help-13

[cedar kiln]

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[vernal basin]

ok so white white black and 14 beans

well first you have a 1/14 of drawing a white beans

then you have 13 beans and 6 white

wait

no I'm stupid awuoefhawuoljef

you have a 1/2 chance of drawing a white bean

then you have 6 white in 13 beans

so multiply 1/2 by 6/13

then you have 5 white and 7 black in 12 beans

1/2 * 6/13 * 7/12 I believe

36/312

[buoyant latch]

7/14 * 6/13 * 7/12

[vernal basin]

6/52

[buoyant latch]

there's still 7 black beans

not 6

[vernal basin]

oops

yeah

so

42/312

7/52

[crimson sedge]

thank youu

.close

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[granite belfry]

how do i do q17?

[rigid ridge]

uwu rotate

[rigid ridge]

solution I: plug in the values
solution II: let tom,harold,patrick be a,b,c. Then a+b+c=9793 and 6(a-29) = 3(b-24) = 4(c - 20)

[flint plinth]

well harold's share minus $24 needs to be 4/(2+4+3) of the total (where the total is after subtracting the $29, $24, $20)

[rigid ridge]

ah nice

that's a better solution

https://cdn.discordapp.com/emojis/947850838313951293.webp?size=48&quality=lossless

[mossy flower]

hmm

[flint plinth]

the lazy man's solution 😁 find only what is asked for

[rigid ridge]

the real lazy man's solution is checking A,B,C,D in order

[flint plinth]

haha yes of course

[granite belfry]

how did u get 4/(2+3+4)?

[flint plinth]

from the fact that their ratios need to be 2:4:3. this is true when to has 2/(2+4+3) of the total, and harold has 4/(2+4+3), and patrick has 3/(2+4+3)

[mossy flower]

we can also subtract the total sum by 29,24,20 and then divide by 9

ryt ?

[flint plinth]

yeah

[granite belfry]

i got 1080 after doing that

[mossy flower]

like 2x + 4x + 3x = 9793 - 29 - 24 - 20

[granite belfry]

ohh

wait yeah

9720/9

is 1080

[mossy flower]

ye

[flint plinth]

yep

[mossy flower]

since harold is 4x so 4 x 1080

[flint plinth]

and then harold's reduced share is 4 x that

[mossy flower]

which is 4320

[flint plinth]

then you add back the 24

[granite belfry]

oh teh answer is A tho

[mossy flower]

oh yes

[granite belfry]

ohh right

thanks everyone

[mossy flower]

add the 24

[granite belfry]

.close

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[lucid sparrow]

do question A and b please

[wicked hill]

what have you tried?

[lucid sparrow]

im completely clueless but i understand that bayes theorum is used

@lusty birch

[elfin hemlock]

Write definition of the sample average

[cedar kiln]

@lucid sparrow Has your question been resolved?

[lucid sparrow]

no

@cedar kiln

[high coyote]

$\overline{X}:=\frac{1}{n}\sum\limits_{i=1}^n x_i$

[wraith dagger]

jnkena

[high coyote]

$\frac{1}{n}\sum\limits_{i=1}^n(x_i-\overline{X})=\frac{1}{n}\sum\limits_{i=1}^n\left(x_i-\frac{1}{n}\sum\limits_{i=1}^n x_i\right)$

$\frac{1}{n}\sum\limits_{i=1}^n\left(X_i-\overline{X}\right)=\frac{1}{n}\sum\limits_{i=1}^nX_i-\frac{1}{n}\sum\limits_{i=1}^n\overline{X}=\overline{X}-\frac{1}{n}\cdot n\cdot\overline{X}=\overline{X}-\overline{X}=0$

[wraith dagger]

jnkena

[high coyote]

@lucid sparrow, do you understand?

For the second one we have

$P(D)=0.05\$

[wraith dagger]

jnkena

[high coyote]

$P(+|D)=0.99$

[wraith dagger]

jnkena

[high coyote]

$P(+|\overline{D})=0.05$

[wraith dagger]

jnkena

[high coyote]

$P(D|+)=\frac{P(+|D)P(D)}{P(+)}=\frac{P(+|D)P(D)}{P(+|D)P(D)+P(+|\overline{D})P(\overline{D})}$

[wraith dagger]

jnkena

[high coyote]

$P(D|+)=\frac{0.99\cdot 0.05}{0.99\cdot 0.05 + 0.05\cdot 0.95}$

[wraith dagger]

jnkena

[high coyote]

$P(D|+)=0.51030927835\simeq 51.03%$

[wraith dagger]

jnkena

[cedar kiln]

@lucid sparrow Has your question been resolved?

[cedar kiln]

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[frigid canyon]

i need some help in understanding about the radius of the Earth

[frigid canyon]

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

well

i saw the geocentric radius and felt that it's fine as radius must change along with latitude

but there seems to be no reason that it changes with longitude as well

[cedar kiln]

@frigid canyon Has your question been resolved?

[frigid canyon]

<@&286206848099549185>

anyone?

[spice tundra]

this is what the ai reckons

the ai gives a better answer the more specific you ask it, so if that doesn't help make it more specific and give it a shot

[cedar kiln]

@frigid canyon Has your question been resolved?

[nova trout]

what ai is that if you dont mind me asking?

[cedar kiln]

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[craggy moth]

Divide 120 in the ratio 5:3

[craggy moth]

it's probably very obvious but i don't know the solution behind this maths equation

[fickle trellis]

Um hi.

[craggy moth]

helloo

[fickle trellis]

So does the question ask you to divide 120 into the ratio 5:3

[craggy moth]

yes

[fickle trellis]

So basically how ratios work here is that

$5x+3x=120$

[wraith dagger]

Muhammad Hussaini

[craggy moth]

right..?

[fickle trellis]

Lemme simplify a bit

You have something known as the common ratio

[craggy moth]

mhm

[fickle trellis]

So if you have to divide something into a and b

You can write the two things as ax and bx

If you gotta divide 120 into a ratio of 5:3

Or one number should be five times something x... and another number should be three times x, and both should add up to 120

That is what it means

So then all you gotta do is put it like this

Common ratio = $x$

One number = $5x$

Another number = $3x$

$$5x+3x=120$$

[wraith dagger]

Muhammad Hussaini

[fickle trellis]

Solve for x and find the numbers

[craggy moth]

okay ill process this in my head for a bit because im still a but confused

so that wouldn't mean 5x+3x +120 is the answer right?

is there an easy way to find the numbers? or do you gotta guess random numbers

oh so 8x=120

soo what do i do after that?

i feel like i got this wrong but

[fickle trellis]

Its going good

[craggy moth]

5x+3x=120

8x=120

[fickle trellis]

8x=120

Yeah

So whats x

[craggy moth]

x=120/8

=15??

[fickle trellis]

Yeah

So x is 15

[craggy moth]

does that mean the final product doesn't have to be a ratio?

omg that makes so much sense now

[fickle trellis]

No... now see what we do here

[fickle trellis]

Refer to this

You are finding those two numbers

[craggy moth]

yes

[fickle trellis]

You didnt know the common ratio until now

Now you know it

15

So plug in the value of x in both numbers

[craggy moth]

so 5x15(75)+3x15(45)

= 75+45 = 120

oh my god that makes so much sense

is that the end of the solving?

[fickle trellis]

Yep so actually the numbers are 75 and 45

Now lets see what that ratio means

[craggy moth]

75:45??

[fickle trellis]

Just for you to understand

YEah

And

75:45 = 5:3

Thats what we were doing the whole time

[craggy moth]

omg

wow

so this is the end?

[fickle trellis]

Did you get it or should I use a different way to make you understand

[craggy moth]

no i do understand but if there is an easier way you could tell me

so you just make the equation into an algebra question

[fickle trellis]

Yeah

[craggy moth]

ohhh okay

thanks so much!!

.close

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[craggy moth]

.reopen

[cedar kiln]

✅

[fickle trellis]

Yeah?

[fickle trellis]

Youre welcome

[craggy moth]

.close

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[mossy flower]

What is the value of |-30 + 80| ?

[quartz vale]

what do you think?

[mossy flower]

i think 50

[quartz vale]

yep

[mossy flower]

oh

so it is not 110

thonxe for confirmation

[buoyant latch]

|| works like brackets

you do what's inside first

[mossy flower]

ok

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[midnight needle]

Can someone help me with these questions? I have to submit it in 5 hours and I am ineligible to compete in exam without them.

[amber pier]

what have you tried yourself

[cedar kiln]

@midnight needle Has your question been resolved?

[midnight needle]

I haven't done anything, this is my friend's graded assignment

He has submitted previous 3 week assignments and not able to do these because he's stuck somewhere, he has exams on 5th June and without these assignments, he can't appear in the exam

And today is the deadline

In 4.5 hours

Please help, his future depends on this

[amber pier]

I am not having none of it

[calm sierra]

getting outside help seems to defeat the purpose of the assignment

also ur friend should be here asking for help, not having u act as a middleman

[ocean hill]

Some solution for this?

[calm sierra]

@ocean hill use a free channel

[cedar kiln]

@midnight needle Has your question been resolved?

[cedar kiln]

@midnight needle Has your question been resolved?

[cedar kiln]

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[crimson sedge]

when 27 is divided by x, the remainder is x - 3. If x must be an integer, what are all the possible values of x

[rigid ridge]

use the definition of a remainder

[crimson sedge]

$\frac{27 - (x-3)}{x}=quotient?$

[wraith dagger]

kube

[lyric jungle]

You can rewrite that as 27 = x*q + x - 3, x,q ∈ ℤ

[rigid ridge]

yes, where the quotient is some integer

[crimson sedge]

this is where im stuck i don't know where to go from here

[lyric jungle]

Simplify everything

Factor where you can

[rigid ridge]

like castroploiin suggests, let the quotient be an integer q

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[dark olive]

how do i do 8c ii

[crimson sedge]

you should make v equal to the vector but just make the value equal to a constant with it

[sage forge]

I don't think it has to be exactly equal to it as it can also be a multiple

[cedar kiln]

@dark olive Has your question been resolved?

[dark olive]

i cant find any values of t that would make v = the given vector

[cedar kiln]

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[boreal kiln]

what is the formula for this question

i forget the formula but i can get everything else done after that

[crimson sedge]

hello

can someone help me w stereometry

[velvet mortar]

This is taken

[devout radish]

Google is your friend

[boreal kiln]

i looked it up already couldnt find it

[devout radish]

Area of a sector?

[boreal kiln]

lmao im so stupid my fault i misspelled sector the first time looking it up

[velvet mortar]

.close

[boreal kiln]

.close

[cedar kiln]

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[minor sparrow]

can someone explain what I is in question 8?

[minor sparrow]

A-2I

i know how to transpose and all that but is I just a diagonal matrix like
[1 0
0 1]

[crimson sedge]

Identity matrix

ye

[minor sparrow]

diagonal matrix + square matrix = identity matrix

understood thanks

and then for question 8 I got

D^2 = [25 0 0 100]

to find D do i just square root?

get [5 0 0 10]?

[crimson sedge]

hmmm

I don't think you can just square root matrices like that

basically

you have matrix D

let D be of form

[minor sparrow]

wait i found the answers lol sorry

[crimson sedge]

[ a b
c d ]

D squared would be

[ aa + bc ab+ad
ca+dc cb+dd ]

from there you get equations with the matrix you got

a^2 + bc = 25

ab+ad = 0

ca+dc = 0

cb+d^2 = 100

solve for a,b,c,d to get all matrices

oh it says diagonal matrices

so b and c are 0

well that makes it easier

[mild spade]

if you care what the solution is

[cedar kiln]

@minor sparrow Has your question been resolved?

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[cedar kiln]

Please don't occupy multiple help channels.

[gray light]

How should this be solvencia?

Solved

I was trying to convert into e

And then get out the log

But I have no idea how

[dire geode]

maybe this will help
https://www.youtube.com/watch?v=6A4pbsXcI84

[gray light]

Alright

Let me see

[somber belfry]

is the exponent just in the numerator or for both

[dire geode]

looks like both
#help-4 message

[gray light]

on both

[bold hinge]

1/e

[cedar kiln]

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[thick bronze]

What's the answer to this and how do I get there?

[dire geode]

there's no question

[cosmic steppe]

You just posted a variable

Like

An equation

If you want an answer, then how about giving us actual information

[thick bronze]

This is the only context mate

I'm trying to get to x to the 4 which is said to be the answer

But none of what I try works

[broken tartan]

use properties of exponents

[cosmic steppe]

You have context and not the whole thing. What are you trying to do? Solve for zeroes or simplify?

Again, we don't know what you're trying to do

[broken tartan]

$\frac{x^a}{x^b}=x^{a-b}$

[wraith dagger]

MinecraftUser525

[broken tartan]

he's tryna simplify it

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

[wraith dagger]

MinecraftUser525

[thick bronze]

I know these but I can't seem to achieve the result

Let me explain where I'm stuck then

[broken tartan]

ok

[cosmic steppe]

So you're trying to simplify

[thick bronze]

(X to the -2) squared, what does that give me

[broken tartan]

x^-4

[cosmic steppe]

You can start with the $\left(\frac{x}{x^3}\right)^2$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

What would that simplify to?

[broken tartan]

$(x^{-2})^2 = x^{-2\cdot 2}$

[wraith dagger]

MinecraftUser525

[broken tartan]

so x^-4

because you can multiply these exponents

[thick bronze]

Yes indeed

But the answer cannot be x to the 4 in the end

[broken tartan]

wdym

[thick bronze]

I don't get how you reach it

[broken tartan]

once you have $x^{-4}$

[wraith dagger]

MinecraftUser525

[broken tartan]

you have

$\sqrt{x^{12}\cdot x^{-4}}$

[wraith dagger]

MinecraftUser525

[broken tartan]

$x^{12}\cdot x^{-4}$

find this first

[wraith dagger]

MinecraftUser525

[cedar kiln]

@thick bronze Has your question been resolved?

[thick bronze]

Yes but that doesn't make it x to the 4?

[broken tartan]

yeah but it's inside of a square root

$(x^8)^{\frac{1}{2}}=x^4$

[wraith dagger]

MinecraftUser525

[thick bronze]

Thank you mate

Lifesaving in terms of my brain cells evaporating

[cedar kiln]

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[cedar kiln]

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[tacit tangle]

A particle is moving at a velocity described by the function with respect to time. Find the acceleration of the particle at time t = 1 s.

[static sage]

this isnt a physics server

basically you want to take the derivative

[crimson sedge]

Bruh

[crimson sedge]

I do this in my math class

[tacit tangle]

oh sorry

[crimson sedge]

Physics is math

[static sage]

moot

[crimson sedge]

No reason for it not to be here

[static sage]

if ur not gonna help go away

[crimson sedge]

Ok

[static sage]

you want to take the derivative

and then find it at t=1

[tacit tangle]

so i have to derive te^t2

[static sage]

yeah do u know how

[crimson sedge]

Basically acceleration is the derivative of velocity

[static sage]

they know 🤦

[crimson sedge]

So find v’ and plug in 1 for t

[static sage]

i literally just said that

[crimson sedge]

I give up

[tacit tangle]

dont fight XD

alright will do that thank you!!

[static sage]

do u know how to do this from here

[tacit tangle]

im still not sure t-t

[static sage]

ok

this is basically product rule

the derivative of f(x)g(x) = f'(x)g(x) + f(x)g'(x)

[tacit tangle]

is this correct (2t^2+1)e^t2

[static sage]

,w derivative of x*e^(x^2)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Induction#7850

[static sage]

youre right

now plug in t=1

maybe idk if you plugged it in correctly you should get the answer

if it makes sense to you then trust yourself

[tacit tangle]

alrightt, a big thankss!

[static sage]

np

[cedar kiln]

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[cedar kiln]

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[unkempt aspen]

Hello, I would like help with factoring ((15-3x)/5)^2

I get (3 (-3x/5)) (3 (-3x/5))

and FOILing I get

9 - 9x/5 - 9x/5 - (9x^2)/5

I am really confused on how to properly square it

Specifically, once I go into the factored form FOILing it out gets me wrong answers and I am going crazy

[cedar kiln]

@unkempt aspen Has your question been resolved?

[cedar kiln]

@unkempt aspen Has your question been resolved?

[thorn turtle]

you can just use (a-b)^2 = a^2 - 2ab + b^2..?

the one you got seems correct for me tho

except it should be 9 - 9x/5 - 9x/5 + 9x^2/25

(last term)

[cedar kiln]

@unkempt aspen Has your question been resolved?

[buoyant latch]

You’re doing it really weirdly

First you should separate the 1/5² away because it’s just gonna confuse you

Then factor out 3 from the top, square it, stick it with the 1/5² on the side out of the way

[unkempt aspen]

I didn't think of that as a possibility

[buoyant latch]

Now you have just (5-x)² *9/25 the ending part you will deal with later

So ignore the 9/25 and focus on the (5-x)²

Expand that first

[unkempt aspen]

I ended up harassing some of my friends and realized that if I kept it as a fraction

I could multiply it together regularly only FOILing the top

I end up getting

(225-90x+9x^2)/25

which I think? is the correct answer

[buoyant latch]

Yes it looks good

[unkempt aspen]

alright, I appreciate you guys looking it over

[cedar kiln]

@unkempt aspen Has your question been resolved?

[cedar kiln]

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[frosty ocean]

Number of ways of awarding the student is $^{39}p_{4}=\frac{39!}{35!}$

[wraith dagger]

QuantumBee

[frosty ocean]

And then, then the four winners can be arranged in 4! ways.
So, the total number of ways should be $\frac{39!}{35!}\cdot4!$

[wraith dagger]

QuantumBee

[frosty ocean]

It's not there in the options.

Where am I wrong?

[bright river]

Here the order in which they are awarded do not matter, so you indeed have to look at the possible arrangements of the winners. Here this reduces the number of possibilities (ex : awarding student 1, student 13, student 28, student 15 or awarding student 15, student 1, student 13 and student 28 is the same "possibility" of awarding students 1,13,15,28)
Hence you should divide by 4!

[frosty ocean]

Alright

got it!

thanks

.close

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[radiant jolt]

someone teach me how to solve this

[cedar kiln]

@radiant jolt Has your question been resolved?

[radiant jolt]

@uncut veldt

[buoyant latch]

Do you know what’s special about completing the square?

[radiant jolt]

wait I'll be back lim stared helping me with

that question

I didn't mean

to have two chanels

he just invited me in that

[buoyant latch]

Dw about it

[radiant jolt]

ok I'm back

alr let's do question 8

wait I minute

for quadratic

is it just like

y-y1=m(x-x1)^2

doesn't matter, how do I know the equation cuz I only have

the vertex

@uncut veldt

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[cedar kiln]

@crimson sedge Has your question been resolved?

[shut reef]

Well

x²*x² would be x⁴

and 2x²*x=2x³

which means it crosses it thrice

[obsidian coral]

The power denotes how many roots there are. So if it's x^3, that's 3 roots

And x^2 is two roots

[shut reef]

If the power is 3, 5, 7... it chrosses three times

if the power is 2, 4, 6... its 2 times

If I remember correctly

ofc it depends on where its located

[obsidian coral]

Well, as I mentioned, the power tells you how many roots, not how many times it crosses. You can have a function with 3 roots but cross the x axis once

[shut reef]

well if its below or above the x axis its once

But in some cases yes

But it seems that it crosses once with those

You can use the quadratic formula or factor those out

oh damn

so

$b^2-5b-36=0$ how do we continue

[wraith dagger]

.,..

[shut reef]

@crimson sedge

Well what's the quadratic formula @crimson sedge

[cedar kiln]

@crimson sedge Has your question been resolved?

[fossil hamlet]

you could use the quadratic formula, so (-b +- root(b^2-4ac) / 2a,, or you could factorise it which is the fastest way

so you think what 2 numbers multiply to get -36 and add to get -5,, which would be -9 and 4

so the quadratic can be written as (b - 9)(b + 4)

[shut reef]

Yes

[fossil hamlet]

and then the roots would be b = 9, -4 because when b is 9 or -4 then the whole expression would be 0, ie the answer

[shut reef]

Yes but he needs to learn it

@fossil hamlet

[fossil hamlet]

yes?

let them read it

[cedar kiln]

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[crimson sedge]

hi

[crimson sedge]

this is a practice test just so yall know

1b is the one that i didnt understand

like what is 2k?

[distant rune]

What grade are you in

Just wondering

[crystal raptor]

k is the unit vector in the z direction

[0,0,1]

[crimson sedge]

12

[distant rune]

Oh ok I’m only year 11 so haven’t done 3d vectors

[crimson sedge]

oh ok

[crimson sedge]

so how do i solve it?

[2,-4,-1] + 2[1,-2,4] - what?

[crystal raptor]

Read what I said carefully, it's basically the same as you're doing for u and v

[crimson sedge]

i dont get it

just add one to u3 and v3 or what

[crystal raptor]

k is [0,0,1] so what is 2k?

[crimson sedge]

0,0,2

[crystal raptor]

So that's what you're taking away

[crimson sedge]

[2,-4,-1] + 2[1,-2,4] - [0,0,2]

is this right

[crystal raptor]

Yes

Simplify and find the magnitude

[crimson sedge]

4,-8,1 is the answer?

<@&286206848099549185>

[crystal raptor]

Where did you get 1 from

Also the question is asking for the magnitude of the vector

[crimson sedge]

could you please solve it

i dont get it

[crystal raptor]

Not what we're here for

Try calculating the 3rd coordinate again

[crimson sedge]

.close

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[rugged tusk]

in group $(ghg^{-1})^{-1} = (g^{-1}hg)$ ?

[wraith dagger]

Michal

[rugged tusk]

is it true ?

[celest ledge]

No

[foggy merlin]

(ghg^{-1})^{-1} = (hg^{-1})^{-1}g^{-1}

[celest ledge]

gh^-1g^-1

[foggy merlin]

gh^{-1}g^{-1} is the result

[rugged tusk]

uhm

thanks

.close

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[crimson sedge]

$(\forall y \in \mathbb{R})(\exists x \in \mathbb{R})[y = \sqrt[3]{x}]$

[wraith dagger]

mahmooz

[crimson sedge]

im not sure whether this function is surjective

cant x be like -8?

and then y = -2?

so its defined for all x and y?

[cedar kiln]

@crimson sedge Has your question been resolved?

[opal matrix]

you are right, it is surjective

[cedar kiln]

@crimson sedge Has your question been resolved?

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[crystal raptor]

What's A_1?

[icy steppe]

it doesn't mention it

[crystal raptor]

Use the definition

[icy steppe]

gotcha will do

[cedar kiln]

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[molten flower]

Sorry I'm not good with graphing at all 😔

[crystal raptor]

Can you find the centre of the circle?

[molten flower]

The centre?

Oh

Uhm

Maybe 9 on each sides

I'm not good with this

I apologize

[crystal raptor]

What are the coordinates of the middle of the circle?

[molten flower]

The coordinates?

Well

[keen rapids]

is it given?

[molten flower]

Given?

What do you mean?

Like any answer options?

[keen rapids]

does it say anywhere else where the center of the circle is

or do you have to find out yourself

[molten flower]

Find it out myself

[crystal raptor]

You just read off from the graph

It's what the dots are for

[molten flower]

Oh

[keen rapids]

if the grid is accurate, just find the dot that's in the center

[molten flower]

Hmm

Lemme try

[keen rapids]

then count how many dots it is away from the origin

[molten flower]

Alright

[keen rapids]

like 2 horizontally and 3 vertically or something

it's not the answer

just an example

[molten flower]

Oh

There's 7 vertically

3,

But the circle goes all the way up to 7

[keen rapids]

no no from the center

[molten flower]

Wait

Ohhhhhh

[keen rapids]

did you find the center?

[crystal raptor]

The middle of the circle

[molten flower]

Yea

I found it

[keen rapids]

now from the center, go down dots till you're at the same level as the origin

[molten flower]

I believe it's 6

Alright

[keen rapids]

we have to count vertical and horizontal separately

[keen rapids]

how many dots did you go down?

[molten flower]

4

[keen rapids]

nice

now go left

[silent yew]

||After moments of straining my eyes the centre seems to be (2,4)||

[molten flower]

I understand that feeling 😭

But I went 4 times

Left

[keen rapids]

was gonna say

lol

[keen rapids]

? should be 2 tho

[molten flower]

Oh

I randomly chose the answer on accident, I got it right though

Lol

[keen rapids]

sooooo basically 2 horizontally, 4 vertically

[keen rapids]

nice

[molten flower]

Yea

Oh

My

God

This next question I hate the most

Alright lemme try to figure it out

Do I close?

[keen rapids]

if you want sure

[molten flower]

Wait I can ask multiple questions?

[crystal raptor]

You haven't finished the question

[molten flower]

I have

I got the answer right

[crystal raptor]

What was your answer

[molten flower]

Even though it was on accident

Trust me bro

I forgot

It was like parentheses 2 and 4

[silent yew]

I don't think u found the answer

[molten flower]

I believe

And the = was 25

Yea I said I chose it on accident

[silent yew]

No, u should do it properly

[molten flower]

Alright

Let's continue then

[silent yew]

Write the equation

On a page

[molten flower]

Ok

OH WAIT

It was (x+2)^2 + (y+4)^2 = 25

[crystal raptor]

• not +

[molten flower]

Yea

Because I went down

[silent yew]

Wrong

[molten flower]

So I'm creating space from the origin

Sorry it was a mistake

But I got my answer

Thank you guys

Oh this problem is easy

Alright

.close

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[dapper wraith]

What did they do to get 3pi/4?

[keen rapids]

if tan x = -1

[dapper wraith]

Ain’t that just -1/4pi?

[keen rapids]

yeah

-1/4pi = 3/4pi (edit: this is wrong)

[dapper wraith]

Ahhh okay makes sense

[keen rapids]

because it's the angle

[dapper wraith]

35 degrees I’m assuming

I just looked at the radians circle

[keen rapids]

wait wait

sorry i was wrong

[dapper wraith]

It’s kl 👍

[keen rapids]

it's because tan(x) is periodic with every pi

so tan(1/4pi) = tan(5/4pi)

that's why tan(-1/4pi) = tan(3/4pi)

[dapper wraith]

Ahhh

Yeah ur right

Idk why I took 5/4pi as negative as well 😂

Thanks @keen rapids for your help appreciate it

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[keen rapids]

np

[cedar kiln]

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[crimson sedge]

hello

[crimson sedge]

is x^2 called "x squared" or "x square"

???????

[keen rapids]

x squared

[rugged palm]

You can also say square of x

[obsidian coral]

Or x to the power of 2

[cedar kiln]

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[crimson sedge]

in how many ways can 1105 be expressed as the sum of two squares of natural numbers

[tribal pier]

that's an interesting question

[crimson sedge]

isn't there a theorem for that

[tribal pier]

I'm familiar with the difference of squares, which can be expanded into some complex number shenanigans, but not across the reals that I'm aware of

[dire geode]

https://www.youtube.com/watch?v=cZXVlhiXSwI

https://www.youtube.com/watch?v=ny7ytjfyXdQ

[crimson sedge]

oh boy

time to dive into another rabbit hole

[dire geode]

highly recommend michael penn videos. he's great

[tribal pier]

let's see... all sums here would imply that one of the squares is less than half while the other is greater than half, so you can technically brute force it by checking all perfect squares such that 1105-n is a square integer, where n is a perfect square less than 552.5

it's not elegant, but you might find some patterns to help with the problem

you'd only have to really check the first 23 perfect squares, so the total number is at most 23 cases

[crimson sedge]

I don't understand

oh so one of the numbers is less than 552.5 and the other is greater than it

[tribal pier]

yep

[crimson sedge]

if one of the numbers is n the other is 1105-n

[tribal pier]

and the square root of 552.5 is about 23.5

so just check the first 23 perfect squares. A little tedious, but not terrible. I'd recommend checking them starting at 23 and going down, since as the chosen square gets smaller, its complement gets larger, and therefore harder to easily check for squareness

[crimson sedge]

hmm ok

[tribal pier]

HOWEVER, I also recommend watching the videos, they're made by a great mathtuber, and probably contain great ways to generalize and save a lot of tedious work by hand

[crimson sedge]

oh one of the sums is literally the first one

23^2 + 24^2 = 1105

[tribal pier]

technically, if you wanted to, you could expand a^2+b^2=1105 as (a+bi)(a-bi)=105, basically asking for the real values of the complex factors of 1105. I'm still brainstorming how I'd do that to make things easier, though

or you could be smart and recognize that it's the equation of a circle with radius sqrt(1105)

[cedar kiln]

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[grand forge]

i need to get $2sin4y$

[wraith dagger]

Mortta

[grand forge]

in the form $pcosec(qy)$

[wraith dagger]

Mortta

[cedar kiln]

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[wooden night]

Why is in the first picture Re() and in the second one Im()?

[cedar kiln]

@wooden night Has your question been resolved?

[dire geode]

Use $e^{iz} = \cos(z) + i \sin(z)$

[wraith dagger]

riemann

[wooden night]

yeah that's what I've done

but why at the end I just need to consider the real part of the result?

[dire geode]

look at the integrand

recognize that $\cos(\pi x) = \mathscr{R}(e^{i\pi})$

[wraith dagger]

riemann

[wooden night]

oh right... thank you

.close

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[ruby cargo]

Hi so i need help with this vector task

[ruby cargo]

I have to find out the values of k and l

[cedar kiln]

@ruby cargo Has your question been resolved?

[cedar kiln]

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[ionic blade]

on part 1 i dont understand what properties i should be using

[balmy apex]

change of base

[ionic blade]

on part 2 i dont understand how the natural log will change the problem

[livid hound]

it doesn't, ln is just log with a different base
apply the same change of base law in part 1

[ionic blade]

how do i apply this?

[balmy apex]

$$\log_{b}(a) = \frac{\log_{x}(a)}{\log_{x}(b)}$$

[wraith dagger]

illuminator3

[balmy apex]

x is any arbitrary number

[ionic blade]

thank you so much

the course hadnt gone through that property

im glad i know it now

[balmy apex]

lmao typical

[ionic blade]

.close

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[marble radish]

can anyone help me real quick? i dont understand how to work out cos of 135

[marble radish]

also im not sure what -cos43 is

[cedar kiln]

@marble radish Has your question been resolved?

[marble radish]

<@&286206848099549185>

[dire geode]

why do you need to know the exact value of -cos(43 deg) ?

[marble radish]

why is it minus cos?

i understand for obtuse you minus 180 but wouldn't that make it 180 --43 because of the negative sign

[dire geode]

that's just what the problem asks for

[marble radish]

so its just aking you to minus cos43

[dire geode]

yes, -cos(43 deg) = minus cos(43 deg)

[marble radish]

can you look at cos 135 i dont understand how to get this either

[dire geode]

,calc cos(135 deg)

[wraith dagger]

Result:

-0.70710678118655

[dire geode]

i don't know what there is to look at?

[marble radish]

how do you get it to be -1/2

[dire geode]

that's not your work?

[marble radish]

no teachers example

[dire geode]

oh wow your teacher's handwriting is awful

[marble radish]

ahah yeah

[dire geode]

did you learn cos(180 - x) = -cos(x)

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Reflections,_shifts,_and_periodicity

[marble radish]

no i dont think sp

should i just write down these 6 formulars?

[dire geode]

what about these?

[marble radish]

no i dont think so '

riemann i understand that cos 135=cos45 but once i get 1/root2 why is the andwer then negative?

[dire geode]

this is wrong

cos 135=cos45

plot it on the unit circle

https://paws.kettering.edu/~ktebeest/courses/unitcircle.html

[marble radish]

i thought that was how refreance angles wiork

oh

[dire geode]

,calc cos(135 deg)

[wraith dagger]

Result:

-0.70710678118655

[dire geode]

,calc cos(45 deg)

[wraith dagger]

Result:

0.70710678118655

[marble radish]

so is -135 = to 45

[dire geode]

yea theta = 45 deg here

so using pi=180, 180-45 = 135

very powerful identity

[marble radish]

oh

so i should just remember the formulars and the sub it in when i need?

ok thanks for the help igtg ive got a maths exam in 20 mins

.close

[cedar kiln]

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[storm anchor]

Hey guys I'm trying to learn geometry and I'm confused on the last part in red.

[upper abyss]

External angles of any closed loop is 360

Because, if you were to follow the triangle's sides, you'd turn around once.

[storm anchor]

Ok thank you as you were typing I just figured it out.

Thank you.

.close

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[crimson sedge]

hi I was just trying to make sure I understand algebra so could someone look over what I did and see if I made any mistakes

[bold vine]

From Line 1 to Line 2 on the RHS the 7 was distributed incorrectly. You should have no 64.4 in the denominator.

The rest looks good though 👍

[crimson sedge]

denominator is the bottom one right?

[bold vine]

Correct - what is below the horizontal bar

[crimson sedge]

this good?

i think i did this very inefficently

[hardy snow]

Yes very good, not inefficient at all. Always better to show all of your work

[crimson sedge]

how could i do it better?

[hardy snow]

Impossible. You did it the best way. You followed all of the rules of math

[crimson sedge]

you said i did it inefficently

[hardy snow]

I said you didn’t do it inefficiently 😂

[crimson sedge]

ohh

sorry im bad at english

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[cedar kiln]

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[cedar kiln]

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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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[queen saffron]

Im a bit stupid, how do I do tan sin and cos rations when there is not big letter to use for reference. just one sidelength and a hypotenuse

[buoyant latch]

Remember SOHCAHTOA

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

So if u have a side length and hypotenuse u can find either angle via sine or cosine

[cedar kiln]

@queen saffron Has your question been resolved?

[queen saffron]

yeah

but what do i use as reference to find the op and adj?

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[cedar kiln]

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[crimson sedge]

what does this mean if Q is a set? ignore the parenthesis

[celest ledge]

I think B^A

Represent all maps from A to B

Depends on the context, like where is it from

It can mean all maps from Q to {0,1}. But you better show me the context

[celest ledge]

I see

[celest ledge]

Then probably this

[crimson sedge]

lol thats ambigous no 2 in that sentence

o wait theres 2 numbers

i dumb

ye got it thnx

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[queen saffron]

ok im kinda stupid

[queen saffron]

i put the opp over the hyp

wtf do i do with this number that i just got

[worldly siren]

what's the question

your trying to get the sin of what?

[queen saffron]

finding lengths thru sin cos

i have both the opp and hyp'

i divide them

now what

[modern compass]

That is sine of some angle

No idea what you’re trying to do, so no idea what’s next

[frigid canyon]

maybe just use pythagoras of you have 2 sides

[queen saffron]

idfk eityher

nah

its a right triangle with hypoyenuse of 18

lower angle of 32

the short and long leg are x and y

wait a fuckin minute

[modern compass]

What is the question?

[queen saffron]

x^2 + y^2 = 18rad2

i could pythag it ig

thew question is to find x and y

thru cos sin ratios

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[cedar kiln]

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Remember:
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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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[void spade]

How do I do this

I have no idea what to do

[grizzled umbra]

it cost
55 rupees 6 hours
then how much it cost for 31 days

[fallen moat]

,rotate

[grizzled umbra]

what rotate

oh damn

that bot

[fallen moat]

Okay, (a) first, to find CR, consider the triangle CBR

[fallen moat]

Please use another (available) channel.

[grizzled umbra]

ok

[silent yew]

@void spade which one are u struggling with?

[void spade]

uh

all of them

lmao

[silent yew]

Did u try the first one?

[void spade]

yes

[silent yew]

Could u do it?

[void spade]

no

[silent yew]

@void spade what is BC?

[void spade]

12

AD=BC

[silent yew]

And u know that angle

So what must be cr?

Do u know what sintheta is?

[void spade]

but i dont know what BR is

[silent yew]

U don't need it

What is sin theta in a triangle?

[void spade]

yes

[silent yew]

If 30° is that angle then what is sin30°?

[void spade]

-0.98803162409

[silent yew]

No

I didn't ask u that

I the triangle BCR, u know that angle B is 30°

[void spade]

ye

angle c is 60

[silent yew]

So sin(B) = CR/BC

[void spade]

bc angle r is 90

ye

[silent yew]

Sin(30°)=CR/12

So now u can figure out CR

[void spade]

oh

ok so CR=6

[silent yew]

Yeah

Now try the other

If u have any problem then ping

But try properly

[void spade]

OHHH

ok

i drew the AC line

[silent yew]

You have to find dq

[void spade]

ye

[silent yew]

How u gonna do it?

[void spade]

do i need to know what QR is

[silent yew]

No

Lmao inwas finding q

But i don't think u need qr

@void spade R u trying?

[void spade]

yes

[silent yew]

I will give u a hint

[void spade]

ok

[silent yew]

For the last two questions u will have to consider triangle DBC

[void spade]

dbb?

[silent yew]

Dbc

[void spade]

dbq

ok

[silent yew]

Lmao no

[void spade]

dbc