help-23

[drowsy moss]

between your 3rd and 4th step you dropped a square

[lean otter]

yup

thank you

BOOM!!!

oh my God, it’s wrong

oh no it’s not

[final loom]

:p Great job

[lean otter]

.close

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[warm prism]

how to get iii

[wind kite]

have you drawn one of those graph visualization thingies

[safe radish]

@warm prism Has your question been resolved?

[warm prism]

yes

[safe radish]

@warm prism Has your question been resolved?

[safe radish]

@warm prism Has your question been resolved?

[warm prism]

fk this

.close

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[terse junco]

quick question, what is x⁻²

[worthy hemlock]

$$x^{-a} = \frac{1}{x^a}$$

[flat frigate]

dldh06

[terse junco]

Woah

just curious no need to answer, why 1 divided by that?

[worthy hemlock]

Property of exponents

[terse junco]

thanks

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[night lance]

Hi, I'm stuck on some homework that I don’t really know how to approach

[night lance]

I'm not sure how to calculate a sinus equation without the use of a calculator

[sonic sail]

ok o mighty lord of reincarnation

[night lance]

Made me giggle thanks

[sonic sail]

first evaluate f at x=2 then evaluate g at x=whatever you got from that

[night lance]

Okay, do I start with g(x)?

[sonic sail]

no start with f

[night lance]

Okay, great

So I'm just supposed to put in 2 at x's place in the equation?

[sonic sail]

yes

[night lance]

Okay

Okay, so I got 10.85

I just shortened pi down to 3.14

Hope that’s okay

But now I'm left with sin(10.85)

[sonic sail]

if you round them off they are not equal to the original numbers anymore

i would only round off at the end

[night lance]

I don’t really know the entirety of pi by heart

[sonic sail]

theres no issue with f(2)=sin(5pi/2 + 3) being an ugly expression

add 2 to its square then youre done

[night lance]

Could you elaborate please 🙏 ?

I'm not sure how to approach that one either given I only have a piece of paper and a pencil

I'm not allowed to use much else

[sonic sail]

calculators not needed at all
just plug in x=f(2) which is sin((5pi/2) + 3) to g(x)=x^2+2 and youre done

[worthy hemlock]

Basically don't simplify

[sonic sail]

sin((5pi/2) + 3) is what you should get as f(2)

[worthy hemlock]

Just take that f(x) value and plug it straight into g(x)

[night lance]

So if I'm getting this straight uhm sin(5pi/2+2) is supposed to go into g(x) like g(sin(5pi/2+3))?

[sonic sail]

yes

thats what it means to plug in x=f(2) to g(x)

[night lance]

Okay, done now how do I calculate this?

[sonic sail]

if youve plugged it in youre done

[night lance]

Seriously? That’s wizardry

[sonic sail]

its called getting the exact answer

a roundedoff answer is not exact

[night lance]

So, this is actually the closest to the exact answer I can get using only my head, paper and a pencil?

[sonic sail]

this should probably teach you not to always rely on calculators

[night lance]

You're right about that!

[sonic sail]

if youve plugged it in thats the exact answer

[night lance]

Can I send a picture of my paper for confirmation?

[sonic sail]

send away

[sonic sail]

you havent plugged anything into x^2+2 yet

[night lance]

Guess it was a good call to confirm

[sonic sail]

g(x)=x^2+2 so replace x by whatever f(2) is if you want to get g(f(2))

[night lance]

Okay, so if I get it straight (I'll send another picture in a second)

[sonic sail]

you can write 5 times pi/2 as 5pi / 2 with 5pi as numerator

[night lance]

Like so?

[sonic sail]

the square of sin(x) can be written as sin^2(x) as well

good for minimizing use of parentheses

[night lance]

Okay, so I can raise sinus to the second power?

like sin^2(5*pi...)?

[sonic sail]

yes

[night lance]

That’s pretty brilliant

[sonic sail]

similar things possible with cos and tan

and their reciprocal functions csc sec and cot

[night lance]

Haven’t gotten to those yet

[sonic sail]

anyhow with that simplification thats it

[night lance]

Awesome! That’s really amazing!

Math is pretty great once you understand it huh?

[sonic sail]

i wish

[night lance]

That’s fair I guess I just feel a bit Euphoric after solving that one (with help of course)

You shan’t go unmentioned 🙂

Up for another?

[sonic sail]

no issues

[night lance]

There’s one more I'm stuck on

[sonic sail]

were here to help eventually

[night lance]

This one says calculators allowed

thankfully

[sonic sail]

and expected to round off or what

[night lance]

Huh?

Oh is it kinda like one per session?

[worthy hemlock]

Like how much to round

[sonic sail]

i dont know what you mean

[night lance]

I’m so confused

[sonic sail]

i was asking if youre required to round off the final answer

[night lance]

Oh no thankfully not

This one is about Vectors

[sonic sail]

ask away

[night lance]

Awesome!

Sorry it took a second I had to write it down and translate it

[sonic sail]

im not certain on what the notation (a,b) means

[night lance]

That’s fair

I'll just figure it out in a jiffy

[sonic sail]

did they say what that notation means

[night lance]

Not really no

[sonic sail]

where that coming from

[night lance]

My assignment

Looks like this

[sonic sail]

oh

[night lance]

But b is the one I'm stuck on

[sonic sail]

you forgot about det

[night lance]

Oh I'm sorry

I mistook it for a word

😅That's embarrassing

[sonic sail]

first form a matrix by putting b next to a as column vectors

you know how to find determinant of (square) matrices dont you

[night lance]

a1 * b2 and such?

[sonic sail]

the matrix formed is a 2by2 matrix

no just put the vector b beside the vector a as columns of a matrix

[night lance]

Oh I think I get it

Like so

[sonic sail]

if it helps heres how i knew about what the notation meanshttps://math.stackexchange.com/questions/3141770/what-is-the-determinant-of-two-vectors

yes then find determinant of that and set it equal to 30

[night lance]

I think I get it

It goes a1 * b2-a2 * b1= 30 right?

[sonic sail]

yes

[night lance]

Awesome!

[sonic sail]

i would rather you not use that notation for multiplication seeing as were talking about matrices
you dont want to mistake it for dot products

your notation earlier is fine

[night lance]

Okay so * instead?

[sonic sail]

works

[night lance]

Okay, I changed it back

[sonic sail]

you should really be using the actual entries of the matrix now

[night lance]

I misunderstood what you said there

So far I'm at 42 - 3t = 30

[sonic sail]

and set that equal to 30

solve for t

[night lance]

I got t = 4

[sonic sail]

looks good

[night lance]

Awesome! thank you for everything 🙂

[sonic sail]

np

[night lance]

.close

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[lean otter]

Hello

[lean otter]

next time post your question directly

I applied chain rule here:

this is help channel

sin(2pix - 3pi) (2pi)

But in the book answer is shown as:

hmmm

[pulsar condor]

$\sin(x-\pi)=-\sin(x)$

[flat frigate]

Mosh

[pulsar condor]

trig identities

[lean otter]

Yes, Thank you for pointing out that 🙂 @pulsar condor

.close

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[lean otter]

Sorry for opening it again.

Then will not be answer negative? @pulsar condor

2pi - sin(2pix)

[pulsar condor]

$f'(x)=-2\pi\sin(2\pi x-3\pi)$ directly.

[flat frigate]

Mosh

[pulsar condor]

to which you then simplify w/ identities to get $2\pi\sin(2\pi x)$

[queen parcel]

subtracting π 3 times will give you a net negative sign, which cancels with the negative in front of the 2π

[flat frigate]

Mosh

[queen parcel]

3 negatives

[lean otter]

.close

.reopen

[safe radish]

✅

[lean otter]

.close

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[night lance]

Hello, kind people of the internet I'm yet again uncertain as to how I'm supposed to approach a question

[lean otter]

do wht the question asks

[night lance]

Yeah, but I have trouble getting started

[lean otter]

in taking out the derivative ?

[night lance]

Okay, I think I might have translated it wrong or in a weird way, but I'm pretty sure I'm supposed to prove it

[lean otter]

yes

[remote bison]

I guess it’s just asking u whether for the function the second condition is true

That dy/dx == x/root(x sq + 1)

[night lance]

Yeah, I'm fairly certain that’s what it meant I've just translated the question wrong

Though I have to do it without any sort of calculator

My only allowed tools are my pen and paper

[remote bison]

U don’t need a calculator for this anyway

[night lance]

That’s likely very true

I just have trouble getting started

I kinda function like an old car with a dead battery

[lean otter]

you know chain rule ?

[night lance]

Okay, I do now that I have translated it

[lean otter]

use it to find the derivaive and put it in the second equation

[night lance]

in x's place?

[lean otter]

in dy/dx

[night lance]

I'm sorry I don’t quite get it

[lean otter]

didi you understand the question ?

[night lance]

No, I didn’t. 😅

[lean otter]

you need to prove something

[night lance]

That I understand

[lean otter]

so first simplfy the LHS

see if it comes equal to RHS

[night lance]

Okay, I'm really bad at simplifying though, so please be patient with me.

[lean otter]

no worries

[night lance]

okay I got y=sqrt(x^2+1) So I guess it's true?

Although I don’t really understand what I've done

[lean otter]

i think this was already given

[night lance]

I stand by my statement then

I don’t get it

[lean otter]

you know F(x) and y mean the same thing.....right ?

[night lance]

I do

[lean otter]

then take out dy/dx and then multiply the result with y(which is F(x) and given )

[night lance]

Okay so dy/dx = y'

and y has to equal the sqrt(x^2+1) which was given

then y'= x/(x^2+1)^0.5 right?

and y*dy/dx=x

and then if I'm not mistaken sqrt(x^2+1) * x/(x^2+1)^0.5=x

[lean otter]

yup

[night lance]

Am I right so far?

[lean otter]

and i think you i solved the question

have*

[night lance]

Oh thank god I can finally go to sleep thx for the help!

.close

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[upbeat canyon]

Is the local truncation error for third order taylor series just the fourth term of taylor series ((x-a)/4!)y''''?

[safe radish]

@upbeat canyon Has your question been resolved?

[broken yew]

ofc not

what about the 5th?

6th?

etc.

[upbeat canyon]

here's the problem it is referring to

"local truncation error" not equation mb

my solution:

[broken yew]

Then give the leading term of that formula...

That Q is also diff from what you asked

[upbeat canyon]

Is the leading term just the equation I have then?

[broken yew]

I've no clue what the full formula is.

Check your book/notes.

[upbeat canyon]

.close

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[prime tinsel]

is there any way to integrate "x^4 / 4x" quickly without by parts?

[plain lion]

yes you can simplify it first

and then its a polynomial

[prime tinsel]

wait shoot I'm absolutely blind

good point

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[sterile vault]

What's the formula for doing Radians to Degrees and Degrees to Radians?

[pulsar condor]

pi radians = 180 degrees

[sterile vault]

hi mosh thanks for helping

so I do

Pi3.492x180?

[pulsar condor]

No

pi/180 is the conversion factor

[sterile vault]

alr

so

I do

3.492x 180/pi?

[pulsar condor]

well idk

[sterile vault]

oh

[pulsar condor]

is 3.492 radians or degrees...?

[sterile vault]

oh

radians

[pulsar condor]

then yes.

[sterile vault]

if I were doing

degrees to radians I would do 50x pi/180?

[ancient escarp]

if 50 is degrees yeah

[sterile vault]

this 1

I know my answer

but idk what to put in box

I got 29.7448813

[pulsar condor]

how did you get 29.7...?

[sterile vault]

basically I did pythag to find the missing side of H

did then sin-1 O/H

[pulsar condor]

so you found the hypotenuse

[sterile vault]

ye

[pulsar condor]

you're not asked for theta....

you're asked for sin(theta)

[sterile vault]

ok well

I did sin-1 o/h on calculator

[pulsar condor]

That's still wrong

[sterile vault]

oh

then what did I do wrong?

[pulsar condor]

regardless of if you say it again

You found theta

[sterile vault]

yee

[pulsar condor]

And as I just said

you're not asked theta=?

[sterile vault]

oh

[pulsar condor]

you're asked sin(theta)=?

[sterile vault]

oh ok ok

I undersatnd now

I just do the O/H

and that's my answer?

[pulsar condor]

only cause you're in Q1, yes.

[sterile vault]

alr

there is another way of answering like uhh

instead of dividing it

[pulsar condor]

no.

[sterile vault]

oh ok

so I have to divide it?

[pulsar condor]

no, you leave it as an exact value.

[sterile vault]

ok

[pulsar condor]

Read the instructions and question btw

[sterile vault]

sorry I'm not good at reading n stuff that's why I had iep in high school

the words always mix me up hehe

oh yeh 1 more question

since I found hypotinuse which is 8.062257748

does that mean I need to round it?

or just leave it at it is as my answer

[pulsar condor]

no

the hypotenuse is sqrt(something)

you leave it as sqrt(something).

You do not approximate it

[pulsar condor]

.

[sterile vault]

oh ok ok got it

so

4/sqrt(65)

like that?

[pulsar condor]

yes.

[sterile vault]

alr sounds good

thank you

[safe radish]

@sterile vault Has your question been resolved?

[sterile vault]

I got a few more

[safe radish]

@sterile vault Has your question been resolved?

[sterile vault]

ye

[safe radish]

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[zinc ledge]

I was just wondering what this partial derivative yeilds exactly

I understand what partial derivatives of 3d funcitons give

with respect to x or y

but i dont know when its both

[frigid geyser]

it means $(f_x)_y$

[flat frigate]

Camilleone

[zinc ledge]

derivative with respect to x * derivative with respect to y?

[frigid geyser]

no, derivative with respect to x, then differentiate the result with respect to y

[zinc ledge]

ohh i think i understand

i dont think you can represent this in 3d right?

.close

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[untold wadi]

Let G1, G2, and G3 be groups, and let f: G1 → G2 and g : G2 → G3 be isomorphisms. Prove that g ∘ f : G1 →G3
is an isomorphism.

[broken yew]

For all of these questions, you want to write the formal definitions

Being as precise with notation as possible

This usually leads you to answer

[untold wadi]

Okay I got stuck again. I'm starting where I want to show g°f is injective. Where a,b are in G1 and f(a)=f(b). Since we know f is injective cuz it's isomorphic, we know its a=b. Then I wanna show g(f(a))=g(f(b)) to be a=b

[broken yew]

Write down the defns of injections for both f and g

$$(\forall a_1, b_1 \in G_1)(f(a_1)=f(b_1)\implies a_1 = b_1)$$
$$(\forall a_2, b_2 \in G_2)(g(a_2)=g(b_2)\implies a_2 = b_2)$$

[flat frigate]

Shuri2060

[broken yew]

Then for your question, you start with any x, y in G_1

$g(f(x)) = g(f(y)) \implies ???$

[flat frigate]

Shuri2060

[untold wadi]

Since we know f is injective, then f(x)=x and f(y) = y. And it's the same for g, so in the end we get x=y from g(f(x))=g(f(y))?

[broken yew]

since g is injective, you get
f(x) = f(y)

[untold wadi]

Oh yeah

I guess I went backwards there

[broken yew]

what u said isnt true

f(x) = x

no

Make sure you know which set everything belongs to

[untold wadi]

f(x) and f(y) are in G2?

[broken yew]

yh

[untold wadi]

And g(f(x or y)) are in G3?

[safe radish]

@untold wadi Has your question been resolved?

[safe radish]

@untold wadi Has your question been resolved?

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[forest parrot]

N

[forest parrot]

Need help with this please

[lean otter]

You can use transformations

or make a x y table

Convert to y=mx+b graph it

You got many options

[forest parrot]

How would I make an x and y table

[lean otter]

You can make a table for x inputs and y outputs

Most people start with -2, -1, 0, 1, 2

[safe radish]

@forest parrot Has your question been resolved?

[safe radish]

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[stark sage]

Let A and B be events satisfying n(A) = 33, n(B) = 29 and n(A∪B) = 35. Calculate the following: $$n[(A\cap B)\cup(A\cap\bar{B})]$$

[flat frigate]

CAT

[stark sage]

i know how to solve inside the parentheses but what do i do after

hi

[deep kiln]

well its an or sign right so you can just add them if it was an and sign it would have to be the minimum of your value

[stark sage]

so for the first set i got 27 and the second i got 6. now for the union..i just add those 2 to get 33??

bc i know theres the rule for unions where you have to exlude the intersection so im just confused on that part??

[deep kiln]

yes but make sure you dont count the union of A and B twice

oh yea thats what Im talking about

[stark sage]

so substituting their values i would get $$(27)\cup(33)= 33$$

[flat frigate]

CAT

[stark sage]

oops i meant for a 6 instead of the first 33

i drew a picture too and it added up...but i was scared about that intersection part

[deep kiln]

P(A∪B)=P(A)+P(B)−P(A∩B) here is the general formula which you were refering to

[stark sage]

yeah!

so im right then that its 33?

is there like a "whiteboard" here on discord bc i would like somewhere to write what im saying instead of typing everything

or like a voice room where we talk instead of type

[deep kiln]

that is what voice calls are for. Some people write on their screens also

since math is hard to translate into text form

[stark sage]

how do i set up voice calls when i need help ?

[deep kiln]

not sure but I know its possible.

[stark sage]

ok so it is 33 then?

[deep kiln]

yes

[stark sage]

alright thanks man!

.done

[deep kiln]

.close

[stark sage]

.close

[safe radish]

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[fast radish]

I would like help with my polynomials hw please

[worldly basin]

So for this your Y-int(s) are where X=0 and X-int(s) are where Y=0

Meaning for X-int(s): 0= your polynomials and find where that holds true

[fast radish]

@worldly basin how to do the end behavior?

[worldly basin]

In the case of #7, one of them is 4 because 4-4=0 and anything X0=0

Lemme check

Okay behavior is basically is it an odd or even function and positive/negative, and how many maxima/minima there are

So you would use the intercepts for main points in your graph

If it is an even function it will have a parabolic shape, whereas an odd one will be more of a line

If it’s positive for even functions they will open upward (like a cup) if negative it will open downward (like a bowl)

For positive odd functions they will have a positive slope, whereas negative ones will have a negative slope (meaning if you went from L->R generally they will increase in value (positive) or decrease in value (negative))

For visuals lemme draw it

(These are all positive btw)

[fast radish]

So how do I solve each letter of 7-9?

[worldly basin]

But basically as the value of X goes to higher powers, the Y values increase exponentially

That was at the beginning of what i said

For y-int make X=0 and vise versa for x-int

[worldly basin]

In the case of 7) one x-int would be (4,0) because 4-4=0 so 0=(0)(x+2) which is true so what other case would make Y=0?

[fast radish]

-2+2‽

[worldly basin]

Yep -2 would be the second one because like you said -2+2=0

So in coordinates (-2,0)

Need anythig else

[fast radish]

How would I graph them?

[worldly basin]

Put points on the 2 x-int you found

And if you wanna go further find the y-int (if any) where X=0 and solving for Y

And then just follow the general trend for odd/even functions

That i drew before

[fast radish]

Just a parabola?

[worldly basin]

For even ones yes positive= pointing up like a cup negative down like a bowl

For odd it was like i drew where the plateau in the middle gets smaller and smaller for higher powers and it increases in Y faster and faster

[fast radish]

I tried my best to replicate your drawing when graphing

[worldly basin]

Right idea but they continue past those intercepts infinitely

So you make the lines with arrows on end past the points

[fast radish]

@worldly basin do I distribute for the 8th one

<@&286206848099549185>

[safe radish]

@fast radish Has your question been resolved?

[wind kite]

ok

what are its roots

[fast radish]

The roots?

X²???

@wind kite

[wind kite]

no

the values for x when y is 0

[fast radish]

I am confused can you explain it more

[worldly basin]

Roots is another way of saying intercepts

And no you don’t distribute the X

You can imagine it as (X-0) effectively if that helps

Or just know when it is 0=x(……..)(…..) what would make that X value=0?

(Hint it is 0)

[fast radish]

Does that mean I solve inside the parentheses of (x+5) and (x-8) for the X's?

well for (x+5) (-5+5) would make a 0. Is that the meaning of this lesson?

[safe radish]

@fast radish Has your question been resolved?

[safe radish]

@fast radish Has your question been resolved?

[safe radish]

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[frail glacier]

wha function should i use to model this?

hm can natural logarithm work?

[safe radish]

@frail glacier Has your question been resolved?

[mortal meteor]

i would model the left part with a straight line and the right part with a sphere or an ellipsoid

[safe radish]

@frail glacier Has your question been resolved?

[safe radish]

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[potent kernel]

a man bought a horse for $60, sold it for $70, bought it back for $80, sold it $90. Now hear me out, i know the answer is $20, but i am getting 10, why aint that right? ( Q: find the total profit)

[potent kernel]

when he sold it for 70, he got 10 as the profit

now he sold something he had bought for 70 at 80, so thats a 10 loss

10-10=0

then he sold something he bought for 80 at 90, so thats a 10 proft

0 + 10 = 10

i know how u get 20, but i wanna know why my way of doin it is so wrong

[hard iron]

isnt this the profit of just the last transaction?

[potent kernel]

ye

[hard iron]

so you gotta consider that + the 1st profit

to get your result

dont you (?)

[potent kernel]

no but like

i get it

but

whys the way i did it wrong

[hard iron]

i dont think is wrong, seems just incomplete to me

[potent kernel]

thats what i wanna know, did i just discover a flaw in maths 🤨

[hard iron]

lol

lemme try again

[potent kernel]

okay

[hard iron]

i got 20 by doing like
60-60=0 to buy the horse
0+70=70-60=10 is the first profit
then it goes 70-80=-10
and -10+90=80-70=10 which is the second profit
the you gotta sum the 2 prof to get 20

i think you missed the last line in your solve

[potent kernel]

i understand till u get 10 as the first proft

how u got the -10 + 90 = 80-70

[hard iron]

probably i had to do it separately

-10 is what he has after buying the horse, 90 is what he gets, 80 is the current cash
then 80 - 70 which is the starting cash make the profit

[potent kernel]

OHHHH

THATS WHAT I MISSED

ok think i got it

thx

👍

[hard iron]

np

also, lookin at what you wrote i got also another explanation to whats wrong

[potent kernel]

psl tell

[hushed mirage]

-10 is what he has?

at what point does he have negative money

[potent kernel]

debt

[hushed mirage]

debt

its late

[potent kernel]

wot

[potent kernel]

pls tellllll

[hard iron]

like, starting from here you count the +10 profit twice and a -10 loss which is true, but then you got 10 - 10 + 10 = 10, which is not the total profit, you gotta consider the ending cash 90 - the starting 60 and then also add the meanwhile profit which is +10 so u get 90-(60+10)=20

i think should be like this

[potent kernel]

lemme read it

[hard iron]

sure

[potent kernel]

so

what u mean is,

i get 10

remaining cash is 30

i minus 10 from 30

to get the actual proft

that way i am getting the profit on what i have

innit?

[hard iron]

i think yes

[potent kernel]

hm

that makes sense

wait what

wait wait lemme read it again i got it all messed up

oh

shoot

got it

thank you

[hard iron]

np

[potent kernel]

👍

[lean otter]

Could someone explain me what Maijer G-functions are and how they work?

[safe radish]

@potent kernel Has your question been resolved?

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[fathom parcel]

I have to find the derivative of R* sin(theta)* e_phi with respect to t. all of them have a factor xt, but i don´t know x. So how can i write down the derivative in general. for example: d/dt(R* e_phi) would be d/dt(R)* e_phi+R*d/dt(e_phi). But how is it when i have three factors which include an t?

[fathom parcel]

So i actually just want to know how the product rule works when i have 3 factors instead of 2.

[quasi bison]

well technically you could just apply the product rule recursively

but writing it out explicitly for three terms is not that bad

you get (f * g * h)' = f'gh + fg'h + fgh'

[fathom parcel]

oh ok. did not think it would be this easy

.close

[safe radish]

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[lean otter]

<@&286206848099549185>

[safe radish]

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[true jetty]

hi

[true jetty]

https://cdn.discordapp.com/attachments/938479969821134848/938479978562064404/unknown.png

how do I find the minimum distance between the plane 1 and the origin

[proper crypt]

what is r * (1, 2, 1) = 2?

[true jetty]

a plane

[proper crypt]

Is that even a plane

[true jetty]

I think the (1,2,1) is meant to be vertical

as in x+2y+z=2

[proper crypt]

I'm currently learning these stuff aswell

but this type of equation seems weird?

variable times vector equal a number?

well

about ur question

the minimum distance should the distance of the vector that starts at the origin and is perpendicular to plane 1

[pulsar condor]

r, not r

r := [x,y,z]^T

[proper crypt]

What is ^T?

[pulsar condor]

Makes it a column vector.

[proper crypt]

And :=?

[pulsar condor]

defined to be.

[proper crypt]

I only use vectors like (1, 1, 1)

[pulsar condor]

cool, r is also a coordinate vector.

[proper crypt]

He's doing something else then?

Oh

r is a vector

[pulsar condor]

yes

hence why it's bold.

[proper crypt]

You multiply each point on plane 2 by (1, 2, 1)?

[pulsar condor]

dot product...

[proper crypt]

Yeah

[pulsar condor]

so no

scaling isn't dotting.

[proper crypt]

well

thats what I meant

i meant dot product

but my question is

wait what

how is it equal to 2 tho?

[pulsar condor]

Open a new channel for your questions.

[proper crypt]

alr lol

[pulsar condor]

Cause you're just flooding this help channel.

[proper crypt]

. i'll bump this

[pulsar condor]

what have you tried?

[true jetty]

im doing this

for the first one

[pulsar condor]

right so yeah, the minimum distance will be the orthogonal distance

[true jetty]

what about the second one

[pulsar condor]

I mean you can always just find the cartesian equation for the plane

[true jetty]

yea

<@&286206848099549185>

how would you work out the 3rd one

[safe radish]

@true jetty Has your question been resolved?

[safe radish]

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[dusky kestrel]

hi

[dusky kestrel]

this is my homework question, i was absent for the beginning of the sine functions unit and im very confused

y=1/5sin(x+30)-2 would this be it

[safe radish]

@dusky kestrel Has your question been resolved?

[crisp lodge]

oof...

that +30 is sus

sin is usually graphed with radians as it's x values, not degrees

also, remember the reflection

[safe radish]

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[lean otter]

https://i.imgur.com/uuxfUbF.png

[lean otter]

i think its [-4.-3) U (1,5)

https://i.imgur.com/er6uSaR.png
THIS TOO. not sure about my answer for second interval tho

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

you can take some points that the graph passes through with a negative y axis

and check the outputs

[lean otter]

passes through: (-1, -4), (0, -2), (6, -1)

[safe radish]

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[ebon rock]

back again with logs :/

[ebon rock]

anyone know where I've gone wrong or what I need to do next?

just realised this may help as it's a multiple part question

[crisp lodge]

it looks right from first glance

[crisp lodge]

this is just fine

[ebon rock]

just need ii)

[crisp lodge]

Okay.. at i) you proved the existence of one such point by showing only one value of y is valid

that is the y coord of the intersection point

so.. you only need to find x

keep in mind its an intersection point

[ebon rock]

yh I think I need to solve for x so I put $7^x = 7^{2x}-12$

[flat frigate]

Flodz

[crisp lodge]

oh

scheise

[ebon rock]

put them equal since its an intersection point, or do I use y?

[crisp lodge]

i got confused by your variable of choice lol

mb

you found y

y=4 right ?

thus 7^x = 4

[ebon rock]

y = 4

[crisp lodge]

this is your solve for x

[ebon rock]

so I just log_7(4)=x?

[crisp lodge]

yep

[ebon rock]

no wonder its a 2 mark question

[crisp lodge]

Now you need the y coord

[ebon rock]

shoulda noticed

[crisp lodge]

which is a natural follow up

[ebon rock]

so then I put x into either of the equations

so 7^x because its just easier

,calc 7^4

[flat frigate]

Result:

2401

[ebon rock]

so (4, 2401)?

[crisp lodge]

Not

quite.. ?

a bit far off

how come x=4 ?

[ebon rock]

wait yh no I haven't even solved x yet, hang on

let me write it down I'm getting ahead of myself

[crisp lodge]

but you did !

you solved for both already !

[crisp lodge]

here is your x !

and your y was computed by solving the quadratic

[ebon rock]

ikik, I've lost my pencil give me a sec 😭

[crisp lodge]

rofl

[ebon rock]

,calc log_7(4)

[flat frigate]

The following error occured while calculating:
Error: Undefined function log_7

[ebon rock]

,calc log7(4)

[flat frigate]

The following error occured while calculating:
Error: Undefined function log7

[ebon rock]

nvm actual calculator it is

0.712 to 3 sf

that's it I think

thanks

[crisp lodge]

yea

looks better

[ebon rock]

I'll be back soon with more questions, logs is the death of me

[crisp lodge]

once you get the hang of it it's a breeze :)

[ebon rock]

this is my final question I need help with

so I tried substituting y in where the was e^x but I never got the answer shown

[flat frigate]

Flodz

[ebon rock]

clearly not what I need

b) (i) btw

[median turtle]

1/y^x is not correct

e^{-x} = 1/e^x and remember y = e^x

[safe radish]

@ebon rock Has your question been resolved?

[crisp lodge]

^

[ebon rock]

so just 20/y, I mightve done that anyway but still I don't get close to what I'm after

[crisp lodge]

get rid of the fraction now

[safe radish]

@ebon rock Has your question been resolved?

[safe radish]

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[signal granite]

What function can i use to plot this situation: every person recruits 6 people starting with 1 person. (basically a pyramid scheme where every person has to recruit 6 more)

[signal granite]

its a simple exponential growth problem but idk 4sum reason

[crisp lodge]

whar are you plotting exactly?

the total amount of people ?

[broken yew]

$$a_n = a_{n-1} + 6(a_{n-1} - a_{n-2})$$

[flat frigate]

Shuri2060

[signal granite]

idk what that means shuri

[signal granite]

amount of people over time/generation

so ig every generation there's an increase of 6 people per person

[broken yew]

Let a_n be people @ time n

According to you, not.

One person recruits exactly 6 and only once.

[signal granite]

yes per generation you add 6 for the new generation

[broken yew]

well think carefully if this describes what you wanted.

[signal granite]

hmmm

i guess it does, thanks bro!

.close

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[sterile vault]

Remind the the formula is

sin17.5= O/H

which is 17.5 = a/0.0865

so sin17.5x0.0865

right?

[tardy lark]

What value are you trying to find @sterile vault

[sterile vault]

c and a

a and b*

[tardy lark]

Ok lets start with a

[sterile vault]

bet

[tardy lark]

whats the formula

[sterile vault]

sin17.5= 0.0865

sin17.5(0.0865)

short cut

[tardy lark]

sinx=o/h right ?

[sterile vault]

ye

0.026011051

[tardy lark]

What is o ?

And what is H ?

[sterile vault]

o is a

O/H

sin

[tardy lark]

What is H ?

[sterile vault]

O=a

[tardy lark]

Yes

[sterile vault]

h is 0.0865

ye

[tardy lark]

Correct

So sinx=a/c right ?

[sterile vault]

ye

yes

[tardy lark]

and Sin(17.5)=a/0.0865

[sterile vault]

yes

that's waht I'm sayin

short cut that shit and do sin17.5x0.0865

[tardy lark]

Yes

[sterile vault]

lol

alr

gucci

0.026011051

[tardy lark]

correct

[sterile vault]

so 0.0260 is my b

a*

[tardy lark]

yes

[sterile vault]

what about b

pythag?

orrr

[tardy lark]

uhm

You could

But you can also use cos=a/h

[sterile vault]

what is fastest

[tardy lark]

i would say cos

[sterile vault]

best

bet*

[tardy lark]

but its pretty much the same

[sterile vault]

so cos72.5(0.0865)

ye

[tardy lark]

yes

Correct

Did you find B?

[sterile vault]

ye

0.026011051

tf

lol

same answer :/

[tardy lark]

why did you put 72.5 as the angle

[sterile vault]

I did 180-90-16.5

17.5*

mb mb

[tardy lark]

no

Its still 17.5

[sterile vault]

you right mb

[tardy lark]

its kk

[sterile vault]

?

oh ok

so it's cos17.5(0.0865)

[tardy lark]

Yes

[sterile vault]

0.824965162

which would be 0.8250

[tardy lark]

Remember SOH-CAH-TOA

[sterile vault]

0.8250*

ye

thanks

but I round correctly tho right?

why is b bigger than c

tf

[tardy lark]

3 significant figures

[sterile vault]

alr

so 0.925

[tardy lark]

So it would be 0.825

[sterile vault]

ok ok

and 0.025

ye?

0.026*

[tardy lark]

Thats 2 significant figure

[sterile vault]

huh

so

0.260

and 0.825

ye?

[tardy lark]

You forgot a 0

[sterile vault]

oki ok

so

0.260, 0.087?

[tardy lark]

Here yoo

Too

[sterile vault]

alr 0.026, 0.087

ye?

[tardy lark]

3 significant figures

not 2

[sterile vault]

oh ok ok

[tardy lark]

0.260 and 0.0825

[sterile vault]

alr bet

[tardy lark]

Is that all ?

[sterile vault]

lemme check

naw theres more

but I'ma try them myself first

[tardy lark]

kk if you need help hit me up

[sterile vault]

yeh thanks man

you actually the best

other people would try explain in long way

[tardy lark]

Just follow the formula and dont skip steps

And you should get the right answer

[sterile vault]

this 1

looks wrong

I used B theta to find the other sides

I did sin 20.2(23.6)

then I did costhen did cos20.2(23.6)

[tardy lark]

b is wrong

[sterile vault]

yeh I thought so haha

[tardy lark]

xd

[sterile vault]

hmm lemme think

I use A theta to find b?

[tardy lark]

what does theta means ?

[sterile vault]

uhh angle

nvm

forget about it lol

[tardy lark]

k

[sterile vault]

so waht yo gonna tell me

[tardy lark]

To solve b

Do

cos(x)=A/H

c = H

A=a

[sterile vault]

oh ok ok

so it would be

uhh

cos20.2(23.6)

I did that 1 already?

[tardy lark]

its sin this tine

Time

For b

[sterile vault]

oh ok ok

to solve b

I use sin

[tardy lark]

yhea

[sterile vault]

alr

so

[tardy lark]

but

You could use cos with A angle

[sterile vault]

sin20.2(22.14843534)

oh fr?

that would probably be easier

[tardy lark]

yhea

[tardy lark]

Same difficulty

[sterile vault]

I already know A angle

180-90-20.2

[tardy lark]

yhea

Good

[sterile vault]

alr so

[tardy lark]

Focus on one angle

its easier

[sterile vault]

formula is uhh

[tardy lark]

A and O changes depending on the angle you chose

[sterile vault]

gulp

not sure

I wanna do

b/23.6

[tardy lark]

Im sure

[sterile vault]

so that would be umm

[tardy lark]

A is the side closest to your angle

[sterile vault]

alr

so it would be a/h

cos69.8(23.6)

😄

8.1 again?

for b

uhh

??

[tardy lark]

O is the farthest side

[sterile vault]

ye

O would be a

[tardy lark]

Yes for b

[sterile vault]

b*

sorry

ye

so

b/23.6

ye?

cos

[tardy lark]

what

[sterile vault]

like uhh

we using cos

right?

[tardy lark]

youre going way too fast

[sterile vault]

sorry lol

[tardy lark]

Write down your equations on a sheet of paper

Don’t freestyle them in your head

[sterile vault]

lemme type here

for ya

alr

[tardy lark]

Is this your exam ?

[sterile vault]

naw

Hw

practice for test tmr

[tardy lark]

ok

[sterile vault]

lol

wdym

sus

8:20PM exam?

lol

[tardy lark]

could be quiz thats worth smth