help-27

[woven radish]

y0shi

[stable storm]

cubroot of both sides give you 9

[lament raven]

i see my mistake

yea it all makes sense now

brain just tired from hours of math lol thanks a lot for the help

[stable storm]

ywyw

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[tame palm]

Could they make that question any more complicated? 😖

[runic reef]

We are getting into integrals

So we know LRAM, MRAM, and RRAM

Oh, it's due Feb 5

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[proper relic]

I'm assuming the curve is a semi-circle

And that the line is tangent to the curve

[lavish tinsel]

yes

it is

[lavish tinsel]

mhm

[proper relic]

Construct a line from the midpoint of the bottom side to the intersection of the curve and the line

The length of this line is 2

[lavish tinsel]

yes

[proper relic]

Now, using trigonometry, determine the distance from the midpoint of the bottom side to the top-right corner

Pythagoras' theorem

Label this side c, the radius line b, and the line segment from the intection to the top corner a

[lavish tinsel]

does x=1 ?

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[devout snow]

@glacial python Has your question been resolved?

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[cyan axle]

I need help finding that angle

[cyan axle]

Like

That ain’t a right triangle no more

[long pasture]

which angle lol

there are so many angles

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[midnight terrace]

how do ya find the vertical one

if its solve for x on the bottom

help :D..

[long pasture]

did you simplify the expression first?

[midnight terrace]

illlll do that now

(x-4)/-1(4x-1)

[long pasture]

good good

now with that, the vertical asymptote would be when 4x-1=0

[midnight terrace]

1/4 RAHHHHHH

ty

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[restive river]

questio 14 pls

[devout snow]

Please don't occupy multiple help channels.

[supple knot]

!1c

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Please stick to your channel.

[supple knot]

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[mellow cairn]

can someone explain these two statements? not sure how they end up with the equivalence to the former, -sin(t), and the latter -cos(t)

[weak cove]

those are just basic trig identities

[mellow cairn]

oh

nice

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[jolly lark]

2/x - 3/2x = 4

i know how to do it if the denominator is a number but this time it's switched around and i don't know how to solve it

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[agile trail]

I need to find e^(At)
I think the eigenvalue is -2 with AM of 3 and its eigenspace is (1 0 0) with GM of 1

[agile trail]

Is Jordan Normal the way I would solve this?
If so, how because I keep getting stuck

[sand dove]

yeah A will be similar to Diag(-2,-2,-2) + E_{1,2} + E_{2,3} and it's really the only place to go to

[agile trail]

yes, sorry I should have been more specific. To find e^(At) I need to find A=P J P^(-1)
It is the finding P I am struggling with

[sand dove]

P is a matrix of generalized eigenvectors, so given e1 = (1,0,0), you want to find e2 such that Ae2 = -2e2 + e1

and then e3 such that Ae3 = -2e3 + e2

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@agile trail Has your question been resolved?

[agile trail]

what do this calculations come from? don't think I've seen them before

[sand dove]

let's let J = Diag(-2,-2,-2) + E_{1,2} + E_{2,3}

you want A = PJ P^-1

So PA = PJ

so writing P = (f1 f2 f3)

[sand dove]

Nvm I'm being dumb I made a mistake here

AP = PJ

so Af1 = ...

Af2 = ...

and Af3 = ...

[sand dove]

If you want to convince yourself that this is true, might as well write what AP = JP means

[agile trail]

wouldn't it be AP=PJ?

[sand dove]

Yes exactly sorry

And f3 corresponds to e1

f2 to e2

and f1 to e3

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[autumn pendant]

This was on my 10th grade math exam. Do note that I don't remember the exact measures that was on the test so this remains an example, but the right call for action was to put both equations to the square and then substract to find a second degree polynomial equation that represents the coloured area. I then proceeded to solve for X whereas we weren't supposed to but I can't understand for the life of me why we dont solve for X here when we can find the measure

[autumn pendant]

Is it possible to find a value for X

[neat solstice]

well

we are given two lengths

and we calculate the area

so the shaded area depends on x

to solve for x, we would have to know that shaded area

which we don't

[autumn pendant]

right

but what if we took that second degree polynomial

moved it to the right of the equation

and put 2x-1 and x+2 to the left of the equation

then algebraicaly solvd it?

[neat solstice]

with "that second degree polynomial", you mean the polynomial that gives the area?

[autumn pendant]

yes

lemme spare you the math and get it

[autumn pendant]

ok

there

right

[neat solstice]

ah so you wanna solve this here?

[autumn pendant]

yes

[neat solstice]

well

you see

we took the stuff on the left

and symplified it

which got us the stuff on the right

[autumn pendant]

i do notice that yes

[neat solstice]

we didn't put any more information in there

so we can't get anything out of it

it is pretty much the same thing

[autumn pendant]

ok

right

makes sense

[neat solstice]

so if you would try to solve for x, you would just end up with 0=0

[autumn pendant]

ok

alright but i dont get why

we cant take the simplified equation

and just use quadratic formula

what do the roots of that equation represent in that case

if its not X

[neat solstice]

pretty much like this:
look at the term x^2+2x+1
we can rewrite this to be (x+1)^2
they are the same however, they mean the exact same thing
so if we try to solve, we would get:
(x+1)^2=x^2+2x+1 |get rid of brackets
x^2+2x+1=x^2+2x+1
0=0

[autumn pendant]

thats a good

explanation now i understand why we couldnt do that

[neat solstice]

roots are x values for which a function is 0
so in this case, f(x)=0 means that the shaded area doesnt exist / is 0

[autumn pendant]

ohh ok

i get it now

thaks

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[wise stirrup]

what do I do here, I'm confused whether this is a question about limits, I don't understand this question in general, thank you! (Calculus/Basic Calculus)

[neat solstice]

it helps to factorize the polynomial in the numerator

[wise stirrup]

what am I finding exactly?

[glass hatch]

hey may i chime in

[wise stirrup]

for sure

[glass hatch]

so that polynomial in that numerator

[neat solstice]

a polynomial of degree n with n roots can be expressed as (x-a1)(x-a2)...(x-an)

[glass hatch]

is factorable by (x+1)

so i think they cancel out or smthn?

[wise stirrup]

hmm okay, the answer said by my teacher is -1, how did it get to that?

[glass hatch]

o

thats impossible

thats dividing by 0

[oblique gale]

X + 1 = 0

You get the domain

That "x= -1"

Wait ywhT

[glass hatch]

i think its 4 above

excluding 4

[wise stirrup]

okay so apparently she said "real numbers greater than 4, excluding -1"

[glass hatch]

yeah thats correct

but why excluding -1

[wise stirrup]

I don't understand this equation as the symbols are confusing me but here's how
"simplify the function. The numerator (x^2 - 3x - 4) can be factored to ((x - 4)(x + 1)). So, the function simplifies to (f(x) = x - 4) when (x \neq -1).

Now, we solve the inequality (x - 4 > 0), which gives us (x > 4).

So, the function (f(x) = \frac{x^2 - 3x - 4}{x + 1}) has a positive y-value for (x > 4). Please note that (x \neq -1) because the original function is undefined at (x = -1)."

[glass hatch]

yeah its true

but she already eliminated

-1 from x > 4

so its redundant

[wise stirrup]

yeah, I'll just ask her about that, thank you guys!

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[small urchin]

How can I, in the Weierstrass theorem, state that there exists a sequence xn of points of [a,b] such that the function calculated in xn : f(xn) tends to its upper limit?

[small urchin]

so lim n->infinity f(xn) = M (sup f [a,b])

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@small urchin Has your question been resolved?

[small urchin]

<@&286206848099549185>

[sand dove]

use the definition of the supremum

Let f([a,b]) = {f(x), x in [a,b]}

if f is upper bounded in R, the sup exists

and by definition there is a sequence that converges to the sup

[small urchin]

for now i have M=supf = sup {f(x):x ∈ [a,b]}

[sand dove]

Can't you use this property?

[small urchin]

no

[sand dove]

what's your definition of supremum

[small urchin]

which is the least of the majorities

but in this case I think it is the maximum value of x, that is, the maximum value assumed by f(x), right?

[sand dove]

the point is you don't know if it's a maximum or not

you don't know if there exists an x such that f(x) = M

[small urchin]

no

[sand dove]

that's what you want to prove

[small urchin]

I don't know if there is a maximum in [a,b ]

[sand dove]

exactly

[small urchin]

ah ok i mean this

but in this case I think it is the maximum value of x, that is, the maximum value assumed by f(x), right?

[sand dove]

yes, that's what the theorem proves IN THE END

but I'm guessing that you want to PROVE the theorem

[small urchin]

yes

[sand dove]

so you can't use the result that it hasn't proven yet

[small urchin]

but so what is M in this case

[sand dove]

M is the smallest number such that f(x) <= M for all x

[small urchin]

it is like a supremum?

[sand dove]

its the definition of the supremum of f([a,b])

Do you have a chapter in your notebook about supremums?

[small urchin]

yes

[sand dove]

I want to know what properties of the supremums in subsets of R you have

[sand dove]

otherwise I can show you how to prove this

[small urchin]

I hold that the upper bound is the smallest of the majorities, and given every epsilon >0 then M-epsilon<x

so m is the smallest of the majorities

[sand dove]

yes ok, we can use the second statement

Do you agree that given any epsilon > 0, there exists x in [a,b] such that M-espilon < f(x) ?

[small urchin]

but M belongs to the real numbers, or is for example +infinity

[sand dove]

Have you not shown that f is bounded?

[sand dove]

because if you reached that part you should certainly have

[small urchin]

no

[sand dove]

ok.
I have to go but basically show :

• If M is finite, apply that "given any epsilon > 0, there exists x in [a,b] such that M-espilon < f(x)" to epsilon = 1/n (which will give you some x_n) and make n -> infinity
• If M is infinite, show that for all A > 0, there exists x in [a,b] such that f(x) > A. Then apply that property to A = n and make n-> infinity

[small urchin]

ok

thank you so much

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[spark cove]

i have this force field

i nedd to find the circuitation around triangle with vertexes on

in COUNTERCLOCWISE direction

so i foudn the right value which i get -1/3

but how do i decide wether it is -1/3 or +1/3

i know positive orientation is when you move along the border you live the area on your left

but how do i know which is the orientation in this case

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[olive oar]

How would you classify matrices according to their shapes and properties?

[heavy current]

what exactly do you mean?

I don’t ever recall hearing about matrices having “shapes”

“properties” is a bit too vague too

[olive oar]

by shape i mean horizontal, vertical, column and so on

[olive oar]

and by properties i suppose should go diagonal, identity, scalar....

or elements is better word

[heavy current]

There is a vector space consisting of all possible mxn matrices where the elements are taken from the field F (think of R - the real numbers) which I’ll denote M_mn(F)

so any mxn matrix with entries in R belongs to M_mn(R)

is that sufficient in answering your question about classifying matrices based on “shape”?

[heavy current]

I mean, matrices of special forms usually just get their own names

e.g diagonal, upper/lower triangular, etc

[olive oar]

see the thing i dont understand about this is, do we put, for example, diagonal matrix in the same classification as scalar matrix?

like im wondering if there is a specific classification or classifications of matrices

[heavy current]

I mean, all scalar matrices are diagonal, but not all diagonal matrices are scalar matrices

one of them is a subset of the other

[olive oar]

oh wait i writen wrong example

i meant for example horizontal and scalar matrix

could they go in same classification

or nah

[heavy current]

scalar matrices are defined to be square to begin with

So no scalar matrix is horizontal and no horizontal matrix is a scalar matrix

The two sets are entirely disjoint

[olive oar]

oh ok

so we can say that there are two classifications based on so called their shape (horizontal, vertical, column...) and on their elements (scalar, identity, diagonal....)?

[heavy current]

I’ll admit that I’ve never heard of matrices being classified by their shapes

But I guess you can do that?

[olive oar]

yeah idk tbh how its called in english cuz in my language is shape lmao

[heavy current]

I see

[olive oar]

well ill go with that then

ty for help

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[thick meadow]

Sorry, Is there a way to isolate λ, given some r in the vector line formula r = a + λb? <@&286206848099549185>

[teal spindle]

only ping after 15 mins

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[thick meadow]

ohh, sorry, it's my first time asking something

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[thick meadow]

I solved it for my self, sorry

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[heady scroll]

i need help

[heady scroll]

this all i have done

i dont know how to solve for m

@thick meadow

@heavy current

.close

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[heavy current]

Why am I getting pinged lol

[heady scroll]

i thought u help

mb

[heavy current]

I’m not active rn

On a bus

[heady scroll]

oh where to

[heavy current]

home

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[wintry sedge]

I'm not one hundred percent sure of where to start from here. What do I set the integral to? What are my a and b values that i subtract and then divide by 3?

[wintry sedge]

<@&286206848099549185>

[tame palm]

What have you tried so far?

[wintry sedge]

I have thought about setting up the integral from 4.3-5.7, and then using 1.4/3 as my deltax over three

And then going from there

[tame palm]

What is the formula for Simpson's Rule?

Actually, why are you even trying to setup an integral? The question said to use Simpson's Rule. 🤔

[wintry sedge]

Since I needed an a and b, i was setting up an integral out of habit to visualize what delta x would be, haha.

formula for simpsons rule is-

[tame palm]

Do you know how to apply Simpson's Rule with the data given?

[wintry sedge]

Not very well, no- this is the first time I've ever seen a problem like this.

In class we used examples like the one you see on page rn

Is delta x meant to be 1?

[tame palm]

Yes, the problem states the measurements were taken in 1 cm increments.

[wintry sedge]

Oh, ok. I might just be overthinking things then.

Let me try it now..

[wintry sedge]

Does this look correct for my equation set up?

[tame palm]

Looks good.

[wintry sedge]

I put it into the calculator, got 21.03

And it said it was wrong

[tame palm]

Hmm, it's possible you may need to include the ends of the region. Even if they are zero, that will affect the coefficents of the middle data points.

Those ends would be equal to one times zero.

[wintry sedge]

Oh, ok- I’ll try that, thanks!

[wintry sedge]

That was it, thank you very much! I'm surprised that including those ends of the region matters.

[tame palm]

yw

[wintry sedge]

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[visual nest]

Hey I have a test coming up and in the revision practice approx 70% so I just want to clarify a few questions, please help

[visual nest]

Most of the questions i dont know are graphing related

[visual nest]

I was sending them, sorry.

[weak cove]

One question at a time

[visual nest]

Its a lot so even a few is okay

alr

[weak cove]

Also, before asking about a question, attempt the question, if you get stuck, then you can ask and describe what you need help with

[visual nest]

Okay, first this one. I am not sure how to work out the equation of a line

[weak cove]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/v/equation-of-a-line-1

[visual nest]

alr

[visual nest]

So in this question the y intercept is 0

y = mx + 0

[dawn lava]

yes

or just y=mx

where m is the slope

[visual nest]

So is the gradient 1 ?

[winter patrol]

no

note that you're dropping down 2 units
so the "rise" would be -2, not 2

[visual nest]

Ohh rigtht

so -1 ?\

[dawn lava]

if the line goes like this \ it’s negative if it’s like this / it’s positive

[winter patrol]

yes, that will be the gradient

[visual nest]

I see

y = -1x + 0 is my answer then?

[dawn lava]

that would be correct but i would just write y=-x

[visual nest]

its correct thanks

ill try the next on ern

one rn*

How am I supposd to do this?Just the change in y/x right?

[dawn lava]

yes

y intercept is 2

[visual nest]

2/-1 = -2right

[dawn lava]

no it would be a slope of 1/2

delta y/delta x can be remembered as rise over run~how far you rise up and how far you go to the left or right

[visual nest]

Why 1/2 I dont really get it ?

[dawn lava]

the change in y is one the change in x is 2

in other words up one over two

[visual nest]

ohh alr I get it

now this one

so the equation is y = mx + c

And then y = mx + -4

[dawn lava]

you can get rid of the plus

+(-4)=-4

[visual nest]

so 2/1x + -4?

[visual nest]

i dont understand

[dawn lava]

you can write y=mx-4

[visual nest]

oh right

[dawn lava]

but yes that’s the correct slope

[visual nest]

If i were to write 2/1x + -4 tho, would that b considered wrong in a test ?

[dawn lava]

ehh depends on the teacher

[visual nest]

Ah alr gotchu

[dawn lava]

it’s not technically wrong it’s just not necessary

[visual nest]

ah

okok

[dawn lava]

mhm

[visual nest]

I think I get these types of equation problems, what abt this one though? Thanks so much @dawn lava

[dawn lava]

are you asking what the equation of the line is?

if so, it looks like y=-x+4

[visual nest]

Like the question is asking to plot it, but what would they mean by x = -2, to x = 3? Does that just mean plot all the points including and between them ?

[dawn lava]

i’m not really sure what that means tbh

[visual nest]

alr np

Thanks, I think thatll be it then

tysm to the ppl thathelped me

it means a lot : )

.close

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[gusty brook]

hello,

I'm working on a 3d fps camera system for my game which uses 3 3d vectors (up vector, right vector and look vector) to handle camera rotation. I'm currently trying to implement yaw rotation for the camera, for that I created a system which detects mouse movements frequently and after implementing factors like sensitivity, it converts that movement into a small difference in angle. (it's a really small amount)

my question is, what are the ways of utilizing that angle and previous 3d vector to obtain a new 3d vector with the angle rotation applied? and how can I do that?

[timber pebble]

theres a thing called a rotation matrix

,w rotation matrix

[woven radish]

Results provided by WolframAlpha

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

Requested by janniku

[limber atlas]

linear algebra coming in clutch

[timber pebble]

gee, not even close

lemme grab one

theres a bunch of info here

https://austinmorlan.com/posts/rotation_matrices/

[gusty brook]

ah

alright

[timber pebble]

in 2D its pretty straightforward

so you may wanna start there (i think this page does)

3D can take a lil orienting yourself, but you can for sure sort it out

[gusty brook]

yeah but 3d kind of melts my brain lol

i'm using the objects around me to understand it

as drawing 3d is not possible

[timber pebble]

i mean you can just google the formulas but it can be a lil like

it takes just a little time orienting yourself to the coordinate system and what the matrices are doing

so going through a derivation may be helpful

[gusty brook]

would using calculus for something like this be a good approach

[timber pebble]

i dont think its necessary

linear algebra is the tool

[gusty brook]

alright

thanks

[timber pebble]

https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions

you can look here too, but i personally find this page incomprehensible

I'm sure some mix of derivations and videos and working through it on your own will crack the code

[gusty brook]

hmm

[timber pebble]

actually, its not so bad

[gusty brook]

ah

3blue1brown has a video about 3d rotation

ill check that

[timber pebble]

for example

this helpful little graphic

[pulsar sand]

I don't know what you're trying to accomplish exactly, but you typically run into problems using that approach in 3d graphics. Most library implementations use quaternions

[gusty brook]

oh this is what i need

i better understand the logic behind it though

[timber pebble]

If jessicak has experience with graphics id listen to her

ive never actually coded anything 3d

[pulsar sand]

See, this video I didn't actually bother to vet, for example

https://www.youtube.com/watch?v=kB7iE8Udq5g

The TLDR is that you need quaternions to give yourself an extra degree of freedom to prevent your movements from getting stuck when you rotate in such a way that two axis of rotation become linear combinations of each other

[gusty brook]

i get the vectoral parts of quaternions but what's with the scalar part of it

what does it represent

hmm i think i get it

alright thanks!

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[devout snow]

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[potent whale]

Does anyone know why the second to last step becomes the last step?

[tender cobalt]

you can move a ln(1/5) out of the ln which then gets absorbed by the C

[potent whale]

Why does it get absorbed by C

[twilit comet]

bc ln 0.2 is a constant too

it's like c_1 + c_2

that's just c

[potent whale]

Ohhh

[twilit comet]

yep

[zenith vortex]

-ln(5) is absorbed into C

[potent whale]

Why does it become -ln|5|

Should it be ln|1/5|

[zenith vortex]

ln(a/b)=ln(a)-ln(b), and ln|5| is the same as ln(5)

[zenith vortex]

ln(1/5)=-ln(5) too

[potent whale]

Okay I understand

Thank you

[twilit comet]

!done

[devout snow]

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[potent whale]

.close

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[grave ore]

I'm confused about how to graph a piecewise-defined function with three pieces

[winter patrol]

apply the same principles as you would two piece graphs

piecewise defined functions tell you how a function behaves / when

look at the condition to determine which sections of each to use

[grave ore]

if my equation is -x and the condition is if x <= -2

[limber atlas]

Also, just as a tip, give a bit more importance to boundary points

[grave ore]

I just pick an x that fits that conditions and put it into the equation?

[winter patrol]

no

[grave ore]

ye

[winter patrol]

you could consider first drawing
y = -x

then only keep the section where x<=-2

[grave ore]

yea

but I first need to pick an x that is less than or equal to 2 and put it into the equation to get my points right?

[limber atlas]

uh

when someone tells you y=-x

[winter patrol]

not really

[limber atlas]

just imagine a line (for y=-x obviously)

[limber atlas]

and when someone tells you, x is less than or equal to -2

just erase the line "above" -2

[grave ore]

ok i understand

let me graph it rq

@limber atlas @winter patrol how is it

[winter patrol]

your middle piece isn't representative of 6-x^2

[limber atlas]

yes

i thought i read it wrong

[winter patrol]

looks more like an abs val function than a parabola

[limber atlas]

x^2 is like a parabola

-x^2 would be a parabola with its mouth downwards

[grave ore]

oh you guys want me to curve it at the y axis a lil more

i see because it is an upside down parabola

[limber atlas]

no....

thats not how a parabola is

you need to make a parabola

[grave ore]

Better?

[winter patrol]

not really, no

plot more plots in between

[grave ore]

💀

I’m running outta space bru

[twilit comet]

then get more paper

never be a miser for paper when doing maths

[grave ore]

I like to draw tiny graphs

[winter patrol]

your connections are a bit too rigid/direct

the whole section should be a bit more curvy

also what's 6-x^2 when x=2?

[grave ore]

atp i might as well redraw the whole graph cuz yall want every damn point 💀

mb no offense thanks for the help

[limber atlas]

because ur drawing it wrong

like you want the exact graph

[twilit comet]

!vol

[devout snow]

Helpers are just people volunteering their time to help you. Be polite and patient.

[shadow salmon]

hello

[limber atlas]

with every point on x "being on" y

[shadow salmon]

u need help?

[winter patrol]

the more points you have, the better the curve will be

[twilit comet]

@shadow salmon look at pinned messages, his question is there

[winter patrol]

a major issue is that you're implying that when x=2, y=0

[grave ore]

bro is not jinwoo 😭

[grave ore]

true but my professor don't care that much

[limber atlas]

☠️

buddy..

[winter patrol]

doesn't mean that you shouldn't

[limber atlas]

maths isnt something your professor owns

[grave ore]

your right i own maths

[limber atlas]

not even gauss would say this

[grave ore]

this is light work I got some real problems for you guys

[winter patrol]

get good foundations, don't get into bad habits

[grave ore]

I will thanks

it's just midnight and i wanna sleep

[limber atlas]

graph it and go to sleep

[winter patrol]

graphing is a crucial component in maths
future profs/teachers are likely not going to be that forgiving

[limber atlas]

any amateur math enjoyer wont be that forgiving

you cant integrate two shapes if you dont know where they intersect

you wont know the slope if you draw the graph even one unit wrong

[twilit comet]

he's right ^

[grave ore]

Oh wow

[twilit comet]

most of stats, calc, and distributions are based on graphs

[grave ore]

So I’d fail calc

[twilit comet]

calculus.

statistics

[limber atlas]

without graphs? yes

[twilit comet]

and distributions.

they make up your world @grave ore , even if you don't see it

so don't take them lightly

[grave ore]

Man I gotta get thru calc 3 and differentials and linear algebra ☠️

[twilit comet]

okay

so

you really

REALLY

need to get better at graphs

[grave ore]

☠️☠️☠️ bro y’all need to see my professors graphs

Bro does not give a shit

[twilit comet]

@grave ore the fact remains

that you are not going to be in college forever

and your future employer will want graphs.

[grave ore]

Hopefully not

[twilit comet]

even in college, this will not be your professor forever.

so get serious and stop blaming other stuff

[grave ore]

You’re right even though I don’t want it to be true

[twilit comet]

there you go, doing the mature thing

they're really not that hard

[grave ore]

im glad you think that because I've spent my whole day on them

[twilit comet]

it's fine

it happens

go get some rest

[grave ore]

one of them is coded in wrong so I was spending hours trynna figure out what I did wrong

💀

[twilit comet]

💀

[grave ore]

But ye

I’ve only had this happen one other time where I checked the textbook answer and showed the professor and it was wrong

[devout snow]

@grave ore Has your question been resolved?

[grave ore]

Kind of

I still got more

@twilit comet

[twilit comet]

?

[grave ore]

Help me

What the meaning of a price demand function

[twilit comet]

im busy sorry

i cant help

i suggest closing this

and opening another channel

[grave ore]

Ok 👍🏻

[devout snow]

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[jade oak]

Factor out -2/5

[devout snow]

@marble otter Has your question been resolved?

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[heavy terrace]

Just want someone to verify if I'm right

[heavy terrace]

If

but there's injectivity in the function of

it means that |A|=|C|

injectivity is basically for all elements in C there are enough elements in A such so every element in C can be uniquely connected to it

or:

injectivity

but since A⊆C

this means essentially that |A|=|C|

also giving bijectivity for the function

ultimately |A|=|B|=|C|

so we can say for sure that B and C are equal in elements

also for A and B

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[honest thorn]

idk where to start with this abomination

[topaz beacon]

i would start by figuring out the rates of biking and walking

[honest thorn]

Car = 2/3 km/min
Bike = 1/3 km/min
Walking = 1/13 km/min

[topaz beacon]

ok then how long would it take to if he fixed the bike and rode it all the way

[topaz axle]

call distance from home x
you can find the location of the first point by solving (time i = time iii)
time ii = time iii will give you the second point
that's all

[honest thorn]

dont reallly undesrtand?

[honest thorn]

isnt it just 44 mins

24+20 from fixing

[topaz axle]

that would only happen if it breaks when he's at home

otherwise the 24 is a smaller number

[honest thorn]

yeah

[topaz axle]

you can find this time for any distance from home

if you call the distance x you get to write equations

[honest thorn]

x-a+24??

where a is the distance from home

[topaz axle]

what's a

there's no second variable

[honest thorn]

idk

[topaz axle]

@honest thornok suppose x = 2.5

that's distance from home where we stopped because of a flat tyre

how much time to get to work then

(if we choose to bike there)

[honest thorn]

its still 44

you're always biking 24 minutes

no matter where you stop to fix

[topaz axle]

right, because you;re adding the time before break

i mean just the after breaking time

[honest thorn]

55/2 mins

[topaz axle]

no 2.5 is distance

and you didn;t add 20 minutes

oh wait you did

you added 7.5 to 20

@honest thornyeah almost right

we're not going home, we're going the other way

so now you have an expression: (8−x) × 3

[honest thorn]

yeah

wait what

why times 3

nvm

yeah

wait why dont u add

20

[topaz axle]

now there's one x where "walk home" is the same time as "fix bike"

my mistake, also add 20

[honest thorn]

-3x+44 = first one

[topaz axle]

this is the first point they are asking about, on one side of it "walk home" is faster, and on the other fix bike is faster

yep

so one equation with x

and then a different one for the second point

[honest thorn]

?

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[river kettle]

20. Let f(x) = floor(x - 3) and if the interval for x is [-1,0) then what is the corresponding functional value of the function
    What does this mean ?

[river kettle]

How can I use the interval

[crisp trench]

If x in that interval what is the f(x)

Im guessing thats what it means

[river kettle]

Oh shi I just understood it thanks 🙏

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[half wedge]

Hi, can anyone tell me what I did wrong with this matrix question

[devout snow]

Please don't occupy multiple help channels.

[half wedge]

Ill post it question and my answrr

[twilit comet]

,rotate

[twilit comet]

there

[half wedge]

Thanks

[twilit comet]

np

[half wedge]

My answer gives me the right answer for the first two columns, but not the last one when i plug it back in

[twilit comet]

idk matrices i cant help u lol

im just here bc of the incident

sorry

wait 15 m then u can ping helpers

[tame palm]

It looks like you are not reducing the matrix correctly.

[half wedge]

ok, so when I do R2 - R1

[tame palm]

You need to use the entire augmented matrix.

[half wedge]

ok, so also the coefficients?

[tame palm]

Yes.

Also, when you zero out the first column of the second row, divide it by -10 to get 1 as a leading coefficient in the second row.

That's the goal and you should do that as soon as you can.

[half wedge]

but wouldnt that mean that 1 = 1/10

which is awkward to deal with

[tame palm]

-10 * -1/10 = 1

[half wedge]

but for the other numbers in the row

[tame palm]

Yes, it will. That's an unfortunate reality of matrix reduction.

[half wedge]

shouldn't i leave it at 10 then

When I do R3 - 2R2, do i include 2 - 2*-2

[tame palm]

No, because even if you left it as -10, when you start reducing the third row, you will be introducing fractions anyways.

[half wedge]

so i divide the whole matrix by 10

[tame palm]

Just the second row.

[half wedge]

oh ok

[tame palm]

And you divide by -10 to make the leading coefficient 1, not -1.

[half wedge]

do i then procede as normal

[tame palm]

Yes.

[half wedge]

so then I do R3 - 4r2

[tame palm]

What step would you do after this?

[half wedge]

I would do R3 + R1

[tame palm]

👍

[half wedge]

including 2 + 0?

[tame palm]

When you have 1 as the leading coefficient, it makes it easier to eliminate the cells in the rows below the ones.

[tame palm]

Yes.

[half wedge]

then i do R3 - 4R2?

[tame palm]

Yes.

[half wedge]

ok, thanks that makes more sense

[devout snow]

@half wedge Has your question been resolved?

[devout snow]

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[glass hatch]

what

[devout snow]

@restive river Has your question been resolved?

[dry geyser]

.close

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[naive mantle]

This cute limit.

[naive mantle]

!status

[devout snow]

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

[naive mantle]

1. I tried multiplying with ln(2x)/ln(2x) to get 1+2x+x^2 = (1+x)^2, but by trying to find the remarkable limit of ln(1+x)/x, I got into the problem of ln(2*0)

[restive river]

apply l'hopital

[naive mantle]

Not taught

[inland seal]

Take 1/x into the exponent

ln((1 + x)^(1/x))

I believe you should be able to see what to do from here

[naive mantle]

Well this is indeed ln of e, but does it still hold for what I have above?

I'd have ln((1+x^2)^1/x

[inland seal]

Your ln(2x) thing works fine, no?

Wait no

That doesn't work lol

[naive mantle]

Yeah...ln(0).

[inland seal]

No but like

ln(a)ln(b) != ln(a + b)

[naive mantle]

Well, I have 1/ln2x

So it would be....hmmm

[inland seal]

$x\ln(\parens{1 + x^2}^{\frac{1}{x^2}})$

[woven radish]

RedstonePlayz09

[inland seal]

This is your limit

[naive mantle]

Wait, wait..

How?

Ohh...did you multiply with x/x?

[inland seal]

Multiply denominator and numerator by x

Yes

[naive mantle]

Yup, makes total sense now

So it's just 0

That's clever as hell man

Thanks for the solution! Have a great day.

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[inland seal]

Np

[devout snow]

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[uneven spire]

How are you supposed to do this problem

[uneven spire]

Simple u-sub doesn't work bc the 2x+1 ends up on the denominator

Oh shit wait is this integration by parts?

[hybrid ingot]

Find x in terms u and substitute x in

[uneven spire]

Ok wait Im confused

I got x=-1 +/- sqrt(u+1)

How is that supposed to help?

[devout snow]

@uneven spire Has your question been resolved?

[supple knot]

Complete the square in the square root

4x^2 + 4x = (2x+1)^2 + ?

[uneven spire]

Yes thats how I got x=-1 +/- sqrt(u+1)
Which doesn't help

[supple knot]

No that's the wrong substitution

[supple knot]

u= 2x+1 is the correct one

[uneven spire]

Ah I see I see

I'll try that way then

Thanks

.close

[devout snow]

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[restive river]

i took the cross product but im not sure how to do the rest

[restive river]

<@&286206848099549185>

[neat solstice]

we can treat them as vectors

their cross product will be orthogonal to both

then we just have to translate that solution to where these lines intersect

[restive river]

yeah im having trouble with this

[devout snow]

@restive river Has your question been resolved?

[neat solstice]

hey, sry for the late response

first things first

we should not have t in both equations

let's use t for L_1 and u for L_2

now

We can get a general Line from L1 to L2 by subtracting L2-L1 or L1-L2

here, we treat the lines L1 and L2 as points that depend on t and u

[restive river]

thanks for helping me btw

[neat solstice]

this will give us a vector that points from one point to the other

this vector gives the distance between the lines
it is the shortest, when it is orhtogonal to L1 and L2

to set it orthogonal to L1 and L2, we can set the scalar product of our vector with the directional vector of L1 and L2 to 0

this gives us 2 equations

[restive river]

like this?/

[neat solstice]

you got v correct

the construction of P2-P1 is also good

[restive river]

was it wrong to set to like 2c, c, 4c

[neat solstice]

i havent done it like that, but that should also work

[restive river]

idk how to solve this though

[neat solstice]

this is what i would do

"Verbindungsvektor r" is your vector v

below, i wrote "v should be orthogonal to L1 and L2"

[devout snow]

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[restive river]

.reopen

[devout snow]

✅

[restive river]

is this the dot product or multiplication

[neat solstice]

dot product

scalar product

im getting more and more confused here as well tho haha

ok i am sure that i have a valid way of doing it now, i checked my results graphically

basically:
-get the directional vectors of L1 and L2
-get their cross product, to get the direction of the vector connecting them (it will be orthogonal to both)

-treat L1 and L2 as points and get their difference->this gives a vector from one line to the other

-set these two vectors equal
so in total, we have a vector connecting the lines and a vector that gives the correct direction
setting them equal gives us the correct one

this gives a system of linear equations which we can solve

if we input t into L1 and u into L2, we get the points where the connecting vector touches the lines

here i checked it graphically and it looks good

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[smoky sentinel]

Can I still simplify this?

<@&286206848099549185>

[wicked turtle]

the numerator and denominator are both divisible by R+r

also: !15min

!15min

[devout snow]

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[smoky sentinel]

oh sorry mb

[wicked turtle]

nw

[smoky sentinel]

.close

[devout snow]

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[devout snow]

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[restive river]

Hey, how do I do this?

I need to do (b)

[dense jay]

this channel is gonna shut down soon, open a new one

[restive river]

Alright

.close

[devout snow]

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[restive river]

my steps are as follows

we're given lambda, 34 meters

and given frequency, 25 Hz

so you apply formula v=f(lambda)

$v=\frac{(34 m \cdot 25 Hz \cdot 1 km)}{1000m}$

[woven radish]

mj

[restive river]

ending up with

$0.85km \cdot Hz$

[woven radish]

mj

[restive river]

simplifies into

$0.85 km \cdot \frac{1}{T}$ where "T" represents period in seconds

[woven radish]

mj

[restive river]

$\frac{0.85km}{T}$

[woven radish]

mj

[restive river]

my problem is here

how is the period 1

isn't period equals to 25 HZ^ -1

[versed jetty]

the period of the wave isn't one

[shell birch]

I don't see how you came to that?

[restive river]

well my steps are above

[restive river]

wdym

oh yeah

it can't be

but how come

[shell birch]

ye but you changed hz to 1/T

[restive river]

the answer suggests that

[restive river]

which is correct since Hz (being frequency) is also 1/period

[shell birch]

f=1/T yes

[restive river]

are you saying that

or do you mean

that Hz isn't frequency

[shell birch]

it is

[restive river]

after we've applied it?

oh ok

im not sure because I believe the math I've done is correct (somewhat)

but I'm just not getting it, is the answer wrong?

or is T actually 1

(i.e period)

[shell birch]

I just don't see why u havent changed 34 meters to kilometers and done the calc?

it gives to 0.85Km/s

[restive river]

yeah i have

im getting 0.85 km * hz

not km/s

[shell birch]

You mean you don't get the dimensional analysis

[restive river]

if you can elaborate on how you've gotten that i would appreciate

it

[shell birch]

Yes then. hz is s^-1 units

but it is not the same as writing T which is the period

[restive river]

yeah 1/T

is what I meant

[shell birch]

if you want to think of it in the sense of f = 1/lamba then 1 hz = 1/ T = 1 / 1s.

[restive river]

could you share a photo of your dimensional analysis if possible?

or type it out with texit works great too

was mines

[shell birch]

Well it is just simply $$ \lambda f $$ which gives $$Kmhz$$ and so then $$1hz = \frac{1}{1s} = s^{-1}$$ so we end up with $$Kms^{-1}$$

[woven radish]

Kernal

[restive river]

okay, so as far as getting 0.85 km * Hz our steps match

^ i think

so then hz is 1/1s?

[shell birch]

So yes. T for 1 hz is 1s, however that is not saying the T = 1 for the wavelength in the question

[restive river]

hmmm okay

I see my mistake

I assumed that Hz was the frequency of the function

which it wasn't

the frequency was 25 hz

so I was wrong in saying

1 hz = 1/T

but rather it's 1 hz= 1/second

[shell birch]

the T for 25hz would be 1/25 = 0.04s.

[restive river]

yeah

okay perfect

thanks for your wisdom

[shell birch]

I wouldn't call it that lmao. I just think u had some confusion but I would look into dimensional analysis a bit if you find stuff like this confusing 🙂

[restive river]

dimensional analysis is a life saver when it comes to remembering units lmao

I just wouldn't depend on it doing everything for me like it didn't here

lol welp, thanks again 🙂

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[devout snow]

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[devout snow]

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[restive river]

don't understand, but if you did dimensional analysis here you'd get 1.3 s?

[winter patrol]

wrong units

[restive river]

I understand frequency is in Hz but

how would you get that

through using velocity and wavelength?

waittt a minute

Hz is 1/s

right

[versed jetty]

yes

or s^-1, if you prefer

they mean the same thing

[versed jetty]

by the way, your second line is wrong here. it should be $\frac{v}{\lambda} = f$

[woven radish]

Out Of Nosh

[acoustic leaf]

the unit for speed is also m/s, not s/m

[restive river]

ohh ok

.close

[devout snow]

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[devout snow]

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[dusty cosmos]

how do i do these 3?

[acoustic leaf]

do you know how to do partial fraction decomposition in general?

[dusty cosmos]

with these types of ones i dont

but\