help-0

[jade birch]

Thanks

I got to do sth, I'll be back in 20 if no one has helped you till then

[sterile zealot]

Okay.

[alpine sable]

yall what's x?

[sterile zealot]

The line CM connects the vertice to the midpoint

1 sec @alpine sable

[alpine sable]

k

if they're equal ik how to solve it

but i dont think they are

[sterile zealot]

So @alpine sable, the area of MBC would have to be 1/4 of the parallelogram, because mirroring over line MC would show a perfect fit for another triangle, and a remaining parallelogram. This being said, the answer is 32 cm2.

Now @alpine sable

Let's get to you

[alpine sable]

yes

[alpine sable]

^^

[sterile zealot]

Equal as in similar?

[alpine sable]

yeah

[sterile zealot]

Because the marks of congruency for the hypotenuse(s) show that the triangles are indeed similar

And the scale factor is 1/2

[alpine sable]

okay well

thanks

i have

another questio

can you help?

[sterile zealot]

Fire away

As in yes I can help

[alpine sable]

its asking for the perimeter of the circle

The bearing of P from Q is 070°. What is the bearing of Q from P?

[sterile zealot]

@alpine sable I sadly don't seem to understand what you mean. You may want another helper.

[alpine sable]

...

[sterile zealot]

@alpine sable here's a hint: try the Pythagorean theorem

Did that help?

[alpine sable]

yes

alright

thanks

[sterile zealot]

Anything else?

[alpine sable]

oooh alr thanks

In the following diagram find the size of the angles marked x and y .

one sec

[sterile zealot]

@alpine sable All quadrilaterals have a total interior angle measure of 360 degrees. Using the provided exterior angle, you can determine the missing interior angle, and thus work from there to determine the values of x and y

Did that help?

[alpine sable]

A yacht starts from L and sails 12 km to M on a bearing 120°
. It then sails 9 km on a bearing of 152° to K. Find ∠LMK

[jade birch]

Did you draw it?

[main dagger]

So, this has more to do with signal theory but maybe someone can help me.

I have an exercise where a causal LTI system responds for a rectangular pulse $$ s(t) = rect(t) $$ with $$g(t) = \Lambda(2t)$$. The task is to find out what the impulse response for this system is. The solution is $$h(t) = \frac{d}{dt} h_{\epsilon}(t) $$ because $$\delta(t) = \frac{d}{dt} \epsilon(t)$$

[ocean seal]

Witchfinder

[main dagger]

I don't really understand the solution and the text book doesn't explain the approach. May someone be so nice and explain it to me?

Especially why h(t) looks like this

[terse iron]

lost

[sterile zealot]

Ah, the sohcahtoa

A way to remember the values of the sine, cosine and tangent.

...ringing a bell?

@terse iron do you got it or do I need to further elaborate

[sterile zealot]

There you go!

@round path bring your question here, the other person is good now.

[round path]

find the shaded

area

[sterile zealot]

Okay, so to start we have the entire shape to consider

[terse iron]

thats it

[sterile zealot]

Shaded and unshaded

@terse iron yes

@round path find the total area, then we will continue.

[round path]

22x44

[sterile zealot]

No, look closer and make sure to get the right dimensions

[round path]

44x44

[sterile zealot]

Correct, evaluate

[round path]

1936

[sterile zealot]

Alright, now keep this number saved

What we do now is try to remove the area taken by the 4 semicircles

They all have the same area, so finding just one will get you the answer for them all

The diameter of all the semicircles is?

[The measure you mistook earlier]

[shell pilot]

I an stuck on this question

Can somebody please help me

[glass lichen]

factor

[untold tide]

Can I ask questions about fourier analysis here?

(I don't know how to get access to the advanced maths section...)

[vale wigeon]

type ,iam adv

in #bots

[untold tide]

thank you!

[untold tide]

Yeah i missed that, cheers

[alpine sable]

Can anyone explain what unit vectors are ?
You can dm me personally 🙂

[vale wigeon]

a unit vector is a vector whose length is equal to 1

that's it

[alpine sable]

How do I solve this for q?
0.2q + 5 + 40/q = 0

[jade birch]

It's a quadratic in disguise

Multiply everything by q

[manic quail]

It has no real solutions though.

[jade birch]

True

[manic quail]

,w solve[0.2q + 5 + 40/q = 0]

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[vale wigeon]

WA is being a bit weird with the form it gives for the solutions

[jade birch]

"+-5i"
huh?

[manic quail]

xD

[jade birch]

I want whatever wolframs on

[vale wigeon]

did this arise from some other problem or were you just given this equation as-is and told to solve it?

[jade birch]

@alpine sable

[vale wigeon]

i pung them with my reply

[manic quail]

pung?

[jade birch]

I thought it was "pinged"?

[vale wigeon]

pinged, but i like to pretend ping is an irregular verb

[manic quail]

Pung sounds better tbh.

[jade birch]

True

[ocean seal]

BinaryVector

[vale wigeon]

did you mean $ba = 0 \implies \mathrm{im}(a) \subseteq \ker(b)$?

[ocean seal]

Ann

[vale wigeon]

if so then... yeah i guess

[tacit breach]

latex is the most simplest but most useless thing you could ever have, its not that hard to use

https://www.codecogs.com/latex/eqneditor.php

[sonic cave]

would this be reflexive or not?

[vale wigeon]

what do you think?

[sonic cave]

hmmm

[vale wigeon]

notice how c doesn't have a loop attached

[sonic cave]

yeah

so it wouldn't be reflexive right? coz x R x and by the definition of R x, x is greater or equal to x?

im not entirely sure so idk

[tacit breach]

That looks hella complex

[vale wigeon]

this wording is garbage

but yes your relation is not reflexive

[sonic cave]

im sorry 😦

[vale wigeon]

cRc is false for your relation, therefore it (your relation) is not reflexive

[jaunty torrent]

Guys
I never sent or used this server before... Idk.. like can I send question and stuff here in tgis exact chat

Heyy Guys*

😅

[vale wigeon]

not right now since this channel in particular is occupied

[sonic cave]

thanks ann

[vale wigeon]

#help-6 is free rn so you can go there instead @jaunty torrent

[jaunty torrent]

ohh okk got it... thank you🙏🏻

[tacit breach]

herm

[knotty garnet]

Hint: what is arc QRS?

[tacit breach]

55?

Im guesing- looks like opposite angles to me

u gonna flex ur latex math skills?

arc qrs is 110

not 55

[knotty garnet]

Latex is extremely useful, it gives just about anyone the ability to elegantly typeset math

What other options do you have?

Is there an alternative?

[tacit breach]

Yes plenty

[knotty garnet]

QRS is not 110

[tacit breach]

I dont know then

[knotty garnet]

You just got that RS is 110

So how can QRS be the same?

Another hint: erase all the lines except QS

[tacit breach]

RQS=55 aswell

bro

alright lol

[manic glade]

10 channels are not enough to not ask a question on top of an unanswered pending question? :/

[sand summit]

How many roots would tan2x have in the range 0<= x <= 3600?

Would it be 80 or 40!

*?

[willow lake]

still no answer

is the statement false

or is the proof nontrivial

[paper temple]

best way to find a function from a function table?

,rotate

[willow lake]

you can infer a polynomial function from a table using polynomial interpolation

https://en.m.wikipedia.org/wiki/Polynomial_interpolation

[knotty garnet]

Couldn't you just take the dual of the polyhedron and see that it is impossible for any face to have 2 vertices?

Or is that too easy

[willow lake]

thanks!

hehe

[manic quail]

You don't have to. Just use the table.

[paper temple]

on the calculator?

[paper temple]

oh wait no lol, i think i understand cos f(2)=0

[manic quail]

Yes, exacty.

[paper temple]

thanks 🙂

[alpine sable]

for questions 4 a and 4b you dont need to find the function

4a just wants you to find f( f(2) )

f(2)=0

f( f(2) )= f( 0 )

f(0)=-1

[paper temple]

thanks you mate! @manic quail pointed it out also. Classic case of just not thinking!

[knotty garnet]

@paper temple also just a quick extra note to re-emphasize that functions aren't always an equation you plug and chug, functions can literally just be pairs of things (input, output) like this table lookup

Or sometimes a definition that is so difficult to compute we don't even know what the values are or if they even exist but that's a bit more esoteric

[paper temple]

oh yeh fair point, so the important thing being there isnt always an equation for them? as they can literally just be random pairs

[knotty garnet]

Yep

[manic quail]

To give you even more information: There would be infinitely many functions which pass through those points.

[knotty garnet]

Functions often times are not that, but they COULD be and that's one way to think about them

[paper temple]

hmm ok im with you for example a set of points in a straight line could be expressed by more than one function

[gentle fox]

Alright so ive got this question on my review and it puzzles me

I am under the assumption that f'(x)= sqrt(x) hence f'(4)= sqrt(4)=2

Or am I completely wrong in how I am trying to solve it?

It could be 0 because there is a horizontal tangent at g(4) and f'(4) = g(4)

Either way, some additional insight would be greatly appreciated

[left spear]

The horizontal tangents only gives you information about g' (specifically: g'(4) = g'(8) = 0), which is not going to be very helpful here as far as I can tell.

The integral of g(t)dt from 0 to x is, by definition, the antiderivative of g whose value at 0 is 0. So I'd consider the h(x) = f(x²) function, derive it and try to find a relation between f' and g.

[neat venture]

How many 16 character combinations will there be if there are 36 different characters?

[gentle fox]

Now that confuses me. I am not familiar with how I can find a relationship between h(x) = f(x²) and f'(x)=g(x)

Or what importance it serves in that matter

[left spear]

f' ≠ g
However if you define h the function such as h(x) = f(x²) then h' = g (because sqrt(x) in the integral then becomes x, so you have an anti-derivative of g)
h is the composite function of f and the square function, so by applying the derivation rule for composite functions, you can link derivative of h (i.e. g) and the derivative of f.

It's useful because once you know that relationship between f' and g you can calculate f'(4)

[gentle fox]

Im sorry, that is all too confusing for me.

That explanation goes way over my head and is unlike anything I had seen or heard before

Thanks for the help though.

[half epoch]

Um, are you doing the same question still? Where did you get an h and how did you figure f’(x) = sqrt(x)?

This looks like a case of the leibniz rule to me

[gentle fox]

I did not say anything about an h

[half epoch]

Actually just reduces to the fundamental theorem of calculus even

[gentle fox]

but I figured, given f(x) = the integral of g(t), then f'(x) = g(t)

[left spear]

That would be true if there wasn't a square root in the integral's upper bound

[half epoch]

It’s just a nice u-sub away from being an u

[gentle fox]

Ive never done u sub for something in the bounds

[half epoch]

Okay, how about we plug x^2 for x and go from there? That should be easy enough to follow

$f(x^2) = \int_0^x g(t) ,dt$

[ocean seal]

Learath2

[half epoch]

Due to the FTC we know $f(x^2) = G(x)$ and that $G’(x) = g(x)$

[ocean seal]

Learath2

[half epoch]

Do you follow so far?

[gentle fox]

So what I gather from this is you squared both sides to eliminate sqrt x

[half epoch]

I plugged x^2 for x. Squaring both sides would not be very useful

[gentle fox]

alright

I see that

that makes more sense

[half epoch]

Now we take the derivative of both sides to get a g(x) on the right side

What would the derivative of the left side be?

[gentle fox]

perhaps f ' (2x)

[half epoch]

Nope, careful applying the chain rule

[gentle fox]

f'(x^2)*2x

[half epoch]

Yep. So overall we have $2xf'(x^2) = g(x)$

[ocean seal]

Learath2

[half epoch]

Now we are looking for f'(4) what do you plug in for x to get a f'(4)?

[gentle fox]

2

[half epoch]

Yep, just check the graph for the value of g at 2

And we are done

[gentle fox]

and thats 2

but thats not a possible answer

[half epoch]

g(2) = 0 not 2

[left spear]

No, it is 2

[half epoch]

Oh wait, lol I misread that, badgraph

Anyway it still works

[left spear]

But here you have 2*2*f'(4) = g(2)

[gentle fox]

ill repost it so we dont have to scroll

[left spear]

So you'd still have to divide both sides by 2x=4 to get the value of f'(4)

[gentle fox]

would it make sense to isolate f'(x) by dividing both sides by 2x

[half epoch]

Just plug x=2 and solve it like you’d solve any other equation

It’s just algebra at this point

[gentle fox]

So 1/2

[left spear]

Sounds good to me

[gentle fox]

Wow

[half epoch]

Yep, that’s what I have aswell

[gentle fox]

Thank you both so much

This is what happens when your professor (in my pfp) gets questions which he never explained how to do before

Thank you again!

[dusky notch]

hey guys Im trying to do some comparison test practice ques but im not sure what to do

what am i supposed to be comparing here if i only have one sum?

[left spear]

You'd want to compare to a series that you know converges - the usual one is 1/n^a which converges when a > 1

More specifically, the greater the denominator the smaller the fraction, so you can see the terms of your series are lower than 4n/5n^3

[dusky notch]

so I would compare 4n/5n^3+3 to 1/n^a?

and take the limit to see what each approaches?

[left spear]

Well 4n/(5n^3+3) < 4n/5n^3 and you can rearrange the latter as 4/5n², which looks a lot like 1/n²

And Σ 1/n² converges

[dusky notch]

how do we know that 4n/5n^3 is larger?

oh since we're adding 3 it makes denom larger

which makes it smaller

so in every comparison case will we always compare to 1/n^a?

[left spear]

Σ 1/n² (or generally Σ 1/n^a where a>1) is prolly the one that you'll find the most in exercises based on series comparison

[dusky notch]

oh that makes sense, thank you!

I appreciate your help

i have 1 more question

so with this one

if we drop the -1 and compare it

since 1/n^a and a is equal to 1 does this mean its divergent?

[noble sinew]

its -1 so you make the number smaller if you remove -1 from denominator

[dusky notch]

oh so as long as the one we are comparing it to is > the original sum then its convergent? and I thought when 1/n^a where a had to be greater than 1 to compare

[noble sinew]

So since n^2/(3n^3-1)>1/(3n) and we know 1/(3n) diverges

then so does the original

(You wrote down +1 in what you posted, when the original had -1)

[dusky notch]

how do we know that 1/3n diverges?

if the denom gets smaller doesnt it apporach 0?

[noble sinew]

pull the constant out of the sum, so we have (1/3)*sum from n=2 to inf of 1/n, which diverges from p series rule, 1/(n^p) diverges for p<=1

[dusky notch]

ooo ok that makes sense

these series are so confusing tbh

theres so many tests

how do u know which one to use?

if not prompted to use a specific one?

[noble sinew]

I use comparison like 95%

[dusky notch]

oh so you can pick and choose which one to use?

so could u use the ratio test on these problems as well

[noble sinew]

But requires knowing some important series to use (the more you know the better)

[dusky notch]

oh like what you said about 1/n, its useful to know whether a compared sum is div/conv

[noble sinew]

Yes you could use ratio

Sometimes tests come back inconclusive and then you have to try something else though

[dusky notch]

is there usually one that typically second best?

like if you start with ratio/comparison

what would be the second best option?

[noble sinew]

Depends on how it looks

But root test more powerful than ratio

[dusky notch]

ah ok that makes sense, thank you for the wonderful insights. I really do appreciate it!

[buoyant vale]

how do i get the critical range

my teacher wants me to solve it this way

[noble sinew]

Have you made your H_0 and H_A?

[buoyant vale]

i have

Ho: p=0.2
H1: p>0.2

[noble sinew]

Assuming critical range is the same as critical region then its just the set of all values where we reject the null hypothesis

[buoyant vale]

how would i get it ?

i cant rememver how to get it but i remember that it is usually in the format X>=y

[noble sinew]

So if the null hypothesis is true then X ~ Binom(5,0.2). So we want to find for what outcomes the prob of that happening is less than 0.05

[strange lagoon]

Can anyone help me witht his question

im thinking its A but not sure

[buoyant vale]

im with you

[noble sinew]

So we want 0.05=P(X>=C_1|X~Binom(5,0.2)=1-P(X<C_1|X~Binom(5,0.2)

Then write out cdf and solve for C_1

[strange lagoon]

are you talking about my question

lol

[noble sinew]

Then remember it is discrete so it can only obtain integer values

[buoyant vale]

to get that id need to do PX>=3

which is 1- PX<=2

right?

[noble sinew]

Well we don't know what values are the critical values yet, in fact P(X>=3)>0.05

hence not part of the critical region

Depending on how much you need to show it might be enough to just show P(X>=3)>0.05 and P(X>=4)<0.05 hence our critical region is {4,5}

but otherwise write out CDF (or sum of PMF's) of binomial and solve

[buoyant vale]

think i got it

thank you

[noble sinew]

$\sum\limits_{i=C_1}^{5}{5 \choose i}(0.2)^i(0.8)^{5-i}$

[ocean seal]

ScapeProf

[noble sinew]

Was a way to solve for the critical region

[crystal cape]

how do i solve thiis

[vale wigeon]

what's the most important thing to know about any geometric progression?

or rather, the two most important things

[crystal cape]

?

first term and ratio

[left spear]

Yeah, you should try to determine the ratio in the first place

Or rather what can p be such that these three terms can be a geometric progression

And the ratio would follow

[crystal cape]

how would i do that ?

[left spear]

Well by definition if it's a geometric progression the ratio between any two consecutive terms is the same, so you have that the second term divided by the first one is equal to the third term divided by the second one

That leads to an equation you have to solve

[crystal cape]

ok

ill try that

that gives me 6p^2 + 10p + 12=0

[vale wigeon]

that's not an equation.

did you mean 6p^2 + 10p + 12 = 42069.777?

[crystal cape]

how did u get that?

[vale wigeon]

i didn't

okay, so how did you get 6p^2 + 10p + 12 = 0?

[crystal cape]

used this

[vale wigeon]

show your work

[crystal cape]

ok

[vale wigeon]

you're clearly missing something that will not be solved just by throwing words around

[crystal cape]

Here's my work

[vale wigeon]

first step after the ratio equation is wrong

$(-2p) \cdot (-2p) \neq -4p^2$

[ocean seal]

Ann

[crystal cape]

oh right

[umbral folio]

how to find the velocity vector at a point?

[left spear]

wait, i made the same mistake
ah no, I just did it in a slightly different way

[vale wigeon]

@umbral folio this channel is busy, please move.

[umbral folio]

ok

[crystal cape]

sorry wrong one

p^2+5p+6=0

so i get -3 or -2 as the possible values

[vale wigeon]

no

you're still insistent on not writing the =0

as if you're allergic to it

[crystal cape]

oh sorry

[vale wigeon]

and no the equation you get is not p^2 + 5p + 6 = 0

[crystal cape]

then?

i got 2p^2+10p+12=0

[vale wigeon]

why do you keep writing expressions instead of equations

equations have equals signs in them

go through the algebra again

show me your work again but now with your mistakes corrected

[vale wigeon]

,rcw

[vale wigeon]

last step.

[crystal cape]

i dont know after this

[vale wigeon]

your last step is wrong.

[crystal cape]

oh yeah

p=6 or p=-1

[vale wigeon]

great

so which is it?

[crystal cape]

6 since its positive

[vale wigeon]

@midnight cedar @alpine sable this channel is occupied, please move.

[crystal cape]

ohk thx

[midnight cedar]

Okk

[crystal cape]

i think i can do it from here

thx

[vale wigeon]

yes, p=6.

great.

[alpine sable]

ok sorry

[crystal cape]

how to solve this

[left spear]

Do you not have a starting point

[crystal cape]

no

[left spear]

The line intersects the curves at points that satisfy both equations

[crystal cape]

so equation of line= equation of curve?

[left spear]

It doesn't really make sense in that context to say that two equations are equal but that's the idea

(it would be y=2x+m(2x+1) and y=6x+4 hence 2x+m(2x+1)=6x+4)

[crystal cape]

and?

i mean there are no values given

so i dont know what to do after that

[vale wigeon]

you need to show the equation 2x^2 + m(2x+1) = 6x + 4 always has two solutions

it may help if you do some algebra to it to write it as a quadratic equation in standard form.

and think about a certain value that you can calculate when faced with a quadratic equation in standard form, and what this value can tell you

[crystal cape]

can u show how to do that?

[vale wigeon]

how to do what

[crystal cape]

this

[left spear]

do you know what the standard form of a quadratic equation is?

[crystal cape]

ax^2+bx+c=0

[left spear]

(almost)

[crystal cape]

now?

2x^2+2mx+m=0

[left spear]

That's not the standard form

[crystal cape]

what bout now

[left spear]

Well that is a standard form but that's not equivalent to what you previously had

Your equation is 2x² + m(2x+1) = 6x + 4
You want to put everything on the same side of the equation, and separate the term in x², the term in x, and the constant

[vale wigeon]

2x^2 + m(2x+1) = 6x + 4, not 2x^2 + m(2x+1) = 0 as you did.

you cannot just ignore some terms of your equation simply because you don't like them

[crystal cape]

i wrote that

he told thats not the standard form

[vale wigeon]

2x^2 + m(2x+1) = 6x+4 : relevant to your problem, not standard form
2x^2 + 2mx + m = 0 : standard form, but has nothing to do with your problem whatsoever

[crystal cape]

yeah what to do after writing that?

[vale wigeon]

nothing

backtrack because you fucked up

[left spear]

☝️

[vale wigeon]

@thorn compass channel busy please move

[thorn compass]

Ok

[vale wigeon]

go back to the equation 2x^2 + m(2x+1) = 6x+4 and turn it into standard form using actual algebra (i.e. not just throwing terms in the trash at random)

@crystal cape

[crystal cape]

ok

[vale wigeon]

and pay attention, pay attention, pay attention to what you're doing

and especially to what you write out here

because remember: i see nothing beyond what you send here

[crystal cape]

how do i put it general form cause theres a m variable here

yeah ik

[vale wigeon]

treat m as if it were a number.

collect all the x^2 terms, and all the x terms, and all the constant terms, as you normally would.

[crystal cape]

2x^2+2x(m-3)+m-4=0

is that right

[round raven]

https://cdn.discordapp.com/attachments/236128981894692864/833404086241984573/Screenshot_34.png

i was sent this question on discor

i got the percentage as 9.68 something something

but the person who sent it says its 1. something

whats right?

i used the sides and and angle using 1/2absintheta to find the area of the triangle

i then found the circles radius by reverse calculating its circumference

later i divided the two

what did i miss?

[vale wigeon]

yes this is right

[crystal cape]

what i do after this

[vale wigeon]

have you ever heard of this thing called the discriminant

[crystal cape]

b^2-4ac=0

[vale wigeon]

no

i didn't say it should be equal to zero

the discriminant of ax^2+bx+c=0 is b^2 - 4ac

what does it tell you about the solutions of your equation?

[crystal cape]

0

[vale wigeon]

speak in complete sentences.

[crystal cape]

the solutions are real and unequal

[vale wigeon]

there are two distinct real solutions, therefore what?

[crystal cape]

b^2-4ac>0

[vale wigeon]

yes great

so now calculate the discriminant for your quadratic

it's going to be in terms of m

[vale wigeon]

great and now you should verify that m^2 - 8m + 17 > 0 is true for all values of m

[crystal cape]

how?

b=root(b^2-4ac)/2a

?

[vale wigeon]

??

no

you should verify that it's never equal to zero

[crystal cape]

ok

no idea then

[ancient bear]

Hello friends

May I tek

[opal sundial]

let's say I have a set of numbers that I want to average out.

how big does a number n have to be to offset the decrease in the result of the mean?

you know since the denominator goes up?

wait does it just have to be >= 1?

[wild shard]

how would I solve for plane cuboid interseion

[hardy geyser]

Help I keep getting the wording wrong

[dire wren]

write 2 equations to solve the system of equations

let q = number of quarters, n = number of nickels

[alpine sable]

is this channel open?

[dire wren]

no..

[hardy geyser]

ok

[mighty copper]

Anyone understand finite difference method (elliptic)

I'm just trying to put my equation into a matrix

[coral frigate]

two particles, A and B, of masses 2m and 3m respectively, are moving on a smooth horizontal plane. The particles are moving in opposite directions towards each other along the same straight line when they collide directly. Immediately before the collision the dspeed of A is 2u and the speed of B is u. In the collision the impulse of A on B has magnitude 5mu.
a) Find the coefficient of restitution between A and B
I need some help here lol
how do you find v1 and v2 for both particles

because for impulse i do

5mu = m(v-u)

since m for A is 2m

I sub in 5mu = 2m(v1 - 2u)

cancel m

5u = 2(v1 - 2u)

5u = 2v1 - 4u

9u = 2v1

v1 = 9/2u, which is not right apparently

the answer book says 7/2u

[daring chasm]

might be more fitting on the physics server

[coral frigate]

oh, thanks

[alpine sable]

can i ask a bio question here

[wind gorge]

Not sure

[upper mesa]

Got a general question for u all
for grade 12 physics
where would I be able to learn more about mirrors?

I think I should do some studying before I start asking questions or bailout so

[ashen wave]

is anyone familiar with factoring quadratic equations?

[mighty copper]

yes

post

[ashen wave]

I just started the unit so I dont know much about it

[mighty copper]

wait

[ashen wave]

I need help with this problem-

x^2+x-6=0

[mighty copper]

https://www.youtube.com/watch?v=ZGmKQa45PVw

You can watch this video, should be able to solve the question after

[ashen wave]

alright ill watch it

[mighty copper]

there are many videos online that show how to solve quadratic equations, id recommend watching one or two

[ashen wave]

what if your factoring a really big number? like with this equation 24x^2+24x-4368=0?

[mighty copper]

You won't ever be asked to do that

[ashen wave]

but I am haha

its in my worksheet

[mighty copper]

Okay

you divide everything by a common factor to make it smaller

[ashen wave]

what?

[mighty copper]

nm

[ashen wave]

oh

[mighty copper]

divide everything by 24

[ashen wave]

alright

so it would be x^2+x-182?

=0

then what?

[ashen wave]

Are you still there?

[mighty copper]

usually you find two numbers that multiply to make -182, but add to make the x coefficient 1

[ashen wave]

what do you mean?

[mighty copper]

if you have $2x^2+3x-10$

[ocean seal]

9ice

[mighty copper]

you get 2 numbers that multiply to make 10

but add to make 3

[ashen wave]

right but didnt you divide out the numbers?

[mighty copper]

Yes, because these aren't really big numbers

if you divide here, you get fractions

we don't want that

[ashen wave]

right ok

[mighty copper]

Okay, so 2 numbers that multiply to make the term without the x

and add to make the term with the x

$2x^2+3x-10$

[ocean seal]

9ice

[ashen wave]

are we talking about that equation?

oh ok

2 and -5

[mighty copper]

so in this case, 5*-2 = -10

and 5+ -2 = 3

[ashen wave]

oops wrong way

alright

[mighty copper]

yh

so

(2x-2) and (2x+5) is our answer

[ashen wave]

oh!

[mighty copper]

its 2x because we kept the 2 infront

[ashen wave]

ok but how do you know when its no like a number before it

hold on let me find an example

[mighty copper]

there was a way I used to factorise really quickly, and was easier too but i;ve forgotten lol

[ashen wave]

I cannt find one but its like (2)()()

(2)(2x-2)(2x+5)

something like that

[mighty copper]

you mean (x-2)(2x-2)(2x+5) ?

not sure what u mean here

[ashen wave]

no its just like one number before it

Ill try to find an example hold on

give me a min

[mighty copper]

$2(2x-2)(2x+5)$?

[ocean seal]

9ice

[ashen wave]

yeah something like that

[mighty copper]

and what does it usaully ask you to do?

[ashen wave]

just like the problem you solved before

but when do you know there is a number in front of the parenthesis

[normal kindle]

can someone help me with this I can’t seem to figure out how my answer is wrong

[mighty copper]

Say you have something like

you've factorised and then you arrive here:

[split hinge]

[mighty copper]

$(4x-2)(4x+10)$

[ocean seal]

9ice

[ashen wave]

alright

[mighty copper]

so this is a factorised form

[ashen wave]

right

[mighty copper]

you can take out a common factor of say 2

to get $4(2x-1)(2x+5)$

[ashen wave]

oh

[ocean seal]

9ice

[ashen wave]

I dont know if this is too much to ask for but do you think you could find a equation just like that but start from the beginning xD? because everytime there is a problem like that I get stuck on the factoring

[mighty copper]

erm, I'm not sure what u mean, I should factorise and end up with an equation like this?

[ashen wave]

yeah I suppose rip

[mighty copper]

Okay, The equation:

$16x^2+32x-20$

[ocean seal]

9ice

[mighty copper]

here we have big numbers, we want to make them simpler

[ashen wave]

alright

[mighty copper]

so lets say we divide by 4

we get $4x^2+8x-5$

[ocean seal]

9ice

[mighty copper]

yes?

[ashen wave]

so this only works if you have a common factor

then you divide them all by it

[mighty copper]

yes

[ashen wave]

okk

[mighty copper]

otherwise you end up with fractions

[ashen wave]

oh right

[mighty copper]

if you cant divide by a common factor, usually you have to use another method to solve the question

[ashen wave]

alright

now what do you do

5 only factors with 1 and itself

[mighty copper]

no, youre forgetting we have a 4 infront of the x^2

usually if the equation looks like this $x^2+8x-5$ then you're right

[ocean seal]

9ice

[mighty copper]

we have a 1 infront of the x^2

but here we have an x^2

[ashen wave]

??? what do you do with the 4 then?

[mighty copper]

you multiply 4*5

so we need 2 numbers that make -20 but add to make 8

$4x^2+8x-5$

[ocean seal]

9ice

[mighty copper]

if it was $x^2+8x-5$

[ocean seal]

9ice

[mighty copper]

we do only 1*5

[ashen wave]

5+4?

[mighty copper]

but its 4 so we do 4*5

[ashen wave]

oh ok we just add that one step

[mighty copper]

its a step we usually ignore if the number infront of the x^2 is 1

but if its not 1 we dont ignore it

[ashen wave]

oh ok

ok so im confused bc when you add 5+4 you get 8 but its a -20 so it wouldnt we need to add the negative to one of the numbers?

[mighty copper]

so you wanted this: $4(2x-1)(2x+5)$

we started with this equation
$16x^2+32x-20$ ;

divide by 4
$4x^2+8x-5$ (-2*10= -20)
$(4x-2)(4x+10) $

if we take out a common factor here

$2(2x-1)* 2(2x+5) $
we get
$4(2x-1)(2x+5)$

[ocean seal]

9ice

[mighty copper]

looks a little messy, but thats all of it

[ashen wave]

ok so wait when you are factoring the -20 I got -54 and 5-4 but when you need to find 8 do you just discard the negatives?

other than that I understand

thanks for helping me btw sorry that took so long

[alpine sable]

whats the answer 😔

im prepping for my ap exam

[mighty copper]

nah its kl

[alpine sable]

is it D

i think its D

right

[mighty copper]

@ashen wave so 5 and 4 dont work for -20

[ashen wave]

oh

[mighty copper]

and we dont ever discard the negatives

although 5*-4 = -20

we cant get 8 from 5 and 4

[ashen wave]

ok ill keep that in mind then

[mighty copper]

but 2 and 10 work for both, we can get 8 and -20

[ashen wave]

oh alright

[mighty copper]

@alpine sable it's not D

it/s C

[alpine sable]

oh bet bet

[mighty copper]

once we bring the power down, we always take away from the power

[nocturne swift]

YES TRUE

AGREED

PERRY AGREES WITH YOU

[ashen wave]

$4x^2+x-3$

[ocean seal]

TheCrabywoomy

[ashen wave]

uhhh can anyone help me out with this

[sterile zealot]

...factor?

Or what?

[winter bay]

@ashen wave if you need help factoring we can help you out

Well I mean I can help u out

[eternal juniper]

yo how are you supposed to solve this? looked through my textbook a few times and couldn't find anything. i assume its just something simple that i'm missing

[livid orbit]

help pls

[alpine sable]

Write |f(x) - 1| = |x^2 - 1| < 0.5, factor, reverse engineer the delta

[eternal juniper]

not sure what you mean

[glass lichen]

what range of f(x) values make |f(x)-1|<0.5 true?

[eternal juniper]

(-infinity,1.5)

[glass lichen]

no

[eternal juniper]

or 0,1.5

[glass lichen]

no

$\abs{a}<b\iff -b<a<b$

[ocean seal]

moshill1

[alpine sable]

3. Four short-order cooks can make 24 omelets in 10 minutes. if a diner gets a to-go order for 90 omelets that needs to be ready in 15 minutes, then how many cooks do they need to complete the order on time?

15?

[alpine sable]

c=#of cooks
o=#of omelets
m=#of minutes to complete

c and o are directly proportional, o and m are directly proportional , c and m are inversely proportional

trick is to realise that the quantity c*m/o will be constant

4*10/24=k

k=5/3

[eternal juniper]

so what are you supposed to do to solve it?

[glass lichen]

Use what I wrote.. then solve the double inequality

[alpine sable]

c*15/90=5/3

10 cooks

[glass lichen]

that will correspond to a range of y values, to which you can find the corresponding x values

then find delta

[eternal juniper]

so 0.5<f(x)<1.5 and then how do you find delta from the x values

[glass lichen]

Yes, so if f(x)=0.5, what's x?

[eternal juniper]

root of 0.5

[glass lichen]

yes, and f(x)=1.5 means x = sqrt(3/2)

[eternal juniper]

yea

[glass lichen]

so if $f(x)\in(0.5,1.5)$ then $x\in\left(\frac{1}{\sqrt{2}},\sqrt{1.5}\right)$

[ocean seal]

moshill1

[glass lichen]

so $\frac{1}{\sqrt{2}}<x<\sqrt{\frac{3}{2}}$

[eternal juniper]

yeah

[ocean seal]

moshill1

[glass lichen]

am I doing this right one sec

[shrewd warren]

Hi can you help me make a normal curve

[eternal juniper]

answers for an example problem if you need it

[glass lichen]

Yeah you're better off just doing the epsilon-delta

then using that to determine delta, given the epsilon

[eternal juniper]

so what's the more efficient way to solve it

[glass lichen]

eps-del

[eternal juniper]

yea what do you do for that

[alpine sable]

Could someone help me with regents review?

Please

<@&286206848099549185>

[regal spruce]

<@&286206848099549185> i need help, how do i find the equation of this function with just the graph

[night blade]

dont ping helpers immediately its so annoying just be patient

it will make you less likely to be helped

[night blade]

same with you

[alpine sable]

Ok

Is this right?

The graph part

[uncut osprey]

I'm a bit too lazy to check the accuracy of the points you've placed, but the general shape and position are correct

[alpine sable]

Ok thanks

Also i have one more question

Ik how to do the last part of this but how would i do the first part

I think i need to find like the vertex

But then what

Oh wait

Or do i use the table

And find out how many feet it is at

Between 1-2 seconds on my calc

[uncut osprey]

It might be easier if you visualize what the equation looks like first

[alpine sable]

The graph would open downards

[uncut osprey]

mmmhm

[alpine sable]

Am i supposed to look on my calc

For the points?

[uncut osprey]

You could if you'd like

[alpine sable]

Wait im so confused

How would i find this on my calculator

Do i look at x value 1?

And see what y is?

[uncut osprey]

Actually I'm kinda confused too on the wording of the question too

[alpine sable]

Or the second after the vertex?

[uncut osprey]

Oh ok the wording makes sense now I think

[alpine sable]

Please explain lol

First off what second was it dropped at loo

Lol

0?

[uncut osprey]

It's asking for the change in height between 1-2 seconds

I believe

[alpine sable]

So do i look here?

Then do i subtract?

[uncut osprey]

Yes

[alpine sable]

Ah i see

Ty

[uncut osprey]

np

[alpine sable]

I may have another question if i get stuck in the next problem

[uncut osprey]

Wait is this a test?

[alpine sable]

No regents review

Ill show u

A pic

Of front page

[viscid yacht]

I’m her sister hi

@uncut osprey

I need help

[alpine sable]

The rest of the info has private school info

[viscid yacht]

Last page

[alpine sable]

Wait anna

He’s still helping me

This channel is occupied

[viscid yacht]

No

I’m her sister and we have the same questions

[alpine sable]

Do i set it equal to zero?

[viscid yacht]

She’s an idiot

It’s a test

[alpine sable]

Oh it cut off to reach the ground

[viscid yacht]

It’s a test

She’s cheating

[alpine sable]

Shut up its not

I sent him a pic

Its regents revuew

Review

[viscid yacht]

Yea of a different packet

She’s cheating

[alpine sable]

If it was a test ud be cheating too

Since we have same@packet

And why would u have a test

Late at night

Could you please help?

Is this right so far and if so what do i do next?

Wait

I think i got it

Ill send u the answer and could u tell me if its right?

I checked on my calc and i believe its 4 and i did it algebraically too:)

Oh lord

Im confused on the next thing

Could someone explain this to me?

Its the last thing i need help on

I forgot about system of equations its been so long

And i really wanna go to sleep after this but my dads forcing me to finish this regents review:(

[cold monolith]

Mario buys some Doritos and some Funyuns and it costs him a total of some amount

x is the price of Doritos, so if you buy 5 Doritos, that would be 5x

[alpine sable]

Wait i have to put these equations in y=mx +b form right?

[cold monolith]

Or Ax+By=C, but yeah

[alpine sable]

Can we do y=mx+b lol

Thats what im familiar with

[cold monolith]

It’s your call but that’s not how the problem is set up to be started

[alpine sable]

Oh-

So im confused now

What equation do i use

[cold monolith]

It will be easiest to start with ax+by=c then solve for y

[alpine sable]

Quadratic formula?

Or slope?

My sister says she did it in slope formula im so confuseddd

Wait but is it still possible to do y=mx+b?

[cold monolith]

If Joe buys 4 Doritos for $x each and 3 Funyuns for $y each and pays $30 total, then you can write a linear equation from that of 4x+3y=30

From there you can turn it into y=-4/3x + 10

[alpine sable]

Ok so for mario

Can we do

[cold monolith]

Note: I made up everything except the x and y parts

[alpine sable]

3x +2y+ 19?

Is that correct for mario?

[cold monolith]

If you replace the 2nd + with an =

[alpine sable]

Ohh i see

OH

So

3x+2y=19

Then for marioo...

I mean

Luigi

2x+4y=24

Right?

[cold monolith]

So far so good

[alpine sable]

So do i use substitution or elimination method? Or wth do i do next loo

Lol

[cold monolith]

Either

[alpine sable]

Wait

When it says

Write a system of equations that describe the situation what does that mean

[cold monolith]

Or since it says to graph the system you could graph both lines and figure out where they intersect

The system of equations is the two equations you just came up with

[alpine sable]

Oh

So do i put then in y=mx+b form now or use my calc and do it

She said to show work so idk which method to use

[cold monolith]

You can graph them however you graph lines

[alpine sable]

To graph it

Oh wait

I have to put them in y=mx+b form to graph from my calc right?

[cold monolith]

Most calculators require that, yes

[alpine sable]

Ok so

Mario was

3x+2y=19

Ima convert it to the formula and can you chec

Uh what do i do here

[cold monolith]

Looks like for Mario you have y=-3/2 x + 19/2

So you should probably rewrite Luigi’s equation now

[alpine sable]

Ok

Thx

Y=-2/4x+6?

[cold monolith]

Can you simplify that first fraction?

[alpine sable]

Oh yes

-1/2

[cold monolith]

Right

Now graph both lines

[alpine sable]

Ok now i need ur suggestion lol

Look what my math teacher did to me

She printed it out but the printer lines are barely visible what do i do 😭😭

Could we skip to the next question

I can graph it and draw the lines later

Im good with that

We can skip to the next question ig

[cold monolith]

Making your own marks and lines is literally what you should do

[alpine sable]

Yea ill do that after we do the next question

Bow

Now

Heres the last thing i need help with

[cold monolith]

The one where you find the price of the snacks?

[alpine sable]

Yes

[cold monolith]

It’s where the lines cross

[alpine sable]

How?

How do you know thats the answer

Could u explain why i mean

The question is the one that starts with determine btw

[cold monolith]

Alternatively, since you now have two equations solved for y, and y is the same in both equations that means the other sides have to be equal too

[alpine sable]

Im confused

[cold monolith]

Y is the price of a bag of Funyuns

In both equations

And it didn’t change from Mario to Luigi

[alpine sable]

Ok

[cold monolith]

So if y=A and y=B, then A=B

[alpine sable]

Ah i get it

Wait

Actually

On the graph

Theres a part im confused on

So

Would there be four lines on the graph?

[cold monolith]

No

There will be two lines

[alpine sable]

Wait

So what would the x -axis be?

Snacks?

[cold monolith]

Unless you decide to count the axes as lines too

The x variable represents the cost of a bag of Doritos

[alpine sable]

What about funyuns?

[cold monolith]

The x axis is a number line for the purpose of displaying that value

The y variable is the price of a bag of Funyuns

That’s what the words say

[alpine sable]

Well dont we need an axis for cost tho?

[cold monolith]

How do you mean?

[alpine sable]

Ait

Wait

Maybe

Id understand better if u can explain what relations the graph is supposed to be showing you?

[cold monolith]

If you pick one of the equations, say Mario’s equation, then any point on that line is showing you how much a bag of doritos and a bag of Funyuns would have to cost for him to buy 3 Doritos and 2 Funyuns and spend $19

[alpine sable]

So would i lable the y axis cost?

[cold monolith]

When x is 0 that would mean the Doritos were free and the Funyuns had to make up the total he spent

No, the x axis is the cost of Doritos and the y axis is the cost of Funyuns

[alpine sable]

OHHH

ok ty for ur help

Im good now tysm

[cold monolith]

The amount he spent determines the location of the line

[alpine sable]

Ye i see

[cold monolith]

Ok, good

[alpine sable]

Thx

[cold monolith]

Ye

[heady light]

This is probably pretty sad, but is anyone half decent with 9th grade algebra?
I have 10 problems im clueless on

[woven thorn]

there is definitely people here who can do 9th grade algebra just drop the problems

@heady light

[fresh salmon]

Hey can anyone help me with some year 10 advanced mathematics area questions?

Just on a call real quick there’s only 1 or 2

[shrewd warren]

Hii help me this

[alpine sable]

posted his entire homework lmao

[heady light]

not all of it

the rest is quadratic functions

and hence why i said “prob pretty sad”

[fresh salmon]

Anyone know how to help? Sorry

[noble cape]

Why is the range of sqrt(x) restricted to positive values? I read this in a few books, but both -2 and 2 should be the images of sqrt(4)

[viral root]

If x + 12 = 15, then x + 32 =?

[oak chasm]

@noble cape The square root symbol is the principal square root, which is generally the positive square root.

[alpine sable]

can someone help me with this questions

[upbeat gorge]

petition to rotate your picture 90 degrees counterclockwise so people don't break their necks

[alpine sable]

,rotate

[alpine sable]

,rotate

[alpine sable]

LOL sorry

[upbeat gorge]

for #8 evaluate it individually

[alpine sable]

idk how to do it

ive been absent for a while from school. was at the hospital

apparently im supposed to know how to do this so im not excused

[short turtle]

how is the answer 6 and 1 ??

[upbeat gorge]

do you know cycles of i, ggwp?

[short turtle]

nope

[oak chasm]

@short turtle Go through all the numbers from 1 to 20. See how many match set A's definition.

[upbeat gorge]

as in $i^1, i^2$, and so on

[ocean seal]

CST

[oak chasm]

Similarly, see how many match both A and B at the same time.

[short turtle]

so the question ask us to find the matches?

[spare sage]

yeah so in normal language its basically asking how many multiples of 3 are strictly between 1 and 20 for part i and how many are both multiples of 3 and 4 and are also strictly between 1 and 20 for part ii

i think im not sure but if its interpreted that way then the answers are 6 and 1

[short turtle]

how bout part ii

[spare sage]

ok so set A is all the multiples of 3 and set b is all the multiples of 4

[short turtle]

intersection between a and b?

[spare sage]

so what would A intersection B be

it would basically be all integers that are in A and B, meaning it must be a multiple of both 3 and 4 right

so how many such integers are between 1 and 20

[short turtle]

so part i is asking to find how many multiples of 3 between 1 to 20 and part ii is asking how many intersections between a and b from 1 to 20??

[spare sage]

i think so

[upbeat gorge]

for reference n(S) is the cardinality of S, or the number of elements in set S, or basically how many things satisfy the conditions of S in your case

[spare sage]

im not solid on set theory but it works out with the answers

[short turtle]

Oo I got thanks so much

[spare sage]

np

[alpine sable]

damn

[ruby plover]

Hello!

My solution to this was (5÷4)×(3×3) = 11.25 but it's the wrong answer.

(5÷4) to get the value of each individual mini square.

(3*3) to get the total amount of mini squares in the second bigger square.

Why is my answer incorrect?

[woeful pulsar]

wait, is this counting squares?

obviously 11.25 is not the total number of squares

[ruby plover]

why would it count the squares

[woeful pulsar]

there are 5 squares in the top diagram

[ruby plover]

it says the value of the first big square is 5

[woeful pulsar]

but they didn't say how they get that value

[ruby plover]

okay so it also counts the square that contains all the mini squares inside

[woeful pulsar]

idk what the question is though