help-23

[sharp venture]

well

-5-2 is -7

and -5 multiplied by -2 is 10

[oblique badge]

what's this whole method called so i can learn more about it

and is it always like this?

[sharp venture]

no clue what its called

but its always like this

search quadratic formula

[oblique badge]

beautiful

thank you so much

[sharp venture]

the method only works when ax²+bx+c=0

[oblique badge]

i see

and what is this different from the previous equation you helped me with

[safe radish]

@oblique badge Has your question been resolved?

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[icy lance]

do you have a question..?

[oblique badge]

yes

in the pic

[hardy lion]

cool picture

whats your question

[oblique badge]

it says

if x+y=7

[icy lance]

yeah but what are you asking about the question

[hardy lion]

here:

[oblique badge]

what is y-x

[hardy lion]

!status

[safe radish]

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

[oblique badge]

i know the quiz is answered but i need explanation

how

4

[hardy lion]

so... 5?

[oblique badge]

mmm

no it's 1

[hardy lion]

is this an ongoing quiz?

[oblique badge]

cause i don't know where to begin

it's just a quiz i'm tryna understand how to solve

for upcoming exam

[hardy lion]

so is it an ongoing quiz?

[oblique badge]

yes

hello?

[wooden garnet]

They won’t answer your question if it’s a quiz you’re currently taking, you’re supposed to do it yourself

[oblique badge]

wait wait

this is not an exam

im studying home

just asked for help like before with some questions

some misunderstanding

I implied that I want to know how to solve it for the BIG exam, currently no exam is being taken

damn it

my stupid english

[trim swan]

@oblique badge Maybe you can factorise x^2 - y^2 ?

[oblique badge]

How so?

[trim swan]

It's a difference of squares, you probably have learned a formula for it

x^2 - y^2 = (x+y)(x-y)

[oblique badge]

Yes that's true but

[oblique badge]

How can i depend it here

[trim swan]

You have
x^2 - y^2 = 7

factorise the left side

(x+y)(x-y) = 7

[safe radish]

@oblique badge Has your question been resolved?

[oblique badge]

And how is y-x is -1?

[trim swan]

Think about it for a second, look at your other equation

[oblique badge]

Wait so

X plus y is 7 in the first bracket

But second bracket

Is

0

[trim swan]

Can't be 0

That would mean

(7)(0) = 7

[oblique badge]

Oh we want 1 cause it's multiplied

[trim swan]

right

[oblique badge]

So 2-1

Which means

Y-x
Is 1-2

Which is -1

[trim swan]

I'm not sure where you got 2-1

but I guess that's the right idea

[oblique badge]

Compensate?

How it should be then?

[trim swan]

Just say

since x-y = 1

y-x = -(x-y) = -1

[oblique badge]

With any number?

[trim swan]

with any x and y, that's true, yes

It's just distributing the negative sign

[oblique badge]

Is that a formula?

[oblique badge]

.

[trim swan]

It's just the distributive property

[oblique badge]

I see

Beautiful

[trim swan]

👍

[oblique badge]

Thank you sir

[trim swan]

you're welcome 👍

[safe radish]

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[hearty berry]

quick question, here obviously both area of the 2 shaded parts are the same, so when i compute the whole area i just get one of them and multiply it by 2 right?

[hearty berry]

i got the same answer in area 1 and area 2, but area 2 was negative

i changed it to positive tho, as its under the x axis

there is nothing called a negative area

[royal kiln]

yeah, it's gonna flip though, that's how you get 2x algebraically

every time you pass through the x axis, you need to flip the sign

well hang on, maybe I'm a lying liar who doesn't remember so good

https://www.wolframalpha.com/input?i2d=true&i=integral+of+Power[x%2C3]dx+from+x%3D-1+to+x%3D1

hrm, I guess it always just depends on the context.

[hearty berry]

i see , thank you

.close

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[sturdy pine]

Can someone help W this

[sturdy pine]

I got 124

It has to be 5 digits

[misty bay]

where is the function not continuous

where is the function not differentiable

[sturdy pine]

247

[sturdy pine]

We don’t know the other digits

[misty bay]

stop typing rnadom stuff in there

and just tell me

where is the function not continuous

and where is it not differentiable

[sturdy pine]

I’m not though

I literally don’t see anything other then 247

[misty bay]

answer the questions I asked

1. where is the function not continuous?

[sturdy pine]

2 4 7

[misty bay]

that's wrong

2. where is the function not differentiable?

[sturdy pine]

I’m in a call with 5 other people we all just see this

247

It’s discontinuous at 2 and 7

[misty bay]

okay so it's discontinuous at x = 2 and x = 7

and it's not differentiable at x = 2, x = 4, and x = 7, right?

[sturdy pine]

And non differentiable at 4

[misty bay]

is that what you're saying?

[sturdy pine]

Yea

[misty bay]

okay so you're saying it's discontinuous at x = 2 and x = 7

where is it not differentiable?

[sturdy pine]

4

[misty bay]

is that it?

[sturdy pine]

.close

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[sharp thicket]

with a parametrically defined function, how can i tell if a point is a collision or intersection point

[spiral bane]

wdym collision

[sharp thicket]

interseection is just that the two lines meet

but collission is when they meet at the same time assuming everything, other than the functions, are the same

<@&286206848099549185>

[spiral bane]

cant you just plug in the t values

if we actually consider collisions as a real thing then they dont intersect unless they collide

like here are two functions of t

where they intersect is where they collide

[misty bay]

Suppose you have two curves: r_1(t) and r_2(t). you can find a collision by using a single parameter t and requiring that the point (x, y) = r_1(t) = r_2(t) for some t

you can find an intersection by using parameters t_1 and t_2 and requiring that r_1(t_1) = r_2(t_2)

[sharp thicket]

👍 thank

.close

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[safe radish]

@wind jasper Has your question been resolved?

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[pulsar spade]

this is what I'm stuck on and what ive done

[pulsar spade]

I have a feeling the integral is wrong, but yeah

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[manic path]

how does sin5x +sinx become 2sin3xcos2x

[toxic stratus]

rewrite sin(5x) as sin(3x+2x) and sin(x) as sin(3x-2x) then apply angle sum formulae

[safe radish]

@manic path Has your question been resolved?

[manic path]

wait what

uh

oh I see

thanks!

.close

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[old burrow]

Hello, so c) of this task confused me - since the restricted functions both give minimum at 0, i would assume (0,-0) is minimum of the unrestricted function $$x_1^2-5x_1x_2^2+5x_2^4$$
but when i draw the graph, it turns out to be a saddle point. how would i come to this conclusion without using a graph/wheres mistake in my thinking?

[flat frigate]

Btmina

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@old burrow Has your question been resolved?

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@old burrow Has your question been resolved?

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[wary marlin]

Hello! I need help with this.

What is the value of x that makes the angle a the largest?

[gritty glacier]

x is side?

x and a arent even related

[wary marlin]

yes, but with what value of x is a the largest?

[gritty glacier]

like

no matter what value of x, it doesnt affect angle a it remains the same

recheck the question

[wary marlin]

no

this is a different value of x

[gritty glacier]

bro

x doesnt even matter

[wary marlin]

yes it does

wdym

the answer should be to make a function f(x) = a, and check for the value of x that gives f(x) its maximum value

<@&286206848099549185>

[safe radish]

@wary marlin Has your question been resolved?

[wary marlin]

does this look like the right function?

<@&286206848099549185>

<@&286206848099549185> :(

[willow gust]

sry I've seen ur prob but it's not in my range ..My apologies 😦

[wary marlin]

https://tenor.com/view/stillesque-gif-25544877

Is ok

[willow gust]

umm can u tell me what u want to get with this function? (ik I can't get u fruitful solution..Just trying)

[wary marlin]

this question

thank you! (you are much nicer than @gritty glacier >:()

[willow gust]

glad to hear that! Anyways in the question, Is the x u've given a side?

[wary marlin]

yes, its the hypotenuse of the triangle

[willow gust]

ok

[wary marlin]

adn as you see here, when x changes, ttha angle a changes aswell

[willow gust]

I see...

Yea That's true! It changes!

Now?

[wary marlin]

.close

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[quiet stump]

let x = points

i am trying to figure out what is the next step when he adds in one point

[vital radish]

In each step he adds x-1 points to the line. With that information you can create an equation ad then solve it

[quiet stump]

why - 1?

[vital radish]

If you have 5 points in a line there are only 4 places in between the points, where you put another point

[quiet stump]

oh right yeah got it

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@quiet stump Has your question been resolved?

[quiet stump]

got it

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@quiet stump Has your question been resolved?

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[thorny dock]

Why is [0,19) not a vector space?

I do not get this explanation

I thought for a set to be a vector space, all elements of the set must respect scalar mult + vector add

so, if I pick any values in the interval [0,19), I can add them and will still get some number in that interval (because it is over F_19)

if I multiply any of the values in the interval... by the same logic, I should loop back around again

because modulo 19

[thorny dock]

are they arguing that [0,19) doesn't respect distributivity?

i.e., they found a counterexample that yields a contradiction when applying distributivity

[peak estuary]

19 times anything should be 0

because 19v = 0v=0

but they gave an element for which this is not true

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[scarlet perch]

I don’t understand part b or c

Particularly the range of the binomial distribution

[rigid inlet]

do you recall how to interpret the two parameters of the negative binomial distribution?

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[rough needle]

why isnt=

[rough needle]

why is a mod 0 = a

how does mod 0 even work

why can you mod 0

[quasi bison]

it doesn't

[rough needle]

Identity elements The elements 0 and 1 are identity elements for addition and multiplication
modulo m, respectively. That is, if a belongs to Zm, then a +m 0 = 0 +m a = a and a ·m 1 =
1 ·m a = a.

[quasi bison]

bad copypaste

but nobody's telling you to take anything modulo zero

[rough needle]

.close

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[outer dune]

Hey Im trying to solve this equasion but i dunno how to even get started

μ0 - 4pi * 10^-7 [(Vs)/(Am)]
n - 5
Iśr - 0,573
2R - 250 ± 5 mm
tgB - 45 degrees

[safe radish]

@outer dune Has your question been resolved?

[outer dune]

<@&286206848099549185>

[safe radish]

@outer dune Has your question been resolved?

[misty bay]

what are you trying to solve for again?

[outer dune]

I need to solve this equasion, but I don't have any information on my worksheets what is it

it is something about calculating magnetic field using a Tangent Galvanometer

[plucky elk]

#old-network for physics server

or be more specific about what math question you want answer

"magnetic field using a Tangent Galvanometer" is not meaningful in math

[misty bay]

honestly this sounds like not solving an equation

but just evaluating the formula at the given values

B_z is the component of the B field in the z direction I think

[outer dune]

I have to calculate what the Bz is by substituting the given values

But I don't know how I can even use the absolute error (250 +- 5mm) in here to calculate it

[plucky elk]

tgB - 45 degrees
those look like 3 variables in your formula

typically one doesn't plug in units of degrees in a formula

try converting to radians

[outer dune]

Okay so I stay with (4pi * 10^-7 * 0.537) /250 +- 5

[plucky elk]

where does error come in the question?

just show the exact question. picture or screenshot

[misty bay]

probably means tangent of 45 degrees

[outer dune]

Srry all in my language but I can translate

[plucky elk]

just translate what you already haven't

[outer dune]

Value Bz has to be calculated for value of rings which equals 5,10 or 15 from equation:

where:
n - value of rings
Iśr - average volume of power coming through rings, designated from 14 measurements (previously as a average of power coming to two directions, and then average of 7 another measurements
2R - diameter of compass rings
tgB - tangent degree of compass needle deflection

[misty bay]

Isr is the current through the rings yeah?

not the "volume of power"

n is the number of rings

2R is the diameter

actually not sure what 2R is

[outer dune]

Yeah

I have somehow to do it into report by this day

[outer dune]

.close

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[eager garden]

where does the +- come from

[safe radish]

Please don't occupy multiple help channels.

[karmic yarrow]

6^2 = 36, (-6)^2 = 36

so +- 6 can both work in this scenario

[eager garden]

oh

ok thx

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[eternal sparrow]

Hi guys can someone please check if I did this question correctly?

[hot thistle]

you did

[eternal sparrow]

But I don’t think the teacher will read it clearly and understand it, how can I rewrite it professionally?

<@&286206848099549185>

[stoic dune]

I think you're fine

[hot thistle]

maybe you can just white out the scribbles

[stoic dune]

Easy to follow the logic here

[eternal sparrow]

I wanna follow this example structure

@kaynex @hot thistle

[hot thistle]

you basically have the same thing

i wouldn't overthink it, your work is correct

[eternal sparrow]

Because the teacher is gonna mark it, and yeha I am overthinking it tbh 😢

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[flat frigate]

Benschko

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[light hatch]

.reopen

[vagrant pasture]

i have a question

[vagrant pasture]

when you have something like 4 times the square root of 10

and they are next to eachother

and you do that times the power of 2

[worthy hemlock]

Like $4\sqrt{10}$?

[flat frigate]

dldh06

[vagrant pasture]

yea

would you multiply the 4 as well

so it would be 16 x 10

if that was in the pythagorean theorem

r u supposed to use parenthesis around your numbers

like say the hypotenuse was 30

or 22

or 25 i mean

would you do

would you do 4^2 + 3^2

or (4)^2 + (3)^2

is anyone there

@worthy hemlock

[white hollow]

you didn't articulate your question very well

what exactly are you asking

[vagrant pasture]

yea ik uh

in the pythagorean theorem

or nvm

like

say you have

and you had parenthesis around that

do you square the 4 and the root 10 or just the root 10

[white hollow]

both

[empty gyro]

depends on where the exponent is

[vagrant pasture]

on the outside of the parenthesis

[empty gyro]

then square both, yes

[vagrant pasture]

ok

ty

[empty gyro]

PEMDAS

[vagrant pasture]

yea

[empty gyro]

or BODMAS these days....

[vagrant pasture]

what

?

[empty gyro]

The kids these days call it BODMAS

But I'm a PEMDAS enjoyer

[white hollow]

BIDMAS supremacy

[worthy hemlock]

Nah that's the Europeans

[vagrant pasture]

i have never heard of the word bodmas lmao

[worthy hemlock]

What's I?

[white hollow]

indices

[vagrant pasture]

it does seem pretty european

in the states nobody says orders

atleast afaik

.close

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[umbral warren]

how to solve this

[gritty glacier]

theyre asking to prove that no positive integer for n will make this equation rational

we know that value inside sqrt should not be negative

thus

[umbral warren]

yeah so how to do that

[gritty glacier]

$n-1 \ge 0$

[flat frigate]

bettim

[gritty glacier]

thus

$n \ge 1$

[flat frigate]

bettim

[hexed dune]

cant you prove that the difference between squares will at minimum be more than 2.

[umbral warren]

ok then

[umbral warren]

idk

[gritty glacier]

so

wiat i messed up sry lol

[hexed dune]

(n+1)^2 - n^2 = n^2 + 2n + 1 - n^2. so 2n + 1 is the difference between each consecutive square. and you have shown that n cant be 0. so if n >= 1. 2n + 1 >= 3

[umbral warren]

$(n+1)^2 - n^2 = n^2 + 2n + 1 - n^2. so 2n + 1 is the difference between each consecutive square. and you have shown that n cant be 0. so if n >= 1. 2n + 1 >= 3$

[flat frigate]

av

[umbral warren]

you mean this

[hexed dune]

$(n+1)^2 - n^2 = n^2 + 2n + 1 - n^2$ . so $2n + 1$ is the difference between each consecutive square. and you have shown that n cant be 0. so if $n >= 1, 2n + 1 >= 3$

[flat frigate]

doctor99268

[hexed dune]

best to use the $ only for the maths part

[umbral warren]

ok

so thats the anwer ?

[hexed dune]

or you could acc do

if you square then entire expression

you get

$n + 1 - 2\sqrt{n^2 - 1} + n - 1 = 2( n + \sqrt{n^2 - 1})$

[flat frigate]

doctor99268

[hexed dune]

n^2 - 1 will never be a square number when n > 0

because its literally always 1 less than a square number

[umbral warren]

bro can you show the steps

cause i didnt understant

[umbral warren]

wdym

[hexed dune]

acc

i need to do a bit of modification

[hexed dune]

all i did was square the equation $\sqrt{n - 1} + \sqrt{n + 1}$

[flat frigate]

doctor99268

[hexed dune]

if we can show that it is still irrational even after squaring it

[umbral warren]

you mean $[\sqrt{n-1}]^2 +[\sqrt{n+1}]^2 $

$[\sqrt{n-1}]^2 +[\sqrt{n+1}]^2$

[flat frigate]

av

[hexed dune]

no, i mean $(\sqrt{n - 1} + \sqrt{n + 1})^2$

[flat frigate]

doctor99268

[umbral warren]

ohh

[hexed dune]

if it was rational

[umbral warren]

would it make a big difference if I did this

[hexed dune]

then it has to be rational when it is squared

[hexed dune]

completely different

and absolutely wrong

[umbral warren]

why do we have to do this

[hexed dune]

if $\sqrt{n - 1} + \sqrt{n + 1}$ was rational, then $(\sqrt{n - 1} + \sqrt{n + 1})^2$ should also be rational

[flat frigate]

doctor99268

[umbral warren]

yes

then

[hexed dune]

$2( n + \sqrt{n^2 - 1})$ this is irrational for n above 1

[flat frigate]

doctor99268

[umbral warren]

ok

now I get it

[hexed dune]

and you can put in n = 1

into the original equation

to show that, that is irrational aswell

[umbral warren]

thanks bro

.close

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[native storm]

Topic: Linear Algebra

Doubt: While calculating Rank of a matrix, when do we know where to stop?

Here's the question:
=> Find the rank of Matrix A.

[flat frigate]

BachToReality
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[native storm]

Here's where I've ended after trying to find the Reduced Row Echelon Form:

[flat frigate]

BachToReality
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[native storm]

When do I know to not continue further row operations?

[safe radish]

@native storm Has your question been resolved?

[native storm]

@meager igloo Sorry for the ping, but can someone help me out here?

<@&286206848099549185>

[worthy hemlock]

When it's in RREF

[native storm]

So, for a 3*4 matrix, is this the RREF?

[worthy hemlock]

No

[native storm]

I thought it'll look like this:
$\text{A} = \begin{bmatrix}1 & a_12 & a_13 & a_14 \ 0 & a_22 & a_23 & a_24 \ 0 & 0 & 0 & 0 \end{bmatrix}$

[flat frigate]

BachToReality

[native storm]

Can I reduce this equation further?

[worthy hemlock]

Most likely because that's not rref

[native storm]

But the given rank of the matrix is 3. That should mean it has 3 independent non-zero rows, right?

[worthy hemlock]

No, it can have up to 3 independent non zero rows

[native storm]

I guess I need to do more reading then.
Thanks for the clarification @worthy hemlock!
You can close this question now.

[worthy hemlock]

.close

[native storm]

.close

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[shell hound]

If 𝑦 = 3𝑠𝑖𝑛𝑥 − 4𝑐𝑜𝑠𝑥, prove that
𝑑^2y/dx^2=+y=0

[shell hound]

please anyone tell me how you can do further questions like this

as well as this one

[split ether]

You mean prove that the second derivative is -y, right?

[shell hound]

I don't know much of this question, this from a chapter named CONTINUITY AND DIFFERENTIABILITY

[split ether]

Is the problem saying -y or +y

[shell hound]

y+

[split ether]

Or you mean d^2y/dx^2 + y = 0?

[shell hound]

no d^2y/dx^2 = +y=0

this from previos exams question of the said chapter

[split ether]

You can't prove that's false

Can you screenshot the question or smth btw?

[shell hound]

my xbox game bar suddenly not working I was to do that, but instead I could send you the whole pdf of questions

[split ether]

Sure

[shell hound]

question number two july 2022

[split ether]

Must have been a typo

Because d^2y/dx^2 + y = 0 is true

Rather than = +y = 0

[shell hound]

hmm, maybe it's they're typing mistake cna you explain what it is

[split ether]

"It"?

[shell hound]

the question ^2y/dx^2 + y = 0 is true

[split ether]

First start by evaluating d^2y/dx^2

So you need to differentiate 3sinx - 4cosx twice

[shell hound]

derviative of a constant is 1. right

[split ether]

Yes, although that fact isn't really relevant here

[shell hound]

so 3cosx-4-sinx

that's it

[split ether]

That's the first derivative, now differentiate it again to get the second derivative

Hopefully you meant 3cosx - 4(-sinx) btw

[shell hound]

yeah, so how do you do second order derivative

I only learned this chapter to find continuity

[split ether]

Just differentiate 3cosx + 4sinx

As if you normally would

[shell hound]

but it's quite similar as the question it self

-3sinx+4(cosx)

[split ether]

Yes

If you factor out the negative sign

You see that the second derivative is simply -y

Hence d^2y/dx^2 + y = 0

[shell hound]

could you explain me more

how do you factor - that you get -y

[split ether]

-3sinx + 4cosx = -(3sinx - 4cosx)

[split ether]

Does the expression inside the parenthesis look any familiar?

[shell hound]

-1(3sinx - 4cosx) can this be right

[lean otter]

hmm math.

[split ether]

That is equivalent

[shell hound]

why did you not put 1

[split ether]

Like I said, that's the same

[shell hound]

so if I need to factor negative just put - out side paranthesis.

what about this question "The derivative of log (x^3) is"

[split ether]

You can either rewrite that as 3log(x) or apply chain rule

[shell hound]

what was chain rule

3 log is the power 3 of x,

[split ether]

No

[split ether]

Never mind what I said about chain rule if you don't know it

[shell hound]

can you quick explain

I might have forgot what it was

[split ether]

Chain rule says that the derivative of f(g(x)) is f'(g(x))g'(x)

[shell hound]

is it d/dx (I) (II)

(II)d/dx(I)-(I)d/dx(II)

[split ether]

No

That's the product rule

[shell hound]

or was it first you do the square then you do the function then you do the angle

[split ether]

Not sure what you mean but that doesn't sound like chain rule

[shell hound]

it means first you derivation the square, then the derivation function eg sin cos etc, then you derivation of angle

I get it now

Power, Function.Angle

.close

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[lean otter]

Hi I have no knowledge about statistics and probability and I was asked if this is correct

[lean otter]

I just wanna know if its wrong and if its wrong whats the correct way for step 5/6

<@&286206848099549185>

[buoyant shadow]

the question is missing

can't tell if it's right

doesn't look right

[safe radish]

@lean otter Has your question been resolved?

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[cyan niche]

hello

[cyan niche]

I have found the solutions to all the parts, but I'm just wondering why x_n is a linear combination of the two solutions?

[peak estuary]

show that the space of sequences satisfying that recurrence relation is a subspace

therefore all elements in the space can be written as a linear combination of basis vectors

which the two sequences (q_1^n) and (q_2^n) are

[quasi bison]

a subspace of the space of all real sequences to be obnoxiously precise

you dont know that its dimension is 2 yet do you tho

or ig you do because you can exhibit a basis

[peak estuary]

well clearly all sequences are determined by the first 2 entries

[quasi bison]

consisting of the seqs (1, 0, ...) and (0, 1, ...) and the rest following from the RR

[peak estuary]

so (1, 0, rest) and (0, 1, rest) are an obvious basis

[quasi bison]

@cyan niche are you familiar w linear algebra at all

[cyan niche]

ok, kinda makes sense

yeah, I've done basic linear alg

[quasi bison]

yeah ok

then it comes down to showing the dim of the solution space is 2, perhaps

[cyan niche]

how would I represent q^n as a vector though?

[peak estuary]

(q, q^2, q^3, ...)

[quasi bison]

(1, q, q^2, q^3, ...) no?

[peak estuary]

they are starting at x_1. and they set x_n=q^n

[cyan niche]

wait so how is this two-dimensional?

[peak estuary]

the space is two dimensional

the elements inside the space are sequences

but that doesnt matter for the dimension

[cyan niche]

so we'd have two sequences, (q_1, q_1^2, q_1^3,...) ,(q_2,q_2^2,q_2^3,...): then how would I go about proving these are basis vectors?

[peak estuary]

show they are linearly independent

[cyan niche]

ok, cool

thanks

[safe radish]

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[deep dune]

hi

[deep dune]

simple question

💀 it isnt in our

assignments tab

[final halo]

https://www.learnalberta.ca/content/memg/division03/inequality/index.html

[deep dune]

ty very much <3

!close

.close

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[trail harness]

Hello, I would appreciate if someone could confirm that I am indeed on the right track

[trail harness]

(On the last line, the first 1/2 is moved out onto the rest of the problem)

[wise venture]

Seems correct to me.

[trail harness]

Well it’s just that it gets pretty ugly right after, having to transform the 7/16 to a 1

[wise venture]

You don't need to do that?

[trail harness]

I dont?

Isn’t the goal of this to make it look like the arctan formula?

[wise venture]

a= (√7/4)

[peak estuary]

oh no a sqrt of 7

how will you live

[trail harness]

Fighting for my life in this calc 2 class 😭

[peak estuary]

I mean you did everything correctly. just dont be scared of a few square roots

be more confident in yourself. you clearly can do this

[trail harness]

Thank you for the kind words!

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[carmine remnant]

Helloo

[hybrid wedge]

Which question?

And

!status

[safe radish]

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

@carmine remnant Has your question been resolved?

[carmine remnant]

1. I don't know where to begin

[hybrid wedge]

Which question?

[carmine remnant]

uhm

at I. all of them if its okay

[hybrid wedge]

O and B are the midpoints in first question

?

[carmine remnant]

yes

<@&286206848099549185>

[carmine remnant]

reallyyy urgent to helpp

[safe radish]

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[safe radish]

@untold anchor Has your question been resolved?

[safe radish]

@untold anchor Has your question been resolved?

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[feral void]

Hi, Need help with the rule of exponent which i forget and really confused right now. There are two solution which i am confused about. Please explain which is right and how using the rule of exponent.

[feral void]

I hope I explained by question clearly

[grim plover]

Yeah

So, how much is 3 - 1/2

[feral void]

5/2

right?

[grim plover]

Yeah

How do you write that?

(Instead of a single power, as a product)

[feral void]

Sorry i didn't get you

could you be more specific

[grim plover]

How do you get -3/2?? It's supposed to be 5/2 only no?

[feral void]

this is the law of exoponent for power

[grim plover]

I meant as x^2 * x^1/2

[grim plover]

But when it's division it's subtraction

So 3 - 1/2

You can't do 1/2 - 3 if it's x^3/x^1/2

1/2 - 3 is means (x^1/2)/(x^3)

[feral void]

So i am learning differentiation from yt and this video explanation got me confusing

is this solution wrong ?

[grim plover]

He did it wrong i believe

It's supposed to be 5/2

[feral void]

i am pulling my hair over this for an hour

[grim plover]

Happens 😂

[feral void]

like i forget my basic math

dammm jesus

[grim plover]

I once did 8+9 = 72 😂

[feral void]

thanku sir for kind help and releasing my stress 🙂

.close

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[thin bridge]

without a lid

[safe radish]

@compact isle Has your question been resolved?

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@compact isle Has your question been resolved?

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[violet birch]

i need help with my homework please

[rigid inlet]

!show

[safe radish]

Show your work, and if possible, explain where you are stuck.

[violet birch]

im not sure what to do in general..

[rigid inlet]

how have you been taught to find probabilities of normal distributions?

[violet birch]

not yet..

but teacher told us to solve it anyways

[rigid inlet]

if they haven't taught you how to find probabilities of normal distributions, you can't solve this

[violet birch]

i know...

what do i search on yt

do i just search probabilities of normal distributions?

[rigid inlet]

or you tell your teacher "you've not given us the tools to solve this"

[violet birch]

she doesnt care

shes mean

tells us to do it ourselves

[rigid inlet]

what has she taught you?

[violet birch]

good question!

wait i found the solution on google

[rigid inlet]

[violet birch]

question is,

how

did we get this

[rigid inlet]

where did you find this?

[compact ferry]

central limit theorem

[violet birch]

google aka classmate sent it

not sure where she found this

[rigid inlet]

looks like it uses functions found on a TI-83 calculator

are you using one of those?

[violet birch]

mhm

question is *what * is an invNorn

[rigid inlet]

it's the quantile function, or the inverse cdf

[violet birch]

how do i input the σ on the calc

im so lost

[rigid inlet]

quite the predicament

[violet birch]

im sorry

im lost lost

[rigid inlet]

ideally you'd have already had a few lessons on this topic, this isn't exactly something you can just solve on the fly

[violet birch]

ideally

unfortunate

[safe radish]

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[lean otter]

This is wrong right?

I got tan^2x/2

[split ether]

Recall that tan^2 and sec^2 are off by just a constant

Which, here, gets devoured by +C

[lean otter]

what do you mean?

[split ether]

Does the trig identity 1 + tan^2(x) = sec^2(x) look familiar?

[lean otter]

yeah

sec^2 = tan^2 + 1

[split ether]

So tan^2(x) and sec^2(x) are the same functions, except with difference of 1

Here that 1 "gets devoured by +C"

[lean otter]

can I turn 1/2sec^2x into tan^2x/2?

since they are the same?

[split ether]

You can do that whenever you have two functions with the same derivative after indefinite integration

[split ether]

Notice that this means that derivatives of tan^2 and sec^2 are equal

[safe radish]

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[lyric belfry]

can someone help me figure out what these angle restrictions mean for my unit circle work?

[lyric belfry]

like in between -180 and 180

does that just mean the entire unit circle?

[safe radish]

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[lyric belfry]

.close

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[true estuary]

can i get some help on part c plz

i have the ausatz written down but thats about it

[obtuse jackal]

1)free family
2) spanning family

[obtuse jackal]

Hint for 2): show that any matrix in U has to be of the right form

[true estuary]

wdym free family

[obtuse jackal]

Linearly independent

[true estuary]

do i need to do this

to show theyre linearly independent?

[obtuse jackal]

Pfff

Hardly ever done that in my entire life

[true estuary]

to show theyre lin inpedenent do i show that theyre coefficients vanish

[obtuse jackal]

Show that if a linear combination is 0, the coefficients are all 0

[true estuary]

ie r 0

ok

[obtuse jackal]

That's the definition and it works very well

[true estuary]

^

[obtuse jackal]

Basically yes

[true estuary]

so now i need to show its a spanning set?

[obtuse jackal]

Yes

[true estuary]

hmmm

bit stuck tbh

[true estuary]

idrk

[obtuse jackal]

did you take that into account

[true estuary]

yh

do i have to show that the matrices in the basis satisfy these condtions?

[obtuse jackal]

look at the definitions

that's all you need

you're in undergrad, show that you have some autonomy

[true estuary]

2x2 matrix

and in complex

Aij = -Aji*

A11 = -A22

[true estuary]

not rly clicking

ive looked but im still kinda frozen

[obtuse jackal]

write equations

find constraints

more precisely

i = j gives what ?

[true estuary]

i=j?

[obtuse jackal]

on the coefficients

[true estuary]

u mean like the vectors

[obtuse jackal]

what does it tell you about A11 and A22

[true estuary]

that A11 is the negative of A22

[obtuse jackal]

what values of i and j give that

[true estuary]

i=1 and j=2

acc

1,2 for both i and j

[obtuse jackal]

so what value of i, what value of j

or if you did, what sets of values did you take to put the equations together to arrive at that result

[true estuary]

well it says in the defn that A11 = -A22 and thats for i = 1 and 2 and j = 1 and 2

[obtuse jackal]

i can't take on 2 values at once

[true estuary]

ok then i = 1

[obtuse jackal]

and j = ?

[true estuary]

1?

[obtuse jackal]

so how did you get A22 ?

[true estuary]

idrk im rly confused tbh

im just going along with the defn

[obtuse jackal]

i = j yields Aii = -Aii*

so it's a number that is its own negative conjugate

has to be pure imaginary

[true estuary]

ok

[obtuse jackal]

oh sorry. I forgot the 2nd said A11 = -A22

[true estuary]

yh

[obtuse jackal]

thought you were trying to deduce it from the Aij property

[true estuary]

nah just the defn

as it says

[obtuse jackal]

yeah sorry

[obtuse jackal]

so it's a pure imaginary

and A11 = -A22

[true estuary]

yh

[obtuse jackal]

so if A11 = ai, A22 = -ai

hence you see it's a U1 + (only coefficients off the diagonal)

then i = 1, j = 2 yields A12 = -A21*

[true estuary]

yh

[obtuse jackal]

what does that tell you about the real and imaginary parts separately

[true estuary]

um, A11 and A22 are imaginary parts

and A12 and A21 are real?

which is true for the matrices in the basis

[obtuse jackal]

what about U3 ?

[true estuary]

since i and -i are A11 and A22 respectively

[true estuary]

wait wdym by U1 and U3?

oh like

1st matrix

and 2nd ok

[obtuse jackal]

basis matrices

[true estuary]

okok

ah rip

yh U3 doesnt agree

with that

as A12 and A21 r imaginary

[obtuse jackal]

what about U2 then ?

[true estuary]

theyre real

so A12 and A21 agree

[obtuse jackal]

so they're simply complex

[true estuary]

and one is negative

[obtuse jackal]

but you have information about how they are linked

[true estuary]

why so? isnt U2 real?

[obtuse jackal]

one tells you about U2, the other about U3

you should arrive at the fact they are spanning from that

(don't forget the other inclusion, even though it is quite obvious, it is still necessary)

[true estuary]

yh yh

so is that it done?

[obtuse jackal]

when you'll have done it yes

[true estuary]

need to do u3

[obtuse jackal]

that's not how you'd write it

take a matrix in U

show it's a linear combination of U1, U2, U3

you don't even have a matrix yet

try to do that on your own

I have to go now

[safe radish]

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[astral matrix]

Would this be positive 36 or negative 36?

[sleek mortar]

i need help with a math problem that requires a long drawn out explanation

[stoic dune]

@astral matrix
Note that ² doesn't distribute over sums.

Unless you're about to place the other 3 terms haha

Would be (-6x)² = (-6)²x² = +36x²

[astral matrix]

Welp ty

.close

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[true estuary]

are u allowed to swap rows

[true estuary]

if u r trying to form a rref

[junior smelt]

it's one of the elementary row operations

[safe radish]

@true estuary Has your question been resolved?

[true estuary]

thx

.close

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[nocturne path]

I just opened a help channel before this and was told to solve Q5 I need to find the point of interception

But I do not know how it do this I am realsing

[glass carbon]

equate the curves

square both sides

(remember about restrictions about x)

[nocturne path]

So 3x+1=5x-x^2

[glass carbon]

yes

[nocturne path]

Ok so it becomes quadratic

It is factorised and x = 1

How do we move forward from here

[glass carbon]

now you have x - coordinate of the tangent

[nocturne path]

Oh shit yeah

I got it

Thanks

.close

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[dim nimbus]

Hello, dont know where to start. I have this system of equations, and I need to calculate this by using Gauss method.
x1+x2+x3=24
8000x1+16000x2+24000x3=520000

[coral ruin]

@nocturne path

There's an easier way if you're interested

just d/dx(1/Sin(x))|x=π/3

[safe radish]

@dim nimbus Has your question been resolved?

[safe radish]

@dim nimbus Has your question been resolved?

[safe radish]

@dim nimbus Has your question been resolved?

[spiral bane]

i dont think you can solve that

theres two equations but three unknowns

[safe radish]

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[cloud lark]

Hey! So i have two dices, one produces 1, 2, 3, or 4 with 1/4 probability each
one produces 1, 2, 3, 4, 5, 6, 7, or 8 with 1/8 probability each
My question is, what is the probablity of NOT getting a total sum of 12 from the two dices, after 100 rolls. Would that be 1/32^100? Since the chance of getting 12 would be 1/4 * 1/8 = 1/32?

[trim swan]

Since 1/32 is the probability of rolling a 12

Doesn't that make (1/32)^100 the probability of rolling a 12, 100 times in a row?

[cloud lark]

uhh you might be right

So 31/32^100 instead?

[trim swan]

Ahh, that sounds good

The probability of rolling anything other than a 12, 100 times in a row

[cloud lark]

Which equals 4.18%

Does that sound right?

[trim swan]

yep

[cloud lark]

Aight, thanks mate

[trim swan]

np 👍

[cloud lark]

.close

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[fiery elbow]

What do i do once i find the equation of a straight line (w logs) t o find K and N

[fiery elbow]

so far, the gradient is 3, so that means n=3 or n=2 i dont remeber which variable to use, but the equation i got was, y=3x+2

[misty bay]

can you write log y = slope * log x + intercept?

[fiery elbow]

i'll do that now

like this? logbase2(y) = 3(logbase2(x)) + 2 ?

[misty bay]

yeah

now here's the interesting part

raise both sides of the equation 2^

to get rid of the logs

see what you get

[fiery elbow]

(how do i do that.)

[misty bay]

do you know the exponent rules

[fiery elbow]

i'm familiar but i forget them

ill look them up

[misty bay]

if you have something1 = something2

then you know that 2^something1 = 2^something2

does that make sense?

[fiery elbow]

yeah i think so

[misty bay]

if you do the same thing to things that are equal

they still remain equal

[fiery elbow]

oh yeah, of course

[misty bay]

so you have $2^{\log_2 y} = 2^{3 \log_2 x + 2}$

[flat frigate]

Saccharine

[misty bay]

can you simplify both sides?

[fiery elbow]

i dont know how to to be honest

can i burn logs?

or is that later

[faint seal]

you can for the left side

but the right side needs some more work

split the exponent

remember that $a^{b + c} = a^b \cdot a^c$

[flat frigate]

kheerii

[fiery elbow]

yeah im trying to use that now, so like, 2(3log2(x) + 2(2) ?

[faint seal]

and $a^{log_a{b}} = b$

[flat frigate]

kheerii