

[naive valley]

sure

[chilly torrent]

thanks for your help!

.close

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[faint spire]

Where to start?

[high badger]

try using integration by substitution

[uncut plank]

I think power rule is enough. But if you want to solve it using substitution, let u = ||√x||

[vale sapphire]

I was thinking about this and now that you mention it it's just the power rule kek

[faint spire]

I can’t solve it with the power rule should I try the substitution?

[high badger]

yes

[uncut plank]

Yes. ||√x = x^½||

[faint spire]

I’ll try again thanks

.close

[lone heart]

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[limpid surge]

So i tried

inverting it

and got that f-1(x,y) = (x-2y, 2x-y)

I'm not sure that this is right

because when I then try to show the composite things is =, it doesn't work

I also have no clue how to prove 1-to-1

[sudden hinge]

For 1-1, use the normal definition. Assume $f(x_1,y_1) = f(x_2,y_2)$ and go on from there, i.e. try to show this implies $x_1 = x_2 \land y_1 = y_2$

[ocean seal]

nvx

[limpid surge]

and then prove by contradiction?

[sudden hinge]

You can make a direct proof by solving the resulting system of equations

[limpid surge]

hmm ok, i'll try that

what about the rest?

[sudden hinge]

can you show how you found the inverse, it does not seem correct

[limpid surge]

uhhh

idk

i tried substituting them

but it felt scuffed

[lone heart]

@limpid surge Has your question been resolved?

[limpid surge]

the way to do this is evading me

<@&286206848099549185> <3

[lone heart]

@limpid surge Has your question been resolved?

[oak perch]

$f^{-1}(x,y)=(\frac{2x-y}{3},\frac{x-2y}{3})$

[ocean seal]

Cogwheels of the mind

[limpid surge]

ty

.close

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[alpine sable]

How I can do this

[flat ore]

what is the relationship between power voltage and current

[alpine sable]

P= V * I

?

[flat ore]

yes

now can you find I

for 90mW and 1.5V

[alpine sable]

135A

?

[flat ore]

no

what did you even do lmao

135 Amp would toast you

[alpine sable]

Yh, with A I mean that

Sry

[flat ore]

?

[alpine sable]

90mW * 1.5V = 135 ampers

[flat ore]

no

it is not I = P * V

$P = VI$

[ocean seal]

ホタル

[flat ore]

$P/V = I$

[ocean seal]

ホタル

[alpine sable]

90 mW is the power and 1.5 is the voltage, What do I have to find?

[flat ore]

Current

[flat ore]

just use this

90/1.5

[alpine sable]

So, 90/1.5?

[flat ore]

yes

60mA

okay?

[alpine sable]

Yes

[flat ore]

now what is the relationship between charge time and current

[alpine sable]

That I don't know

[flat ore]

$I = \frac{q}{t}$

[ocean seal]

ホタル

[flat ore]

Current is charge flowing per unit time

now the question wants you to find the time

so

$t = \frac{q}{I}$

[ocean seal]

ホタル

[flat ore]

now q is 3000mAh

and I is 60mAh

[alpine sable]

3000mAh/60mAh

[flat ore]

once you divide you'll get the the time in hours

[flat ore]

not 60mAh, its 60mA

unit of current is Ampere, not Ampere hour that is charge

[alpine sable]

Ok, I understand now

So, the answer is 50mAh?

[flat ore]

no

[alpine sable]

Nono

50h

[flat ore]

no

yes

[alpine sable]

Sorry, I didn't see the keyboard, I'm on cell phone 😅

So, every exercise, would I do it this way?

For example, use these formulas because i had to find the current, right?

[flat ore]

yes

just remember your formulae

relating everything

and substitute what's given

to find what's asked

[alpine sable]

OK, thanks u bro

.close

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[lone heart]

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[alpine sable]

does anyone know how to solve the integral

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[balmy narwhal]

let u = 10^2(x-12.5)*ln(10)

did u try that

[lone heart]

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[last tangle]

for B, do i have that $\mathbb{P}(X=1\cap Y=1) = \mathbb{P}(X=1\cap Z=1)$?

[ocean seal]

Rœmer

[lime shore]

umm very long question

i will try to solve it

[last tangle]

you only have to know that X and Y take values in +- 1 and Y = XZ to answer my question

[last tangle]

well?

[lime shore]

bro wait im gonna do this in last im solving short ones first

[last tangle]

wdym?

[lone heart]

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@last tangle Has your question been resolved?

[lone heart]

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[lone thistle]

how do I cut ( y') this equation?

[limpid spade]

?

what y'

[lone thistle]

y' is a cut equation

<@&286206848099549185>

[merry coral]

asks question
gets asked to elaborate
doesn't elaborate
pings helpers

[lone thistle]

i don't need to elaborate

[spark creek]

Do you mean differentiation

[twin pine]

derivative?

[lone thistle]

is that what it's called? Im sorry

the translation from my language is "cut"

[spark creek]

Fair enough

[lone thistle]

yes, I know that 5/x will turn into -5/x^2, but I don't know what to do with the other number

nor how do I solve it from there

[spark creek]

You do you know what x² turns into?

[lone thistle]

i need to multiply 0.16 by 2?

[limpid spade]

when derivative is cut loll

[spark creek]

Yeah

[lone thistle]

i apologize for my poor translation

[worn fox]

what language is that? interesting

[lone thistle]

so it's -5/x^2 - 3/25x?

[merry coral]

I don't think so

[lone thistle]

because 0.32 = 3/25

[merry coral]

,w solve 3/25

[ocean seal]

Results provided by WolframAlpha

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Requested by Chunkin#4952

[limpid spade]

oof

[lone thistle]

hebrew

[merry coral]

it's -5/x^2 +0.32x

I believe

,w d/dx 5/x + 0.16x^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chunkin#4952

[merry coral]

positive 0.32x

but ye

[lone thistle]

so now I put 1 below the 0.32 and do cross multiplication?

[merry coral]

this is already fully simplfied

[lone thistle]

oh, I wonder why it's positive

[merry coral]

cause d/dx +0.16x^2

= (0.16)(2)x^(2-1)

or

0.32x

[spark creek]

This

[spark creek]

Same thing

[merry coral]

ik

[lone thistle]

Is it? I have to get rid of the x^2 below the 5

[spark creek]

Mb

[merry coral]

add those together gets this

kinda ew

[lucid merlin]

help

pls

[lone thistle]

where did the x^3 come from

[lucid merlin]

A primary school made money by having tickets and a bazaar at a May 17 event.
They used 75%
75 : %
75%
of the money at camp school for 7th grade.
They used 2/3
\ frac {2} {3}
3
2

of the remaining money on upgrading the schoolyard with new play equipment.
25%
25 : %
25%
of the money they had left then they spent on summer closing.
Then they had 1800 kr
1800 : \ mathrm {kr}
1800kr
again, which they saved for next year's May 17 event.
How much money did the school make at the May 17 event?

😳

HELP

[spark creek]

x² was the denominator

[lucid merlin]

godsh

[spark creek]

Use a different channel sir

[lucid merlin]

which one

[lone thistle]

listen, they're trying to help a handicap person

[merry coral]

#❓how-to-get-help

[merry coral]

nice test question

[lone thistle]

you make it look too complicated

can I work with that?

It's a + *

In between

like, I can multiply 0.32 by x2 and multiply 1 by 5?

though where does the - take effect? are both 5 and x^2 in minus?

[spark creek]

It's acceptable if you leave the answer in this format
@lone thistle

[lone thistle]

so 0.32x - 5/x^2 is my y'?

[spark creek]

Yes

[lone thistle]

thank you

an extra question, please ?

0 = 0.32x -5/x^2

how do I separate the x^2 from the 5?

[lone heart]

@lone thistle Has your question been resolved?

[lone heart]

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[oak mesa]

Hello, I need help concerning a number theory problem
how can I find the remainder of the division of 2^(pq) modulo 2^(p) - 1?

[hybrid silo]

hi

how to do

https://i.gyazo.com/b210ca67c9a2f623f6e56b0b99a3846f.png

[lament glen]

read #❓how-to-get-help

[placid zinc]

You were so close haha

[hybrid silo]

whaty

[oak mesa]

.

[placid zinc]

Try another higher

The "rest" of the division?

[oak mesa]

the remainder*

sorry

[placid zinc]

Do you just want to know what 2^(pq) is when reduced (mod 2^p - 1)?

Yeah yeah okay

[oak mesa]

yes exactly

[oak mesa]

Did you find any solution?

<@&286206848099549185>

<@&286206848099549185>

Hey please can anyone help me with this problem Xd?

<@&286206848099549185>

!close ....

!close

.close

[lone heart]

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[spice mauve]

would you please solve this 🙂

[merry depot]

how many elements are in R_1?

[lone heart]

@spice mauve Has your question been resolved?

[spice mauve]

12 i guess

[merry depot]

how many elements are in the intersection?

(meaning you need a point that is both (x, 3x) and (x, x^2))

[spice mauve]

is 11 correct answer?

@merry depot

[merry depot]

should be

[spice mauve]

tysm

may i ask some more ques?

[merry depot]

sure

[spice mauve]

Cardinality of R1 ∩ R2

and cardinality of R3

[spice mauve]

is the answer 6? @merry depot

[merry depot]

what's your reasoning?

[lone heart]

@spice mauve Has your question been resolved?

[lone heart]

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[feral sonnet]

ok so basically i want to make a formula that will multiply a number by two for a specific number. So like 64 original number then 3 times i want it individually multipied by two

[lament glen]

so 64 * 2 * 2 * 2 = 64 * 2^3 right?

[feral sonnet]

what would that equal

[lament glen]

will original number also be a power of 2, always?

[feral sonnet]

yes

i think

[lament glen]

then you just add the exponents

[feral sonnet]

i know nothing about math

[lament glen]

$a^b \cdot a^c = a^{b + c}$

[ocean seal]

Doggo

[lament glen]

you can make use of this

[feral sonnet]

oh thanks

let me try it

[lone heart]

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[next cliff]

Hello there

[next cliff]

Can anyone explain how I would estimate theta using maximum likelihood estimation?

I'm confused as to how to setup a likelihood function

[lone heart]

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[merry coral]

find the area

[lone heart]

Please don't occupy multiple help channels.

[ocean seal]

Chunkin

Results provided by WolframAlpha

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[worn fox]

bro no

[merry coral]

$$f\left(x,y\right)=x^{2}+\left(y-1\right)^{2}-\cos\left(x\left(y-1\right)\right)$$

[ocean seal]

Chunkin

[merry coral]

look it's a function now

[lament glen]

I might just be dumb but don't you need to separate the x and y first to get the function?

you can always apply the Wolfram Alpha theorem

[worn fox]

you do, and we've told him theres no way to do it but he wont give up

[lament glen]

yeah I tried to use Wolfram Alpha theorem and it failed

[lament glen]

close enough to a circle of radius 1 actually

I'd say the area is 6

good enough

why find an accurate answer when you can have free time

[limpid spade]

area is actually

2.9746762955529314904939768732072660583586595261147266304759719278

[lament glen]

which is approximately 6

[limpid spade]

very true

i was wrong saying it was pi

6 is closer to 2.9746762955529314904939768732072660583586595261147266304759719278 than pi

[lone heart]

@merry coral Has your question been resolved?

[hollow shale]

Oh god he's made another channel

[lone heart]

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[merry coral]

[lone heart]

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[proper tangle]

the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is
$$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.$$

[ocean seal]

vin100

[swift shore]

Do you know how to find the distance between two points

[fervent bobcat]

Midpoint?

[lament glen]

Just to visualise the formula
To find hypotenuse (which is our distance) we can apply pythagorean theorem:
$$d^2 = |x_1 - x_2|^2 + |y_1 - y_2|^2$$
$$d^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2$$
$$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$

[ocean seal]

Doggo

[lament glen]

we can get rid of absolute values when squaring which is what happened from line 1 to line 2

[fervent bobcat]

So do I fill in both points into this formula?

[lament glen]

yeah

[fervent bobcat]

Ohhhhhh dayum I'm stoopid

What's that formula called?

[lament glen]

¯_(ツ)_/¯

[fervent bobcat]

Loll

[lament glen]

distance between two points I guess

not sure if it has a fancy name

[fervent bobcat]

And how do I know when to use it?

[lament glen]

if you have two points and want the distance you use the formula

then again, you can always draw a triangle and derive the formula when needed

[fervent bobcat]

Wait so do I find the distance from b to c using that formula

[lament glen]

yup

[fervent bobcat]

And if so why does it say d4

[lament glen]

you find distance then take the 4th power

at least I think that's what it means

[fervent bobcat]

So I just multiply it on the calculator once finding the distance

[lament glen]

yeah

[fervent bobcat]

Ohh OK thanks

I think I understand how do I close this help thing

[lament glen]

you do .close

[fervent bobcat]

Thanks man

.close

[lone heart]

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[gloomy wolf]

Am I approaching this in the right way? I am primarily skeptical of the 2nd to last centered line, where I take the limit of the "end" of the fourier series of f as the starting index goes to infinity

oops i shouldve read the whole rules- this is certainly not pre-university. my bad

.close

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[barren elbow]

This is the lines from an answer sheet in a textbook. How do you get from the second line to the third line?

[gloomy wolf]

$a\left(\frac{x}{2}\right)^2 = a\cdot\frac{x}{2}\cdot\frac{x}{2} = \frac{ax^2}{4} = \frac{a}{4}x^2$

[ocean seal]

JamesH

[gloomy wolf]

and $\frac{x}{2}\left(2a-b\right) = x\cdot\frac{1}{2}(2a-b)$ and then distribute the $\frac{1}{2}$

[ocean seal]

JamesH

[barren elbow]

distribute?

[worn fox]

they said second line to third line

[wet sentinel]

A pebble is embedded in the tread of a rotating bicycle tire of diameter 60cm. If the wheel rotates at 4 revolutions per
second, determine the relationship (equation) between the height, h, of the pebble above ground, in centimetres, as a
function of time, t, in seconds using a sine function. Assume that at t=0, the pebble is located halfway between the
ground and the top of the tire.

someone please help

[gloomy wolf]

i should read

thanks

[worn fox]

#❓how-to-get-help

[gloomy wolf]

it seems that they evaluated for some given values of a,b, and c is the only thing that makes that happen i think

probably makes sense in the context of the problem but not without

[worn fox]

yes you need to provide the whole question

[barren elbow]

one sec I'll send the question

Entire solutions

[worn fox]

so you have two equations for the same graph

one involving a,b,c via transformations

and one given to you at the bottom of the question

they have just set those equal to eachother because they are the same graph

now you need to find a,b,c by comparing coefficients

[barren elbow]

I understand up until the second line of this

how do you start comparing coefficients from this though

[gloomy wolf]

you have that the 2nd and last line need to be equal to each other

so you need to match their coefficients

the last line has x^2 coefficient of 1/2

the 2nd line has a/4

therefore a/4 = 1/2. which gives you a

you follow a similar process of matching coefficients for the x and constant terms

[barren elbow]

OMG I finally understand

Thanks so much @gloomy wolf

They're just comparing coefficients

[gloomy wolf]

😉

[barren elbow]

.close

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[quick jolt]

how do I find BC, this is my work so far and I’m stuck at trying to find the base to AQC so I can use Pythagorean to find BC

[gloomy wolf]

you can fully solve both triangles APQ and BQP using law of cosines + law of sines

you found BQ^2 (take the square root to get BQ)

you can use law of sines to get angle PQB

then you can use law of cosines to get side AQ

after which you use law of sines to get angle AQP

ok actually wait-

[quick jolt]

starting from point B or point Q

[gloomy wolf]

it doesnt matter, its an angle 🙂

they are the same

i was slightly mistake nthough

actually nvm

just find ALL the angles

jk sorry im going back and forth

[quick jolt]

ok this is my updated work I’ll work on finding all the angles

[gloomy wolf]

if you can find angle PAQ

, then you know that $\sin(\angle PAQ) = \frac{\overline{BC}}{7+22}$

[ocean seal]

JamesH

[gloomy wolf]

so use law of sines to get angle PAQ, then you can solve for BC

[weary pivot]

Can someone help me with stats ?

[quick jolt]

where did you get the 22 from in 7 + 22

[worn fox]

#❓how-to-get-help

[stuck grail]

Presumably they meant $7+15$

[ocean seal]

Fyriole

[quick jolt]

that’s what I thought thanks

I got 13.1 as my answer for BC

thanks for the help guys

.close

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[alpine sable]

it says here that sin(a) = 1 and -45 < a < 45
how is that possible?
when I algebraically solve this I end up with sin(90) = 1

[alpine sable]

does this have to do with the unit circle?

[tacit arch]

where does it say g = 1 ?

[alpine sable]

forgot to add that part

[alpine sable]

can you check now?

Is it possible to get a value less than or equal to 45 and greater than or equal to 45 for a?

when sin(a) = 1

[tacit arch]

G and g are different

Where does it say G = g?

[alpine sable]

They are both the same

[alpine sable]

That was the auto correct by the application

Assume G and g are the same, now if you can help that would be great.

[tacit arch]

,w plot sin(x) for -pi/4 < x < pi/4

[ocean seal]

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[alpine sable]

What is that

[tacit arch]

max value of sine on your given interval is 1/sqrt(2),

,calc 1/sqrt(2)

[ocean seal]

Result:

0.70710678118655

[tacit arch]

and that's less than 1

[alpine sable]

I dont get it

[alpine sable]

can you explain what this is

[tacit arch]

it's a graph if the function

[alpine sable]

ok

but why -pi/4 < x < pi/4 instead of -45 and 45?

[tacit arch]

oh i thought this was degrees

Is it?

[alpine sable]

doesnt say so

[tacit arch]

then there are a lot of solutions

[alpine sable]

how?

[tacit arch]

,w plot sin(x) for -45 < x < 45

[ocean seal]

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[tacit arch]

15ish solutions

,w solve sin(x) = 1

[ocean seal]

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[alpine sable]

is there a way to solve using a unit circle?

[tacit arch]

do you know radians?

[alpine sable]

nope

I understand very little though

[tacit arch]

uhhh, were you taught radians?

[alpine sable]

not yet

we used the unit circle but not with radians

[tacit arch]

what units are 45 then?

[alpine sable]

what you mean

[tacit arch]

https://upchieve.org/blog/2021/4/18/what-are-radians

[alpine sable]

ok

[tacit arch]

i'm pretty sure the 45 is 45 degrees

and your formatting just omitted the $\circ$ character

[ocean seal]

riemann

[tacit arch]

Just like how it lower cased the G

[alpine sable]

yea

I was going to say the first solution worked

but I have question

why did you used -pi/4 instead of -45

[tacit arch]

pi/4 radians is equal to 45 degrees

it's like 1 kilometer = 1000 meters

the conversion to remember is 180 degrees = pi radians

[alpine sable]

man this is confusing

you know any trignometry playlist?

[tacit arch]

https://www.khanacademy.org/math/trigonometry

[alpine sable]

can you explain how you got 0.70710678118655 from this

[tacit arch]

,calc sin(pi/4)

[ocean seal]

Result:

0.70710678118655

[tacit arch]

,calc sin(45 deg)

[ocean seal]

Result:

0.70710678118655

[tacit arch]

the graph looks like it's increasing from left to right. so the maximum is the right most point

[alpine sable]

i graphed it

[tacit arch]

yup. that's because 90 degrees = pi / 2 radians

which follows from 90 degrees = 180 / 2 degrees = pi / 2 radians

[alpine sable]

so that is the max correct?

[alpine sable]

you learnt all this from here?

[tacit arch]

no, but khan academy is great

get a real trig textbook if you want to learn properly

[alpine sable]

i have one

[fervent timber]

this is impossible; you did something wrong when you calculated g

[alpine sable]

?????

[fervent timber]

there are no solutions for a in that interval

[alpine sable]

that was written by my teacher

[tacit arch]

try skimming through it

you should be able to find an explanation for 180 deg = pi rad

[alpine sable]

why do radians exist tho

[fervent timber]

just tell them there’s no solution then

[alpine sable]

great way to fail assignment

[fervent timber]

don’t worry about it if you haven’t covered radians; it’s advanced stuff

it’s an advanced concept but also super useful

[tacit arch]

https://en.wikipedia.org/wiki/Radian#History

[alpine sable]

So coming back,

I say sin(0.70....) = 1?

or sin inverse

ok it works

arcsin is sin inverse right @tacit arch ?

just to know before i close

,w plot sin(x) for -pi/4 < x < pi/4

[ocean seal]

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[alpine sable]

.close

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[weary pivot]

I would like to get help with stats

[weary pivot]

Is it correct?

I feel like my working out is very messy

Do u know how I could write it better?

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@weary pivot Has your question been resolved?

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@weary pivot Has your question been resolved?

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[slim mason]

I’m not really understanding how to approach 5

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[severe gyro]

i solved the expression and got 729g^3y*4sqrty^2

im meant to solve for r, s, and k

i got r and k correct but i cannot solve for s

for r i got 3 and k i got 729

for s i tried 4/2 and 2/4 and both were wrong

[languid portal]

why not divide both sides by kg^r and take the log_y of each side?

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[wary stream]

What is the correct answer?

My suggestion, convert to yards first

It'll be easier

Because 36 is 36 ft^3

Then you divided by 3 yards

That's 36 ft^3/3 yd

The units don't match for the conversion

1 ft = 3 yd

1 ft^3 = 27 yd^3

That was the mistake

Yeah, it'll make it easier

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[real solar]

Why did you close the other one? But yeah looks right at a quick glance

Integral is setup right

Yeah looks good

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[gilded kiln]

im having trouble understanding the difference between what a period and a cycle of a graph is

[gilded kiln]

is the cycle of a graph half it's period?

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[alpine sable]

Cos theta + i Sin theta = ?

[lapis panther]

e^(iø) ?

[alpine sable]

Thank you :)

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[cedar kraken]

ik how to do part A

4x+10y=80 is the answer for part A

[lapis panther]

hey

[cedar kraken]

hey

[lapis panther]

so yk the wire is of 80 cm and part of it used for square and the other is for rectangle

[cedar kraken]

yep

[lapis panther]

and in a) they have given "length of the side of square is x cm"

[cedar kraken]

yes

[lapis panther]

and now yk u can find the length of the all sides of square = 4x, right?

u get it this?

[cedar kraken]

yes 4x is the perimeter of the square