help-0

[indigo jetty]

how would you make lg x the subject?

[leaden goblet]

getting rig og lg 5 and then lg 2

rid of

[indigo jetty]

it would be easier if you expanded the brackets first

[leaden goblet]

oh

[alpine sable]

Log5*log5=log25 is that how it works or is it log10

[indigo jetty]

neither

[leaden goblet]

huh

[indigo jetty]

it's (log5)^2

[alpine sable]

Oh

[leaden goblet]

oh

[indigo jetty]

as i mentioned, treat lg 5 as just a number

[alpine sable]

2•log5 basically

[indigo jetty]

no

it's different

[alpine sable]

Ok

[indigo jetty]

log 5^2 and (log 5)^2 are 2 different numbers

[leaden goblet]

how do i times the lg 5 and the lg x

do i just leave it as it is?

[indigo jetty]

just leave it as it is

[leaden goblet]

so it will be (lg5)(lgx)?

[indigo jetty]

yes

[leaden goblet]

lg5^2 +(lg5)(lgx)=lg2^2+(lg2)(lgx)

is that right

is seems wrong

[indigo jetty]

it should be (lg5)^2, and (lg2)^2

[graceful bloom]

Heu

Hey

[leaden goblet]

oh yea

ok

[indigo jetty]

make lg x the subject

[leaden goblet]

but i do not know how to bring the other lgx over

[indigo jetty]

move the terms with lgx to one side, and the rest to the other side

[unkempt cloud]

Find the domain of the equation first (here because of the power of (5x)^lg5 and (2x)^lg2 are irrational so this equation's domain is x>0) and then cross multiplying to make the equation become:
(5x)^lg5=(2x)^lg2 <=>10^((lg5)^2)×(x)^(lg5)=10^((lg2)^2)×(x)^(lg2)
<=>(1/10)^((lg2+lg5)(lg2-lg5))=x^(lg2-lg5)
You got the point now, the equation becomes f(g(x))=f(h(x)) with f(x)=x^(lg2-lg5); g(x)=(1/10)^(lg2+lg5) and h(x)=x ; now the solutions of the equation will be equal to the solutions of g(x)=h(x) that satisfy the conditions of both f(x), g(x), h(x). And your solution is a point so you don't need to proof something else.

[alpine sable]

Natsumi is typing since an hour

[unkempt cloud]

I don't know if my answer is correct; but I hope it would help you.

[gaunt coyote]

Can we switch to DM ? Iam at work and can’t follow the whole chat currently

[alpine sable]

Ok

[gaunt coyote]

Thanks

[leaden goblet]

i got (lgx)(lg5-lg2)=(lg2)^2-(lg5)^2

[leaden goblet]

THANK YOU

i would see later

[leaden goblet]

@indigo jetty is this it

[indigo jetty]

yes

so now make lg x the subject

[leaden goblet]

lgx=lg2-lg5

is that it

then x=-3

wait no

is it x=0.4

[indigo jetty]

are you allowed to use a calculator?

[leaden goblet]

nope

[indigo jetty]

ah ok

so just divide the whole expression by (lg5-lg2)

now notice (lg2)^2-(lg5)^2

does it resemble a^2-b^2?

[leaden goblet]

yes

OHHHHHH

I SEE IT

[indigo jetty]

but

be careful of your signs

cos the denominator is lg5-lg2

not lg2-lg5

[leaden goblet]

yes

i put minus sign infront then i swap the lg2 and lg5

for denominator

[indigo jetty]

yes

[leaden goblet]

i got lg x= -(lg2 +lg 5)

so what do i do now

[indigo jetty]

look carefully

remember all your log rules

[leaden goblet]

ok

do i multipy the minus in?

so it lwill be -lg2 -lg5

[indigo jetty]

no need

[leaden goblet]

wait what

oh

[indigo jetty]

the expression is screaming to you that it simplifies to a very nice number

[leaden goblet]

its lg10

[indigo jetty]

yes

[leaden goblet]

which is 1

[indigo jetty]

gd

[leaden goblet]

so

[indigo jetty]

so what is lg x?

[leaden goblet]

0.1

[indigo jetty]

kk

you got your answer

[leaden goblet]

OMAI GAWD

[indigo jetty]

now, good practice, verify your answer

[leaden goblet]

THANKYOU

YES I WILL

[indigo jetty]

sub back into the original equation and make sure you get the same answer

👍

[leaden goblet]

OK THANK YOI

YOU

[shell comet]

What is the procedure to go from the step of the first green arrow to the second green arrow?
I hope my translation is not so bad

[indigo jetty]

It would be easier if you go back to the original series at the top, and write out the series term by term

then you notice that you can split up the series into odd-indexed c and even-indexed c

then apply the expressions in the first green arrow to all the c

[shell comet]

Ok, imma try...

[mellow dome]

how do I go about doing this?

I've found the angle between l and π1

but I don't understand what I meant to do to get the equation of the plane perpendicular to π1 including l

[indigo jetty]

basically, pi2 contains l, so it contains the direction vector of l, which is one vector that defines pi2. Now you need another defining vector for in pi2. Notice that if pi2 is perpendicular to pi1, what can you tell about the normal of pi1?

[mellow dome]

it'll be a vector parallel to pi2, I get that

but I need like a Cartesian equation

not the uhhh

the 3 vectors and a point one

I just need a general methodology type thing so I can figure it out meself

[indigo jetty]

you need at least 2 defining vectors to get the defining normal vector of pi2, and then you can get the cartesian equation from there

[mellow dome]

cross product of two vectors on the plane?

[indigo jetty]

yes

[mellow dome]

perfect, thank you!

I need coffee lmao

[indigo jetty]

the most important form for planes is the r.n form

because you can switch between vector and cartesian

[mellow dome]

r.n=0?

where r is a vector on the plane and n is the normal's unit vector?

I think?

[indigo jetty]

r.n = a.n

a is a point on pi2

easiest is to get it from the line l

which is the origin

[mellow dome]

oop okay

thank you!

[indigo jetty]

so yeah r.n = 0

👍

[hazy kraken]

if i have a sample which is right skewed, can i still compute the 95% confidence interval normally using this formula?

i can take the natural log of the variable to obtain a more normal looking distribution, but do i need to do this?

[alpine sable]

if the sample is large enough (usually n >30) then the central limit theorem would apply

so the sampling distribution of the sample means would be approximately normal

[hazy kraken]

ahh okay, so even though the sample data doesn't look normally distributed, n>30 means the distribution of the sample means would be normally distributed so any confidence interval would be valid

why would it be better to transform the data to make it more normal though?

this is actually part of a set of practice problems where it asks me to compute the confidence interval

but the previous question asks why it would be beneficial to take a log transform before analyzing the sample data (because the dataset becomes less skewed)

i'm just not sure whether that ties into this question or not

[alpine sable]

i'm guessing the benefit would be by transforming the data to make it more normal, you could use a confidence interval even with a smaller sample size where n<30

[hazy kraken]

oh we're given a sample of 500 which is pretty right skewed

and it's asking why taking the natural log would make it better

i just said that it makes the distribution way less skewed

but the next question asks for the 95% confidence interval of the population mean

so i don't know whether to keep the log transform

maybe that would fudge the numbers because then i'd have to undo the log to find the confidence interval

i guess since n>30 i dont need to change the sample and i can just assume they intended for the questions to be independent?

[hazy kraken]

like i get that this is a benefit but we're already given a sample and the only effect that taking the natural log has is making the histogram more symmetric

[alpine sable]

oh if it's given that the sample is pretty large already then idk what the benefit of a log transform would be

maybe it'd give a better approximation?

[hazy kraken]

that would totally mess up the numbers though right? if i took the log, then found the confidence interval (for the next question), and then did undid the log

like i think the weirdness of the former question is confusing me

it asks what the benefit is of doing a log transform of a sample of 500

and i said: to make it more symmetric (i dont even know what implications this has, it just sounds good)

next question is to compute the 95% confidence interval of the pop. mean

does the log thing have anything to do with this is my confusion

[alpine sable]

i think it wants you to use the log transform to compute the confidence interval for the next one

[hazy kraken]

okay

thank you for all the help btw

[hazy kraken]

how do i do this?

im taking the mean +- sd/sqrt(500) of the log transformed sample

and then i got the interval

do i just undo the log?

[alpine sable]

yeah you apply the inverse of the transformation

[hazy kraken]

alright, thank you so much

[night sigil]

not sure how to do the last part because the function has multiple equations in it

[torn falcon]

M = 6n - \sum_{i=1}^j\ (6 - f_i) = 6(N-1 - j) + \sum_{i=1}^j\ f_i

Hello, I am new herw.

here

to post formulas, is that of the Latex use?

[spare fern]

Use $ sign at the start and the end

Use $ sign at the start and the end

[torn falcon]

M = 6n - $\sum_{i=1}^j\ (6 - fi)$ = 6(N-1 - j) + $\sum{i=1}^j\ f_i$

[ocean seal]

Fantinatti

[torn falcon]

Thank you sir.

[spare fern]

No need to call me sir

[torn falcon]

This is the formula for the DOF (Degree Of Freedom). Why do I have "-1" on it? Because the last resource can't be changed? Fixed? Just to clarify this idea.

[sinful shore]

Someone help me with this

6c

@ when someone can help me <@&286206848099549185>

[strong furnace]

How do you determine the domain of inverse function if you're given the actual function?

[sinful shore]

i tried it

i did ln(y+1)=x

which gives -0.63

and then plugged that into ln(x+1)=y

which gives -1

so my teacher is probably smoking crack @strong furnace lol

@strong furnace U had a question, I assume you figured it out?

[strong furnace]

Not really

[sinful shore]

this question a typo made by teacher?

cause idk how to solve it lol

[strong furnace]

I can't give the solution without giving away the answer so let me think how I can convince you without doing that

[sinful shore]

idc about the answer

tell me the proccess of doing it

i have a test in 2hours

and this is study guide questions

[strong furnace]

You're supposed to find the domain of inverse function

[sinful shore]

of ln(y+1)=x

[alpine sable]

when you do dy / dx or d / dx how do you know where to write that?
heres a problem as an example:
Find dx/dt when x = e^t
I know that I would take the derivative of e^t and get e^t but would I write that as follows?
dx/dt x = e^t
dx/dt = e^t
?

[strong furnace]

Actually never mind I am smoking the same stuff as your teacher

That seems to be a typo

[sinful shore]

mhm

@strong furnace yep like i though

though

thought

but i would find the domain of the inverse @strong furnace then what?

[strong furnace]

If this was a proper problem then -1 would not lie in the domain of its inverse

f^-1(f(-1)) should have been the problem

[sinful shore]

@strong furnace how would u do 8b

ik the proccess but how do u get 0.08 out of 3 and 5

i wanna know so i dont get stuck on that during test

[signal otter]

Hi can someone tell me about algaber with an know one number please quickly tomorrow I have tast

[alpine sable]

hi im super stuck on this ...

,rotate

[alpine sable]

wdym??

[signal otter]

I didn't understand what are you saying

[copper summit]

unknown?

[alpine sable]

do you know the formulas for surface are / volume of a sphere?

[alpine sable]

no

[strong furnace]

The base is 10 I assume?

You have to use log(2*5)=log2+log5=1 in this case assuming log(10)=1 is trivial

[cosmic cypress]

hi everyone, i was playing around with a physics equation and stumbled upon a strange thing that i'm not sure if it's entirely correct (and i quite feel it's not)

the equation for the relativistic addition of velocities tells that
u = (u' + v) / (1 + u'v/c^2)

so, for a school homework i had to evaluate the derivative of this equation (respect to u'), and i think i discovered thath
du/du'=(dt'/dt)^2
does this make any sense?

[signal otter]

I want the way of this

Answer please

[tacit whale]

make y the subject of formula

y= 4-x

then substitute it into the above equation to solve

[onyx cargo]

Is this how you’re supposed to do this? Should I be getting a negative 36

[alpine sable]

i think you dropped a negative

36=(x-3)^2

x=-3, 9

then find the y-coordinates and you're good to go

can somone help me get ready for a fractions math test involving bedmas

[swift ravine]

@onyx cargo what math are you in btw

ok

[alpine sable]

dm me if you can help

[swift ravine]

what math are you in

[onyx cargo]

Calculus and Vectors

[alpine sable]

grade 8

[swift ravine]

ok i can help you

[alpine sable]

ok

great

[onyx cargo]

Ah thank you

[alpine sable]

give me any question involving bedmas

[swift ravine]

accept freind request

so i can dm you

[smoky goblet]

Can anyone give me a question with Hands on Equations-

[alpine sable]

ok thank you

[sinful shore]

Anyone wanna help with precalc

any in here smart lol

[vast blaze]

People here may help if you post the question you want to ask

But before hand, please read #❓how-to-get-help first

[sinful shore]

ok sure

Is this correct?

have a test in 15 min

needa know if my work is right so i know how to do it during the test

[thorny mirage]

help

[shell comet]

Don't post twice!

[stuck plaza]

twice lol hes spammed it on every question

[past arch]

@thorny mirage sorry for bad handwriting
Maybe this helps you

Text in curly bracket is explanation

Wooops

[alpine sable]

Is there anyone to help with physics?

[shell comet]

me

[alpine sable]

Aight

[shell comet]

dm

[cloud kiln]

Since no one is using this channel rn, I’ll ask tm question

[cloud kiln]

Resolve into two or more factors:
$2a^2x^2 - 2(3b-4c)(b-c)y^2 + abxy$

[ocean seal]

Prak

[runic dock]

I don't understand

[cloud kiln]

Which part

sec x = 1/cos x

[runic dock]

3rd to 4th step

1-cos4ø

[cloud kiln]

Can you edut and highlight it

Cos4x = 1 - 2(sin2x)^2

[runic dock]

cos2x = 1 - 2sin^2x right

[cloud kiln]

Yep

[runic dock]

I still don't understand

[cloud kiln]

Or 2cos^2x - 1

What do you not understand?

[runic dock]

what should i do for 4ø

[cloud kiln]

The angle is just doubled

Do the same for cos4x as you do for cos2x but double the angle

[runic dock]

(2-2sin^A)×2

[cloud kiln]

?

What

[runic dock]

?

[cloud kiln]

Where did this come from

[runic dock]

is thwre other way to do it

[vast blaze]

Hint: ||cos(4x)=cos2(2x)||

[cloud kiln]

^ do this

[runic dock]

ok

So if it's 8x it will be 1-2sin^2 4x

[cloud kiln]

Yes

[runic dock]

yes ok

Thanks

[cloud kiln]

Resolve into two or more factors:
$2a^2x^2 - 2(3b-4c)(b-c)y^2 + abxy$

[ocean seal]

Prak

[cloud kiln]

Anyone???

Ping me if you get here I am closing discord and moving on from this question for jwp

Now

[thick shard]

Could anyone please help me with this? I'm stuck.

I tried factorising it. Doesn't work.

[wooden anchor]

Hi! I'm really stuck here in the graph. We need to start Y AXIS from 0. The highest Y value is 23. How do I number the Y AXIS?

[brave ice]

make every 1 cm 3?

[honest moth]

help pls

[alpine sable]

who was first

[honest moth]

i think you?

idk

[alpine sable]

i can help you with yours

[honest moth]

really?

thanks

[alpine sable]

It's C

It says -2(x + 2)

[honest moth]

thanks bro

[alpine sable]

Which is -2 * x and -2 * 2

[honest moth]

oh ok

[alpine sable]

So the correct answer would be x = 11

[honest moth]

thanks

[alpine sable]

You catch my drift right

[brisk tree]

Is you question about continuity?

[alpine sable]

My question?

So x is kilometres

and y is the price in my local currencies

so for between 0 and 10 km bus ride you pay 36

They ask me to write up the function for f

but the function changes depending on what x is

so what am i gonna do

I am using Geogebra btw

[brisk tree]

It's fine, f is then a piecewise defined function

[alpine sable]

does that mean I should write f(x) multiple times

what does a piecewise defined function mean

this is what i got so far

what should i write next?

[brisk tree]

Means that the interval is broken up into pieces like (0,10], (10,20] and so on

[mellow dome]

how do I do the last part?

[alpine sable]

aight got it, thanks

this correct though right

[brisk tree]

Yeah

[hybrid pike]

@brisk tree can I dm u?

I need help with geometry

[brisk tree]

Okay

[calm helm]

ive been puzzling over this for some time now
the common ratio for between the 1st and 2nd term is different than the ratio between the 2nd aand 3rd term
wouldnt this make it not a geometric progression?

[brisk tree]

You gotta find out x that makes this sequence a geometric sequence i think

1/x=x/(2x^2+x)

[calm helm]

hmm ok ill try that thank you!

[neon olive]

https://cdn.discordapp.com/attachments/779055760520773643/844240154449412156/unknown.png

im helping my friend out but idk how to do this

[calm helm]

wait actually, I tried this but it just simplifies to x=0

which doesnt work for a geometric progression

[brisk tree]

I don't think so let me check

2x^2+x=x^2

[calm helm]

this is D

[brisk tree]

So x=-1

[neon olive]

ok

[calm helm]

ohhh that makes sense

[alpine sable]

how to do this

[glass lichen]

$\log_4(x)=\frac{1}{2}\log_2(x)$ by change of base

[ocean seal]

Mosh

[buoyant yacht]

can someone help me with this pls

[glass lichen]

so you want $\log_2(x+4)=-\frac{1}{2}\log_2(x)=\log_2\left(\frac{1}{\sqrt{x}}\right)$

[ocean seal]

Mosh

[glass lichen]

since the bases are the same it's equivalent to solving $x+4=\frac{1}{\sqrt{x}}$

[ocean seal]

Mosh

[glass lichen]

@alpine sable

[alpine sable]

tq

[weak tendon]

Having trouble integrating this

[lapis fjord]

Can you please help with my homework

I dont understand it

[glass lichen]

split the fraction, then use u-sub for one and the other will be an inverse trig

[weak tendon]

ok will try that

I treat 4 as 2^2 right

[glass lichen]

factor 4 out of the denom for the inverse trig integral

then x^2/4 = (x/2)^2

[alpine steeple]

Can someone explain the steps taken to get the bottom equation?

the j is a complex number

[glass lichen]

multiply by i/i

ie realise the fraction

[lapis fjord]

I dont understand this

[alpine steeple]

where does the minus come from?

[glass lichen]

i^2=-1

[alpine steeple]

I see so they have multiplied top and bottom by i?

[glass lichen]

like I said. . yes

[alpine steeple]

great thanks 👍

[glass lichen]

$\frac{1}{if_n}\cdot\frac{i}{i}$

[ocean seal]

Mosh

[alpine steeple]

Thats perfect thanks

[weak tendon]

this one is still not clicking for me

is it just this rule???

[glass lichen]

u=x^2+4

[weak tendon]

ok I'll try that

[alpine sable]

how would i go about this?

would i just use the limit definition and check if f(c) = the limit?

[glass lichen]

Definition of continuity

[alpine sable]

f(c) = the limit of f(x) as x approaches c?

[glass lichen]

$\lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=f(a)$

[ocean seal]

Mosh

[alpine sable]

ahhh so i would just check if the limit exists at 4?

how would that give me k sorry

[glass lichen]

f(4) is clearly 0

[alpine sable]

yea

[glass lichen]

so you need the sided limits to converge to 0

[gleaming matrix]

Can someone help me to solve this? (c is the speed of light)

[alpine sable]

oh so i just set the limit equal to 0 and solve for c?

i think im misunderstanding

;-;

[glass lichen]

yes

[alpine sable]

OH

thank you so much

wait mosh

just checking

this should equal 0 ?

because thats the limit on the left side

[glass lichen]

that shouldnt equal 0

[alpine sable]

oh

[glass lichen]

$\lim_{x\to 4^+}f(x)=0$

[ocean seal]

Mosh

[alpine sable]

how would that get me k? i think thats where im missing something

[glass lichen]

cause you can find that limit as a function of k

[alpine sable]

would that be

$\lim_{x\to 4^+}f(k)=0$

[ocean seal]

CAESAR

[alpine sable]

this?

im kinda confused sorry

i know that the left and right side limits have to be the same

[weak tendon]

so I got the wrong answer here should be -1/2 ln(x^2 + 4)

[alpine sable]

and that f(4) has to equal those

but im not sure how i could get k from knowing that the graph is continuous

[glass lichen]

$\lim_{x\to4^+}f(x)=16k-8-1$

[ocean seal]

Mosh

[alpine sable]

OHHH so youre setting the right sided limit equal to the function and just plugging in 4?

[glass lichen]

yes

[alpine sable]

and then we know that the right side limit goes to 0?

so we would just solve for k?

i got 9/16 = k i think

thank you btw

[thick sigil]

Hello everyone

[surreal bone]

derivative of phi(u) = u^3, u(x,t) = x^2*t^2 + x + 1? can someone explain how to find it?

[thick sigil]

whats everyone's input on 2a)?

My exams done just checking if I did it right

I got neither A or B has first order stochastic dominance

But some of my mates are saying B dominates A in first order

[rugged sinew]

What is 25 % of 200

[short olive]

50

[next sequoia]

Can someone help me with this¿?

[arctic ferry]

Doing a mock paper before my exams does anyone know how to do epsilon - N proofs like these

[alpine sable]

You may find it helpful to note that 0 < n < n+4

[arctic ferry]

I've found it converges to 0

[stray frost]

Posted in another but someone is spamming Q's in there. I got everything aside from D. How does U become root gd?

[arctic ferry]

Could you help me out with what this means ?

[alpine sable]

Choose a channel other than questions 0 if you don’t want questions to get spammed out

How would you start the proof?

[alpine sable]

And is this for the first one?

[arctic ferry]

Yeah this is

I'd probably start by saying it converges to 1 and say a = 1?

But I feel I've skipped something but automatically saying it converges to 1

[alpine sable]

What does say a = 1 mean?

[arctic ferry]

In the notes it desribes the value the sequence converges to as a

Or am I wrong?

[alpine sable]

Ok sure

Arbitrary notation though

So you want to prove the sequence a_n converges to 1

[arctic ferry]

I think I just want to show it converges

And I have to use the epsilon to N proof apparently

[alpine sable]

Converges to 1 implies it converges

[arctic ferry]

Yeah

I don't know how to do that though using the e-n proof

[alpine sable]

Sorry then, I don’t have time to go through that from scratch

[arctic ferry]

Okay thanks anyways

[arctic ferry]

Just one thing though, do I need to find a value of epsilon first?

[alpine sable]

No, what you’ll be “picking” is N

I give you any epsilon, you give me an N back which makes some properties hold (the implication in the definition)

Since you need to find an N for every epsilon, N will depend on epsilon

[arctic ferry]

So to prove this I need to show for any epsilon > 0, there is a number N ?

[alpine sable]

Yes, a number N such that...

[arctic ferry]

A number such that for all n > N, | a_n - a | < e?

Im not sure how to show that bit though ^

[alpine sable]

Yes, that’s the idea

[arctic ferry]

So to clarify I should pick a value of N or e to start?

[alpine sable]

Let epsilon be any positive real number to start

And pick a value of N which is in terms of epsilon (deciding what to pick is the tricky part)

[surreal furnace]

can someone help me with my nmath hw

[analog locust]

wait

how is this +3?

I thought c should be -1?

is this a mistake from the book?

[indigo storm]

Any mistake?

[alpine sable]

confused with d

[indigo storm]

D should be 6yx⁴-12y³x⁴+2yx³

[alpine sable]

Thank you

[indigo storm]

Did you check?

Answer

[alpine sable]

I'm doing it on paper right now

[indigo storm]

O

[alpine sable]

@indigo storm Can you tell me what steps you took with solving it

[indigo storm]

O wait

I did it on my mind

I'll write steps

[alpine sable]

You're really smart

[thick sigil]

can anyone answer this?

or have an idea on whether im right or wrong

[alpine sable]

Thank you

[oak chasm]

,rotate

[oak chasm]

@indigo storm Looks fine, except you usually put variables in alphabetical order.

[kindred crater]

Huh

[indigo storm]

When you multiply 2yx³ with 3x you should multiply 2×3×y×x³×x

[indigo storm]

Yey

[knotty garnet]

You are correct, first order neither is dominated

[indigo storm]

I wanted to help him

[knotty garnet]

B does not dominate A because there are 3 options that are nonzero, and A does not dominate B because B's maximum is higher than A max

[crisp quest]

I have a question

Where the therefore part is, I can't figure out how they went from there to the next line

oh nvm

jeez louise

lul

no help needed for me

[violet haven]

matrices, what's the process in solving this?

[alpine sable]

brute force matrix multiplication would work

[violet haven]

how do i do 3 tho:(

[alpine sable]

go from right to left

you'd have to do two multiplications

[violet haven]

so i do 2 first and then the last one into that?

[alpine sable]

yeah

[violet haven]

ohh that makes sense thank you

[alpine sable]

the ones on the right and left are supposed to be rotation matrices right

[violet haven]

yeah

[alpine sable]

in that case there might be an easier way, but i'm not sure

[violet haven]

replace x and y with the values given, so 1. is 200 = 258+10, check if they're even on both sides. if 258+10 is not 200 then the variable values are not a solution to the equation

goddamn i meant 25*8+10

did that answer your question or did you need help w something else?

[gray sundial]

How does (cos^2 x - sin^2 x) = cos 2x ?

[knotty garnet]

I have a roundabout method which is longer but gives a more general more satisfying answer

Would you like that?

[gray sundial]

Yh sure

[knotty garnet]

So are you familiar with complex numbers?

[gray sundial]

Yes

[knotty garnet]

Are you familiar with the idea that complex numbers can be written in both rectangular and polar form?

[gray sundial]

Nope

Actually it looks simple

I know it now

[glass lichen]

do you know DMT?

[knotty garnet]

ok excellent

[gray sundial]

No whats that

[knotty garnet]

so here's an interesting thing about complex numbers

if you want to multiply two complex numbers

you multiply their magnitudes and add their angles

voila, complex numbers multiplied

[glass lichen]

if $z=r(\cos(t)+i\sin(t))$ then $\forall n\in\mathbb{Z}, z^n=r^n(\cos(nt)+i\sin(nt))$

[ocean seal]

Mosh

[knotty garnet]

mosh im getting to that

[alpine sable]

anyone please help

[violet haven]

yeah so if 260 = 25 * 10 + 10 then it means the variable values given are a solution to the equation. it needs to be even on both sides. then the last one you can try out other values for x and y to try to make it even^^

[gray sundial]

Yh so Modulus-Argument form?

[knotty garnet]

yeah do you know the concept behind why that's true?

[glass lichen]

yeah, so if we assume z is on the unit circle $\abs{z}=1$, then let n=2 $$(\cos(t)+i\sin(t))^2=\cos(2t)+i\sin(2t)$$

[ocean seal]

Mosh

[glass lichen]

then by comparing components you get the desired result

[gray sundial]

Oh ok thanks I get it now

Thanks @knotty garnet aswell

[quick talon]

is the relationship for "the Average wrist circumference, by age" continuous or discrete

[sharp bramble]

What is a possible value of x so that the distance is √29 between the two points with the given coordinates: (-9, -5) (x, -3)

[warm junco]

can someone help me with this im so stuck

[violet haven]

it tells you to make up your own values for x and y, so you can just put in a random value for x and solve it and then your answer is y. for ex. if x=5 then 25*5+10=135 and 135 is your y

[gray isle]

you can determine whether your function is linear or quadratic from the first and second differences

[quick talon]

8 139.46
9 147.31
10 150.12
11 152.65
12 154.46
13 162.04
14 162.50
15 168.64
16 170.45
17 169.59
18 170.05
19 170.82 (are their outliers?)(edited)

\

[sharp bramble]

What is the equation of the Line of Reflection if triangle LMN is reflected as triangle L'M'N' as shown?

[zenith chasm]

x = 1

[soft dagger]

Hi so I've been having troible with this problem my girlfriend asked me about and I want to seem smart

Can anyone help?

[arctic ferry]

Can anyone help, this one's tough for me

[soft dagger]

Wait I still need help?

[knotty sleet]

Hahahahahah

Best thing I've read all day

[soft dagger]

I need help 🤣

[knotty sleet]

Ok

[knotty sleet]

So basically as X goes to negative infinity you see the graph also goes to negative infinity

As X goes to positive infinity the graph also goes to positive infinity

[soft dagger]

I see that yes

[knotty sleet]

That's all you need to say for 'end behaviour'

[soft dagger]

Oh

That's it?

[knotty sleet]

The number of real zeros is the number of times it crosses the X axis

[soft dagger]

Okay thank you!

[knotty sleet]

Or touches

Touches counts as one (repeated) zero

Np, good luck impressing your gf hahaha

[soft dagger]

I will!

[rigid imp]

How to solve 429.5 = 578 (sin(x))

[upbeat dirge]

solving this would be: 8x tan (55) right?

[thick sigil]

can you explain why? My idea was random variable A has a higher pay-off for x = 2 and the random variable B has a higher payoff for x = 5. Hence neither dominates

[sly mantle]

@upbeat dirge is this quiz graded?

[thick sigil]

But some of my friends came out with combining the payoff

[knotty sleet]

Make sure you know precisely what surjective means and what needs to happen for it to be surjective 🙂

[upbeat dirge]

No! its a practice quiz to go over what we learned in preparation for a real quiz, and my teacher sent a video but it has not explained how to find the sides using trig! I tried looking it up and I think i've gotten the hang of it, but when I used this equation it gave me a really big negative number so I wanted to make sure my equation is right!

[thick sigil]

and with their idea, it looks like B can also > A w/ first order stochastic dominance

@knotty garnet

[knotty sleet]

This channel is getting flooded 😅

[upbeat dirge]

i'm not asking for the answer btw, i just wanted to make sure my method is right!

[thick sigil]

nvm i just saw this thanks!

[alpine sable]

is there an equal sign missing?

[upbeat dirge]

is there supposed to be an equal sign in this equation?

[alpine sable]

every equation has an equal sign lol

[sly mantle]

i'm suspicious bc of 'quiz' in the url and the points attached to each question. i'll take your word that it's practice

[alpine sable]

it should be tan(55 degrees) = opposite(x)/adjacent(8)

[upbeat dirge]

proof :)) it says quiz because it's canvas!

[rigid imp]

just gonna repost cause I got flooded~
How do you solve 429.5=578(sin(x))

[alpine sable]

so u solve for x by multiplying both sides by 8 to get x = 8tan(55 degrees)

[upbeat dirge]

Thank you so much! I will try that equation, I really appreciate it! And sorry for the dumb question, i'm not really the brightest when it comes to math

[alpine sable]

no problem everyone has their weakness/strength

[thick sigil]

isnt this just sin^-1(429.5/578)

[alpine sable]

lmk if im right

[rigid imp]

thats what i thought but that doesnt give me the answer on the key

[alpine sable]

did u change to radians

[upbeat dirge]

I believe it worked! If i'm correct, the answer should be 11.42

Thank you so much once again!

[alpine sable]

np

[split flume]

yeah you gotta change it to radians

[blissful cliff]

Hey can anyone explain to me the inequalities?

[alpine sable]

of?

[blissful cliff]

Of ?

The argument in general I didn't really understood it

[rigid imp]

Should I be setting this up differently? I did 429.5=1/2(34)(34)sin x

[alpine sable]

area = 1/2 base x height

ur base is the side opposite the obtuse angle

[gray isle]

your initial set up is fine

[bleak spade]

someone help

[rigid imp]

Getting a different answer with it than whats on the key tho. I’m getting 48 degrees from that while the key says 132

[gray isle]

note that sin(x) = k
has two solutions for 0<k<1 and0 < x < 180°

you are told your angle is obtuse

[alpine sable]

oh tru

🧠

[gray isle]

use the appropriate shift to get your obtuse solution

[rigid imp]

Care to elaborate? Only really one way i can think of to set this up

[gray isle]

apply properties of the unit circle and/or sine

subtract you acute angle from 180°

[rigid imp]

Ok, that works for the answer, but I don’t get how that really makes sense/how to show the work

[gray isle]

properties of the unit circle and/or sine

sin(x) = sin(180° - x)

note that sin(x) = k
has two solutions for 0<k<1 and 0 < x < 180°
x = arcsin(k) , 180° - arcsin(k)

[alpine sable]

How do I get x and Y

[gray isle]

trig

sine, cos, tan and/or special triangles/angles/ratios

[alpine sable]

So it's sin

?

Wait

[winged ledge]

?

[bleak spade]

someone help pls

[raw zephyr]

Top one i think LOL

[winged ledge]

yeah i put taht

xd

what about .that

[raw zephyr]

hold on

[spring patrol]

can someone pls help me out on question 5

[raw zephyr]

i think its the top

[novel siren]

there are no real solutions, the square root of anything can never be negative

[real sinew]

There's no real solution s

[raw zephyr]

my brain hurts

[winged ledge]

thanks

lol

[raw zephyr]

whats the question

[gray isle]

this looks like an answer key

[spring patrol]

somneone help pls

[carmine coyote]

does anybody have an answer for this

[strong furnace]

standard parabola has directrix at x=-a if that helps you , you can rotate this parabola to get what you want

[raw zephyr]

1. (a) x²+6x (b) x²+4x (c) x²+8x

   (d) x²-10x (e) x²+7x (f) x²-5x

sorry if i was a little slow LOL

hold on i'm doing some more for you

[strong furnace]

you're not supposed to do that :/

[raw zephyr]

??

[strong furnace]

giving answers straight

[raw zephyr]

if it was i wouldnt give the answers

cause of the rules

[strong furnace]

its not just about the test , you're supposed to help them get there not just give them the answers thats in the rule as well

[raw zephyr]

ok

[carmine coyote]

anybody?

[knotty mist]

no idea what im doing, help

[gaunt coyote]

hello

anyone here can help me with a very complex math/excel question?

i tryd it several times now no luck so far with some ppl

@gaunt coyote me if u think u can help me i will explain then everything

[solar tapir]

[alpine sable]

stuck

[gaunt coyote]

i asked so many times its no so easy to explain it

[solar tapir]

You need to ask first

[wild nest]

Anyone here?

[remote heron]

😄

[wild nest]

The sum of two numbers is 46. One number is 12 less than the other. What are the numbers

[remote heron]

sounds like a system of equations

[wild nest]

I need to make the into a linear equation

[remote heron]

have you been able to make any progress so far

[wild nest]

No

[remote heron]

lets say a is the lower number, and b is the higher number

can you write an equation for b?

like if i tell you the lower number, whats the equation for figuring out what the higher number is, given the information in the prompt

[wild nest]

Idk

[solar tapir]

@remote heron

Can I try making a question?

[remote heron]

hmm can you identify the piece of information that might help you here

[wild nest]

We’ll just take the lower number and Minus it from 46

[remote heron]

to toopy you mean?

[solar tapir]

@wild nest Get an equation for this part only: The sum of two numbers is 46

[remote heron]

sure

[wild nest]

Ok

[solar tapir]

What did you get?

[wild nest]

23

[solar tapir]

Channel busy

[solar tapir]

That's not an equation

[winged ledge]

Mb

[wild nest]

A + b = 46

[solar tapir]

That's better

So that's your first equation

[wild nest]

Ok

[solar tapir]

Now get another for

One number is 12 less than the other

[wild nest]

A-12 + b = 46

[solar tapir]

That's not correct for the statement

[solar tapir]

Make an equation for this

[wild nest]

I don’t know how

[solar tapir]

You don't know how to state that a number is 12 less than the other?

[wild nest]

Not in an equation

[solar tapir]

What is substraction used for?

[wild nest]

To get rid of numbers

Math?

[solar tapir]

If I am 30 years old and you're 15 years old, how many less years you have than me?

[wild nest]

15

[solar tapir]

Then make an equation for this

[wild nest]

Ok

Sorry but I’m stumped and i forgot all math

You probably think I’m an idiot and that’s ok

[solar tapir]

Focus on this situation

[sudden hawk]

u need help with this?

[solar tapir]

M = Max's age

T = Toopy's age

If I am 30 years old and you're 15 years old, how many less years you have than me? You said 15

So you can say M = T + 15

So once again

[wild nest]

Oh

[solar tapir]

Make an equation for this

[wild nest]

A = b +12

[solar tapir]

OK

So now

you got 2 equations

[wild nest]

Yes

[solar tapir]

A + B = 46

A = B + 12

The second equation can be rearranged, if you wish so, to

A - B = 12

Solve the equation system

[wild nest]

Which one

[sudden hawk]

If you need help with simultaneous equations I would recommend putting one variable to one side and then substituting.

[solar tapir]

The equation system is

A + B = 46

A - B = 12

[wild nest]

Idk man

[solar tapir]

What methods of solution did they teach you?

[wild nest]

I don’t remember

That’s why I’m here

[solar tapir]

Then, with all respect

Pick a book and read about solution methods

I suggest you to check substitution and elimination

[sudden hawk]

yes

[solar tapir]

Otherwise, me solving this for you would be doing nothing for your learning

And the ability to solve linear equations system is important

You already got the equation system, so you're about 80% done

[solar oasis]

can someone help with this. i dont know where to start with the polynomial

[solar tapir]

What's the formula of a perimeter?

[steep steeple]

depends what shape

[steep steeple]

just add up all the sides like 4a for a a square

[solar tapir]

True

For a rectangle

[steep steeple]

2(l+w)

just add the length and width and then multiply that by 2

[teal rune]

How to find X?

please help

[sudden hawk]

is a polynomial just a quadratic

[teal rune]

yes

it is

[sudden hawk]

k thx

[strong furnace]

no, polynomial can have any degree (n ) n in W , a polynomial with degree 2 is called quadratic

[timid wind]

can someone prove the divisiiblity rule for 8 and 9

<@&286206848099549185>

ping me when u there

[muted raft]

You can just google search this?

[teal rune]

12 - 6root3

what is this in simplest radical form

[timid wind]

wait true

ill just google

[gray isle]

12 - 6root3

[teal rune]

\

what is x tho this was my original question

[outer elm]

60

[strong furnace]

incenter is the intersection of angular bisectors , you have to use this and the fact that tangents are perpendicular to radius

[somber oak]

Anyone know how to answer it?

[gentle notch]

anyone help me please

its the last question

[ionic jewel]

28 = 4*7 and 63 = 9*7

[gentle notch]

idk how to do anything

@ionic jewel what about mine?

[somber oak]

no lol

It’s a surf

Surd

[ionic jewel]

i have no idea what a surd is but i was giving you a hint

[somber oak]

I don’t think Americans learn it

[gray isle]

aka radicals

[ionic jewel]

yes I learned this math, my hint should be helpful if you know radical (surd?) rules

$\sqrt{ab} = \sqrt{a}\sqrt{b}$

[ocean seal]

bunny

[strong furnace]

for non-negative numbers 🙂

[somber oak]

oh I thibj I’ve got the question mixed up

yeah your right

[gentle notch]

@ionic jewel

[ionic jewel]

stop pinging me

[gentle notch]

plz help me out

[ionic jewel]

no

[outer elm]

lol

[gentle notch]

bruh you helped him

[ionic jewel]

you posted on top of his question

I was helping him

not only were you rude, your question looks unfun to solve

[gentle notch]

can you help me now?

[ionic jewel]

im not interested in helping

no

i cant

[gentle notch]

can anyone help me out?

[somber oak]

Use photomath

[gentle notch]

how was I being rude lol?

just asking a question???

[ionic jewel]

you posted on top of someone elses question, then pinged me twice when i was clearly helping someone else instead

[gentle notch]

yes, cause I know that I will be unanswered if I dont

[gray isle]

the irony

[outer elm]

bro just leave it lol

[strong furnace]

<@&268886789983436800> le epic troll @alpine sable

[gentle notch]

ok, I am sorry for being rude

[solar tapir]

Calm down both and return to math help

[gentle notch]

ill just go to the geometry section

yall are no help

[solar tapir]

Pick another channel and ask there

[strong furnace]

what have you tried?

[gentle notch]

i thought ABG was a triangle

and since tangents share a common endpoint \

the tangents are congruent

so the triangle is isosceles

[strong furnace]

ok

[gentle notch]

so 180 - 30 = 150

and since base angles are congruent in an isosceles triangle

150/2 = 75

[strong furnace]

how does that help us in finding what they are asking for?

[gentle notch]

so both angles equal 75

they are asking for the measurement of angle BFG right?

[strong furnace]

yes

[gentle notch]

so

m<BFG = Arc BG?

wait no

[strong furnace]

F is not the center

ye

[gentle notch]

doesnt make any sense

ok

yeah thats kinda where Im stuck

[strong furnace]

I will tell you how I would look at this problem

the tangent angle

we have to use this info

but this is not doing much as of right now

lets look at the other piece of information

they have given an arc

[gentle notch]

ok whose measure iis 50 degrees

[strong furnace]

now angle of arc is the angle subtended by a chord at the center

and we know something about the angle subtended by a chord at the center

we can find the angle subtended by this chord at any point on the circle using the relation

do you see how we could use this to get closer to what we need?

[gentle notch]

ummm not really?
the angle of arc is 50 degrees right?

[strong furnace]

yeah

[gleaming matrix]

<@&286206848099549185> 🙏🏽

[teal rune]

uh

whats the answer tho

I dont think

I got it right

<@&286206848099549185>

[outer elm]

@teal rune bro i told you

its 60

[teal rune]

I got 60

damn

ok

[ashen condor]

is dis 60?

<@&286206848099549185>

[outer elm]

how did you get to that?

[ashen condor]

ah, i can't get exact result, but here is my reasoning so far:

• In a circle, any two inscribed angles with the same intercepted arcs are congruent.

let me draw

I know it has to be > 45 because of this

[rich basin]

How do we know whether this statement is true

if we don't know whether they logically follow

[outer elm]

@rich basin bro wait cant you see that we're in the middle of something? ask in a different channel

[rich basin]

Sorry

[ashen condor]

almost done

ok, im not sure if its correct but let me post it

[polar kindle]

Hi, I want to define a domain of possible inputs of a random fuction, this domain is the same as the image, how can I write this mathematically? (sorry for my bad english)

[ionic jewel]

$-1 \leq x \leq 1$\
$-1\leq y \leq 1$

[ocean seal]

bunny

[ionic jewel]

or
$-1\leq x,y \leq 1$

[ocean seal]

bunny

[ionic jewel]

or something like

[polar kindle]

Can I write this: $f(x) = -1\leq x,y \leq 1$

[ocean seal]

madeira

[ionic jewel]

i cant read that

no you cant

f(x) makes it a function

what I wrote is a range of x and y

what you could do is

$f(x,y) = {(x,y) | -1 \leq x,y \leq 1}$

[ocean seal]

bunny

[ionic jewel]

but thats not what you want

the domain is just not written f(x) =

[echo pike]

I need some help

[polar kindle]

how can I research about it to better understand?

[loud oriole]

@echo pike

[echo pike]

Thank you ❤️

[sweet grove]

Yes I wood like some help pleese my home work says 2-3 and we haven’t learn that

[polar kindle]

thank you btw

[sweet grove]

Could you help me

[echo pike]

one more question

[lean atlas]

so if i have 10 letters and they can be either lowercase or uppercase how many total possible combinations r there?

[faint sundial]

So my brother is making macaroni shapes in real life which needs 6 table spoons but we want to know in a measurement cup (measures in cups) how much milk we need. All I know is that there’s 16 tablespoons in 1 cup and we need 6 tablespoons and 1/2 a cup is 8 tablespoons and 1/4 cup is 4 so if we need 6 tablespoons how much of a cup would we need?

[glass lichen]

1/4 cup is 4 tbsp, then 1/8 cup is 2 tbsp, so 1/4 + 1/8 = 3/8 cups

(assuming 16tbsp = 1 cup is right)

[faint sundial]

So if we need 6 tablespoons and 1/4 cup 4 tablespoons and half a cup is 8 tablespoons so half way between 1/4 cup and 1/2 a cup is 3/8 cups?

[glass lichen]

yes the average of 1/4 and 1/2 is 3/8

1/16 th of a cup is 1 tbsp, so 6 tbsp is 6/16 = 3/8 cups

[elder kindle]

Hi

So I'm learning about the shell method and using it to solve this problem:

So I figure I rotate this shape here

And I think it would make this sort of shape, could be wrong

[gusty gorge]

indeed the shape it makes is very unaesthetic

[elder kindle]

I understand why the radius of the shell is 2-y, but my teacher says the height/depth of the shell is 2-x, which I don't understand. As such I can't move forward with the problem

[elder kindle]

Does it look about right?

[alpine sable]

where can i quickly learn about trig?

[elder kindle]

Using this channel. Also read #❓how-to-get-help before asking questions

[gusty gorge]

hmm, imagine that the funny-looking curve is a set of (x, y) points for a second here

they actually are defined like that, but that's a conversation for another day

let's say we're considering the shell indicated by the red line

the radius is 2-y, as you've correctly noted

and do you agree that the height of the shell is the length of the red line?

[elder kindle]

Yeah the x

[gusty gorge]

the x?

[elder kindle]

The length on x axis becomes the height of the shell

[gusty gorge]

that's not a precise statement

do you agree that the height of the shell is precisely the length of that red line?

[elder kindle]

Yeah, I just thought I knew what the red line was :P

[gusty gorge]

right, and that red line has a length of 2-x

[fading musk]

can someone help me with 2 9th grade math assignments?

[wheat pecan]

whats the property that states that 2x = x + x ?

[elder kindle]

Why is that?