help-10

[vast wren]

A

[uneven palm]

do you understand the goal of system of equations?

[vast wren]

(2, 15) and (-4, 9) are your answers

[uneven palm]

don’t give answers

[vast wren]

but why are these your answers?

[vast wren]

ik, one sec

[uneven palm]

:/

[timid silo]

for that one it just throws me off that theres two numbers so i guess i think thats the final answer since you need a x,y

[uneven palm]

@timid silo this is important to understand

[vast wren]

because it’s a quadratic equation

there has to be two solutions

(for discriminant > 0)

you really need to review your material

or study maths from another source

wait one sec

@timid silo https://www.youtube.com/playlist?list=PLybg94GvOJ9FoGQeUMFZ4SWZsr30jlUYK

[timid silo]

ill look into that, thanks

[vast wren]

you should definitely look into it

[timid silo]

what about ordered pairs? i got one of them but im confused pasted the ;

[uneven palm]

in a broad sense, what are solutions to a system of equations?

that’s really important to understand

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

im not really sure what you mean by that

[ivory sierra]

Not know if is this question but i would say b

[timid silo]

i already finished that xd

[timid silo]

on to this now, but currently still stuck.

[ivory sierra]

What if you make a grafic?

[nocturne minnow]

Post your work

[ivory sierra]

Isnt it quadratic? The shouldnt you develop for -3 and look for the other solution?

[timid silo]

what would?

the first part is

but

i dont know how to get the second x,y

[nocturne minnow]

One, don't give out answers

Not the purpose of the server

[ivory sierra]

Ok see

The exponent of the x will tell you how many solutions are there

[ivory sierra]

Therefor, for what i can understand, x should have two solutions for the f(x)=-3

They are giving you one, the first ordered pair

[nocturne minnow]

FYI, you are over complicating it. There is a much simpler way than whatever you are doing

[ivory sierra]

me?

[nocturne minnow]

And the OP found that answer, I believe, as they stated "I got one of them"

[nocturne minnow]

Do you know what it means when it says f(x) = -3?

[ivory sierra]

So i would suggest, for complete process, solve the ecuation for “-3”, and it should give you the 2 (which is already in the ordered pair), and the other solution you are looking for

[timid silo]

nope

[nocturne minnow]

That's over complicating it, because it seems like that's just guessing

[ivory sierra]

Ok there it is

f(x) = ecuation

[nocturne minnow]

It means the output, or y value is -3

[timid silo]

whats the output?

[ivory sierra]

-3

[nocturne minnow]

So you have the function, f(x) = x^2 - 5x + 3 and knowing f(x) = -3. That means the output is -3, so you can replace f(x) with -3

What is that function when you plug in -3?

[ivory sierra]

when the function gives you -3, what values are in x?

[timid silo]

so i replace the (x) with -3?

[nocturne minnow]

Not helping, there's a easier way than whatever this is

[nocturne minnow]

Not exactly, you replace f(x)

That entire part with -3

[ivory sierra]

No no no, the result of the function will be f(x), all f(x)

[timid silo]

i put that in a calculator and i got 3,2

[nocturne minnow]

What does that mean?

[ivory sierra]

What did you do exactly?

[nocturne minnow]

I asked you what the equation is when you plug in -3 for f(x)

[ivory sierra]

Ah yea

[timid silo]

-3=x^(2)-5x+3

[nocturne minnow]

So is 3,2 a coordinate point?

[nocturne minnow]

The roots to this?

I wasn't asking you

I already know what it means. I'm making sure the OP knows

[nocturne minnow]

Well, of you solve this, you will get the solutions of x that has the y coordinate of the value of -3

[timid silo]

i mean

the 3,2 is for this

[ivory sierra]

Do you know how ordered pairs works for equations?

[timid silo]

not really

[ivory sierra]

Ok, you know how functions are represented?

[nocturne minnow]

Here's a video, might be helpful
https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-solutions-to-two-var-linear-equations/v/ordered-pair-solutions-of-equations-2

[timid silo]

like the picture im assuming?

[ivory sierra]

ok, lets see

Functions are represented on a 2D plane

Absises (horizontal line) are for “x” axises

Ordenates (vertical line) are for “y” or “f(x)” axises

Ordered pairs are coordenates in that plane, as in (x, y) and (x, f(x))

being x the values of x

and f(x) and y, what the equation value

Ordered pair: (x, y)

[timid silo]

so what equation would i do to find the second pair of x,y

or is it 3,2

[ivory sierra]

Ok, you put the ecuation in the calculator, and it gave you 3 and 2

Right?

[timid silo]

yes

[ivory sierra]

You know what that means?

[timid silo]

not really

[ivory sierra]

It means x can be all 3 or all 2, and still gives you -3

Those are solutions for x

[nocturne minnow]

.

[timid silo]

ohhh okay i get that

[ivory sierra]

Annnnd this

[timid silo]

wait so was i right? xD

[ivory sierra]

not exactly

3 and 2 are solutions for x in that ecuation

3 is x
2 is also x

[ivory sierra]

Look at the form of ordered pair, you need a x value, and y value in order to get coordinates

[ivory sierra]

Analize the order pair they are giving you

[timid silo]

-3=x^(2)-5x+3 will this give me my answer ?

[ivory sierra]

You got 2 and 3 from doing that, right?

[ivory sierra]

The ordered pair they are giving you is

(2, -3)

Your solutions for x are 2 and 3

And (x, y) is the form of ordered pairs

[timid silo]

yes i did

so do i replace x with either of those numbers?

[ivory sierra]

There is one already used in the first ordered pair

[timid silo]

this?

[ivory sierra]

We already passed that part

y is f(x) too

You already solved the equation, all right with that

[timid silo]

so this just tells me that f(x) is -3 right?

after that i replace them with -3 and get -3=x^(2)-5x+3

[ivory sierra]

Yes

[timid silo]

but after that i dont know what to do with 3,2

[ivory sierra]

ok right

3 and 2 are for x

[ivory sierra]

x^(2)-5x+3

if you change x for 3, it will give you -3, and if you replace x for 2, then it sill give you -3 too

Those are solutions for x

[ivory sierra]

(x, y) is literally that

x value (solutions for x)
y value (also as f(x))

[timid silo]

do i put this in a calculator?

[ivory sierra]

no

You dont need calculator anymore actually

[ivory sierra]

Lets see the orderes pair they gave you

[ivory sierra]

(2, -3)

x value 2
y value -3 (also as f(x))

And if x means solutions for x… and y means the result… then…?

[timid silo]

okay thanks!

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

@celest zodiac Has your question been resolved?

[celest zodiac]

would I just say they are both in rref form?

[obtuse pebble]

@celest zodiac Has your question been resolved?

[royal basin]

them both being in RREF has nothing to do with their similarity, so no

also, "reduced row-echelon form form"

these matrices are both in JNF though.

[fierce lagoon]

The matrix memories are flooding in dear god the pain never ends

[brave bramble]

Kek I do that all the time

rref form

[fierce lagoon]

What's JNF though

I've never heard of that with matrices

All I know that rref is like the "solution" and doesn't show similarity at all, if anything

Google tells me "Jordan Normal Form" and that's beyond my ken

[royal basin]

yes it is

[royal basin]

"ATM machine"

[fierce lagoon]

Jordan's a funny name

[tardy epoch]

DC Comics

[obtuse pebble]

@celest zodiac Has your question been resolved?

[obtuse pebble]

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[sly pivot]

Hey guyz if i have 1.7l of fuel consumption on 100km while going 27kmh how many liters of fuel consumption on 100kmh will i have if i go 40kmh?

[glad canopy]

This question needs more background info

Is there a specific relationship between speed and gasoline efficiency? There may be a function for that

[obtuse pebble]

@sly pivot Has your question been resolved?

[sly pivot]

No its just 1.7l/100kmh speed: 27kmh

I just wanna know how many liters of fuel on 100kmh consumption is when speed will be 40kmh

[obtuse pebble]

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[obtuse pebble]

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[mellow halo]

Someone help fast is
x ^2 multiple 2x

[mellow halo]

2x^3

Is that the ans?

[sweet cobalt]

Yes $x^2 \times 2x = 2x^3$

[warm shale]

Jammy

[sweet cobalt]

Do you understand why?

[obtuse pebble]

@mellow halo Has your question been resolved?

[obtuse pebble]

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[drifting helm]

Is multiplying a vector the same as multiplying a matrix, it is, right?

[timid silo]

wym

[drifting helm]

Oh sorry. I was thinking mostly of a vector multiplied by a matrix with the appropriate proportions. (Such as 4x1 vector times 4x4 matrix)

What I basically wonder is, can I treat a vector as a matrix?

[kind hawk]

you can't multiply a 4x1 vector times a 4x4 matrix. what you probably mean is 4x4 matrix times 4x1 vector

do you mean whether you can treat nx1 vectors as matrices with just one column?

then yes

[obtuse pebble]

@drifting helm Has your question been resolved?

[drifting helm]

Oh yeah, exactly. Thank you very much, gonna start a linear algebra course soon. For fun.

[obtuse pebble]

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[timber hatch]

I’m unsure on how to do question 1a and b and have already attempted to create an equation for it but I’m unsure if it’s correct as it doesn’t make sense on how it can help me find the length and breath. If I could get support on how to complete it I would be very grateful!

[timid silo]

suppose the short side is x

[timber hatch]

Ok

[timid silo]

then what does it say about the long side

[timber hatch]

That it is different?

[timid silo]

yes by how much

[timber hatch]

5m

[timid silo]

so how would you represent the long side in terms of x

[timber hatch]

84m^2 - X - 5 = long side?

[timid silo]

since the
short side = x

then
long side = short side + 5m = x + 5

[timber hatch]

Oh right

[timid silo]

now how do you calculate the area of a rectangle

[timber hatch]

L x b

[timid silo]

okay so what would the area of the rectangle be in this problem

[timber hatch]

84m^2 = x + 5m + x?

[timid silo]

hmmm not quite

it should be *

[timber hatch]

Wdym?

[timid silo]

84 = L * b = (x + 5) * x

multiply

[timber hatch]

Ohhh right

[timid silo]

now you have (x + 5) * x = 84

[timber hatch]

But instead of writing short side do you write x

[timid silo]

wym?

[timber hatch]

Wait I’ll write it out

Nvm in the equation should I just use x?

To represent the short side

[timid silo]

sure

and since u have (x+5)*x = 84

u solve this quadratic equation

x^2 + 5x - 84 = 0

[timber hatch]

Yeah

Sorry I don’t know what to do from there

[timid silo]

do u know the quadratic formula

[timber hatch]

No sorry

[timid silo]

okay so lets say u have an equation ax^2+bx+c=0

then $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

[warm shale]

Jester

[timber hatch]

Ok

[timid silo]

so what are a, b, c in our problem

[timber hatch]

Length, breath and area?

[timid silo]

no in x^2+5x-84=0

[timber hatch]

Oh right

Yeah sorry I don’t know

[timid silo]

so a = 1 b = 5 c= -84

ax^2+bx+c=0

x^2+5x-84=0

[timid silo]

so u plug in the a, b, c here to find x

[timber hatch]

Ok

In the quadratic formula?

Ok

I’ll work it out hol on

Hold

How do you know if it’s plus or minus?

[timid silo]

they are both plausible

u mean $\pm$

[warm shale]

Jester

[timber hatch]

Yeah

[timid silo]

yeah there are two x's

x1 and x2

[timber hatch]

Ohhhhh

-12

7

[timid silo]

now x cant be -12

because its a side

so u take 7

x = 7

[timber hatch]

Ok

[timid silo]

now what is the long side

[timber hatch]

x + 5 / 7 + 5

[timid silo]

yes

[timber hatch]

12

[timid silo]

which is 12

[timber hatch]

Yeah

[timid silo]

and thats it

lets check

[timber hatch]

Oh

[timid silo]

7 and 12 differ by 5

and the area is 7 * 12 = 84

[timber hatch]

Oh right

[timid silo]

alternatively u couldve guessed 7 and 12 but i thnk ur teacher wont accept it

[timber hatch]

So now I have to show it

I’m working

In

Oh right ok thanks so much

How do I leave this channel

[kind hawk]

write .close

[timid silo]

.close

[obtuse pebble]

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[leaden shoal]

what next to solve for a,b and c?

[leaden shoal]

help

[noble dust]

Maybe we can divide by c-a and b-a and b-c and then equate pairs of equations to get three simpler equations

@leaden shoal

[timid silo]

from 12 u get 3

so i think 3 wont help

[noble dust]

We can divide by c-a because of a=c then the first and second equation will be the same but 7 is not equal to 13

[noble dust]

Oh okay

[leaden shoal]

hmm how?

[noble dust]

16(c-a)=12(b-a) which gives 4c=3b+a and the others will give you similar equations and so you might be able to use that

12(b-c)=4(c-a) giving a+3b=4c

Oh I was wrong

[leaden shoal]

?

[noble dust]

Sorry about that

[leaden shoal]

its fine

[noble dust]

I'm not sure about this, maybe someone else can help

[leaden shoal]

ok

[obtuse pebble]

@leaden shoal Has your question been resolved?

[obtuse pebble]

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[timid silo]

what

[restive ridge]

"it's arithmetic by its definition"

lol

[timid silo]

yeah

[restive ridge]

that's like saying

"let a = b, prove that a = b"

[pine sail]

Didn't we do something very similar just a moment ago?

[pine sail]

Exactly.

[harsh lantern]

prove that a = a

[pine sail]

If each term can be written as previous term plus some constant, then it's arithmetic already.

[solar trellis]

They probably require you to show that x_n+1 - x_n = constant for all n

[heavy summit]

yeah

[heavy summit]

^^

[pine sail]

Then do it. Smh.

That is what we did earlier anyways.

[heavy summit]

.close

[obtuse pebble]

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[short lily]

hi, i want make sure if i underestand it right that wang tiles will give never repeating pattern

[short lily]

https://demonstrations.wolfram.com/MakingPatternsWithWangTiles/

[short lily]

here are showcase pics

[short lily]

so basically its infinite pattern that will never repeat

yes?

[obtuse pebble]

@short lily Has your question been resolved?

[obtuse pebble]

@short lily Has your question been resolved?

[obtuse pebble]

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[graceful bone]

I'm not sure how to calculate the curl for this

I've never seen a problem structured like this

[tardy epoch]

https://math.stackexchange.com/questions/836041/curl-of-cross-product-of-two-vectors

[graceful bone]

hmmm

We haven't seen anything like this formula...

plus I'm not sure what I woudl even do since I'm not given r

[gloomy valve]

alternatively, evaluate the cross product first and then do your usual curl

r = (x, y, z)

[graceful bone]

How do you come to this conclusion?

[gloomy valve]

r is usually the position vector (x, y, z)

convention

[graceful bone]

oh, really? we always use r as the name of our parameterization, but I've never seen it default to <x,y,z>

[gloomy valve]

as a scalar parameter or as a vector?

[graceful bone]

as a vector

parameterizeing a surface

[gloomy valve]

something like r(t) = (x(t), y(t), z(t))?

for a surface you only need 2 scalars u, v to parameterize it

[graceful bone]

so I should take curl(<cos(t),sin(t),0>X<x(t),y(t),z(t)>)?

[gloomy valve]

im pretty sure thats what they mean here, yes

[graceful bone]

awesome, I will give that a try, thank you!

is this what you would expect for the cross product?

I'm not sure how to differentiate these...

do I get rid of the t's in r?

I don't know why this thing is throwing me off so much

[tardy epoch]

Because you wrote F = (cos(t), sin(t), 0)

that's not F

F is the resulting cross product

[graceful bone]

oh right right

this seem right? now curl(F), yea?

[tardy epoch]

assuming your cross product is right yea

[graceful bone]

hmm, well I'm getting <0,0,0> for the curl.... and the homework site is saying that's not right

oh wait, nvm one sec...

ok, yea I'm still stuck... It looks to me like the curl should be <2cos(t),2sin(t),0>

figured it out! the given vector is <0,cos(t),sin(t)>

should have read my unit vectors better

thanks y'all!

.close

[obtuse pebble]

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[gentle kayak]

helppls

[gentle kayak]

longest chord is the diameter

aka 50

and idk how to find the shortest chord

[knotty crow]

consider this one

[gentle kayak]

but

i can find shorter chords tho

like thathow do i find the length of the chord tho

[knotty crow]

but it need to pass through P

so?

[gentle kayak]

OH

its

50-15 = 25

wait

i meant 35

typo

typo

[gentle kayak]

is it 35

[knotty crow]

no, why?

[gentle kayak]

bcz longest WAIT

it said

LONGEST PASSING THRU P

i sped ;-;

[knotty crow]

longest passing through P is the diameter, as you said

[gentle kayak]

and thats 50

cuz the radius= 25

wait

im stupid

ITS IN THE THING

its 15 ;-;

wait

it cant be THAT easy

[knotty crow]

find length of the blue chord I've mentioned

can you?

[short lily]

.reopen

[gentle kayak]

wait

um

[short lily]

cant just someone tell me

[short lily]

you, do you know?

[gentle kayak]

how do i find the length of the chord

[gentle kayak]

know what?

[short lily]

if wang tiles are infinite and never repeating pattern

[knotty crow]

consider right triangle

[gentle kayak]

um

[knotty crow]

whose hypotenuse is the radius

[gentle kayak]

like this?

[knotty crow]

nop

[gentle kayak]

so how do i draw it

im confused; -;

[knotty crow]

find leg at the top then take it twice to get the chord's length

I guess you know Pythagorean Theorem

[gentle kayak]

YEA

um

[thick oracle]

Hi

[gentle kayak]

wait

OH THATS HTE

SO

OHHH

i got it

thanks

HI MASTER OOGWAY

ITS 10

I GOT 40

FOR THE CHORD LENGTH

[knotty crow]

yes

it's right

[gentle kayak]

i took notes

help with that

i confused

i put 180 its wrong

idk why

[thick oracle]

That triangle doesnt seem equilateral at all

Oh

Its abc

[gentle kayak]

ya

[thick oracle]

Ok

Where does E come from?

[gentle kayak]

idk

[hexed agate]

What is circle F?

[thick oracle]

The name of the circle

Try to calculate every angle you can

[gentle kayak]

im so cofnused

[thick oracle]

Why

Arc bed cant be 180

Cuz bd isnt diameter

[gentle kayak]

OH

THATS WHY

so how do i find it

[thick oracle]

.

Write them on the photo please

So i can help you

[gentle kayak]

i was in restroom sorry

all ik

[thick oracle]

Read the first 5 words

Of the problem

[gentle kayak]

wait

SO ITS

60

60

60

that took alot of itme

[thick oracle]

Oh yeah thats smart

Now

What is angle acd?

[gentle kayak]

120

[thick oracle]

Good

Now

What is arc acd?

Wait

[gentle kayak]

120

[thick oracle]

No

[gentle kayak]

????????????

[thick oracle]

Cuz C isnt the centre

[gentle kayak]

oh

what does Collinear mean

[thick oracle]

On the same line

[gentle kayak]

ok

wait

i can find arc BD and subtract it from 360

i meant BAD

[thick oracle]

To get what,

Wait a sec

Nevermind

[gentle kayak]

so how i solve it

[thick oracle]

We need to think more

Take every word

And write as much info as we can out of it

[gentle kayak]

master Oogway

i have to go

could u dm me ur way or solving it and the answer pls

thanks

[thick oracle]

I'll send it if i will be able to solve it

Bye

[obtuse pebble]

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[knotty crow]

What's your problem?

I mean what you're asking about

[strong tendon]

how do i find the midpoint of a vertex?

i think that's what the question is asking me to find but i'm not sure

[knotty crow]

of the vertices

I guess question is asking about the midpoint of the segment created by vertices of the given parabolas

[strong tendon]

i graphed the 2 parabolas but they don't make contact how will i find what it is asking for?

[knotty crow]

Can you find the vertices?

[strong tendon]

how do i do that?

[knotty crow]

you can use graph you've just done or the formulas (analytic way)

[strong tendon]

i'm not sure i understand what you mean

cuz i thought vertices were only for shapes

[knotty crow]

first one has been already given in vertex form

[strong tendon]

so do i make the other equation into vertex form?

[knotty crow]

you can but I'd use other property

which says arithmetic mean of roots is axis of symmetry (x-coordinate of vertex)

in this case roots are x = - 14 and x = - 10

mean is (-14-10)/2 = -12

y(-12) gives y-coordinate

[strong tendon]

but how would i find the midpoint of the vertices?

[knotty crow]

can't you find the midpoint of two points?

[strong tendon]

do i need to find the midpoint of the x's and y's

[knotty crow]

yes, basically this is what midpoint formula says

[strong tendon]

oh ok i think i understand a bit

so i just need to find the aos and vertex and then i need to use the 2 vertex's x1 and x2 and y1 and y2 to find the midpoint so then i get my final point that the problem is looking for?

[obtuse pebble]

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[strong tendon]

.close

[obtuse pebble]

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[graceful bone]

I got this right, but I don't totally understand

I thought curl=0 => grad

and I'm not sure what the "curl test" even is

[tardy epoch]

what does your textbook say the curl test is

[graceful bone]

we don't have a textbook

[tardy epoch]

notes then

[graceful bone]

I'm pretty sure we haven't covered it.

[tardy epoch]

or look here to see what it could be
https://tutorial.math.lamar.edu/classes/calciii/curldivergence.aspx

[graceful bone]

there's no "curl test" on that page

and I couldn't find one when I googled it, which is why I asked here.

[tardy epoch]

sounds like it's something your teacher invented then

[graceful bone]

huh

weird

[cedar lichen]

Why are the second two answers not green like the first one

[graceful bone]

not sure, but they are correct.

Just went through all of our class notes and didn't find any "curl test"

[wary vigil]

there is a "curl test" for conservative fields

if the curl of a field is not 0

then the field is not a gradient of a function

and therefore not conservative

but if it is 0

it does not necessarily mean it is conservative

because there are irrotational fields that are not conservative

meaning

$0 = \nabla \cross \vec{F}$ but $\vec{F} \neq \nabla f$

[warm shale]

Katharine

[graceful bone]

So, would the only way to find that this isn't a gradient to be attempting to solve the diff eq for the potential function and deciding you can't find it??

Or is there a better way I'm missing

[wary vigil]

it's very very difficult to know for sure if a field is a gradient of some function unless you can find that function or generate the field from that function

basically if you integrate the gotten field to both x and y

and you can combine them into a single function

as in

f = h(x) + g(y) + constant

then you know for sure it is a gradient field

[graceful bone]

I guess I'm just confused what the point of this exercise is... It really wanted me to try to find the potential function, fail, then decide it wasn't a gradient?

and thank you, btw, for the answer!

[wary vigil]

the second answer contradicts the first in my opinion

because it does satisfy the "curl test"

by giving

$\nabla \cross \vec{B} = \vec{0}$

[warm shale]

Katharine

[wary vigil]

which would be the point of the test in my opinion

to find if the function is definitely not a gradient field

[graceful bone]

interesting. I wonder if this has the wrong option marked as correct, then....

[wary vigil]

because if the curl is not 0 then it is definitely not a gradient field

[cedar lichen]

Maybe it doesn't satisfy the curl test because a curl of 0 is indeterminate as to whether its conservative or not? As in, maybe the test is to check if a vector field isn't conservative, like how the divergence test checks if an infinite sum isn't convergent?

[wary vigil]

yeah but then the third answer doesn't make sense

[graceful bone]

This makes sense to me, though I find it strange that this popped up when my prof hasn't even mentioned any "curl test" at all.

[wary vigil]

because the third says it is not a gradient field

but if it fails to give a definite answer

it means it could be a gradient field or not

curl being 0

means it could be a gradient field but it is not guarranteed

it's called a necessary condition

a gradient field necessarily requires the curl to be 0

but the other way around is not necessary

a curl of 0 is not necessarily a gradient field

i would try to ask for clarification from your professor

[graceful bone]

I definitely will. Thank you again.

.close

[obtuse pebble]

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[dawn sonnet]

Could you help me solve this

[dawn sonnet]

I multiplied the top and bottom by x^2 and got

I dont know how to proceed from here

[heavy thicket]

Factor the denominator first

[graceful bone]

I'm not a helper, but you should plug infinity into those and see what happens

[heavy thicket]

Wait a second

This is infinite limit

[dawn sonnet]

yea

[long peak]

If you've got an infinite limit it would probably be easier to show that a function less than or equal to that diverges to infinity

which would let you consider just replacing the denominator with 2

[dawn sonnet]

I simplified till here

[graceful bone]

perfect, now plug in infinity

inf-3 is essentially inf

[dawn sonnet]

if i plug in infinity i get inifinity

[graceful bone]

yup

the function diverges

[dawn sonnet]

Ohh

well then thanks

[graceful bone]

np, I was just still in here from getting help before you lol

[dawn sonnet]

lool

.close

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[dusk fox]

For this do i have to find the equation of line Aand B

and after thatmake a perpendciualr line from D touching to the line AB?

[turbid sail]

Yes

[dusk fox]

is that the actual fastest way of finding the shortest distance

[turbid sail]

Is this a intro linear alg class

I’m assuming?

[dusk fox]

yes

[turbid sail]

Or high school

[dusk fox]

like 10thgrade

or ages of 15 years olds

[turbid sail]

I mean the shortest distance will be the line perpendicular to that line and the point

[dusk fox]

like this

and where the point meets is the shortest distcance

[turbid sail]

Yes the length of that

Is the shortest distance

[dusk fox]

and then i will have to find the distcance from point D to the intersecting point?

point D is (11,3) and (9,7)

now where i am stuck is how will i find the distcace betwwen those 2 points

[turbid sail]

Pythargorean theorem

[dusk fox]

oh really

[turbid sail]

I gotta head out I’ll be back in 30 if no one else can help ya

[dusk fox]

😦

[turbid sail]

Yeah look up formula for length

Oh a line

Of

[dusk fox]

the lines arent even straight how can i find the lenght

[turbid sail]

They are straight

It’s linear

I’ll be back sorry I gotta go

[dusk fox]

ok

<@&286206848099549185>

.close

[obtuse pebble]

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[fickle tangle]

Hi

[fickle tangle]

Does anyone have any idea what series could represent { 1473, 1376, 984, 480 }?

I'm lost trying to figure out a function that could represent it

Or, if that's not possible, does anyone know what function represents { 1473, 1376, 492, 80 }

[shadow jewel]

they could be a domain and range

[heavy thicket]

It’s a sequence

[shadow jewel]

oh

[fickle tangle]

^

[heavy thicket]

The objective is to find a pattern

[fickle tangle]

Yes

[heavy thicket]

What have you tried

[fickle tangle]

This is a Taylor series for context, but I can handle the rest once I figure out the pattern of a sub n

[heavy thicket]

Oh

[fickle tangle]

Well I just solved out the first 4 terms of the taylor series of f(x) = x^5 + 4x^3 + x centered at a = 4

Now I just have to find this a sub n pattern

[heavy thicket]

Idk Taylor series

[fickle tangle]

Ah, thanks for the help still.

[heavy thicket]

👍🏼

[fickle tangle]

🤔 Anyone else got an idea?

...

.close

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[maiden swift]

about part b.

[heavy thicket]

Set x equal to 0 and 10

Then find the y values

Then you can use change in y/change in x

[maiden swift]

this is just for part b?

[heavy thicket]

A

[maiden swift]

oh im good for part a

its aprt b

[heavy thicket]

You need B

Just explain in words

[maiden swift]

yes

[heavy thicket]

For every minute, there will be an average of x bacteria added to the alive list

[maiden swift]

but what does tyhe (a)'s sign + or - do to this questiuon

[heavy thicket]

• is increase - is decrease

[maiden swift]

so our a value will increase the amount over of bacteria removed by the substance

[heavy thicket]

I think so

On average New bacteria

Not sure though

[maiden swift]

hows this looking for a

[obtuse pebble]

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[tardy epoch]

Explain what

What even is the original question

[stone leaf]

So x is any value from 2-6.
If you take yhe equation and replace "x" with the x value you can solve the equation and get the y-value.
So let's use 6 as an example here:
If you replace "x" with "6" in the equation you get y=4
So on the graph where the x-value is 6, the y-value will be 4

You're essentially asked to then take all points on the graph using the limited possible x-values. That will draw the curve shown above.

The range would be numbers including and between the largest and smallest possible y-values you get from the limited possible x-values

Lowest point on the graph is when x=3
The equation solves to y=-5
Highest y is 4, lowest y is -5
Range for those x values is -5<=y<=4

That help at all?

Awesome! Use the .close command if that's all, then!

[timid silo]

Hello

Muplicative inverse of 1/-18-34i

Dat minus on 18 will it change

When we rationalise

?

Oh shit

It's occuppief

[stone leaf]

Hey sorry I'm back now

Yeah pretty much! The question just asked for the range.
Range is what values y can be

Excluding more advanced stuff that's going to mean "what is the highest y value and what is the lowest y value" and then the range is every number between and including the highest and lowest

So if you say that
Y is greater than or equal to -5
And also y is less than or equal to 4
You're covering every value between -5 and 4

So 2,-4 is in there already

No, they took the equation and replaced "x" with "6"

[fierce lagoon]

The 4 is the maximum output on the domain

If the domain is $\left{x\in\bR | x\in[a, b]\right}$, then the range is \left{y\in\bR | \min_{x\in [a, b]}f(x) \leq y \leq \max_{x\in [a, b]}f(x)\right}$

[warm shale]

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

[fierce lagoon]

And all that's saying is that the range is the lowest output on that domain to the greatest output on that same domain

That is, the input and output are real numbers and don't deal with complex numbers and shit like that

So for this, the minimum for $f(x), x\in [0, 5]$ is -5; the maximum is 4. So the range is $-5 \leq y \leq 4$

[warm shale]

Umbraleviathan

[fierce lagoon]

minimum to maximum outputs

That's the range

[obtuse pebble]

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[delicate lion]

Question: we write gradient of the cost function of machine learning in vertical, not in horizontal? or (2 x L)? What is the meaning of writing gradient components in vertical order? thank you

[brave bramble]

None

Write it horizontally if you want to

Like, if x is vertical, and A is a matrix, then Ax makes sense

But if x is horizontal, you'd do xA instead.

Mind you, that's also just a convention. You could swap it and life would go on. You'd probably confuse many ML teachers though.

Markov Chains do vectors horizontally, so it is done somewhere.

@delicate lion

[delicate lion]

I revised linear algebra a while ago, and in linear algebra, horizontal has "span" or "dimension" meaning

do we need to think of the components of gradient has some dimensions?

[obtuse pebble]

@delicate lion Has your question been resolved?

[brave bramble]

You're misremembering.

[brave bramble]

Hmm?

[obtuse pebble]

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[night dew]

Am i solving it right?

[obtuse pebble]

@night dew Has your question been resolved?

[obtuse pebble]

@night dew Has your question been resolved?

[night dew]

<@&286206848099549185>

[timid silo]

why are you diving by powers of 10 in the first line of working?

second line looks fine though

,w sum 7*(sum 1/10^j from j=1 to i) from i=1 to 20

[warm shale]

Results provided by WolframAlpha

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

Requested by Toby#2275

[timid silo]

,w (7/81)(179+10^-20)

[warm shale]

Results provided by WolframAlpha

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

Requested by Toby#2275

[timid silo]

your answer is correct

[obtuse pebble]

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[night dew]

Ooh tnq

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[timid silo]

I dont really know where to start with the following:

Let X, Y be two random variables with Y > 0. Compute the pdf for X/Y in terms of the joint density function fX,Y (x, y).

[solar trellis]

let Z = X/Y

Z is a rv

find the cdf of Z

[timid silo]

I think im still a little lost

Im unsure about how to express the cdf of Z and then to put it in terms of the joint pdf

[solar trellis]

$F_Z(z) = \mathbb{P}(Z\le z) = \mathbb{P}(X/Y\le z)$

[warm shale]

giannis_money

[solar trellis]

think about how the set ${ (x,y) : x/y \le z}$ looks like in the $x-y$ plane

[warm shale]

giannis_money

[obtuse pebble]

@timid silo Has your question been resolved?

[solar trellis]

call this set A

[solar trellis]

then this

$= \mathbb{P}((X,Y)\in A) = \iint_A f_{X,Y}(x,y) \dd{x}\dd{y}$

[warm shale]

giannis_money

[obtuse pebble]

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[unique vessel]

Can someone clarify if I'm doing this correct?

[warm canopy]

all checks out

if you can use desmos, you can check this by graphing the two functions and seeing if they're the same (thats what i just did to check, but remember to convert to radians)

[rose oyster]

is this 10th grade

?

[obtuse pebble]

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[timid silo]

Hello there is a transition out lecturer did wheb he wanted to know if this set is independant or no {u-v+w,v-2w,u+w}
Where you do linear combination
a(u-v+w) + b(v-2w) + c(u+w) =0

[timid silo]

But then he did the transition

u(a+c) + v(-a+b) +w(a-2b+c)=0

Why did he do that

[warm canopy]

you were probably told that {u,v,w} are independent

[timid silo]

Yes

[warm canopy]

so hes rearranged it so that you just have u,v,w and coefficients

bc u,v,w being independent tells you something about an equation like that

[timid silo]

He wants these scalars here

To be 0

AHHHHHH

Thats why

[warm canopy]

right because u,v,w are indep, you know a+c=0, b-a=0... etc

this will lead you to conclude a,b,c are all 0

[timid silo]

Yess

And they are

I did matrix

What if we wanted to know if the set {u+v,v+w,w+u,u+v+w}

Spans R^4

We just equal it to (a,b,c,d)

?

And if there is solution then it spans it

[warm canopy]

you can do that, or you can also test for linear independence again, because you have a maximal list of vectors, if its LI, then it spans

3 LI vectors in R^3 span R^3

[timid silo]

They are independant

[warm canopy]

4 LI vectors in R^4 span R^4

[timid silo]

If they are independant i just do that right?

[warm canopy]

if you can show they are independent, then this implies they are spanning, because maximal independent sets are spanning

[timid silo]

@warm canopy sorry for the ping
And thank you ❤️🙌

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[obtuse pebble]

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[peak hamlet]

Is Q3 trial and error?

[high lily]

no

set up an equation; applying the formula for area and solve for x

[peak hamlet]

1/2 (17)(x)(sin 68)

7.88x=150

150/7.88 = x

X=19

Or 19.04 without rounding

[peak hamlet]

I don’t know why I didn’t think to use the original formula

Thanks

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[crisp dune]

How do I find area of shaded region here?

[trail musk]

Integrate

[heavy thicket]

Have you tried definite integrals

[crisp dune]

I have but I’m failing to do it properly

[heavy thicket]

What have you got so far

[crisp dune]

Well from 0.356 and 1

I integrated the red function

And tried subtracting that by integral from 0 to 1 for blue function

Idk if that’s right so far

And then

From 0 to 0.356 for red function

And basically multiplied all of this by 2 because functions are symmetrical

[trail musk]

Nope

[heavy thicket]

What about -1 to 0

Forgot that?

[trail musk]

Just integrate (red-blue) over the intersection points

[crisp dune]

Doesn’t that answer the -1 to 0?

[crisp dune]

Could u write it out?

U*

[crisp dune]

Yeah so *2 because symmetry?

[heavy thicket]

Of course

[trail musk]

You're making this way too complicated lmao

$\int_a^b$ (red - blue)

[warm shale]

Mr. Gamer

[trail musk]

Where a and b are the points of intersection

[crisp dune]

But the question is, is my working out correct?

[trail musk]

I'm not sure your signs are correct

You need the magnitude of the area

[crisp dune]

Ok

[trail musk]

Not the signed area

[obtuse pebble]

@crisp dune Has your question been resolved?

[obtuse pebble]

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[stiff grove]

what is the difference between the average rate of change
(AROC) and instantaneous rate of change (IROC)?

[cedar lichen]

Average rate of change is the average change over some interval, while instantaneous rate of change is the change at a precise instant of time

[stiff grove]

can I say that AROC is the average change inside a range of values, while IROC is the instant change at a certain value?

[void pelican]

yes

[stiff grove]

great thx

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[stiff grove]

.reopen

[obtuse pebble]

✅

[stiff grove]

can someone help me determine this equation?

.close

[obtuse pebble]

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[undone marlin]

hi can someone hit me with a representing periodic behaviour with sinusoidal functions question and then slide me the answer IN SPOILERS ||so like this||

[undone marlin]

that way i wont see it

actually ill just google problems related to my question i guess

thanks

¯_(ツ)_/¯

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[lofty whale]

Which graph would it be 🤔

Vertices (+-2,0), foci (+-3,0)

[obtuse pebble]

@lofty whale Has your question been resolved?

[lofty whale]

<@&286206848099549185>

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[plush valley]

guys how can i rotate a parabola?

[plush valley]

$\y =frac{x^{2}}{90}

[warm canopy]

https://www.youtube.com/watch?v=BPgq2AudoEo

[plush valley]

thx

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[elfin tangle]

How would I even start this?

[warm canopy]

what is the biggest value that sin can take?

[lusty cedar]

and the lowest as well, basically you need the bounds for the first one

[elfin tangle]

idk how to get that lol

[warm canopy]

think/look at the graph of sin(x)

[elfin tangle]

ok

isnt it

12 and -12

[warm canopy]

thats the max and min of 12sin[30(t-5)] yes

becuase the max and min of sin(t) is 1 and -1

[elfin tangle]

yex

ohh

[elfin tangle]

i need to

+14

[lusty cedar]

for reference

[elfin tangle]

max is 26

min is 2

[lusty cedar]

exactly

[elfin tangle]

so then what?

[lusty cedar]

what do you think about period?

you did this one right

you might be able to do that one as well

[elfin tangle]

i mean when i put it in desmos it glitches out

so i cant really find period

[lusty cedar]

don't plug in entire functions

try sin(2x) and sin(3x) and so on and try to figure out what it should be

[elfin tangle]

wdym

[lusty cedar]

try plotting them

notice that there is a pattern

[lusty cedar]

in fact you can do that without plotting

sin(2x)=sin(2x+2pi)

sin(2x)=sin(2(x+pi))

so it will repeat in pi

[elfin tangle]

yes

[lusty cedar]

so what do you think about sin(30x)?

[elfin tangle]

its really compressed

[lusty cedar]

so?

can still be figured out

[elfin tangle]

how

[lusty cedar]

don't need to use desmos

[elfin tangle]

why

[lusty cedar]

sin(3x)=sin(3x+2pi)

[elfin tangle]

i have to graph it at 24 hours

[lusty cedar]

sin(3x)=sin(3(x+2pi/3))

[elfin tangle]

wha

[lusty cedar]

please tell me you noticed the pattern

[elfin tangle]

i did on the graph

[lusty cedar]

hmm

and?

[elfin tangle]

but idk what to do with it

[lusty cedar]

SHM?

[warm canopy]

go elsewhere

[lusty cedar]

do you know what a SHM is?

[elfin tangle]

no, what is it?