help-36

[lyric summit]

such a projeciton on yz plane

so phi walks form - 90 degrees till moment

when red lcurve meets blue one

if y^2 + z^2 = a^2, and z = b < a, then

y^2 = a^2 - b^2

and if y >0

then y = sqr ( a^2 - b^2)

so cos phi = sqr ( a^2 - b^2) / a^2

so phi = arc cosine etc

[sour torrent]

Okay I won’t say I totally understand but this was really helpful

[lyric summit]

yes forgive mei cant nicely describe you in english

but calulus is not hard here

[sour torrent]

Np it was understandable ^^

I’ll close for now and do similar practice problems

[lyric summit]

ok

[sour torrent]

Thank you so much ❤️

[lyric summit]

yw )

[sour torrent]

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[steep ridge]

Given a system of 3 linear equations (Ax +By +Cz +D=O, A1.., A2.., A3..) in 3D-space, what are the solutionspaces and the conditions for the coefficients?

I did this for two planes first, then did this one but was told to find a systematic method for it and use pivots, and idk how that works here

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[rose ravine]

can anyone confirm if my logic for these is any good?

a)If x is an element of m|x and n|x then it mujst be true that x=mk for some k in Z and x=nj for some j in Z. Suppose x is 12. In this case, it would be possible for m to be 4, to be 3, n to be 6, and j to be 2. This would then mean that the intersection of the sets must be a subset of mn|x. However, mn in this case is 24 while x=12. 24 does not divide 12 so the intersection of the sets is false.

b) If x is an integer such that mn|x is true, ti must also be true that x=mnk for some k in Z.

x=mnk is the same as x=m(nk) while m is a valid integer. Thus m|x is true.

Similarly, x=n(mk) while n is a valid integer meaning n|x is also true.

Thus, x is an element of both m|x and n|x, making x an intersection of the sets. mn|x is then a subset of that intersection and the statement holds true.

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[austere snow]

where did the cosx go?

[royal gust]

2sin(x)cos(x) = sin(2x)

Keep your trig identities nearby, if you aren't strong with them

[austere snow]

ah ok

so wait wb this

where did the 2 go?

and how did pie become 3 squared over 2?

[royal gust]

sin(2π/3) and sin(π/3) happen to be the same thing, I don't necessarily see why they swapped one into the other though.

sin(2π/3) = √3/2

[austere snow]

so its just unnecessary

[royal gust]

Could have just went directly from sin(2π/3) into √3/2

Hopefully you know your special angles off by heart, and none of this is surprising

[austere snow]

isn't that the unit circle? (I think that is what they call it)

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[torpid dagger]

so x = i?

i know it is but does that qualify as a solution?

or can you really answer a question like x = ? with an imaginary number

[celest crane]

Yes, as long as there is no constraint on the solution such as "give all Real solutions."

[torpid dagger]

thanks :))

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[austere snow]

is this so far correct?

[austere snow]

ok now I fixed that, how do i progress forward with this to find the extreme values

[cedar flame]

find x

[austere snow]

Ok I will be fixing that and pay much more attention next time, but after that what do I do?

[cedar flame]

If $a\cdot b = 0$ , either $a=0$ or $b = 0$

[soft zealot]

vedu

[austere snow]

oh yeh isn't the bottom just v^2?

[austere snow]

what does that have to do with my question

[cedar flame]

you use that to find the values of x

[cedar flame]

i think ur confusing chain rule with quotient rule

[austere snow]

ah, just like how I did the last part right?

[austere snow]

prob tbh

[cedar flame]

r u asking if u did the derivative correctly?

[austere snow]

really helpful, thank you so much man.

I will try to do mine all over again and send another SS

is this better

so like tihs?

yes I do understand all the steps

ok so now i try to find the X

2x^3=0
x=0

1-x^4=0
x=1

so its 1?

[soft zealot]

nox💫

[austere snow]

my book says 1 tho

ah ok

now for the second problem

B)

do i use the chain rule as well?

can I use geogebra

is this correct up to now?

outside

ok man thank you so much for the help, I will look over at your example rn

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[flint perch]

and the answer

[void valley]

W czym problem?

[flint perch]

the bounds I have are 0- 2pi for theta, 0-4 for radius and 2r-8 for z

not sure if bounds are correct

[void valley]

theta - ok
radius - ok
how did you get 2r-8 for z?

outer ones should be constant

[flint perch]

z=8

and z=0, but if I do z=0 that would mean a cylinder instead

2r because z=2sqrt(x^2+y^2)

[void valley]

So try to change the order of integration or (that's what I would recommend) transform it to double integral

[flint perch]

but it says triple in the question?

ok ill change order

wait but how for order

you always want dzdrdtheta

[void valley]

Notice that

You can project that circle and get the region (let's say it's D) described as:

[flint perch]

yes

wait

no isnt it x^2+y^2<=16?

[void valley]

ye, mb

[soft zealot]

Modus

[void valley]

Now, the integral becomes

[soft zealot]

Modus

[void valley]

And now you can apply what you already did, I mean poolar coordinates

[flint perch]

oh

wait I'll send a picture,

why would this be wrong?

its also 8-2r

for bounds, where you just put in the equation instead

[void valley]

no problem, it's fine

anyway it works that way as well, I mean you got (8-2r)r^3 what seems correct

[flint perch]

you said it was wrong tho?

[void valley]

Ouch, I misunderstood I guess, I treated it as one thing instead of 2r and 8, maybe that's the thing

[flint perch]

okok

thank you!

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[tranquil pine]

Find the range of y= (1-sinx)/(1+sinx).

All in all I’m getting -1 <= (1-y)/(y+1) <= 1

[tranquil pine]

How do I proceed

[cloud zephyr]

hint: || can y be negative ||

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[tranquil pine]

im using the error bounds theorem in terms of midpoint rule

tryna find n

i got n = 816947

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[patent creek]

A distributor promoted a product based on each data and experience before. For a supply of x thousand items, cost per item is settled as $p = p(x)$ thousand rupiahs, which expressed as $p(x) = \sqrt{x^2-6x+18} , 1 \leq x \leq 8$. The distributor also set the amount of supply every week. In t week, the market received the supply of $x = x(t)$ thousand items which expressed as $x(t) = 1 + \sqrt{t} , 0 \leq t \leq 49$

This product would reach the cheapest price on t-th week with t = ...
(A) 1
(B) 3
(C) 4
(D) 6
(E) 8

[soft zealot]

sho

[patent creek]

<@&286206848099549185>

[craggy plank]

[craggy plank]

Is the answer C?

or you don’t have the answer

[patent creek]

i don't

[craggy plank]

okay

!status

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

[patent creek]

1

[craggy plank]

Do you know how to find the vertex of a quadratic function?

[idle blaze]

i also got c 🙂

[craggy plank]

yeah, that give me confidence. Appreciate it

[patent creek]

by deriving the function

?

[craggy plank]

Can you tell me in what condition, you’ll pay the least money per item?

[patent creek]

oh, 1?

x = 1

[craggy plank]

?

Find the vertex

It’s incorrect

[patent creek]

p'(x) = 0?

[craggy plank]

Here

Ignore the root

[patent creek]

which vertex? y or x axis?

[craggy plank]

The quadratic function

[patent creek]

i only know this and discriminant😭

if y then -D/4a

if x then -b/2a

[craggy plank]

do you know -b/2a?

The way you find the vertex of a quadratic function

[patent creek]

3?

[craggy plank]

yes

[patent creek]

then i input 3 to the function?

[craggy plank]

yeah

It says the cheapest

So just plug 3 into the second function

And find t

[patent creek]

x(3)?

[craggy plank]

x=x(t)=3

What you want to find is t

[patent creek]

OHHH

YEAHH

i got it

[craggy plank]

Congrats

[patent creek]

thank youu

[craggy plank]

type
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To close the channel

[craggy plank]

Npnp

[patent creek]

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[reef patio]

how do I solve this

[warm ether]

is your question about the one point you dont have

[reef patio]

yes

and how to find the y cordinate

[warm ether]

its because you cancelled the (2x+3)

[warm ether]

sub your x's into either equation

(2x+3)=0 is a solution

[reef patio]

but didn't I cancel it out?

[warm ether]

you did, in your second line

you divided by 2x+3, neglecting that 2x+3 could be 0

[reef patio]

oh ok

got it

by either equation you mean

[warm ether]

wdym

[reef patio]

(2x+3)(2x-3)(x+2)=0?

[warm ether]

im not sure what youre asking

[reef patio]

this

[warm ether]

into either of the original equations given

[reef patio]

ok

[warm ether]

if you get the same y for each one with an x, then you know that x is right

[reef patio]

Thank you!

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[teal robin]

I was wondering how to determine based on contour lines which has a greatest change in altitude and how does that differ from steepness?

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[barren depot]

hi can someone tell me how im wrong on the thrid one

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[hallow vale]

<@&286206848099549185>

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[hallow vale]

<@&286206848099549185>

[static stump]

Yeah. Seems about correct.

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[storm void]

isnt it just 0.0006

[gritty solar]

you need to find the probability that it was found on the condition that it was stolen

the automobile is stolen, thats a given

[storm void]

P(b/a) thingy so

[gritty solar]

there's no probability in it being stolen

[storm void]

p(a) is stolen

[gritty solar]

Yeah

[storm void]

how do i get the intersection?

[shrewd storm]

It’s the first value

[storm void]

thanks

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[livid meteor]

I dont understand what Im doing wrong haha. I tried using "C" instead of "c" yet webassign doesn't understand what Im doing

[wind badger]

Have you tried inputting c as a vector like i, j, k

[livid meteor]

Let me see about that

Huh that seems to work. May I ask why c would be a vector in this case?

[wind badger]

because it's a vector valued integral

when you integrate each entry of the vector (here expressed as xi + yj + zk) you have a different constant of integration for each one, so you group them into the vector c

[static stump]

You can't randomly introduce a scalar to a vector integration. However, you can add a scalar in each component of the vector.

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[turbid flume]

Can someone help with 10 f) please

[turbid flume]

i know the x value

i just dont know how to find the y value

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[tardy vortex]

y=ax+c so plug in ur value of x into that

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[uncut gorge]

Im supposed to solve this question using first principals and i have no idea what to do now

[marsh temple]

generally the next step at such a crossroad is to multiply by the conjugate

[uncut gorge]

like this?

[marsh temple]

not quite

first combine this into one fraction

then if you multiply by the conjugate of the numerator, things will cancel nicely

[uncut gorge]

ohhhh

[uncut gorge]

now what do i do lol

[marsh temple]

that's not the conjugate

so you first do that step correctly

[uncut gorge]

oops, i forgot to write +

[marsh temple]

indeed

you also didn't correctly combine everything as you lost the h in the denominator

[uncut gorge]

where

[marsh temple]

between these two steps, what happened to the /h bit?

[uncut gorge]

oh

i didnt forgot

maybe i did

ok maybe i did

@marsh temple anything else i have to do?

[marsh temple]

you can simplify a little more

[uncut gorge]

i honestly dont know how

[marsh temple]

you don't know what $\left(\sqrt{x+1}\right)^2$ is?

[soft zealot]

Steakanator

[uncut gorge]

would that be x+1?

or would it be ^3/2

[marsh temple]

this is a question you should be able to answer on your own

[uncut gorge]

i should, but i'm kinda uh

lets say

special

[marsh temple]

well you'd better remedy this gap in your knowledge

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[uncut gorge]

its x+1 right?

[marsh temple]

!occupied

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[urban shoal]

any idea for b)

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[grim basin]

How does strong induction work without weak induction?

[grim basin]

If you already proved P(1), then tried to prove P(2) to an arbitrary P(n), how would you even do that without weak induction?

Oh nvm I misunderstood strong induction

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[winged tulip]

Let $(X_n)_{n \in \mathbb{N}}$ be sequence of random variables, where
$X_n \sim N(0, n)$.
How to prove this sequence DOES NOT follow weak law of large numbers?

[soft zealot]

redve

[silver maple]

So what is the weak law of large numbers

[winged tulip]

if $S_n = \sum_{k=1}^{n} X_k$, then $\frac{S_n}{n}$ converges to 0, but sum of probabilities of all those variables will be pain to compute

[soft zealot]

redve

[winged tulip]

I know theorems to proof something follows the WLLN, but it's implication. They doesn't work backwards

like Markov-Chebyshev theorem, if that's the english name of the theorem

but this limit implicates that sequence follows the law, but it doesn't have to mean sequence which doesn't has that limit does not follow the law

[silver maple]

This is what I found in Wikipedia

[winged tulip]

but that law assumes, that all X_n has the same distribution, doesn't it?

while in my example they all have different variance

[silver maple]

We need the random variables to be iid but they are not in this case. But it does not say anything about convergence probability for non-iid

[silver maple]

yep that is correct

[winged tulip]

if it doesn't say anything about it, do I need it in this case?

[silver maple]

Yeah I guess you could state that

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[winged tulip]

@spring depot

<@&286206848099549185>

turns out I pinged user with name Helper lol

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[winged tulip]

seccs

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[undone whale]

hi

[undone whale]

How do I do part 2

I got fx equals this

[static stump]

Differentiate f(x), substitute the point to get the slope at that point, write the equation of line from that point.

[undone whale]

but if i differentitate fx i get a quadratic

how can a quadratic be a tangent

[static stump]

That quadratic is not the tangent. It's the bahviour of the derivative.

Substitute the point in that quadratic. You'll get the slope at that particular point.

[undone whale]

so f prime (0) is the gradient?

at point x = 0 and y -1/2

[static stump]

Yep

[undone whale]

then do i sub into y= mx plus c

[static stump]

Yep

[undone whale]

and thats eqn of tangent?

[static stump]

Acutually, (y-y0) = m(x-x0)

That's it.

[undone whale]

okay

thank u

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[formal comet]

Hi can someone explain

[sacred cargo]

me again

[formal comet]

Llalalalala

[sacred cargo]

this fortunately is very simple :)

where are you lost

[formal comet]

):

10/5

I don't really know much what to do since you can't root the 2

[sacred cargo]

Let's do it then :)

when you have a root, the exponent goes on the numerator, and the root goes into the denominator

[formal comet]

Hahahahaha thankss

[sacred cargo]

always

so that's how we get (5^\frac{10}{5})

[soft zealot]

dp

[sacred cargo]

then, what's (\frac{10}{5})?

[soft zealot]

dp

[tranquil pine]

You should think of 2^10 as a number x. Now take the 5th root so it's x^(1/5). Now exponents can be multiplied: (2^10)^(1/5) = 2^(10/5) = 2^2

[sacred cargo]

@formal comet

[formal comet]

Sorry hahahahahaha

[sacred cargo]

still there?

[formal comet]

Sorry i was overthinking it hahahahahha

[sacred cargo]

understood it?

[formal comet]

I get lost when you will say this

Hahahahaha

[sacred cargo]

ok

for all $x,y,z$, $\sqrt[z]{x^y} = x^{\frac{y}{z}}$

[soft zealot]

dp

[sacred cargo]

this is a rule that always works

and that's what your textbook did

in this case, x = 2, y = 10, z = 5

[formal comet]

What

[sacred cargo]

let's ignore that for now :)

[formal comet]

Waittt

I kinda divided 5 and 10

Then i get 2

[sacred cargo]

YES

that's it :)

[formal comet]

ohhhhhh

Why did i spend several minutes overthinking ):

Hahahhahahaha that was pretty clusmy of mee

Thanks againn

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[quiet garden]

Help

[quiet garden]

My third one is wrong

Idk why

[sacred cargo]

My guess is calculator mistake

[quiet garden]

So what is the correct answer

[quiet garden]

That’s what I did

[sacred cargo]

I'm gettin g-80.06

oooh

i see

You're calculating the position when t = 0.002

but that's not what the instructions say

it's 0.002s after 2s

so 2.002

[quiet garden]

Oh

I got -71.03 for .001 seconds

Is that right

[quiet garden]

I just tried it and got -71.06

[sacred cargo]

yeah that's correct

I put 40 and not 49

your solution is correct, I mean

[quiet garden]

Ok so what do I do for B

Is the answer 0?

Actually 22+22/2?

@sacred cargo

[sacred cargo]

no :)

let's think for a second together

do you see that the time is getting smaller and smaller

so we first had

[quiet garden]

Yes

[sacred cargo]

0.01 seconds

0.05

and when you were calculating

your numbers were getting closer to a number?

[quiet garden]

-71

[sacred cargo]

so -71,3; -71.15;-71.06

yes

that's your answer

it's getting closer to -71

[quiet garden]

How was I supposed to calculate it though

Like in the equation

[sacred cargo]

Have you learnt derivatives?

[quiet garden]

No

[sacred cargo]

then you aren't supposed to calculate it

just getting closer and closer

seeing it approaches something

and that's why they made you calculate multiple numbers

to see the pattern

[quiet garden]

Ok

Can u help with this too

I don’t understand what to do

@sacred cargo

Bruh

[sacred cargo]

oh so you do know about derivatives

or are just about to learn about them

What you have to do is just calculate what youre told

$$\frac{f(a+h)-f(a)}{h}$$

[soft zealot]

dp

[sacred cargo]

in this case a is 4 and h = 0.1

so

$$\frac{f(4+0.1)-f(4)}{0.1}$$

[soft zealot]

dp

[quiet garden]

So I put the whole f(x) equation outside

[quiet garden]

I know basic ones

[sacred cargo]

I mean the easiest way is to do f(4.1)

[quiet garden]

So the equation times 4.1?

[sacred cargo]

f(4)

[sacred cargo]

Substitute x for 4.1

[quiet garden]

48.71

[sacred cargo]

ok

$$\frac{48.71-f(4)}{0.1}$$

[soft zealot]

dp

[sacred cargo]

try to do the rest

[quiet garden]

Why is it shown as f(x) when it’s f(a)

[sacred cargo]

I do not understand the question

where it's shown as f(x)

[quiet garden]

The normal equation

F(x)=x^2+9x-5

[sacred cargo]

yeah

[quiet garden]

I got 17.1 for first one

[sacred cargo]

the only important thing is that it's the same letter

f(x) = x^2+9x-5; f(u) = u^2+9u-5

all mean the same thing

[sacred cargo]

correct :)

The rest is litearlly the same thing

[quiet garden]

I got -1.69 for the second one

I think it’s wrong

Nvm I forgot to divide it

I got 16.9 instead

[sacred cargo]

yess

[quiet garden]

Thanks

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[sleek mulch]

this is sorta a weird question but if π is defined as the ratio between a circle's circumference and diameter, why does it end up being irrational?

[tranquil pine]

oh

circumference of a circle with rational diameter is always irrational , i just know this thing but cant really explain it

until maybe i think on it

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[loud heron]

how to find aysmptotes for csc sec and tan

[loud heron]

question 5 for example

[formal trail]

it may be easier if you rewrite them as a fraction of sines and cosines

[loud heron]

like this ?

1/sinx

and 1/cosx

?

[formal trail]

yes

[loud heron]

csc would be 1/sinx ?

[formal trail]

yes

[loud heron]

okay but im a little confused on how that helps

[formal trail]

generally if you have a function that can be expressed as a fraction, a vertical asymptote happens wherever the denominator approaches 0 (as long as the numerator doesn't approach 0 at the same time)

[pseudo knot]

,rotate

[soft zealot]

Couldn't find an attached image in the last 10 messages.

Feb 25, 2024, 9:13 PM

[loud heron]

okay wait i get you so basically if i were to graph a sin graph the aysmptotes for csc would be where the sin graphs touches 0/x-axis?

or no?

[formal trail]

yes

[sleek mulch]

asymptotes for csc exist where sin = 0 because csc = 1/sin, so just solve for sin = 0

[loud heron]

yo bruh no way it was that easy thank you !🙏 🙏 😭

[sleek mulch]

in this case 2sin(2x)

[loud heron]

lemme try it out then resend it

[sleek mulch]

👍

[loud heron]

okay my sin graph a lil funky

but did i do that right?

also lowkey didn’t know if the phase shift is right

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@loud heron Has your question been resolved?

[sleek mulch]

looks right to me, there isn’t any phase shift

idk how many periods your teacher wants you to graph

usually mine would have me graph until 2pi but whatever

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[sonic quartz]

I need help integrating this I can’t get u sub to work or by parts to work

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[sonic quartz]

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[sonic crescent]

could anyone explain why this boolean expression is true:

y' + yz = (y' + y)(y' + z)

[sonic crescent]

it is not intuitive to me

but once i understand this step i will understand absorption law

[tough tiger]

What is y’ and y ?

It’s like y’ = opposite of y ?

[sonic crescent]

yeah it's the negation of y, so if y = 1, y' = 0

[tough tiger]

Okay

Develop the right part of the equation

So that we can we see wich elements are missing in the left part of the equation and why there are useless

(Or in Boolean, always equal to 0)

[sonic crescent]

the right side simplifies to

(1)(y' + z)
y' + z

[tough tiger]

That’s actually an even better result than the one we want to show

But let’s just do basic maths here and forget for one moment about Boolean

[tough tiger]

Well actually you Boolean expression is not true

Just take y= 0 and z=1

And you’ll see this is not right

[sonic crescent]

y = 0, z = 1
y' + yz = (y' + y)(y' + z)

0' + 0 * 1 = (0' + 0)(0' + 1)
1 + 0 = (1 + 0)(1 + 1)
1 = (1)(1)
1 = 1

[sonic crescent]

this is what i got

[tough tiger]

Oh my god I forgot we were in Boolean by bad

[sonic crescent]

haha it's ok

[tough tiger]

I was like 1=2

Okay so let’s say y’ + yz is true

[sturdy cypress]

you;re asking about one step

show the whole thing instead

[sonic crescent]

the whole thing?

[sturdy cypress]

you said i don;t understand this step

[sonic crescent]

ohh

[tough tiger]

The problem in this step is that it is a law in Boolean

So the all thing won’t really help

[sturdy cypress]

what

[tough tiger]

Well this equation is a law in Boolean

[sonic crescent]

y' + yz = (y' + y)(y' + z) (idk how we got this)
y' + yz = (1)(y' + z) (complement law)
y' + yz = y' + z

thus absorption law is proved based on other laws

[sturdy cypress]

are you sure that's how it starts?

[sonic crescent]

yeah, to be completely honest i was using chat gpt to try and understand the proof of absorption law, and this is how it demonstrated it.

this was the first step

[sturdy cypress]

well it doesn't make sense to me

[tough tiger]

You could see this step like that :
If y’ is true then okay everything fine because 1 absorb everything with +

[sturdy cypress]

yeah that's distributive law

like alexis said, they just didn't name it

[tough tiger]

Since y’ equal 1 or 0. Let’s suppose that y’ equal 0. In this case you have 0 + yz = (0 + y)(0+z) that simplifies to yz=yz and everything fine. So in both case the equation is right

I don’t find this law really intuitive

So maybe don’t try so hard to intuitively get it

The use of + and * is not the most logical thing when it comes to distributive law, because obviously in math + doesn’t distribute on * @sonic crescent

[sonic crescent]

rightt i think that is where the confusion is coming from

[tough tiger]

So just focused on learning this distribution law and forget about math when using + and *, for those step using distribution law

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[willow heron]

I’m very lost so idk what question to ask but I’ll try my best, what do the zeros have to do with anything in the problem?

[dense crescent]

i'm guessing it's because whatever a or b value you get, it's certain to be that length
say you have (12, a) and (b,5), it'd be more difficult to find as you'd have to account for the difference in positions

[willow heron]

So since the coordinates are more specific, it is easier to find side lengths right?

Is that what you’re saying or did I misinterpret it

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[craggy plank]

I would choose C

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[dense crescent]

i'm currently stuck on this. i already did a direct comparison but it doesnt work cause it'd be done wrong. i can't use cauchy's condensation test since we haven't been taught it, so i have to do it differently; i can only use the

nth term test
p series test
geometric series test
(limit) comparison test
integral test
telescoping series test
alternating series test
ratio/root test

[dense crescent]

https://cdn.discordapp.com/attachments/1166868215956250624/1211490822722289714/IMG_7544.jpg?ex=65ee63c0&is=65dbeec0&hm=f72dbb02ccd1f88c76b666262e45db223534c03e138677ef257e72aa763f0402&

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[dense crescent]

wouldn't you have to use the rule 1/n^p?

or is it just like

any similar

[lyric summit]

1. si integral est gives you divergence

it is clear right ?

integral test

[dense crescent]

yeah

[lyric summit]

makes 1 ) series divergent

ok

and now

you use it

in comparison test

in 2 )

[dense crescent]

ooh

i was just like confused on what series to use during direct comparison

what i am/ am not allowed to use

[lyric summit]

yes i understand

but this you can use

[dense crescent]

ooh

okay that makes more sense

i just needed that

thank you

[lyric summit]

yw

[dense crescent]

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[mild portal]

If X is a gaussian random vector, then are its coordinates X_1, …, X_n jointly gaussian and then we can write X ~ N(mu, sigma)? y/n

[mild portal]

building on this, what is an example of 2 univariate gaussian random variables X_1 and X_2 that isn’t jointly gaussian? the only example i can think of is the trivial one, if both have variance 0. then i think there isn’t a valid continuous pdf because the density of two points is 0

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[white raven]

Help with the Second 🙏🏽

[soft zealot]

smidgin

[signal vector]

Actually you only need the first limit, since the second limit is a consequence of the first

@white raven

[white raven]

Yea I know but I can’t figure out what identities use to solve it

[signal vector]

Use these

[soft zealot]

smidgin

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[white raven]

Ok lim tan 3x /x is 3

And sin 8x / x is 8

What about the cos😅

@signal vector

Ohh I understand

Cos 8x lim is 1 as x approaches 0?

The lim is 64/3

Tank you

The first what is not defined because if I factor out an it may be divide by 0?

[signal vector]

Think about the sequence a_k=0 for all k

[soft zealot]

smidgin

[white raven]

Yes it think it is. Do you mean constant 0 sequence?

[signal vector]

Yes I mean constant 0 sequence

[white raven]

So if I factor out an the limit isn’t defined?

[signal vector]

In this case, will $\frac{19a_n^2+17a_n}{6a_n^2+17a_n}$ be defined?

[soft zealot]

smidgin

[white raven]

No because an may be equal to 0

[signal vector]

Right

So you cannot say anything about the first limit

For some sequences like a_n=1/n, the limit is defined and equal to 1, but in other cases like a_n=0, it is undefined

[white raven]

Tank you🙏🏽🙂

The second is right?

[signal vector]

Yes

[white raven]

Tank you for helping 🙂

Close.

.close

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[sacred egret]

😦

[white tiger]

the 135 degree angle is made by two angles

[sacred egret]

do i subtract 135- the 90 degree

angle

[white tiger]

yes

and whats that equal to

[sacred egret]

45

[white tiger]

and so 45 is equal to?

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[vale bane]

can someone check the middle column?

Im deriving the entire blue function btw

im starting off with deriving the expression inside the brackets

i put it into a derivation calculator and it gave me a different answer

does anyone know where I went wrong?

and sorry for the messy working out

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[vale bane]

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[fluid bay]

someone explain me this with mod method

[vital crag]

use fermat's little theorem

,calc 103/17

[soft zealot]

Result:

6.0588235294118

[vital crag]

,calc 103 - 17 * 6

[soft zealot]

Result:

1

[fluid bay]

103/17

=6.05

then what

did you do?

[vital crag]

.

[fluid bay]

but they said 103 that is 104-1 in which 104 should be prime but it isnt

[fluid bay]

and the ans is 12

not 1

@vital crag

help

[vital crag]

oh should be 16 not 17 here

,calc 103/16

[soft zealot]

Result:

6.4375

[vital crag]

,calc 103 - 6 * 16

[soft zealot]

Result:

7

[vital crag]

,calc 7 ^ 7

[soft zealot]

Result:

8.23543e+5

[fluid bay]

but how to get the ans

this is not 12

[vital crag]

shush

[solar glade]

Do you know binary exponentiation?

[vital crag]

,calc 49 - 3 * 17

[soft zealot]

Result:

-2

[fluid bay]

yeah but i wanna do it with mod

[fluid bay]

what?

[vital crag]

,calc (-2) (-2)(-2) * 7 + 17 * 4

[soft zealot]

Result:

12

[vital crag]

get this from fermat's little theorem

[vital crag]

then do what samuel said

[fluid bay]

hmm

[vital crag]

7 = 2 + 2 + 2 + 1

[fluid bay]

thanks .close

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[loud heron]

Just need someone to check if this is correct

[loud heron]

Only reason to why idk if it’s correct is because on question 16 my teacher did and got 6pi and on 14 i did as well but he put 11pi/2 as the last plot which confuses me bc shouldn’t it be 12pi/2 ?

also i’m not sure if aysmptotes are correct

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[loud heron]

<@&286206848099549185>

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[loud heron]

man no it’s okay tho bye bye chat

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[copper barn]

having trouble with boolean algebra and am not sure if the following simplification and use of demorgans theorem is correct

[rain compass]

it is not as you would have to switch the middle + for a *

[copper barn]

mb

i dont know how to get from step 2 to 3

this is as far as i am able to understand

looks even worse now

<@&286206848099549185>

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[grave oyster]

Can someone help me with this problem?

[vital crag]

do you know how energy and power relate

[grave oyster]

integral of this function would be energy?

the area under the line from 0 to 30 seconds?

[vital crag]

yes

add the rectangles

[grave oyster]

so area of rectangle 1 which is 45*15?

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[grave oyster]

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[ancient monolith]

is this necesssary

cant i do it withought

and if so i dont understand why

if there equal

[vital crag]

Show your attempt

[ancient monolith]

actually looking at it i cant cause the integral of cot^2 isbnt given

i think that why i got it wrong

ohhh i did cosec^2 = 1-sec^"

whoopsie

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[pine ridge]

is this correct

<@&286206848099549185>

[void valley]

wait, where does ln thing comes from

Are you trying to apply logarithmic diff?

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[twin brook]

Given the function f(x)=3 sin (-2x-4)+3 create an explicit expression for g(x)=-1/3f(2(x-1))+2.

[neon slate]

!status

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

[summer shoal]

you should find out what f(2(x-1)) is and replace it in g(x)

f(2(x-1)) is f(2x-2) so you replace all Xs in f(x) with 2x-2

pay attention to signs and multiplications

[twin brook]

got it thanks

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[slow swan]

hi

[slow swan]

what i tried:

8
8^-2
1/64

i feel like the answer is really obvious but i just cant figure it out

[rotund wolf]

is it not just 1

[slow swan]

nope

i got it

thanks though

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[scarlet vigil]

Hey I’m practicing for discrete math, I’m just not sure about one of my answers here. 4b, I’ll send my work in a sec

[scarlet vigil]

I just need to simplify to the shortest form in 4b

idk how to say it in English, hope it’s understandable enough

This is what I got but I’m not sure

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[scarlet vigil]

<@&286206848099549185>

[tranquil pine]

Seems correct to me, but if you're not sure you can always try to make a truth table

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[stark apex]

how did the 1000 become 0

Ik the quotient rule was used

ohhh ok

ty

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[tranquil pine]

Hi

[onyx umbra]

hello

[tranquil pine]

On the answer sheet, the x-axis is shown as (2.5 , 0). Why isnt it (-2.5 , 0)?

[onyx umbra]

okay

so

let's start at the x-intercept header

yeah?

we have $0=5-2x$

[soft zealot]

Oreo

[tranquil pine]

So plus 5 on both sides

Wait

Or plus 2x on both sides

[onyx umbra]

so it doesn't matter

[tranquil pine]

Thats why its positive

[onyx umbra]

but adding 2x is easier

yes

[tranquil pine]

OHH

[onyx umbra]

you forgot to change the negative sign

[tranquil pine]

thank you 🙏

[onyx umbra]

no problem

[tranquil pine]

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[digital crescent]

this is so easy but my brain just died

[shut gazelle]

Opposite angles are equal and adjacent sum to 180

Use those properties of a parallelogram

[digital crescent]

?

so like

4x+13=5x-12

[shut gazelle]

Yes

[digital crescent]

what about 4y+7?

[digital crescent]

4y+7=180?

[shut gazelle]

You can solve for x here

Then do it again because you know the value of x

[digital crescent]

ohh

yeah I remember now

thxs

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[crisp carbon]

"A basis is a linearly independent set that is as large as possible. T or F"

[crisp carbon]

i thought the answer was false, a basis is the smallest set possible that spans the subspace, but that was incorrect

A.
The statement is false because a basis is a linearly dependent set.
B.
The statement is true by the definition of a basis.
C.
The statement is true by the Spanning Set Theorem.
D.
The statement is false because a basis is the smallest independent set that spans the subspace.

[warm ether]

a basis has to be linearly independent

oops i cant read

its true

the largest a set can be while being linearly independent is the dimension of the space

thats the largest possible linearly independent set

[crisp carbon]

ohhh

i didn't connect the "as possible" with "linearly independent".. somehow

thanks :)

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[rugged escarp]

how do you find the direction of an vector if you have the magnitude

[craggy plank]

You can’t

[tiny gorge]

you don't have enough information if the magnitude is all you have

[warm ether]

is that all you have

[rugged escarp]

i have the sin and cos too

[craggy plank]

Where did you guys emerge? 💀

[rugged escarp]

sorry

i just remembered

[warm ether]

so you have the angle it makes essentially

[rugged escarp]

inverse tan

[tiny gorge]

this is a vector in two dimensions then?

[hybrid heath]

!xy

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[rugged escarp]

yea

[tiny gorge]

do you know how to get x and y from r and theta (polar coordintes)

[rugged escarp]

yea

[craggy plank]

You can use polar on this

[rugged escarp]

but this is opposite

i remembered how to do it now

[craggy plank]

!done

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[rugged escarp]

tan inverse y/x

then subtracy it from 180

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[deft kayak]

nk