help-27

[sage socket]

oh

hmm

that's true

[small raptor]

do you know implicit differentiation?

[sage socket]

I do!

it's pretty straightforward

but the equation givin is not very nice

[small raptor]

its easier if you split the exponant

[sage socket]

what does that mean

[patent marsh]

nah it's not the prettiest lol, but it shouldn't be too bad. Just split up the e factors and you'l be golden

[sage socket]

split the exponent

[small raptor]

$e^{x+y} = e^{x}e^{y}$

just an example btw not your actual question

[woven radish]

Mortta

[patent marsh]

there we go lol

[small raptor]

oops!

[patent marsh]

haha it happens

[sage socket]

let me think about that

what's the goal then

if I have x and y

2 and 4

[small raptor]

dont worry about x and y for now,

[sage socket]

okie okie

[small raptor]

just differentiate

implicitly

[sage socket]

gotcha

[small raptor]

and find dx/dy

[sage socket]

right right

following

[quaint citrus]

Idk if u would be able to use it on a test, but if ur interested in studying more in math, there’s a method of differentiating these types of equations using partial derivatives that’s much easier, might be worthwhile to check out if ur interested. Just a side note tho, focus on this problem for now

[sage socket]

for sure

I haven't gone over those yet

I have a workbook that does though

my professor recommended not to go onto those chapters though :p

I got 2e^2x * e^-y dy/dx + e^2x * -e^-y = x^2 * -1/y^2 + 2x * y^-1

so far

all good?

the next move is to get dy/dx on one side IIRC

sorry it took me a sec to do that

[quaint citrus]

I didn’t check it but yea do that and we can go from there

[sage socket]

okie

[small raptor]

tell me

how did you get e^2x e^-y

[sage socket]

oh darn

I needed to do chain rule

[small raptor]

You tell me

[sage socket]

should be 2e^2x * -e^-y

using chain rule

wait sorry

so

let me just edit the top

[small raptor]

looks better

[sage socket]

peep the edit

[small raptor]

erm

you have it on the wrong side

$e^{2x}e^{-y}$

[woven radish]

Mortta

[small raptor]

use product rule

uv' + vu'

u = e^2x, v = e^-y

u' = 2e^2x

v' = -e^-y dy/dx

[sage socket]

oh

you mean the terms?

because it's addition

does it really matter?

ik it would for quotient rule

cause of the subtraction

[small raptor]

Im just confused why your dy/dx is on your e^-y and not on your -e^-y

[sage socket]

OHHHHH

yeah that was a mistake

mb

so

I moved everything with a dy/dx on the lhs

and everything without to the rhs

I can factor out dy/dx

divide what's in the () over to the rhs

and boom

I have dy/dx

[small raptor]

im confused

theres supposed to be a dy/dx on the right hand side too no?

[sage socket]

why??

OPMG

YOU'RE RIGHT

[small raptor]

because you differentited y^-1

[sage socket]

wait

I did that

I moved that over

already

that's why I was able to factor out the dy/dx

sorry if my hand writing isn't legible

[small raptor]

all g

mines not any better trust

ok now you know y and you know x, plug em in

[sage socket]

oh lord

I'm getting

a horrible looking number

-4(e^2-2) / 21e^2

[devout snow]

@sage socket Has your question been resolved?

[sage socket]

sure

[devout snow]

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[sage socket]

to me, the question is just asking me to find the 2nd deriv of the position function. Then, I need to find where that 2nd deriv is zero.

[sage socket]

for finding the poistion and velocity at those times, I'm assuming I'd plug in those values that I got from finding when the 2nd deriv is zero?

[lyric hornet]

then plug in those t values into the first derivative for velocity and the normal function for position

[sage socket]

omg

woooo

it sounds like I got it

.close

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[cinder berry]

I wanted to know how this works

!status

[devout snow]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[cinder berry]

1

<@&286206848099549185>

[west palm]

Hi

Do you know sine rule

[cinder berry]

yes

wait

no

I thought you said sine

[west palm]

Oh k

[cinder berry]

I too lazy to solve this I'm just gonna close this channel

thank you anyway tho

🙂

.close

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[devout snow]

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[cunning perch]

I don't understand any of these questions at all

I dont even know what mutually exclusive means and what union means

I try to look at definitions and stuff but it just doesnt click

i guess my understanding of question a is it is 0.1/0.4

so 1/4

but b and c I don't get at all

[topaz axle]

it's all about overlapping circles
union is like total area covered, by at least one of the circles
if 0.3 and 0.4 together cover 0.5, the overlap has to be 0.2

[cunning perch]

how is it 0.2

im a bit confused sorry

[topaz axle]

i can't explain stuff

[cunning perch]

oh

oh wait

I think I get it

Because

to find A|B

you need to do AnB/B

and we dont know AnB

so its

x/0.4=0.5

so x=0.2

wait

is A|B the same is AUB?

[topaz axle]

no

[cunning perch]

oh

[topaz axle]

you've seen 4 of your friends yesterday
you've seen 2 of your friends today
but you only have 4 friends
how is it possible

[cunning perch]

so is what I did wrong

[cunning perch]

sorry yeah continue

[topaz axle]

because you've seen some of them twice, the sum 4+2 is not equal to 4 but it's more

and like i literally can't handle the fact that you don't get it
it's a huge problem it ruins my mood for like 6 minutes

[cunning perch]

What does P(A|B) mean

Maybe I'd understand if I knew what it meant

I started learning this a couple min ago

[topaz axle]

you pick a random point in the rectangle, if it happens to be in some circle, that event happens. P(A) is the size of circle A and P(B) is the size of circle B.
P(A∩B) is the size of the overlap and the union is like size of them togeher but without counting overlap twice, just how much of the rectangle is inside one of the circles
P(A|B) is the ratio of intersecting part, A∩B, to B
it means that instead of picking a point anywhere, you pick a random point inside circle B, because you are certain that B happened.

[cunning perch]

Oh so it's P of A given B happened

[topaz axle]

yeah

you read | as "given"

[cunning perch]

Yeah

Oh wow I get it now

[topaz axle]

if they are mutually exclusive, just means they don't overlap

[cunning perch]

Because to find the overlap of the two

You add them and subtract the union

Oh ok thank you

[topaz axle]

great

mood unruined

[cunning perch]

So it's just 0?

[topaz axle]

yes

[cunning perch]

Ok now I get it

Thanks

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[shy topaz]

Hi, can someone help me with 10.2? I don’t understand why tan y = k/AB
is ABE a right angled triangle?

[devout snow]

@shy topaz Has your question been resolved?

[fleet inlet]

oh

is that a 3d diagram

wow

i did not see that

yes ABE is a right angled triangle as the netball post is vertical

and the players are on a horizontal plane

then you use trig

soh cah toa

[devout snow]

@shy topaz Has your question been resolved?

[shy topaz]

awesome :), thanks!

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[lime swan]

Can someone give me a suggestion on how to resonantly solve this problem im stuck

[lime swan]

Or do I just have to do 100000 steps until I solve it?

[devout snow]

@lime swan Has your question been resolved?

[lime swan]

yeah I just finished it this problem was specifically made to waste as much of your time as possible

.close

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[harsh flume]

how would you do this

ive tried making equations but im not sure where to go with them

[devout snow]

@harsh flume Has your question been resolved?

[harsh flume]

<@&286206848099549185>

[red heath]

name them and try cancelling something

[worn schooner]

Wait

[red heath]

in the equations

[worn schooner]

Make set equations of intersection, union, etc

It'll come out, if you do it right

!nosols

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[red heath]

i didnt solve

🤨

[worn schooner]

No, i didn't target you.

I just wanted him to know that we can't show him the ans but only guide him

[harsh flume]

this isn't hw

so I need to use set notation

[worn schooner]

Do you know the formula/equation to find total people in this?

[devout snow]

@harsh flume Has your question been resolved?

[harsh flume]

.close

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[nimble zodiac]

back at it again

[nimble zodiac]

let’s get it

Not sure how to rearrange numbers that are being multiplied or divided this isnt something i usually do

question 10

[nimble zodiac]

Oh wait

i just got that answer

wtf

tysm tho

[livid monolith]

all g

its a formula so make sure to remember it

[nimble zodiac]

will do

thanks

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[hidden dragon]

Is the range of g(x) in fog(x) a subset of domain of f(x)?

[restive river]

It has to be, no?

[hidden dragon]

So can it be equal as well or just be a proper subset?

Well I have sorted it out on my own so nvm and thanks.

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[worthy kraken]

Viewport size = screen size / device pixel ratio;
So for iPhone 12 pro: viewport size = 1170 x 2532 pixels, 19.5:9 ratio anyone can calculate that?
I guess the result will be 390 x 844

[main gull]

That answer looks fine

[worthy kraken]

Could you elaborate how can we calculate that?

[devout snow]

@worthy kraken Has your question been resolved?

[devout snow]

@worthy kraken Has your question been resolved?

[worthy kraken]

Anyone can do the math how can it be calculated? 1170 x 2532 and 19.5:9 to 390 x 844?

[whole badge]

Firstly, your question is rather passive aggressive, that attitude may discourage people to help you.

secondly, I'm not sure about how to do it but 1170/19.5*9 = 540, not 390 so I think your answer is wrong

[devout snow]

@worthy kraken Has your question been resolved?

[worthy kraken]

Got this information:
Screen size (resolution) is the number of physical pixels present on a screen.

Viewport or Viewport size is the number of software pixels (CSS pixels) present on a screen. Usually, viewport size displays as viewport width in pixels to viewport height in pixels.

Device Pixel Ratio (DPR) or CSS Pixel Ratio is the ratio between the physical pixels (screen size or resolution) and CSS pixels (viewport). Depending on device specification, one CSS pixel can equal one or mode physical pixels. Modern devices have screens with high pixel density resulting in the difference between screen size (resolution) and viewport.
Summary:
Screen Size (Resolution) = Viewport size × Device Pixel Ratio.
Viewport size = Screen Size (Resolution) / Device Pixel Ratio.
CSS Pixel Ratio = Screen Size (Resolution) / Viewport size.

Viewport size = screen size / device pixel ratio;
So for iPhone 12 pro: viewport size = 1170 x 2532 pixels, 19.5:9 ratio anyone can calculate that?
I want to find out the viewport size

[devout snow]

@worthy kraken Has your question been resolved?

[devout snow]

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[idle tiger]

Hello. Please help me with this. Would be really appreciated

@dry robin

.close

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[hidden hinge]

What did I do wrong here?

[topaz beacon]

remember that square roots have a plus or minus at the front

given the initial condition, you have to choose either the plus or the minus

[hidden hinge]

oh ok

[hidden hinge]

thank you

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[hidden moth]

Alright back with the trig identities, I can get the tan side to be tan theta + cot theta but that obviously doesn't equal the other side

[weak cove]

rewrite tan and 1/tan in terms of sine and cosine

and then make them have common denominators for adding

see what shakes out from that

[hidden moth]

something like this?

oh wait no the other way around

[weak cove]

so, the things you are multiplying by, you can't just do that

[hidden moth]

ok

[weak cove]

to make them have common denominators, you have to make the one on the left

the sin/cos

have a denominator involving a sine like that one on the right has

so multiply it by sin/sin

this is fine, because multiplying by 1 is all you are doing and it doesn't change the equation

but it also makes the denominator sin(theta)cos(theta)

and then the one on the right, it already has the sin and needs the cosine, so multiply it by cos/cos

[hidden moth]

that's what I was trying to get at

ahh

but then won't the trig functions be squared on the top?

A HA they = 1

thanks austin!

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[thorn sage]

Original message edited

[thorn sage]

It's d

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[thorn sage]

Whops

[devout snow]

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[hidden dragon]

If a is any real constant, and I have function f(x)=(a-x)/(a+x), can I say that range of f(x) is R-{-1}?

[hidden dragon]

Because I was taught that, to find range of linear function/linear function I got to remove the ratio of coefficient of x from whole real number set.

[restive river]

I think you mean R-{-a}

[magic thicket]

,w plot (1 - x) / (1 + x) over [-10, 10]

[magic thicket]

that's the domain

[hidden dragon]

Like, range of (ax+b)/(cx+d) would be R - {a/c)

[restive river]

Oh whoops

brain

[woven radish]

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[magic thicket]

idiot WA

[magic thicket]

yes

[hidden dragon]

No I already know that domain is R-{-a}.

[magic thicket]

because each branch is the half line above or below -1

[hidden dragon]

Ohh

,w graph (2-x)/(2+x)

[woven radish]

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[hidden dragon]

So range is R-{-1} for sure?

actually there is a question

In which f is defined from R-{-a} to R

When it should have been from R-{-a} to R-{-1}

[magic thicket]

either is fine

you don't have to define functions in such a way that they are surjective

[hidden dragon]

Oh that's true

Ty

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[neat turtle]

On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?

[devout snow]

What step are you on?
1. I don't know where to begin
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3. I got an answer but I'm told it's wrong
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6. None of the above

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[devout snow]

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[verbal coral]

Hi i need help

[jaunty mantle]

<@&268886789983436800>

[jaunty mantle]

Have you tried labeling the f’ f’’ and f’’’?

[verbal coral]

yeah

@jaunty mantle

[jaunty mantle]

What’s the slope of f(x) at this point

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[proud zodiac]

hey

[proud zodiac]

i need help with math pre calc

[tall knoll]

what about it do you need help with?

[proud zodiac]

What do i put in the

other boxes?

0 0

am i suppose to put this in a calculator?

[near stone]

Hint: use a unit circle

,tex .unit circle

[proud zodiac]

tex.unit circle?

[woven radish]

Akira

[proud zodiac]

okayy what should i do now.

[near stone]

As the theta you need to replace it based on the number given on table like this 6sin(3(0)/2) etc

and if you want to check your answer use a calculator

[proud zodiac]

okay

how do iuse the calcultaor

it seems easier

ay

hey

[near stone]

are you using a real calculator or online?

[proud zodiac]

none

i should use online

right

[near stone]

if you don't have a calculator irl then yes use the online

[proud zodiac]

ok

what do i put on it

[near stone]

start with 0

6*sin(3(0)/2)

[proud zodiac]

okay

mmm

confusion

[near stone]

,calc 6*sin(3(0)/2)

[woven radish]

Result:

0

[proud zodiac]

o

[near stone]

,calc 6*sin(3(15)/2)

[woven radish]

Result:

-2.9230470747631

[proud zodiac]

OKOK

[near stone]

does it says you need to write it as fraction? just curious

[proud zodiac]

i write it like -2.92

,calc 6*sin(3(30)/2)

[woven radish]

Result:

5.1054211472047

[proud zodiac]

,calc 6*sin(3(45)/2)

[woven radish]

Result:

-5.9941288802078

[near stone]

so you're all good now?

[proud zodiac]

No

i need to learn to graph it

it has to be a flower

let me fill this in , itll take 1 minute.

,calc 6*sin(3(60)/2)

[woven radish]

Result:

5.3639799816033

[near stone]

do you know desmos?

[proud zodiac]

not really

im NEW to math lol.

,calc 6*sin(3(75)/2)

[woven radish]

Result:

-3.3746483343981

[proud zodiac]

,calc 6*sin(3(90)/2)

[woven radish]

Result:

0.53021211662401

[proud zodiac]

,calc 6*sin(3(105)/2)

[woven radish]

Result:

2.448574931035

[proud zodiac]

,calc 6*sin(3(120)/2)

[woven radish]

Result:

-4.806915814403

[proud zodiac]

,calc 6*sin(3(120)/2)

[woven radish]

Result:

-4.806915814403

[proud zodiac]

,calc 6*sin(3(135)/2)

[woven radish]

Result:

5.9472288394791

[proud zodiac]

,calc 6*sin(3(150)/2)

[woven radish]

Result:

-5.5805692680272

[proud zodiac]

,calc 6*sin(3(165)/2)

[near stone]

oh btw if you want to continue calculating those use #bots its free

[woven radish]

Result:

3.7998452327837

[proud zodiac]

HELPFUL

TY

[near stone]

np

[proud zodiac]

,calc 6*sin(3(180)/2)

[woven radish]

Result:

-1.0562756788273

[proud zodiac]

#bots

ok

@near stone

how could i graph this now?

[near stone]

use desmos

https://teacher.desmos.com/activitybuilder/custom/57055922bcf5db6607684ae3#preview/368d373d-e3b3-42d4-92d7-67b3f5b04255

[proud zodiac]

mmm

idk

okay

what do i put here

i think i did this wrong.

are the nubmers correct?

#bots

yeah..

umm its not right??

@near stone

.close

[devout snow]

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[near stone]

replace the theta and as you see the point, it shows you

[near stone]

.close

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[near stone]

.close

why this bugged

[devout snow]

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[tight geyser]

Hello i am going to send my work for this momentarily but my answer i got isnt a possible one and i wanted to see if someone could spot where I went wrong.

[tight geyser]

Am looking for the Area.

.close Nvm i think i see it

[devout snow]

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[lavish canopy]

Need help w/ #40, plz

Could someone pinpoint where I’m going wrong?

Here’s my work

I feel like the answer key might be wrong

[devout snow]

@lavish canopy Has your question been resolved?

[lavish canopy]

<@&286206848099549185>

[devout snow]

@lavish canopy Has your question been resolved?

[lavish canopy]

Plz help

[devout snow]

@lavish canopy Has your question been resolved?

[lavish canopy]

<@&286206848099549185>

[devout snow]

@lavish canopy Has your question been resolved?

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[devout snow]

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[modern magnet]

hey

[mild comet]

[modern magnet]

I am trying ot make an arch in minecraft but I am trying to make it start at certain x and end at certain x

I am currently using the sin function but I do not know how to control when it finishes

How could I make so it starts at 0 and ends at 4?

[restive river]

https://donatstudios.com/PixelCircleGenerator

🤷‍♂️

[modern magnet]

?

[lost trout]

to control the height of sin(x), change the coefficient of sin(x) and to change the width of sin(x), change the coefficient of x

[restive river]

I used to use this for Minecraft pixel art

[lost trout]

i recommend you play around with this

[modern magnet]

it's related to math more than mc

[modern magnet]

let me experiment with it

[lost trout]

this is for getting started

[wooden veldt]

Just add to your x > 0 by changing it to say π > x > 0

[modern magnet]

this worked

ty

[lost trout]

yup

you're welcome

[devout snow]

@modern magnet Has your question been resolved?

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[hearty nexus]

$y = 5\sin(-180x) + 25$ is the same as $y = -5\sin(180x) + 25$

[hearty nexus]

?

[woven radish]

rynite

[mild comet]

yes

[hearty nexus]

they output the same graph, I know one is a reflection across the X and another across the Y

[hearty nexus]

Ok

[livid dagger]

yes as sin(-x) is equal to -sinx

[lyric hornet]

Odd functions

$cos(x)=cos(-x)$ is an even

[woven radish]

XxMrFancyu2xX

[hearty nexus]

alright

Thanks.

.close

[devout snow]

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[lyric hornet]

yw!

[devout snow]

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[hearty nexus]

another question, graph i (blue), which is $y=-5\sin(180x)+25$, when changing to cos, can the equation be either $y=5\cos(180(x-1.5))+25$ or $y=5\cos(180(x+1.5))+25$?

[woven radish]

rynite

[hearty nexus]

to me its anyways translating the graph horizontally so it starts from the max, whether its -1.5 or +1.5

just confused because in the answers it's -1.5

[void hound]

can someone explain how they got 4 and 0 pls?

[mild comet]

#❓how-to-get-help

[void hound]

i can't send messages on there

[mild comet]

have you read it

[void hound]

I did but I don't understand what its saying

[mild comet]

Yes

[mild comet]

it says you can ask your question in a channel like #help-39

[void hound]

oh i see thank you

[devout snow]

@hearty nexus Has your question been resolved?

[hearty nexus]

👍

[devout snow]

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[restive river]

helllo

[restive river]

i dont know where to start from

[winter patrol]

do you know how to convert radical form to exponent form?

[deep cove]

You may want to revise on "Law of Indices".

[restive river]

revise is a nice word

i havent learnt that lmao

but in this case, it would be...

y divided by 4?

?

[winter patrol]

no

[mild comet]

what do you use instead of “revise”?

[restive river]

learn

[restive river]

nope

also hey again ramonov

[mild comet]

“revise” means something more like “study”

[restive river]

yeah but i cant study something i never learnt. that would make it a new topic/piece of content that i need to learn

[winter patrol]

revise means you look back on stuff you're previously learnt

compare $\sqrt[n]{a^m}$ to $\sqrt[4]{y}$
what are $a,m,n$

[restive river]

back to topic since im acting like a weirdo

[woven radish]

ℝamonov

[restive river]

what does the question want in the first place/

[winter patrol]

it tells you

the want something in the form
$$y^{\text{some fraction}}$$

[woven radish]

ℝamonov

[restive river]

but the entire thing is y

[winter patrol]

wdym

[restive river]

its mainly comprised of ys

how do you do it

[winter patrol]

read above

what I asked you

[restive river]

still lost

sorry

[winter patrol]

don't overthink

[restive river]

y^4/y?

[winter patrol]

no

that's not what I asked and no

focus only on the numerator for now, and converting that to exponent form applying the identity at the bottom right

compare $\sqrt[n]{a^m}$ to $\sqrt[4]{y}$
what are $a,m,n$

[woven radish]

ℝamonov

[restive river]

so how do we even start

[winter patrol]

read ^

[restive river]

read

[winter patrol]

that's how you start

[restive river]

i dont really get what any of that means

[winter patrol]

which part

[restive river]

lost me at exponent

[winter patrol]

exponent form is something in the form
p^q

[restive river]

oh

so 4^5?

2^2?

like that

?

[winter patrol]

is something in exponent form

[restive river]

okay

so y^4/y?

[winter patrol]

NO

again stop trying to skip ahead

[restive river]

okay

[winter patrol]

focus only on this

compare $\sqrt[n]{a^m}$ to $\sqrt[4]{y}$
what are $a,m,n$

[woven radish]

ℝamonov

[winter patrol]

for what values of
a,m,n
will these be the same

don't overthink this

[restive river]

oh

so y is a, 4 is n?

[winter patrol]

yes, and what about m

[restive river]

0?

[winter patrol]

no

[restive river]

or is it 1?

[winter patrol]

1

[restive river]

how

oh okay

[winter patrol]

y^1 = itself

[restive river]

then we do this?

y^ 1/4?

[winter patrol]

() around the (1/4)

that'll be your numerator

[restive river]

i dont get it

y^(1/4)

[winter patrol]

yes

[restive river]

so this is our numerator?

over y?

[winter patrol]

yes

[restive river]

so the ans is y^1/4
-------
y

like this?

[winter patrol]

that's just the first step

y^(1/4)
() are needed to communicate clearly in text

[restive river]

okay

[winter patrol]

and then apply that quotient law

[restive river]

but whats the next step

[restive river]

what law

[winter patrol]

quotient law
the second one in the list with division

[restive river]

oh

hows that useful here

marking scheme says this

WAIT

y/y is y divided by y

so we can use the second law

y^(1/4)

 y

same as divided by

right @winter patrol ?

rip youve given up lmao

[mild comet]

this is equivalent to the original expression

[restive river]

yea

[winter patrol]

y/y is y divided by y
not an accurate description of what you have
you have (y to the power of something) divided by y (or y^1)

[restive river]

okay

[winter patrol]

and the second law above is applicable here

[restive river]

okay

while were here..

for ci

i got (y-2)(y+24)

why isnt that the correct answer/

marking scheme says (y+6)(y-8)

@winter patrol

oh wait

nvm

sorry for the ping

.close thanks

[devout snow]

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[mild comet]

What is A and what is B

[devout snow]

@restive river Has your question been resolved?

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[kindred fern]

Hello. I need help with thinking and solving the problem. I am trying to practice my math as a 7 grade. "Find the length of the cathetus in an isoscelus right triangle with the hypotenuses equal with 6sqrt3"

[kindred fern]

Until now I did - BC^2 = X^2 + X^2 => 2x^2 = 6sqrt3, but I don't know if its correct or how to calculate it

<@&286206848099549185>

[strong saddle]

@kindred fern your setup is close, however you need to also square the 6sqrt3 term in your setup using the Pythagorean thm

[kindred fern]

then it would be 6sqrt3 squared, so, 36 * 3 = 108. 108 = 2x^2 | : 2, sqrt(54) = X, what now?

if ab = ac, AB = sqrt(54), AC = sqrt(54)

Don't think that's good

also, 54 it's prime number

[strong saddle]

so

you can simplify sqrt54 as 3sqrt6 because 54=9*6

then that is the length of each cathetus in your isosceles right triangle

@kindred fern

[kindred fern]

Yes.

Thank you so much !

[strong saddle]

np

[kindred fern]

.close

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[eager harness]

Hi

[eager harness]

How can we here deduce the right side from the left side

i.e why:

$$x^8 = 3 \mod 11 \implies x = 2 \mod 11 \lor x = 9 \mod 11$$

[woven radish]

szahu420

[stone stump]

for these small values you can just bruteforce

it obviously helps here that the exponent is even so if x is a solution, then also -x is

[eager harness]

in the third row that would mean I have to calculate 2^10 mod 13 , 3^10 mod 13 and then 4^10 mod 13

of course the reminder probably cycles, so it's not that much of calculations

[stone stump]

if you use fast exponentiation thats doable in your head

for these numbers anyway

[eager harness]

ah I see the fast multiplication algorithm

but I still have to check all of them right?

[stone stump]

i.e. square-and-multiply

[eager harness]

is there a guarentee that there is only going to be 2 solutions?

[stone stump]

no

x^6=1 mod 7 has 6 solutions

[eager harness]

so I do have to check all numbers mod 13

so in this I do have to check all numbers between 1, 12?

[eager harness]

could you link that?

[stone stump]

only 1 to 6

just google it

[eager harness]

I see thanks

[stone stump]

2^10 = (2^5)^2 so if you can figure out 2^5 then 2^10 is easy

2^5 = 2^4*2 so you need to figure out 2^4

then 2^4 = (2^2)^2 etc

[eager harness]

I see thanks

.close

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[hidden dragon]

Is f(x)=0 the only function which is both, even and odd?

[stone stump]

try proving it

[hidden dragon]

I have alr proved it then, by using the two equations, f(x)=f(-x) and -f(x)=f(-x)

That f(x)=0 seems to be the only solution but just wanted to confirm in case m wrong

[stone stump]

yes its the only one

f(-x) has to be both f(x) and -f(x) at the same time which is only possible for f(x)=0

[hidden dragon]

Oh

[hidden dragon]

What if domain is changed, won't there be infinitely many different functions which is both even and odd?

[stone stump]

change to what

[hidden dragon]

Like f(x)=0, x belongs to R and g(x)=0 where x belongs to R-{-1,1} would be different functions but still even and odd

by removing symmetrical domain

So it won't be correct to say that f(x) and g(x) are equal function

[stone stump]

well ok...

[hidden dragon]

Because their domain aren't same

[stone stump]

g is still the zero function on its domain

for each fixed domain only the zero function works

[hidden dragon]

Yeah but I studied that if domain is different then functions can't be identical

[stone stump]

yes they arent

but that's not really the point here

[pseudo basin]

if you want to be that pedantic about it then for each zero-symmetric subset D of R there exists precisely one function f: D -> R which is even or odd, and it is the constant zero function

[hidden dragon]

Zero function you mean f(x)=0

[stone stump]

f(x)=0 for all x in your domain

the last part I didnt specify before because that was implicit

[hidden dragon]

Ohh I see

[stone stump]

you always implicitly mean "for all x in whatever domain"

[hidden dragon]

Ohh, that makes sense

Thank you both Ann and denascite

.close

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[hidden dragon]

f: R-{2}->R, f(x)=0. Which of the follow is f(x).
A)Even B) odd C)Even and odd both. D) neither odd nor even.
I want to confirm my answer. My answer is D.

[topaz axle]

makes sense

[hidden dragon]

I see

That means D is correct, thank you!

.close

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[topaz axle]

i don't know why i even answered i have no clue

[hidden dragon]

.reopen

[devout snow]

✅

[hidden dragon]

You said makes sense though..

[topaz axle]

it makes sense, because the graph can't possibly be symmetric if it has a single hole that's not at 0,0

[hidden dragon]

I also thought the same that's why I picked D but when I put -x into f(x) it gives both even and odd

What you say makes sense!

[topaz axle]

i don't know however how evenness is defined, maybe it's somehow totally fine

[hidden dragon]

Evenness should be defined by symmetry I think and hence the name

So I'll be obstinate with the answer D, thank you!

Now I'll close the channel then!

.close

[devout snow]

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[devout snow]

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[jovial mauve]

The economy of a country consists of exactly two industries: mining and manufacturing. It was expected that the economy would grow by 18% if mining grew by 10% and manufacturing by 20%. However, if manufacturing grew only by 10%, then, for the economy to still grow by 18%, mining needs to grow by what percent?

[jovial mauve]

I get 50% and the answer is mentioned as 37.5%

Can someone verify?

[supple knot]

just show your work

[pseudo basin]

yeah this answer is not readily verifiable from just the input data

[jovial mauve]

[pseudo basin]

ok my answer matches yours

so either we made the same mistake or the book is wrong

can you show both your sol and the book's sol

[jovial mauve]

The book did not give solution to this problem

It is just written 37.5%

I will show my work

(Economy - Mining) : (Manufacturing - Economy) = 8 : 2 = 4 : 1
Thus, (Mining - Economy) : (Economy - Manufacturing) = 4 : 1
So, (x-18) : (18-10) = 4 : 1

x is the growth percent of mining industry

[pseudo basin]

hm

looks dodgy to me, but might arrive at the right answer.

this is how i did it, somewhat abridged:

d := original mining production
m := original manufacturing production
[d for dig ~ mine]
take original economy size as 1 for simplicity

original economy: d + m = 1
proj growth: 1.10d + 1.20m = 1.18

d + m = 1
1.10d + 1.20m = 1.18
subtract => 0.10m = 0.08
=> m = 0.8 => d = 0.2

manuf only grew by 10%
=> new manuf volume = 0.88
to get to 1.18 total, mining must grow to 0.3
0.2 -> 0.3 = +50% growth

[cosmic jacinth]

Okay so, I did it, and I arrive at 50% too.

I used Desmos haha, so my work might not be of use here

[jovial mauve]

.close

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[signal panther]

Finally, the x_3 x_4 plan is considered in R^4 , i.e. the subspace V = {(0,0, x3, x4) ∈ R 4 | x3, x4 ∈ R}. Show that the common set U ∩ V is a line through the origin and determine a direction vector for this. Where U = {b1,b2,b3}. What i have tried is the take the basis vectors from U and set them to be equal to the vector in V then found the echelon form. Since the first 2 vectors in V are always 0. Is it safe to assume the the line through the origin is L = {0,0,-3x_3,x_3+x_4}? The basis vectors b1 b2 and b3 are the coloumn vectors in the non reduced matrix

[devout snow]

@signal panther Has your question been resolved?

[devout snow]

@signal panther Has your question been resolved?

[devout snow]

@signal panther Has your question been resolved?

[devout snow]

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[void hound]

need help with a question

[void hound]

I don't understand the concept of convergence. Could you explain it using this example?

@royal thorn

@dry robin

[devout snow]

@void hound Has your question been resolved?

[void hound]

.close

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[distant root]

hi there just wondering the beet way to solve this

[torn vessel]

Use $P(A \ or \ B) = P(A) + P(B) - P(A\ and \ B)$

[woven radish]

Zybikron

[placid rover]

venn

maybe.

[distant root]

what is p(a and b) again

is that just the prob of either right

like combine them

[torn vessel]

do you know what mutually exclusive means?

[distant root]

oh mb i forgot ab that part

yea i think

like they don’t overlap

[torn vessel]

yep

[distant root]

wait so what would it be the

then

[torn vessel]

it means A and B can't happen or is empty. So what's the probability?

[distant root]

im confusing myself i think

im sorry

[distant root]

wait so if they are mutally exclusive then i can’t find p(a or b)

nvm

im dumb sorry

thank you for your patience

[devout snow]

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[devout snow]

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[craggy sequoia]

I am stuck on this probability question. I have no idea about the rules of cards.

[lavish oar]

do u know how many classic card have

[craggy sequoia]

52 total cards right?

[patent marsh]

yep! How many cards in a suit?

[lavish oar]

can you give a minute i will make a flow chart about everything

[craggy sequoia]

okay.

[craggy sequoia]

what is a suit?

[patent marsh]

hearts, spades, clubs, and diamonds

[craggy sequoia]

i'm guessing 52/4

13?

[patent marsh]

bingo

so what is the probability of getting a heart if there are 13 total hearts out of 52 cards?

[craggy sequoia]

1/4

0.25

[patent marsh]

yep!

so that's P(A)

[craggy sequoia]

right

[snow basin]

PLZ HELP ME

PLEASEEEE

[craggy sequoia]

@snow basin wrong help channel

[snow basin]

😔

[patent marsh]

#❓how-to-get-help

[craggy sequoia]

use an open help-channel to paste your query.

[patent marsh]

I saw that before the edit. dont' troll

[snow basin]

HELPPPPAFSRFSWSF

[devout snow]

Please read #❓how-to-get-help

[snow basin]

ur pfp is troll enough

[craggy sequoia]

I saw it too :I

[snow basin]

check forums

plz

someone check forums and help me

[craggy sequoia]

could you wait your turn please?

[lavish oar]

okay, ping me on ur form

[main gull]

Read #❓how-to-get-help, don't beg for help either, or try to get attention to your question, that's how you can get muted or banned

[snow basin]

I DID

WTF

WHAT DOD I DO

[craggy sequoia]

rae please

occupy another help channel

wait your turn

all you have to do

all the helpers are alseep right now

[snow basin]

why i gotta wait jus help me

someone help

plz help

[craggy sequoia]

wait until tomorrow and someone will have answered your query

you have to wait

none of the people who know how to do your question are online currently

[snow basin]

uhm

my grades lock in like 30 mins

im desperate

[craggy sequoia]

yikes

[patent marsh]

advice: dont' wait until 30 min

[snow basin]

too late for that :3

[craggy sequoia]

😆

[snow basin]

i didnt do it all semester

whoops

[craggy sequoia]

anyway Mellow would the probability of both events be 0.25?

[patent marsh]

@craggy sequoia check out this tree

[patent marsh]

yes correct

[craggy sequoia]

thanks. @patent marsh @lavish oar

.close

[devout snow]

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[upper spire]

repost ur question here

<@&268886789983436800>

ping mods

[devout snow]

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[restive river]

why does the cos tend to 0 here?

[pseudo basin]

it's not the cos itself that tends to 0 but what's inside the cos

i.e. π/n

[restive river]

yea I will need a little depper explanation

π/n what does this have to do with it

[pseudo basin]

as n approaches infinity, what happens to 1/n?

[restive river]

0

duck

.close

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[lavish oar]

$$ 0 < \frac {1}{2x-4} < \frac 1 2 $$
$$ 0 < 2x-4 < \frac{(2x-4)^2}{2} $$
$$ 4 < 2x < \frac{(2x-4)^2}{2} + 4 $$
$$ 2 < x < \frac{(2x-4)^2 + 8}{4} $$

[woven radish]

JXHN

[lavish oar]

either
x > 2

oh wait a sec

yeah nha

$$ x < \frac{4x^2 - 16x - 16 + 8}{4} $$
$$ x < \frac{4x^2 - 16x - 24}{4} $$
$$ x < x^2 - 4x - 6 $$
$$ 0 < x^2 -5x - 6 $$

[woven radish]

JXHN

[old stag]

I really think you'd have a better time if you noted that if 1/y is positive, then so is y. There's nothing stopping you from just multiplying by 2x-4 in the first step and solving a linear problem instead.

[lavish oar]

$$ 0 < (x-3)(x-2) $$
x > 3 and x > 2

[lavish oar]

i was doing the same thing but that will only give one part of the answer

and the process/assumation is wrong too

@pseudo basin

<@&286206848099549185>

i got x > 2 and x > 3 by intesection x > 2 but the answer is x >3 : (

[old stag]

Intersection means the region where both conditions are satisfied.

Where x>2 AND x>3

[lavish oar]

ohhhhh

.close

[devout snow]

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[trail stratus]

what does the last statement mean??

the question\

[sonic smelt]

It says that the limit of a_n does not exist

What's confusing you there?

[trail stratus]

why

Why does it not exist?

[sonic smelt]

It oscillated from -1 to 1 constantly

Informally speaking

But we can do a proof

[trail stratus]

Like this?

[sonic smelt]

Yeah, except it happens at infinity

Not at the origin

[trail stratus]

ahhh, yeah I remember this in calculus 1

thank you

I'll restudy the proof

[devout snow]

@trail stratus Has your question been resolved?

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[finite briar]

Question: is (x^2+1)^4 = (x^4-6x^2+1)^2 + 16(x^3-x)^2 an identity

So I tried putting in values, it works out

But algebraically it doesn't

[finite briar]

,rotate

[finite briar]

Can someone point out the mistake here?

Also pls mention me when u respond

[devout snow]

@finite briar Has your question been resolved?

[finite briar]

<@&286206848099549185>

[finite briar]

<@&286206848099549185>

????

[junior otter]

lemme go through ur working

[junior otter]

@finite briar i am getting the same answer as you

[pseudo basin]

hold up

Question: is (x^2+1)^4 = (x^4-6x^2+1)^2 + 16(x^3-x)^2 an identity

this?

@finite briar i think you're going about this in a complicated way

easier to just expand (x^2+1)^4 and 16x^2(x^2-1)^2

and (x^4-6x^2+1)^2