help-13

[graceful karma]

Satisfying whole number

[astral dagger]

,w 15/sin(arctan(15/8)

[wraith dagger]

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Requested by Cold#1033

[astral dagger]

confirmed!!!!!

[graceful karma]

Epic

[astral dagger]

whats next tho?

[graceful karma]

Thats it

Minus plugging it in ofc

[astral dagger]

17sin(1.08 + ?)

whats the ?

[graceful karma]

Well wt is just always gonna be there I think

Then we solved for a

[astral dagger]

a = 1.08 rad

[graceful karma]

,w arctan(15/8)

[wraith dagger]

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Requested by PapaBread#3820

[graceful karma]

Reasonable

[astral dagger]

the answer is 17 sin(ωt + 1.081) tho

[graceful karma]

Yeah

[astral dagger]

ye so is a the second variable

[graceful karma]

Yeah

[astral dagger]

ahh i see what symbol is that

i thought wt was a

[graceful karma]

I didnt want to type out α every time

Alpha

[astral dagger]

ohh so that was alpha not a

xD

ok thanks for helping me ive got a ton of these to get through so thanks

[graceful karma]

Np

[astral dagger]

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[vestal ingot]

does anyone know how to solve the 1 3 13 16 23 = 20 krypto

[vestal ingot]

the calculator does not account for imperfect fractions

there is a way to solve it

my math teacher said there is a solution but it uses fractions

i have looked all over the internet

and i could not find anything other then this

https://brainly.com/question/25619199

not from my class

no one else in my class cares

i think it is just a coincidence

my math teacher showed me a script that a student wrote that could solve it

like we used seemingly impossible cryptos and it found a solution to them

no, he wants me to try to figure it out

but i have spent over 5 hours on this

and i cant seem to find the answer

[sinful zealot]

need help

[kindred plinth]

Like they said, use #❓how-to-get-help

[vestal ingot]

do you know anyone else that may be able to solve the krypto

[kindred plinth]

I kind of want to try writing a script for it now, I've never heard of this puzzle before

[vestal ingot]

well the person wrote the script to solve it in one night and was in 6th grade

that is pretty insane

they were brilliant

they scored like top 10 in mathcounts at states

anyways if you find the answer please dm me because i really want to figure this out

?

like the answer

wait a sec

how in the

wait how

you have a 400 iq

wait acctualy how

wait no

you used 3 twice

wait nvm

this cant be true

ima fact check this

send them to me

how are you solving this

did you like find a script

like how

can u send it to me

thank you so much

i did

you saved me like 10 hours of my life

ok

ya you figured it out so you deserve to answer that question

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[livid monolith]

Can someone join voice and help me with this question?

[bright surge]

uh
i'll try

[livid monolith]

Can you hear me?

[bright surge]

i mean

you have this?

it must be?
else we can have (a+b near 14) or (a+b near -31)
which is impossible

the tangent line is perpendicular to the radius of a circle

(you know what i mean)

(probably)

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[kindred pike]

where does the 2x come from on this one?

[wraith dagger]

hvna

[crimson sedge]

Not sure why it's factored out because that's incorrect

[kindred pike]

can you explain where the 2x comes from

i assume its the dt but idk

[crimson sedge]

The last term of the integrand in the middle part of the equation

there's a -1

It integrates to t

And then evaluates to x62

x^2

which if you take the derivative is 2x

[kindred pike]

awesome ty

[crimson sedge]

Non problem, good luck

[kindred pike]

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[coarse marsh]

hii, can someone please explain how my teacher got -1? i think it should equal 0/0

[coarse marsh]

nvm i get it ^^

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[ripe jungle]

anyone know a good math website with old tests for all grades?

[crimson sedge]

what tests

[ripe jungle]

math. geometry

school tests?

[crimson sedge]

do you just want to practice or what

Since you said grades in your original question, I'll assume you mean grade school math

http://www.math-tests.com/

[ripe jungle]

no im writing next week. and im sweating cuz im top in my grade now. i've done all the local school tests... i just need more

[crimson sedge]

This is a collection of grade school math tests

[ripe jungle]

thank you so much

[crimson sedge]

Anytime!

[ripe jungle]

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[potent glen]

I understand every part of this problem except for the portion circled in red. Where does the 5e come from?

[potent glen]

I understand that you're supposed to find the limit by replacing n with infinity, but I don't get how that results in 5e. I probably would have said its infinity/infinity or even 5/1 by looking at leading coefficients

[wraith dagger]

hvna

[potent glen]

gotcha, I think that makes sense. Is there a name for this rule? I don't have it in my notes

[crimson sedge]

The limit definition of e

[potent glen]

wonderful, thank you.

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[neat heart]

I'm not sure what do do with h) and i) the rest was easy. I guess i need to transform the bounds 2 and 5 somehow.

[neat heart]

I've only done this randomness variable transformation the other way arround

[cedar kiln]

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@neat heart Has your question been resolved?

[neat heart]

<@&286206848099549185>

[glass wigeon]

I think there might be more context, what probability model does it want you to use?

[neat heart]

I'm looking for P(2<X<=5) for lnX ~ N(0,1). So i know that ln X is standard normal distribution but i don't know what distribution X is.

[glass wigeon]

ah, i understand what this is about, the letters are not the answer options, they are the parts of the question, my bad

[neat heart]

yes they are different questions 🙂

[glass wigeon]

it has been a little bit since i have taken stats, do you know the formula for the transformation of sdev?

you should be able to use that to set up an equation

[neat heart]

does sdev mean standard normal distribution?

[glass wigeon]

sdev means standard deviation

[neat heart]

oh okay

like sqrt(Var(X))

[glass wigeon]

... let me check

[neat heart]

hm so the sdev is the sqrt of the second parameter

so in this case 1

[glass wigeon]

I believe so, and but i forget how the transformations affect the variance, which you also need to use that equation

I'm sure you have done the transformations before, this should just be the reverse of those (but I learned this in a different country so I don't know how much it is different)

[neat heart]

The only transformation i have done before is P(X^2 < 4) which i transformed to P(-2<X<2)

that was basically just solving the inequation

but i'm not sure how to do the transformation when it's given for the distribution

[glass wigeon]

sadly, I'm not sure how to help you then. most of this notation is very different than anything I have seen before, i would give more if i could

[neat heart]

thanks for trying 🙂

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[crimson sedge]

how can i determinate this?

[crimson sedge]

what are the options

👀

(sin^2x)^2 - (cos^2x)^2
(sin^2x)^2 - (1-sin^2x)^2
sin^4x - 1 -2sin^2x + sin^4x
2sin^4x-1-2sin^2x

[mighty drift]

simpler to do a difference of squares

[crimson sedge]

oh wait you have a point

[graceful karma]

The squares are simply different

[mighty drift]

(sin²x + cos²x)(sin²x - cos²x)
(sin²x - (1 - sin²x))
2sin²x - 1

[crimson sedge]

okay this

[graceful karma]

Do you know how to start

[crimson sedge]

start what

[graceful karma]

The problem

[crimson sedge]

i barely remember this class ill re-study it later on my own

[crimson sedge]

👍

ill send another question i barely remember

this

@crimson sedge@graceful karma yall know anything about this

[tribal spoke]

Sin^2= ?

@crimson sedge

[crimson sedge]

wym

[crimson sedge]

factor out cos x
cos x (sin^2x-1)
cos x ( cosx^2)

cosx^3

its pi/2, 2pi/2 i think

find points where cosx^3 is 0

so

$\ cosx^3 = 0$

[wraith dagger]

senku

[crimson sedge]

find for all points it's true

within that interval

peace out

[mighty drift]

it's actually -cos^3(x) but whatever

[crimson sedge]

Oh wait

[tribal spoke]

You are not helping giving out the answer like that @crimson sedge

[crimson sedge]

wait so this is the correct answer?

[crimson sedge]

Yeah sorry

I'll leave

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[crimson sedge]

how would i write x is less than or equal to -9 and greater than or equal to 3 in interval notation

[crimson sedge]

@crimson sedge

<@&286206848099549185>

ok

the question i was answering was

Solve the inequality $x(x + 6) > 16.$

[wraith dagger]

d-static

[crimson sedge]

but my answer

(-inf,-9] U [3,inf)

is wrong

[graceful karma]

^

[crimson sedge]

?

why?

not correct

no, it renders correctly

no infinity symbol

can you explain how you got it?

wdym?

wait

i think that it should be (-inf,-8) u (2, inf)

based on your graph

the inequality is non-strict

it works

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[remote yoke]

Hi

[remote yoke]

So i dont really understand

What the question is asking

x = 0 doesnt make sense

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[remote yoke]

Thank you

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[hollow fox]

How I can solve these questions?

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@hollow fox Has your question been resolved?

[hollow fox]

<@&286206848099549185>

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@hollow fox Has your question been resolved?

[leaden otter]

For 1) and 2) try seeing what happens when you divide both, numerator and denominator by the degree term.

For 3) try to factorise the numerator

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[last oyster]

Can anyone help with this question? 14 b?

[harsh slate]

@last oyster Do you know Calculus?

[last oyster]

yuh

[harsh slate]

Ok, I think it's a optimization problem

To find the maximus of a funcion you take the derivative, and check f'(x) = 0

Then check if it's a maximun or a minimun

[last oyster]

ok one sec

[harsh slate]

The function in this case is the one in a

[last oyster]

is f'(x) (-2x^2+25)/(2√(25-x^2))?

[harsh slate]

,w derivative of (1/2)x sqrt(25-x^2)

[wraith dagger]

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[harsh slate]

IT seems

[last oyster]

so i make this =0 to find max or min right

[harsh slate]

Yes

[last oyster]

dont i have to derive twice?

[harsh slate]

Yes, but, you can check with the first derivative, around the point. For example, if it's a maximun, the function is increasing in the left and decreasing in the right. That means, the derivative is positive in the left of the point and negative in the right

You should have obtain two points, right? one positive and one negative. So, just focus in the positive since x represente length

And do that argument

[last oyster]

ok so x=√(25/2)

[harsh slate]

In this case you're looking for a global maximun, so, you have to check in all the domain of the derivative

[last oyster]

and i sub it in f(x) it gives me 6.25

[harsh slate]

Yes, but did you check is a maximun?

A global maximun

[last oyster]

so i have to derive twice right

[harsh slate]

Yes, but you can do in another way

The one I told you

Check that in the left of the point the derivative is positive and in the right is negative

Do you understand why it should be a maximun

?

[last oyster]

i dont know how to do your other way i dont udnerstand

[harsh slate]

Check, if the function have a local maximun in c

Local means, the maximun is around an interval, this is f(c) is maximun for an interval around c,

$f(x) \leq f(c), \forall x \in (c-d, c+ d)$

[wraith dagger]

Enigsis

[harsh slate]

If you find that, f is decreasing in the left of c and increasing in the right of c, then, it means f(c) it's actually a maximun, since all the point around that point are less

if x < c and f is increasing on the left that means f(x) <= f(c). And if c < x and f is decreasing on the right, that means f(c) >= f(x)

I think in this case that works

[last oyster]

ohh yeah i got it

alright i tested for it and it got maximum

[harsh slate]

But the second derivative method is more general I think

[last oyster]

so 6.25 is my answer

thanks

[harsh slate]

Yes, I think so

[last oyster]

yeah answer says 6.25 just checked

[harsh slate]

,w critical points of (1/2)x sqrt(25 - x^2)

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[harsh slate]

Hmm

,w maximun of (1/2)xsqrt(25-x^2)

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[harsh slate]

That's how you check

[last oyster]

👍

[harsh slate]

If you want to be sure

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[wide swan]

Is there a way to reverse solve this question or something? I'm not entirely sure how to approach this question. Can anyone help?

[sudden magnet]

ok so

[wide swan]

So far, I don't think it's (A) or (D). Because (A) is too small and (D) feels like it's way too much.

[sudden magnet]

multiply all of the chances

for example a chance that a crocodile makes it to 1 year old is 0.25*0.55

[wide swan]

Alright, I'll do that first.

[sudden magnet]

13.75% chance that it survives

you want to do that for all 5 and you should get a pretty small percentage

yeah

[wide swan]

On a calculator it gets 0.0097329375. As a decimal.

I multiplied them all together.

[sudden magnet]

are you sure you multiplied correctly

[wide swan]

I'll check again.

That's correct, I misclicked a number.

0.007486875

[sudden magnet]

this problem is basically
55% (chance that it reaches 1 year old) of 20% (chance that it survives after hatching)

etc

[crimson sedge]

Hi

[wide swan]

So then, that's 0.007486875/1=0.007486875? Same thing?

Oh

[sudden magnet]

multiply 0.007486875 by 100

[wide swan]

1/0.007486875=133.5670757158

[sudden magnet]

you get a 0.74% chance that it survives

yes

correct

[wide swan]

Oh, so 133 crocodiles to each lay an average of 50 eggs?

[sudden magnet]

1 in about 133/134 eggs will reach 5 years old

[wide swan]

Doesn't the question asks the number of crocodiles?

So it was three.

Ok

Interesting, thanks for your help!

I'll close this now.

[sudden magnet]

np

[wide swan]

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[dry dirge]

how you proof that these are equal ?

[dry dirge]

I know sin(x+y) and also know sin(x+y+z) but I can not make these two sides equal

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[toxic plank]

ive tried alot of methods nothing is working

[upper abyss]

Remainder theorem.
P(n) = 2n

[toxic plank]

oh ty

i missed that lesson makes so much sense

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[tribal scroll]

how would u do 10 b

[cedar kiln]

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@tribal scroll Has your question been resolved?

[hollow thicket]

https://tenor.com/view/explaining-explaining-meme-cala-gif-23733782

me when funcions

[radiant topaz]

You have to find P(X >4)

[rare ferry]

calculating the limit of your mom

[hollow thicket]

:=

:0

[tribal scroll]

yeah i did that, it was part a

i need help with b

[radiant topaz]

Use the binomial approximation

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[crimson sedge]

U know when u got harmonic form equations

[crimson sedge]

like this

how do u know if u should turm them into

sin(a + b)

or cos (a+b)

or does it not make a difference>

[cedar kiln]

@crimson sedge Has your question been resolved?

[true glade]

It can be converted into both a sin and cos term here

Because there's a negative in the middle it can either be sin (a - b) or cos (a + b)

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[still panther]

hey could someone help me on questions 5 and 8

[still panther]

<@&286206848099549185>

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@still panther Has your question been resolved?

[tall eagle]

I only know the answers of polynomials with only one variable

you need the answers of 1,3,4,6,7?

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[deft jasper]

would anyone be able to help with part B? I have work for part A if youd like to see what im working with but im confused what part B wants

[cedar kiln]

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[deft jasper]

<@&286206848099549185>

[deft jasper]

<@&286206848099549185>

[cedar kiln]

@deft jasper Has your question been resolved?

[deft jasper]

<@&286206848099549185>

[deft jasper]

<@&286206848099549185>

[deft jasper]

<@&286206848099549185>

[slim valley]

@deft jasper Hello 🙂 would you mind showing part A so i can better understand?

[deft jasper]

ofc one sec

this is an example from lecture notes but its basically the entire discussion of what part A is

[slim valley]

@deft jasper Thank you 🙂 i am not totally sure on the physics parts of it, but i will give it a go. if i cannot help i am very sorry but i will try

[deft jasper]

thats totally ok, im barely getting most of this as is, i cant expect someone else to pick up my slack, i just hoped someone had good knowledge on this that would be able to run me through how and why

[slim valley]

I love physics and its nice to see some physics questions here every now and then, but this is outside of my territory. just give me a sec while i research all of the names and functions you will be using

[deft jasper]

yeah it is a physics based question its more math than physics

[slim valley]

i take what i can get 😄

is uniformed the same a homo?

[deft jasper]

wym?

[slim valley]

it states the electric field does not change right?

over distances

[deft jasper]

yeah

constant field

[slim valley]

yes, idk why its called homogenisk here, but its what i thought, thats very good makes things easier

[deft jasper]

very much so yeah

[slim valley]

would you mind confirming by understanding of this question @deft jasper
We have a sphere in a uniformed electric field
The sphere has an electrostatic potential that does not change(?)

the question wants us to consider a variation where the electrostatic potential on the surface of the sphere is given by a function?

[deft jasper]

yes

that is correct

[slim valley]

I noticed it is 2:09 but i will stay awake for this 😄

[deft jasper]

oh well if its that late for you dont worry about it really, i dont wanna trouble u

[slim valley]

https://royalsocietypublishing.org/doi/10.1098/rspa.2015.0064

does this mean anything to you?

[deft jasper]

not particularly

[slim valley]

so you have not gone through this?

[deft jasper]

not to my knowledge

[slim valley]

good, i didnt understand that

ok, lets take a look so far and just make sure i understand what the question is about

we want to use Harmonic polynomial representation @deft jasper formula to get a educated guess of the surface potential?

ignore all of which is in the top left corner

i can barely keep awake, anyhow. there is a great wikipedia page on it you can follow this and solve it.
https://en.wikipedia.org/wiki/Spherical_harmonics
sorry its just too late

[deft jasper]

nah ur good

yeah i think ur on the right track, ill just do a bit more reading

[slim valley]

that normally solves it. if i can do it you can do it 😄

[deft jasper]

thank you!

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[clear grail]

someone please help me solve this step by step

[clear grail]

its optimization

v scary problem ;-;

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[thorny prism]

Hey so I don't so much need help with the problem itself here but I need help visualizing it. What does it mean by same Orientation?

[thorny prism]

Okay cool.

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[unique falcon]

Quick question: for questions like this, do i just take the definition of hyperbolic cosine, plug ln(x^2+8) and differentiate it like normal?

[foggy merlin]

if you want but its too long

[glad kestrel]

just use chain rule

[foggy merlin]

^

derivative of cosh(u) is u'sinh(u)

[unique falcon]

ooh right right, big brian

[unique falcon]

wait... that work even with hyperbolic trig functions?

[foggy merlin]

?

its just chain rule? what is the problem ?

[graceful karma]

It works with anything

[unique falcon]

ok, welp, looks like i didn't understand the my lec about hyperbolic shit at all. TY for the help guys

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[polar vector]

can someone explain wtf im doing wrong

[livid hound]

can you show your work

especially where arcsin(sqrt(2)) is coming from

[polar vector]

oh wait im chilling lmao i did it completely wrong lolol

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[sand ether]

Would calculating the determinant of this matrix and showing that it is non-zero be enough to prove that for any point in the image space, there will be a unique point in xyz space which maps to it

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[crimson sedge]

How to calculate x^(-y) like 5^(-1) in paper without calculator?

[tidal bough]

X^(-y)=1/x^y

[crimson sedge]

Thank you

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[peak bough]

Hi. I'm just making sure if my answers are correct?

[lunar thistle]

hello

[peak bough]

no. 1 is a cubic function. I put none of these bc cubic function is not in the choices

[livid hound]

what other choices were available

[radiant topaz]

I need to know options

[peak bough]

Only exponential equation, exponential function, exponential inequality, and none of these

i'm not sure with my answer to no. 3

[peak bough]

@radiant topaz @livid hound here

[livid hound]

then yeh, 1 would be correct

[peak bough]

how about 3?

[livid hound]

that'd probably be what i'd select

their use of e in Q4 is dodgy though

[peak bough]

Ohh yea I didnt notice the e in 4

[livid hound]

they should've used a different variable

supposedly its intended to be a variable as the equation would otherwise be false

[peak bough]

Yeah. but ill just put an explanation why equation is my answer

Thank you so much

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[upbeat carbon]

How can I show that all ℤ-basis of ℤ^n are composed of n vectors ?

[cedar kiln]

@upbeat carbon Has your question been resolved?

[upbeat carbon]

(I'm sorry for the ping) <@&286206848099549185>

[dense wing]

wdym

you mean how to show a basis of Z^n has n vectors..?

[upbeat carbon]

Yep

[dense wing]

that's definition of basis

a n dimensional vector space has n vectors in a basis

[upbeat carbon]

Let me rephrase it : How can I show that two basis of ℤ^n have the same cardinality

I'm working with free Abelian groups, not vector spaces

And by basis I mean a family that

1. Is free (i.e. you can't write on of the vectors with the others)
2. Every element of Z^n can be written with the vectors in the basis

[upbeat carbon]

Nevermind, I found how to do it

.close

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[hallow stream]

I tried to apply x -> inf rules here but that doesnt work. Does -inf change how to solve it?

[hallow stream]

I thought it was just N > M, and A/B > 0 so ans is inf

[upper abyss]

Well yeah, it isn't the same haha.

The numerator is larger and therefore dominates. That's enough to think through the limit

I suggest thinking about why the x → inf rules work, and how they might change here

[knotty badge]

You can apply Robida Law

[upper abyss]

If you are really stuck, try dividing top and bottom by 1/x³

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[real tartan]

we can't divide by 0, but we can divide 0 by other numbers right?

[real tartan]

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[tall eagle]

yeah

[real tartan]

.reopen

[cedar kiln]

✅

[real tartan]

oh al right

.close

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[crimson sedge]

can you actually do this

if its a + c

just multiply by a different constant instead?

seems wrong

how can they change it from an addition constant which graphically would be a translation or something, to a multiplication which graphically would be like a stretch?

[cedar kiln]

@crimson sedge Has your question been resolved?

[dense wing]

C=ln(A)

[crimson sedge]

between these two lines

they didnt log anything did they?

they just combined two of the logs

and the +c at the end turned into now multiplying them?

[sly iris]

Yeah

[cedar kiln]

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[marsh pecan]

they did it in 1 step what was done is simply replacing the constant with ln(A)=C as mentioned and then combining the terms

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[marsh pecan]

its like replacing $\sqrt{4}$ with 2, essentially the same thing they just did it without mentioning it

[wraith dagger]

james ash.

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[gleaming cave]

what is the definition of rotation

[gleaming cave]

[euclidean n-dimensional case]

geometry teacher didn't define it

[glass wigeon]

I got "Rotation has a central point that stays fixed and everything else moves around that point in a circle." from mathisfun

[tribal spoke]

Are you talking about matrixes of rotation ?

[gleaming cave]

under that definition this is a valid interpretation of rotation

[gleaming cave]

don't know what those are so probably not

[sly iris]

No

That's translation

[gleaming cave]

yes so then what is the definition of rotation

[sly iris]

Each point on that shape is a vector that can be described with a magnitude r and angle θ

[gleaming cave]

you mean corresponds to?

[sly iris]

Just add some dθ to θ to get the rotation

I guess in this specific scenario: the direction of the arrow should always be tangent to the circle at every point

[gleaming cave]

ok first what do you mean "each point on that shape is a vector"

just arbitrary vectors?

[sly iris]

Yeah

[gleaming cave]

wait doesn't the definition of angle measure make this definition circular

[sly iris]

Theta = s/r

No not really

An increase in angle measure just corresponds to an increase in sector length

[gleaming cave]

wait wait

i think you mean to say that each point on the shape corresponds to a vector from the center to said shape-point?

[sly iris]

Yes

What else could that have meant

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[crimson sedge]

.close

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[regal oak]

is x = 3?

[cedar kiln]

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[ruby nest]

Can someone please help me step functions

[cedar kiln]

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[ruby nest]

<@&286206848099549185>

[glad kestrel]

nobody can help you if you don't have a question

[ruby nest]

@glad kestrel Can u go on call with me so that I can present my screen and we can do my assignment together plz

[fossil hamlet]

send a picture of it

[ruby nest]

@fossil hamlet @glad kestrel

<@&286206848099549185>

<@&286206848099549185>

[clear grail]

can someone please explain how to solve this step by step

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[raw saffron]

I need help with this question please, I do not understand

[raw saffron]

thanks

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[digital sentinel]

need help with this question

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[radiant topaz]

Sum of all terms / number of terms is mean

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[crimson sedge]

I need help with this question. I am unsure how u would go through with solving this type of problem.

[crimson sedge]

I’m liiike pretty sure I’d be failing if it wasn’t for this server 😭

<@&286206848099549185>

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[kindred sand]

r u trying to sketch the graph of the function lol

or what

[crimson sedge]

,close

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[delicate pike]

Can someone help me out on how to solve this using sin and cos I don't understand how I start it or if I'm even using the right formula

[delicate pike]

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[livid hound]

"a common factor of a^3 is a^4"
that statement makes no sense
wouldnt the only factors of a^4 be a^2 and a^1 / a
recall the definition of exponentiation

that's not what you wrote though

[viral cloak]

That is not what you said at all.

Woops, sorry, Ramonov. All yours.

[livid hound]

anyway

recall the definition of exponentiation
(and exponent laws)

a^1 = a
a^2 = a * a
a^3 = a * a * a
etc

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[crimson sedge]

I really need some help with that thanks

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

well what did you try

@crimson sedge

give me a second to write it

this should follow very quickly from properties of dot product

Recall that U⊥ = {u ∈ R^n | "u, v# = 0 for all u ∈ U}. Since
0 ∈ U⊥, U⊥ &= ∅. Let u, v ∈ U⊥ and k a scalar. Then by definition of U⊥,
"u, v# = "v, U# = 0 for all w ∈ W. Now for all u ∈ U,
"u + v, u# = "u, w# + "v, u# = 0, "ku, w# = k"u, u# = 0.
Hence u + v ∈ U⊥ and ku ∈ U⊥. Thus W⊥ is a subspace of R^n.

Basically this is the proof.

yes

just W is my U and V is the R^n

should have I changed anything else?

no

thanks @crimson sedge

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[winged dawn]

Can somebody tell me how do i start solving 1/2 * tan(2*arctan(x)) ?

[cedar kiln]

@winged dawn Has your question been resolved?

[graceful karma]

Try using the tangent double angle formula

$\tan 2x = \frac{2\tan x}{1-\tan^2 x}$

[wraith dagger]

PapaBread

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[vital spire]

I know that BD is median,and that bc =2ac and i need to calculate dbc

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[vital spire]

<@&286206848099549185>

[regal oak]

do u have values ?

the concept to be applied is Pythagoras theorem ( since only 90 deg is given )
else u can use trigo if u know other angles

[vital spire]

no, that all

[vital spire]

may you explain the Pythagoras theorem?

[regal oak]

base ^2 + perpendicular ^2 = hypo ^2

this is pythagoras theorem

[vital spire]

so bc = 2x and ac = x so x^2 +2x^2 = 3x^2 which is ab

then what

got it

.closed

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[zinc adder]

Help

[zinc adder]

<@&286206848099549185>

[crimson sedge]

what's ur problem

[zinc adder]

Here

[crimson sedge]

make a table an mention how many faces of squares there are?

[zinc adder]

Number 1

I don’t get it

We jus started this unit

And the teacher didn’t even explain like wtf

[crimson sedge]

oh yeah i know this

pretty much

[zinc adder]

Ok

[crimson sedge]

count how many letters there are in between each letter

in this case the difference between b - e is 2

[zinc adder]

Ok

Why it says

[crimson sedge]

so that would be e,f,g,h

[zinc adder]

Discribe In words

[crimson sedge]

the difference is 2

[zinc adder]

Oh ok

[crimson sedge]

you says that the sequence from B skips every 2 letters in between

[zinc adder]

Ok

Alr

Ok what abt

The table one

@crimson sedge

<@&286206848099549185>

Ugh

<@&286206848099549185>

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[crimson sedge]

try to solve it urself then when you get stuck tell someone

[zinc adder]

Oki

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[gray light]

Where am I wrong?

[regal oak]

it isn't clear

[gray light]

Sorry

Let me draw it then

[gray light]

Here it is

[regal oak]

its crt

[gray light]

Sure?

I shouldnt be working with non exact roots

[regal oak]

ya

[gray light]

unless i messed something in the sqrt

38+-sqrt1444-960 ?

/20

Should be like that?

[regal oak]

ur eq is crt

[gray light]

Hm

Oh im dumb lol

Ok i got another one

[regal oak]

not clr

[gray light]

The c one

Okay let me draw

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[gray light]

<@&286206848099549185>

[regal oak]

its wrong ig

[gray light]

Where

[gray light]

ik

[regal oak]

x-2 ^2 = x^2+x+1^2

not -

(x-2) ^2 = x^2+(x+1)^2 this is the right one

see the denominator

@gray light

[gray light]

Oh

I see

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[crimson sedge]

can someone check my work for #3

not sure if it's correct

[languid valley]

How do i do this my brain cant process this

[crimson sedge]

<@&286206848099549185>

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[crimson sedge]

<@&286206848099549185>

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@crimson sedge Has your question been resolved?

[sand fog]

Essentially you want to find two equations, one for each cab company, to represent the cost of a trip given the distance travelled

Then you want to solve for when these two equations are equal

But please create your own help channel if you need help

[crimson sedge]

bruh its not even his help thread

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[cedar kiln]

@crimson sedge Has your question been resolved?

[tawdry rivet]

If you just wanna check the answer, you can use wolframalpha 😁

Btw, missing

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[lone mantle]

is this error

[graceful karma]

What's the linear equation [2]

[lone mantle]

2y=x+9

i thought it was supposed to be 2y=9.5 not 2x=9.5

it is from worked solutsions mannual from cambridge a level math book

[graceful karma]

Only one of those is true

[lone mantle]

I am asking if

they mistyped

y with an x

[graceful karma]

Non

I imagine it was very purposeful

[lone mantle]

why

then

[graceful karma]

Cause only one is correct

And the rest have to be wrong in one way or the other

[lone mantle]

there is no such thing as "only one is correct"

[graceful karma]

Oh wait I thought that was a multiple choice question for a sec

Sorry about that

[lone mantle]

lmaooo

dw

do you think they mistyped it

[graceful karma]

Hmm

Yeah

Cause you're substituting in x

There shouldn't be any xs left

[lone mantle]

.close

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[summer lotus]

1. What is compact and non-compact in representation theory (unitary theorem)

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@summer lotus Has your question been resolved?

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[summer lotus]

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[charred skiff]

I’m confused on the first example

[sleek fox]

Oh uhm.

wrong chanell

[charred skiff]

My

My

Mb

[bleak hearth]

Do you know how to find the area of a circle?

[sleek fox]

i forgot lmao

[bleak hearth]

Is it written in anywhere like your notebook?

[sleek fox]

ik the formula

A=piR^2

[bleak hearth]

do you know what is the r in your question

[sleek fox]

oh sh

my calculator only does it to 1 dp

[bleak hearth]

you can expand the numbers first, multiply them then divide them accordingly

if you expand the numbers with a power of 10 dividing be simpler

[sleek fox]

yeh i got it right lol

[cedar kiln]

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[pallid skiff]

hi, so I’m trying to figure out this question. the topic is factor theorem, I just don’t understand how you can find the algebraic values

[pallid skiff]

Question 9

,rotate

[pallid skiff]

I know how to do it, it’s just the methodology for this specific thing

when you don’t know the values of the cubic

.close

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[grave jay]

What have I done wrong?

[graceful karma]

You prob wrote the equation wrong

Cause thats the proper solution that you got

[grave jay]

oh ok, ill send more of the question

[grave jay]

my bad, it is -3 for the second fraction. Thanks though

.close

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[mighty compass]

help me

[mighty compass]

.close

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[viral cloak]

wth manel??

[cedar kiln]

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[ebon sphinx]

guys how do I complete the square for 2x^2-4x-7?

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[worldly wigeon]

Hi

[worldly wigeon]

I have a question

[south burrow]

did you read the message stating what you must do in this channel??

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[daring talon]

lol

[hollow quiver]

😠

[daring talon]

hey

[hollow quiver]

y=x+3

y=2x

done

[daring talon]

man

[hollow quiver]

my turn

[daring talon]

it was that simple?

[hollow quiver]

yeah

what are two possible things you can do to 3 (the input) to get 6 (the output)

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[crimson sedge]

i learned a seperate way to solve these types of problems our teacher taught us and none of these steps are what im familiar with, can someone help me and give me the correct order of letters? thanks

[obsidian coral]

How would you solve for x in that problem?

[lofty charm]

hi

[crimson sedge]

first we’d find the opposite version of the number in the middle

then if it monies we’d subtract it from the number that’s to the right of number side or if it was plus we’d add it

[lofty charm]

um guys

[crimson sedge]

then we would divide the result by the number with the variable

[obsidian coral]

Which number and what exactly do you mean by opposite version?

[crimson sedge]

the middle one between the number with the variable so if a number was like -6 it would be 6

[lofty charm]

how to make 5 to easiest fractaion

[obsidian coral]

Don't interrupt an occupied channel, read #❓how-to-get-help

[lofty charm]

oh ok sorry

[obsidian coral]

But in that problem though

[crimson sedge]

so in that case since there is a minus sign in front of the 8 we usually consider it as -8

then make it an opposite

so then it would go to 8

or positive 8

[obsidian coral]

So the opposite is adding 8, correct?

[crimson sedge]

yes

[obsidian coral]

After you add 8 to each side, what should you do next?

[crimson sedge]

add the number or subtract it to the number to the right of the equal sign depending if it has a minus or plus sign

if it helps i can send a picture of the proces

[obsidian coral]

You add 8 to both sides, what is the next step?

[crimson sedge]

oh we would usually on add 8 to the number that’s right to the equal sign

[obsidian coral]

So in that problem, first step was adding 3 to both sides

In the original question you asked, we add 8 to both sides

What is the step after adding 8 to both sides?

[crimson sedge]

adding the number to 1?

[obsidian coral]

We did that step already. Adding the value to both sides is that step

We add 8 to both sides

What is next

[crimson sedge]

dividing?

[obsidian coral]

Yes

[crimson sedge]

and then we divided 4 from 4?

[obsidian coral]

That's in that problem, but in the original that you asked

[crimson sedge]

.close

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[coarse rose]

Jaysen has 25 marbles. He divides the marbles into 5 piles so that each pile has a different number of marbles. The largest possible amount of marbles in the biggest pile is ______ marbles

[bold vine]

Think about trying to make 5 groups of marbles with 25 marbles

The key fact here is that each group needs at least one marble

[coarse rose]

Uhhhh

[bold vine]

Well you can first imagine starting by creating 5 piles, 1 marble each

[coarse rose]

Ok

[bold vine]

Now if you want to put as many marbles as you can in one pile, then you can dump everything else into one pile

[bold vine]

This maximizes the number of marbles in a specific pile

[coarse rose]

9 marbles?

Take one marbles from each pile?

[bold vine]

No, unfortunately

[bold vine]

Start here

You have 5 piles, each with 1

And 20 in your hand

[coarse rose]

Yes

[bold vine]

If you want the largest possible number of marbles in one specific pile, then dump all 20 into that one pile