help-13

[crimson sedge]

Is it clear now?

[ashen plume]

from where are you getting pt ^2 = pa * pb

actually dont tell me

let me figure this out

[crimson sedge]

look for congruency

[cedar kiln]

@dusky plume Has your question been resolved?

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[late owl]

Let U ∈ Z
n×n be a unitary matrix, that is, det U = 1. Let R ∈ Qn×n be a rigid rotation
matrix, that is, R · RT = I. Define Lˆ = U · L · R where L is n.I I is identity matrix

[late owl]

how can we comment about the Lattice generated by Lˆ has a basis consists of n orthogonal vectors each of length n

.

[cedar kiln]

@late owl Has your question been resolved?

[late owl]

.reopen

<@&286206848099549185>

no

[cedar kiln]

@late owl Has your question been resolved?

[late owl]

no

<@&286206848099549185>

[cedar kiln]

@late owl Has your question been resolved?

[cedar kiln]

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[thick blaze]

Is the ans 2.5π?

[whole ember]

,w integrate 5sin(x)/x from 0 to infinity

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by R31_#9293

[thick blaze]

👍

But idk how to calculate this on paper

I used wolfram alpha like you :/

Fine, thx for helping

:)

.close

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[civic coral]

this is the graph of function 2x+3=0

but i can't understand what the graph looks like this, i mean we dont have an "y" in this case right

[tropic oxide]

equation, not function

[civic coral]

got it

[whole ember]

no matter which value of y you choose, x will always be -3/2

[tropic oxide]

the idea is that moving up or down on the coordinate plane does not change the answer to the question "does our point satisfy the equation"

[civic coral]

but we dont have y in the equation of 2x+3=0

[whole ember]

that's why the x isn't affected at all along the graph

[tropic oxide]

and so for any point on the xy plane that satisfies your equation, an entire vertical line comes with it

[civic coral]

i got it, since we dont have y in our equation. so y could be either infinity or -infinity

is my understanding, correct?

[whole ember]

y could be anything from -infty to infty

[civic coral]

yes

i think i got it thank you

ohh one last question

why does the slope be approximately to infty

i heard that the slope of a vertical line will be close to infty, is there a reason

[whole ember]

recall how you find the slope of a line

[tropic oxide]

no

if you want to talk about the slope of a vertical line at all, it will be infinity, not "close to" it

in calculating the slope of a vertical line you are going to divide by zero

[cedar kiln]

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[crimson sedge]

If the equation: $a^{3}(b-c)(x-b)(x-c) + b^{3}(c-a)(x-c)(x-a) + c^{3}(a-b)(x-a)(x-b)=0$ has two equal solutions, then we can say that:

[wraith dagger]

feliipe

[cobalt prawn]

Did u try it

[crimson sedge]

yes

I actually I tried to factor the first two terms, in this case a^3 and b^3

[cobalt prawn]

At a glance I think e

[crimson sedge]

and maybe see if there's common factors afterwards with c^3

but nothing really changed

at least by the way I did ofc

[cobalt prawn]

Ok i am outside I might look later

[crimson sedge]

to my brain

e looks the most correct

[crimson sedge]

i have no idea what this means

the answer is letter A

sheeesh

[cobalt prawn]

Yeah probably

[crimson sedge]

wdym "probably"?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[crimson sedge]

.close

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[limpid canopy]

There is two functions $f,g = N -> N$ I know that f and g are surjective functions, and that $f(n) = g(2n)$. how can I find if g is an injective function?

[wraith dagger]

Shachar

[celest ledge]

It’s not true

[limpid canopy]

Whats not true

[celest ledge]

Your statement

[limpid canopy]

I need to prove that g not injective

but if my question is to prove its not injective I cant use this answer

[celest ledge]

This is a counterexample:

g(2)=1, g(n)=(n/2)-1 when n is even, g(n)=n when n is odd

f,g are surjective but g is not injective

[elder tapir]

Who is f ?

You don’t mention it in your exemple

[celest ledge]

f(n)=g(2n)

[elder tapir]

Ah yeah sorry

[celest ledge]

I can make a simpler counterexample, just let g(n)=n/2 when n is even, g(n)=n when n is odd

f(n)=g(2n)

[limpid canopy]

the thing is that im not sure if I can use a counterexample to prove that g is not injective

[celest ledge]

?

[celest ledge]

g(1)=g(2)=1

[limpid canopy]

ye I know there is a counterexample, but isnt counterexamples used to disprove things, not prove them?

[celest ledge]

As I said

Your statement is wrong

I disproved it

By having given you a counterexample

[limpid canopy]

i think i typed it wrong, my question is to prove that if f,g surjective then g not injective

[celest ledge]

…

Okay then…

[limpid canopy]

by giving counterexample you are not proving anything

[celest ledge]

Not my fault alright

[limpid canopy]

Its not yours, its mine

[celest ledge]

You gave me the wrong statement and you just corrected it one minute ago

Okay I can prove your new version now:

g(1)=n

Since f: m—>g(2m) is surjective

There exists m from N such that g(2m)=n

So g(2m)=n=g(1)

[limpid canopy]

wdym by f: m -> g(2m)

[celest ledge]

And 1 doesn’t equal 2m, so g is not injective

…

f is such a map, mapping m to g(2m)

[limpid canopy]

you took g(1) because there is no f(1/2)?

[celest ledge]

I took g(1) because 1 doesn’t equal 2m for any m

You can choose any odd number you like,

[limpid canopy]

ok i think i got it, ty for helping me

[celest ledge]

g(7)=f(m)=g(2m) for some m and 7 doesn’t equal 2m therefore g is not injective

Np

[limpid canopy]

and sorry for making it hard to help me

.close

[cedar kiln]

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[celest ledge]

Not at all, as long as your problem is solved

[cedar kiln]

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[tame cloak]

solve from elimination method

no idea i havent even done anything

[elfin hemlock]

Do so the coefficient in front of one of the variables are the same in the two equations

[tame cloak]

what?

[sonic thistle]

sqrt 8 is 2sqrt 2

[elfin hemlock]

What?

[sonic thistle]

you need to multiply the first one by 2sqrt2

and the second one by sqrt3

then add them

so the y cancels

[elfin hemlock]

He doesn’t have to do that, no

[sonic thistle]

?

its the easiest method

[elfin hemlock]

Just as easy to do it for x

So its just doing what I said

[sonic thistle]

but y already has -

[elfin hemlock]

And?

[sonic thistle]

easier

[tame cloak]

alright i have found the answer

shall i share it?

[sonic thistle]

yeah

how did you do it

[tame cloak]

not me

.close

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[tender moss]

X is 70

So what is y?

[hushed spoke]

can you find the angle supplementary to 70?

[tender moss]

Is it 35 by any chance

110?

Is y 35

[hushed spoke]

is it cyclic?

[tender moss]

Yh

[crystal raptor]

You should find another angle of the y triangle using a circle theorem and the fact that x=70

[tender moss]

Ok

One sec

So

So is y 20

[sonic thistle]

yes

[tender moss]

Id the midpoint is 140

[sonic thistle]

yes

[tender moss]

Yeah ok

Thanks

[crystal raptor]

Well done

[tender moss]

.close

[cedar kiln]

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[drowsy basin]

I need help on how to calc the difference in proportions

[lament sonnet]

What did you try?

[drowsy basin]

I've been lost this whole unit but I tried doing this formula and it didnt really work out

[lament sonnet]

Could you show what you did? The formula is correct

[cedar kiln]

@drowsy basin Has your question been resolved?

[drowsy basin]

do you know what z and q1 and q2 would be in this case? and sure

[lament sonnet]

z is the number such that P(Z>z) = 0.025, where Z-N(0,1). q = 1 - p

[drowsy basin]

Oh ok I had something else for that, I got the question correct now thanks

[cedar kiln]

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[wide light]

Not sure how to do part iii

For auxiliary equation I get

M = sqrt(9-k) -3

Mark scheme don’t make sense to me

Waiiit

I get it

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[cedar kiln]

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[radiant mountain]

i need help ty

[cedar kiln]

@radiant mountain Has your question been resolved?

[gleaming cloud]

how would you check if a function is a pdf?

[cedar kiln]

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[lethal sedge]

I need help with this question please

I am a bit stuck on where to start

[winter trench]

Have you begun the questions or are you still at the start

[lethal sedge]

still at the start

kind of stuck there

[winter trench]

well x^2+y^2=r^2

so you can switch and put that into the sqrt

to get sqrt(-r^2+49/256)

[lethal sedge]

oh ok

but where do I go from there

im sorry im pretty lost on this one

our instruction has been pretty limited on this section

[winter trench]

ok just gimme one sec to work this out lol

[lethal sedge]

all good thanks

@winter trench should we communicate in dms instead

[winter trench]

Nah here works

[lethal sedge]

oki sounds good mate

[winter trench]

next you have to get the limits on integration in terms of r and theta

[lethal sedge]

yes that is where I wasnt sure how to get those bounds

[winter trench]

since it is a hemisphere we can use intuition to say that theta goes from 0 to 2pi

which is just all the way around the circle

[lethal sedge]

I assume that is the first bound right but how would the second be determined

@winter trench

[winter trench]

That would be the outside bound

You usually want to do rdrdtheta

[lethal sedge]

yes

I would need an inside bound but im not sure

[winter trench]

Ok and then r is a little trickier to find

[lethal sedge]

how to determine that

yea

[winter trench]

R will hit one point and then the next and those will be the bound

[lethal sedge]

would i solve for 0

like the square root

[winter trench]

since it is a solid over the origin R hits 0 first and that would be the l9ower bound

[lethal sedge]

sorry how do I do that

im rlly sorry

i dont know how to do that

[winter trench]

Do you have an idea of what the shape looks like

[lethal sedge]

yes I do

I just dont know how to solve for it

I feel like I should keep x^2 and y^2 for solving for it

instead of subbing in r^2

-r^2*

[winter trench]

It wants it in terms or r and theta though and in this case subbing in r is much easier

[lethal sedge]

oh ok

so I have sqrt(-r^2+49/256)

from there what do I do

do I set that to 0

[winter trench]

I would square both sides

[lethal sedge]

the other side would be 0 right to begin with?

[winter trench]

give yourself z^2 = -r^2 + 49/256

[lethal sedge]

oh ok

and then what do I do

solving for r would contain z tho right

and how would I have z involved

wouldnt I set the square root = 0 instead of z

@winter trench

sorry for the ping

[winter trench]

If you set z=0 then you have the the outermost r can be

[lethal sedge]

okay

[winter trench]

and when we set up the intergral we will do it in the form ∫∫zdA

[lethal sedge]

so I just have z

[winter trench]

∫∫zdA = the area of the shape

[lethal sedge]

so I have the z^2 = -r^2+49/256

what should I do next

[winter trench]

Solve for r when z =0

[lethal sedge]

so -49/256 = -r^2

so r^2 = 49/256

r = 7/16

[winter trench]

Yes

[lethal sedge]

and -7/16

[winter trench]

nope

it would be 0

for the bounds wise

[lethal sedge]

oh so 0 and 7/16

[winter trench]

yes

[lethal sedge]

why would 0 be the lower bound again

[winter trench]

You start r from the origin

and the first time it touches the shape is the inner bound

[lethal sedge]

wouldnt that be 1

[winter trench]

Since this shape is solid over the origin it hits there

No since the shape is a solid over the origin

[lethal sedge]

oh ok

so it would

first integral from 0 to 2pi

[winter trench]

r hits first at 0 and then leaves at 7/16

[lethal sedge]

second integral from 0 to 7/16

and what are we integrating

so I know it would be drdthetha

[winter trench]

zrdrdθ

[lethal sedge]

what is zr

im confused sorry

could you like type the integral in mathway.com and show me

like a screenshot so I can see it

[winter trench]

ok so we are integrating over area and that is dA

dA = rdrdθ

[lethal sedge]

oh ok and this needs to be done too sorry

how do you do this part

[winter trench]

You can find the height by setting r=0

[lethal sedge]

when do I set r = 0

in the square root?

[winter trench]

in the original equation

that will be the height

[lethal sedge]

but r is not in the original

you mean in z = sqrt(-r^2 + 49/256)

and make it z= sqrt(0+49/256)?

is there any way you could show me what I should do like in mathway.com

or something so I can see it easier im so sorry

[winter trench]

yes

when it is z = sqrt(-r^2 + 49/256)

Height should be 7/16

[lethal sedge]

height = radius?

bc we solved for r and it was 7/16

so is the height = radius?

bc u said height should be 7/16

[winter trench]

Yes

[lethal sedge]

when did we subtract the upper surface from the lower surfave tho

[winter trench]

Yeah idk what it means by that tbh

[lethal sedge]

oh ok

[winter trench]

I just know the the height will be when r=0

As you can see by the shape

[lethal sedge]

u mean z =0

right

bc radius cant be 0

[winter trench]

you want to solve for height?

[lethal sedge]

yes

[winter trench]

then when r=0

[lethal sedge]

oh ok

[winter trench]

r=0 when the height is maximized in this shape

[lethal sedge]

when did we substitue polar coords

bc it says thats needed too

[winter trench]

We already did that

polar coords are r and theta

[lethal sedge]

okay

could you show me the finished integral setup

on mathway

and screenshot it so I could see it

sorry for the inconvenience

[lethal sedge]

oh ok

got it

let me solve it and check one second

WOW

you were right

omg

I checked by putting in r = 7/16

here

these two were equal

you are a genius!!!!

thank you!!

[winter trench]

np

[lethal sedge]

the height and radius are both 7/16 right @winter trench

[winter trench]

Yep

[lethal sedge]

okay got it

thanks

sorry last thing

i promise

it is 0 to 2pi bc thats the full circle right

or like whats the explaination

[winter trench]

Exactly

[solid kiln]

is this a linear equation?

[dire geode]

this channel's occupied. read #❓how-to-get-help

[solid kiln]

oh sorry, stuff has changed since I was last here

[cedar kiln]

@lethal sedge Has your question been resolved?

[lethal sedge]

.close

[cedar kiln]

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[gray blade]

verify:
1 / (1+cosx) = csc^2 - cscx * cotx

[gray blade]

I don't know where to go from here

or if this is the right way even

[zenith shadow]

You're almost there, use $\sin^2=1-\cos^2$

[wraith dagger]

Maldor

[gray blade]

okay so that makes it (1 - cos) / (1 - cos^2)?

[zenith shadow]

Yeah now the bottom is a difference of squares

[gray blade]

ohhh

that makes sense thank you!

.close

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[gray blade]

verify: (cos / sec-1) - (cos / tan^2) = cot^2

[gray blade]

not sure how to begin

[cunning loom]

Do you mean sec$(x)^{-1}$ or sec(x)-1?

[wraith dagger]

Kimbomanjaro

[gray blade]

$sec(x)-1$

[wraith dagger]

kihei

[gray blade]

sorry i like to remove the variables to make it easier

[loud anchor]

we hav

,, \csc^2(x) - 1 = \cot^2(x)

[wraith dagger]

vin100

[loud anchor]

expressed in terms of sine and cosine

,, \frac{1}{\sin^2(x)} - 1 = \frac{\cos^2(x)}{\sin^2(x)}

[wraith dagger]

vin100

[cedar kiln]

@gray blade Has your question been resolved?

[cedar kiln]

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[crimson sedge]

how could i find the diagonal lengths?

using trig

[cunning loom]

A rhombus is regular, so all the other sides will have length 5.4. Then use trig on the triangle whose angle you have.

[cosmic steppe]

Triangel

[crimson sedge]

wait my bad

forgot diagonals were perpendicular

oh my god

thank you so much

.cloose

.close

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[hollow hamlet]

is h(4) 0 and h'(4) -1?

im on part b

and I will share my work so far

so someone can check it

[cunning loom]

h'(4) is -1 yeah, although I think h(4)=-2.

[hollow hamlet]

hmmm interesting why?

[cunning loom]

You have a graph of h(x)

Go along to 4 and down to -2

[hollow hamlet]

it would make more sense in the equation but not sure how to get it

wow totally missed that

reading the y wow

thanks

[crystal raptor]

I have final answer when youre done btw Thegend

[hollow hamlet]

okay I will share mine as well almost done

im getting 1.75

[crystal raptor]

agreed

[hollow hamlet]

thanks a ton

[crystal raptor]

no worries, well done

[cedar kiln]

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[lucid palm]

What's going on in dy?

[lucid palm]

I understand that it's integrating with respect to t so y(t) makes sense but

I just can't grasp exactly how change of variable happened there

like algebraically

[upper abyss]

I agree something there isn't making sense

Anything happen before this point? What's the original question?

Or are you asking why
∫ dy/y = ln(y) + C?

[lucid palm]

ah sorry forgot to include original question

this is the question invovled

since we can't really get elementary form for \int e^-x^2 dx we do need some dummy variable trick I think

but that notation doesn't make sense to me

on y side

[dire geode]

Just leave your answer as an integral

[lucid palm]

i mean I'm fine with leaving as integral

[lucid palm]

this part is what I'm not confident in

$\int^x_4 \frac{dy}{y}$ transforming to $[ln(y(t))]^x_4$

[dire geode]

Use separation of variables

[wraith dagger]

sunho

[lucid palm]

I think the solution meant $\int^{t=x}_{t=4} \frac{dy}{y}$

[wraith dagger]

sunho

[lucid palm]

but still I'm not sure how change of variable happen to make it ln(y(t))

[dire geode]

It's just dummy variables. Do the integral

[lucid palm]

\int dy/y is ofc trivial

i guess I'm not getting how dummy variable works

[dire geode]

You don't put limits until after evaluating the integral

[dire geode]

This is wrong

[cedar kiln]

@lucid palm Has your question been resolved?

[lucid palm]

but then if you do integral verbatin it's

ln(x) - ln(4)

which doesn't make sense

[upper abyss]

Oh that's true, what's even going on with those bounds?

I wouldn't use the bounds at all. Evaluate the +C using the initial condition instead

[lucid palm]

Evaluate the C using the initial condition?

How would you do with \int e^-x^2 dx

if it's without bounds

I tried without bounds first and stuck at that point

[dire geode]

Nope

[dire geode]

It's ln(y(x)) - ln(y(4)). You skipped a step

[lucid palm]

why tho

[dire geode]

That's what the evaluation means

[dire geode]

This is just wrong

[lucid palm]

I said that I know it's wrong

idk this is not being helpful at all

Imma just leave

.close

[cedar kiln]

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[versed portal]

hey how do i solve this?

[jovial ravine]

have you learned 30-60-90 triangles?

do you know the ratio of the sides

[versed portal]

no 😦 sorry

missed alot of school so this whole thing is new to me

[jovial ravine]

oop

oh i see

[versed portal]

insane how you miss 4 days of school and you are so behind

[jovial ravine]

yep it goes fast

[versed portal]

so where do i start to solve this problem?

[jovial ravine]

first you need to know the ratio of the sides

wait frick i made a mistake

its a 60 not 90 oops

so in a 30-60-90 triangle the side lengths are like this

the shortest side is 1

the longer leg is r3

and the hypot is 2

[versed portal]

ohh i see

wait thats not hard?

i just have to sub in 12 for r3

[versed portal]

and solve rest?

[jovial ravine]

oh wait

[versed portal]

or 2 i meant

[jovial ravine]

mhm

[versed portal]

OHHH

[jovial ravine]

sub it for 2 yeah

and use the ratio of the sides

👍

[versed portal]

thank you!

[jovial ravine]

npnp

[versed portal]

really appreciate it

[jovial ravine]

find the answer and ill check it

[versed portal]

ok

[jovial ravine]

oh

ok so

the thing is

i didnt read the problem correctly

!

but you can also do that

but you can also just do the tangent of 30

[versed portal]

?

[jovial ravine]

theres nothing wrong with doing this thing but its a bit more complicated

[versed portal]

oh ok

what is tangent of 30?

[jovial ravine]

did you find the side lengths of this triangle?

[versed portal]

also i got 6,12 and 6r3

[jovial ravine]

yeah that looks right

so you know what tan is right

[versed portal]

nope

[jovial ravine]

oop

yeah u have a bit to catch up on

[versed portal]

i think i learned in online school but ngl i forgot

yea

ik abt this

[jovial ravine]

okok

so to take the tangent of the 30 degree angle

you do opposite/adjacent

and you know the values for both of them

[versed portal]

6r3/6

[jovial ravine]

and simplify that and u got your answer

[versed portal]

oh so its just r3

[versed portal]

how would i input it in to this tho?

[jovial ravine]

yep

[versed portal]

iim guessing leave the other spots blank?

[jovial ravine]

its 1r3/1

try that

[versed portal]

hmm i got 2/3

[jovial ravine]

woihefaiw give me a second

i have no idea why thats wrong....

WAOIEFHAI

IM

SO DUMB OOPS

[jovial ravine]

i put 30 where its supposed to be 60

i reveresed them cuz im dumb dumb

[versed portal]

so what changes

oh so the opposite and adjacent are swapped?

it would still be a 1-3-1 though

[jovial ravine]

so then itll be 1/r3

and that can be rationalized

[quiet tulip]

can someone help me calculate AD^C

[jovial ravine]

go to a #help place

and someone will help u ther e

[quiet tulip]

ok thanks

[versed portal]

ahh

so it becomes r3/3

thank you! so much

realyl helps

especialyl cause im so bhind hlol

[jovial ravine]

👍 👍 👍 np

try asking your teacher for extra help if you need

and hopefully theyll give it

[cedar kiln]

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[cedar kiln]

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[signal moat]

Is it okay to write the roots of a quadratic function using cases like this?

[dense hornet]

i would prefer if the third equal sign is replaced with a =>

or <=> would fit the context better

[cedar kiln]

@signal moat Has your question been resolved?

[signal moat]

But is it incorrect to write it like this?

[dense hornet]

write it like the picture?

[modern compass]

that's fine

[loud anchor]

$\implies$ and $\iff$ mean "implies" and "if and only if" respectively. both fit well into the context.

[wraith dagger]

vin100

[modern compass]

my only issue is the notation $\lambda_{1,2}$ I'd rather see something like "With $i=1,2$ let $\lambda_i =\ldots$" because I regularly see things like $\beta_{i,j}$ as a double index notation, hwere here you mean it as two different indexes.

[wraith dagger]

Zybikron

[cedar kiln]

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[upper garnet]

F(x,y,z)=(x,y,0) and E the part of the sphere surface x²+y²+z²=1 inside z=sqrt(x²+y²)
surface integrals over vector fields
for parameterization i have (sinthetasinphi,sinthetacosphi,cosphi)
so for dsigma i become (-sinphicosthetacosphi,costhetasin²phi,-costhetasintheta)
now if i do F*dsigma
integrandum becomes zero
what did i do wrong

[cedar kiln]

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[upper garnet]

<@&286206848099549185>

[cedar kiln]

@upper garnet Has your question been resolved?

[cedar kiln]

@upper garnet Has your question been resolved?

[cedar kiln]

@upper garnet Has your question been resolved?

[upper garnet]

.close

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[south remnant]

.reopen

#help-12

there was some personal information in the previous image

[warm vector]

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side. This is why you must flip the sign whenever you multiply by a negative number.

[south remnant]

oh ok thanks

[cedar kiln]

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[vernal pike]

$19_{ten}=number_{two}$, what's number?

[wraith dagger]

AuHasard

[vernal pike]

converting from base 10 to base 2

1*10^1 + 9*10^0 = 10+9 = 19

[cedar kiln]

@vernal pike Has your question been resolved?

[cedar kiln]

@vernal pike Has your question been resolved?

[glacial pollen]

to convert from base 10 to base 2, you keep dividing by 2 on each step @vernal pike

if it divides evenly, you have 0, if it doesnt divide evenly, you have a 1

[vernal pike]

Can you show me please?

I am new to this.

[glacial pollen]

okay so watch this process

does 2 divide 19?

2 | 19 = 1
2 | 9 = 1
2 | 4 = 0
2 | 2 = 0
2 | 1

the base 2 would be the reverse of it, aka 19 = 10011 in base 2

[vernal pike]

I don’t understand this. What did you do there?

[glacial pollen]

division

so each step im dividing by 2

if it is divisible by 2, then the remainder is 0

if it is not divisible by 2, then the remainder is 1

[vernal pike]

@glacial pollen Yeah so eg 19/2 is 9 and the remainder is1, then 9/2 is 4 remainder 1, then 4/2 is 2 remainder 0, etc. I get it now.

How did you get the numbers 19, 9, 4, 2, 1?

[glacial pollen]

so 19/2 is not divisible by 18/2 is divisible and 18/2 = 9

and so on

[vernal pike]

@glacial pollen Yeah but that was on my question, how did you get the numbers 19, nine, four, two, etc.?

Why do we divide those numbers by two?

[glacial pollen]

there are only two numbers available to us in base 2 right

so we need to represent 19 using powers of 2

19 = 2^0 + 2^1 + 2^4

or we can write it also as

19 = (1)2^0 + (1)2^1 + (0)2^2 + (0)2^3 + (1)2^4

in order to find the numbers in brackets we divide by 2, thats the simplest explanation i can think of righ now

[vernal pike]

ok thanks i will think about this

.close

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[reef hemlock]

T : P3 → P3 ved T (p) = p(0) + p(2)t − p(0)t^2 − p(2)t^3.
find (p) for p(t) = 1 − t^2. is p an eigenvector for T ? and if so
what is the eigenvalue
T(p)= 1 +(-3)t - t^2 - (-3)t^3 = 1 - 3t - t^2 + 3^3

T(p)=λ(1 - t^2) = 1 - 3t - t^2 - 3t^3

=λ(1 - t^2)=(1 - t^2)(1 - 3t)

=λ=(1-3t) no p is not an eigenvector for T

and
repeat last task for p(t) = t - t^3
T(p) = 0 + (-6)t - (0)t^2 - (-6)t^3 = -6t + 6t^3 = -6(t-t^3)

t(p)=-6(t - t^3) = λ*p(t)

=-6(t - t^3) = λ(t - t^3)

= -6 = λ
is this correct?

[cedar kiln]

@reef hemlock Has your question been resolved?

[reef hemlock]

<@&286206848099549185>

[cedar kiln]

@reef hemlock Has your question been resolved?

[reef hemlock]

.close

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[smoky tangle]

is there a way to calculate min. val. of f(x) in a non brute force like way?

[smoky tangle]

an example for N( 24 because 864000000 is 24 hours in milliseconds)

and its derivatives

[cedar kiln]

@smoky tangle Has your question been resolved?

[smoky tangle]

i would be thankful if someone could at least identify what field of mathematics it is

<@&286206848099549185>

[cedar kiln]

@smoky tangle Has your question been resolved?

[smoky tangle]

<@&286206848099549185>

[smoky tangle]

<@&286206848099549185>

[smoky tangle]

<@&286206848099549185>

[dire geode]

Yea stop pinging every 15 minutes

[smoky tangle]

<@&286206848099549185>

[smoky tangle]

.close

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[woeful hill]

I had a quick question for completing the sqaure

[woeful hill]

in this problem why did my professor not simplify it to -x(x-5)

[livid hound]

because that wouldn't be completing the square

[woeful hill]

can you elaborate a little more

[livid hound]

completing the square is a process that can be used to convert a quadratic expression to vertex form which allows you to identify min/max

[woeful hill]

nvm

i think i got it

thank you

one last question

I'm trying to understand what my professor did here

his plugging in method doesn't make sense

ahhhh

I think I see

the p is what we're looking for, which is why he plugged the formula to p and ignored s?

[cedar kiln]

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[elder parrot]

It says: Show that the following vector is covariant. So that it transforms like shown below.

[elder parrot]

Any ideas on how to show that

I really do not see how

[cedar kiln]

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[loud anchor]

the second term of the velocity is wrong

[harsh jasper]

qwq

i dont understand how is velocity 15 but t=0?

did i integratewrong?

oh

[loud anchor]

you can check with ,w

[harsh jasper]

its 20t

[loud anchor]

the degree of t is missing

[harsh jasper]

?

OH

OMG

+c

.close

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[real bone]

I am not sure where to start for this one

Since ln would not bring down any exponents here

[dire geode]

,w derivative 6^x

[wraith dagger]

Results provided by WolframAlpha

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

Requested by riemann#2529

[dire geode]

i think you have your derivatives remembered wrong

[mighty drift]

Just use l'Hospital's rule

[real bone]

Yea

Ok

I'll just do the derivative then

[mighty drift]

It literally asks you to

[real bone]

Can I use ln rules to make it all on one line?

Like 6^xlnx-8^xlnx-lnx?

[upper garnet]

there is a common factor

[crystal raptor]

You have not differentiated the top and bottom?

[real bone]

Ohhh

Yep

[upper garnet]

bottom is x not 1/x

[crystal raptor]

Also there won't be any lnx floating about

[real bone]

Why not?

[upper garnet]

.

[real bone]

Oh

It's lna not lnx

My bad

[upper garnet]

what's ln(a)

[real bone]

The formula is f=a^x f'= a^x lna

[upper garnet]

yeah so a is either 6 or 8 here

[real bone]

Yes

I am tempted to multiply by x/x

[mighty drift]

It's not 1/x

The denominator is x so its derivative is 1

[real bone]

But the derivative of lnx is 1/x

Does ln not apply to the denominator?

[crystal raptor]

Do you see lnx anywhere in the original question

[upper garnet]

^

[real bone]

No but we applied ln to both sides

[upper garnet]

huh

[crystal raptor]

Why did you do that?

[real bone]

Oh wait

No we didn't

[upper garnet]

ln(3!4) is a constant

[real bone]

Sorry it came from the derivative

How do I get rid of the 6^x and the 8^x?

[upper garnet]

plug in zero

[real bone]

Oh lol

Ok ty

[mighty drift]

Fun fact. l'Hospital's is not required for this

[real bone]

Really?

[mighty drift]

If you factor 8^x out of the numerator and rearrange a bit, you can recognize a derivative

[real bone]

How do you factor out an 8^x from a 6^x?

Unless you mean 6^x-1(8^x)

[mighty drift]

6^x / 8^x = (3/4)^x

[real bone]

So you dive everything by 8^x/8^x?

[mighty drift]

Factor out

[real bone]

I don't get the division

[mighty drift]

Using the fact that 6^x = (3/4)^x * 8^x

[upper garnet]

8^x*(-1+6^(x)/8^(x))

[real bone]

Ohhh

Ok so what's the trick from here?

[mighty drift]

To recognize that it looks like a derivative

[real bone]

Like

(F(a+h)-f(a))/h?

[mighty drift]

Yes

[real bone]

So you would recognize that 3/4 is basically a

But how would you get the ln part?

[mighty drift]

What ln ? There's no ln in this method

Also a=0

[real bone]

Well the answer is ln(3/4)

[mighty drift]

Yes

[upper garnet]

it's multiplied by a constant

[mighty drift]

Because the derivative of (3/4)^x has ln(3/4) in it

[upper garnet]

wait

isn't it (6^x-8^x)/x * ln(3/4)

[dire geode]

you guys really got tricked into doing extra work

[mighty drift]

I'm actually surprisingly good at that

[real bone]

Ok ty guys

.close

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[astral trellis]

Hey, I want a gif visualization in which a gaussian distribution smoothly transitions into a uniform distribution. Where should I get one?

[foggy merlin]

google... ?

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[fair hare]

@rough falcon

[fair hare]

I found the solution to your problem from earlier

simplifed to

[wraith dagger]

Chunkin

[fair hare]

and finally without gross absolute value signs 🤮

[wraith dagger]

Chunkin

[cedar kiln]

@fair hare Has your question been resolved?

[cedar kiln]

@fair hare Has your question been resolved?

[cedar kiln]

@fair hare Has your question been resolved?

[cedar kiln]

@fair hare Has your question been resolved?

[fair hare]

hell no bot imma be here for years

[rough falcon]

Oh, that wasn't my problem, it was just an example I gave for piecewise defined functions, sorry 😅

[fair hare]

😳

well I solved it

[rough falcon]

That does look kinda cool tho
I'll look at it a bit and try to figure out what you did, it'll certainly be helpful!

[cedar kiln]

@fair hare Has your question been resolved?

[cedar kiln]

@fair hare Has your question been resolved?

[solid quarry]

any 2 real functions can be mixed together

its not that interesting

[fair hare]

🎉

1 day anniversary of #help-13

[tropic oxide]

do you... actually have a question to ask here or do you just want to hog this channel for no reason

[dire geode]

.close

[cedar kiln]

Channel closed

Closed by @dire geode

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tulip summit]

Does it make sense for the B part something like sin(theta)= 2b/a ??

[cedar kiln]

@tulip summit Has your question been resolved?

[cedar kiln]

@tulip summit Has your question been resolved?

[tulip summit]

<@&286206848099549185>

[cedar kiln]

@tulip summit Has your question been resolved?

[tulip summit]

.closed

[fervent mason]

Please use .close instead @tulip summit

[tulip summit]

.close

[fervent mason]

Don't use ` for .close

[tulip summit]

.close

[cedar kiln]

Channel closed

Closed by @tulip summit

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[still granite]

How do I find the pronumeral of the letters

[still granite]

I know that c=17

I just need to find d and e

[opal matrix]

Note that ACB is a right triangle since AB is a diameter

[still granite]

Ok

[opal matrix]

So d=73

And since ABCD is cyclic, d+e=180

So you can solve for e

[opal matrix]

This is since c+d=90

[still granite]

Got it

[still granite]

Why does it equal to 90

❓

I've found the answer to each pronumeral

btw

[still granite]

But it's just this part ^^^

Anyways I will just close this question help chat because it seems like your idle

.close

[cedar kiln]

Channel closed

Closed by @still granite

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[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[opal matrix]

Because you have triangle ABC with angles 90, c and d, and they add up to 180. Sorry for not replying but i was in class lol

[opal matrix]

.close

[cedar kiln]

Channel closed

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[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[viral kayak]

Anyone tryn help me with my quiz thing

[viral kayak]

💀

[lament sonnet]

You are not allowed to ask for help on quizzes. The server does not support cheating and academic dishonesty

[viral kayak]

Oh ok

.close

[cedar kiln]

Channel closed

Closed by @viral kayak

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[silk stream]

How is question c when simplified equal to 2?

[silk stream]

I get 7^n / 4 cause you cancel out the 7^n-1

[vestal bear]

because you're able to combine the numerator

7^2n+1

[zinc harbor]

8*(7^n-1)/(4*7^n-1)=2

[vestal bear]

Loh wait

Its addition

Split the fraction

[silk stream]

???

[zinc harbor]

What do u mean ???

[grand raft]

You need to do:
7^n-1(1+7)

This will be the top

Because you take out the 7^n-1

[zinc harbor]

This is the sol

[vestal bear]

splitting the fraction is a better way to get the answer

Less complex

[silk stream]

How do you get 8?

For the numerator

[zinc harbor]

7^n-1 + 7* 7^n-1

=(1+7)7^n-1

?

[silk stream]

It’s 2?

[zinc harbor]

^

[vestal bear]

nb

mb

Nvm

[silk stream]

How do you do this?

How did you get there?

[zinc harbor]

This is the numerator

[silk stream]

But it’s 7^n + 7^n-1

[zinc harbor]

factor a 7 from the left term

do you know what 7^n means?

[silk stream]

7 to the power of n

[zinc harbor]

What does that mean,

[gray condor]

$5^t$ x $5^{2t}$x $5^{-2}= 5^{-2}$

right?

[wraith dagger]

Rylo

[zinc harbor]

(c)

Chap

[silk stream]

Haven’t done that yet

[gray condor]

ahh

[silk stream]

Not sure

[zinc harbor]

okay that’s where your problem is

When learning maths you need to understand what the symbols mean

7^n=7*7*…7, multiplied n times

[silk stream]

Mhm

[zinc harbor]

so can u see why 7* (7^n-1)=7^n now?

[gray condor]

$8(7^{n-1})/4(7^{n-1})$

[silk stream]

No?

[zinc harbor]

Tell me what the left hand side means

and tell me what the right hand side means

[wraith dagger]

Rylo

[gray condor]

wdym no

it’s 2

[zinc harbor]

Rylo can you stop I posted that above

[silk stream]

7 multiplied by 7^n-1 is equal to 7^n

[gray condor]

ok,

[zinc harbor]

do you know why?

[silk stream]

No clue

[zinc harbor]

i mean what does “7*7^n-1” mean

[silk stream]

7 multiplied by 7^n-1?

[zinc harbor]

go on, what does 7^n-1 mean

[silk stream]

This but take 1 every time?

[zinc harbor]

Wdym

[silk stream]

The 7^n is 7*7 … 7

[zinc harbor]

7^n-1 = 7 multiplied by itself …

[zinc harbor]

Finish this

[silk stream]

7^n-1 = 49?

[zinc harbor]

I’m not sure where this is coming from

7^n-1 = 7 multiplied by itself n-1 times

[silk stream]

7 multiplied by itself is 49???

[zinc harbor]

yeah only when h multiply it by itself once

Not n-1 times

[silk stream]

Oh

I kinda got it

Thanks

[zinc harbor]

Np

[silk stream]

.close

[cedar kiln]

Channel closed

Closed by @silk stream

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallen vine]

When calculating a definite integral, why do we take the steps that we do

[lament sonnet]

Google Fundamental theorem of calculus

[fallen vine]

Ok thanks :))

[cedar kiln]

@fallen vine Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lunar mica]

Hi, how can I solve this recurrence ?

[upper abyss]

Any method you're expected to use? There's a few

[lunar mica]

nope

master theorem clearly doesn't work. I tried the substitution method but I'm stuck after doing the substitution.

[dire geode]

plug in small n, say n=2,3,4 and find a pattern