math-help

[left knoll]

I UNDERSDTAAAAND

lmaooo

ya'll are life savers istg

[cyan night]

yes

[left knoll]

can u give me more problems if you can blue?

[cyan night]

as i introduced to u before, a function simply requires an input and an output. for every input, there's 1 and only 1 output. the problem helps us determine what's the input and what's the output, in order for our function to be in correct order. the problem often states" y is a function of x", means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x.

[cyan night]

so this problem wants you to indicate 2 abilities, 1 is you know how to apply geometry theorems and 2 is you know how to write a function

u can ask ur prof for more problems i personally dk any lol

[cyan night]

for 1 input there could only exist 1 result, but an output can be the result of many inputs, for example, y = f(x) = x^2, both x = 2 and x = -2 would result in y = 4. but if u input x = 2 u cannot have both y = 4 and y = -4 for example. on the graph, the "undefined function" is represented as a vertical line on the graph. this verticle line indicates that for 1 input there are many outputs, or 1 value of x, many values of y exist. as aforementioned, this is invalid

[left knoll]

omg i was gone for a min

hhaha

you're very kind

[cyan night]

do u get it

dont be afrad to as

ask

afraid

[left knoll]

Blue is a maths enthusiast

[left knoll]

ITS AMAZING

[left knoll]

understooood

[left knoll]

You're amazing too zay 😩

[left knoll]

okayy

[cyan night]

i actually dk really well the term "y is a function of x", biii corrected me so i learnt from it

[left knoll]

i, academically suck pls

blue is awesome, im glad you're into math

[cyan night]

yay thank you

[left knoll]

ur very smart

❤️

[cyan night]

hmm i doubt that 😂

quentin is a master

[left knoll]

gotchuuuu

[left knoll]

Doing good in academics doesn't necessarily define "amazing" 😩 for example you're an amazing singer !!!!!

omg both of u are awesome

[left knoll]

ahh but singing wont do anything for my future ahem

tis just a hobby

[cyan night]

@opal rock

basically

[opal rock]

Yes Blueberry I'm here

[left knoll]

winnie da pooh

[cyan night]

parabola is a way to express quadratics on a graph

it is a symmetrical butt

[left knoll]

Tch tch noo just give your best in everything you do ᕦ(ò_óˇ)ᕤ

[cyan night]

shape of a but

it has symmetry

a parabola has a vertex

[left knoll]

lmaooo you know im right !! Thank you, you too, whatever happens happens

[cyan night]

the vertex could be the absolute min or max of the parabola

depending on if its faced up or down

you can find the vertex

if the quadratic has a solution

the x coordinate of the vertex is the average of the x intercepts' x coordinates

for example quadratic x^2-3x+2

= (x-1) (x-2)

wait

yeah

so its intercepts are 1 and 2

so the vertex's x coordinate is 1+2/2 = 1.5

to find the vertex's y coordinate u simply input its x coordinate to get the ouput

y = (1.5-1)(1.5-2) = -0.25

[left knoll]

you must kidnap me and teach me all the math u know

[opal rock]

His like 13 years old he has a very limited amount of knowledge of mathematics so don't worry

[cyan night]

what

[opal rock]

Ok I see it

[cyan night]

bruh

u dont patronize one person to make another better

[left knoll]

thats... rude

[cyan night]

haha jk its fine

anyway good luck both of you

[left knoll]

No

rude

[cyan night]

dw i forgive

[left knoll]

age dont matter bish

imma smack yo ass

[cyan night]

oh no

[left knoll]

winnie

[opal rock]

I'm sorry Blueberry I sincerely apologise I won't make fun or mock you

[left knoll]

good

[cyan night]

no problem dont fight

ok bye

[opal rock]

Thats true or else we will get in trouble by the police

[cyan night]

HI KNIGHT

[left knoll]

That's contradictory to him

[cyan night]

what

[opal rock]

See ya Blueberry 👋 Thank you for the quick parabola lesson I will hold on to that for sure

[cyan night]

okok

[cyan night]

WHAT

[left knoll]

What

[cyan night]

wdym

[cyan night]

WDYM

[left knoll]

Oof okay dumb question

[cyan night]

hmm

[left knoll]

Uhh

What bii did

After this part

How did it become 1/2 ^d^2

[cyan night]

ok

so

do u know how to calc the area of a square based on diagonals?

she isnt correct actually

it should be a = x^2/2

[left knoll]

Double the sides ?

[cyan night]

its actually the product of 2 diagonals divided by 2

[left knoll]

How so

[cyan night]

cuz its diagonal^2 divided by 2, not just diagonal ^2

the 2 diagonals in a square is equal

hence it is x*x = x^2

[left knoll]

Ahh okay

[cyan night]

the correct answer should be

[left knoll]

What ab the d then

[cyan night]

d/2*sqrt.2

[left knoll]

Ooooo

[cyan night]

she forgot to divide x^2 by 2

[left knoll]

Okay

[cyan night]

so x^2/2 is the area of the square

and we already have x = d/sqrt.2

so it is just (d/sqrt.2/2)^2

= (d/2sqrt.2)^2

[left knoll]

Damn

Okay

I get the gist of it

😂

I need more practice is all

Thank you!!

[cyan night]

ya np any questions just ask here

[left knoll]

Thank u thank u

Appreciate it

[left knoll]

I'mma write all this down too

[cyan night]

okok

ill give u an image

[left knoll]

Okay I've got one more question

😩

[cyan night]

ok

i will give you an image

[left knoll]

Yeeeeesss

This is the same exact one in my book lmaoo

[cyan night]

u see the vertical line here

it isnt a function if it has a vertical line

or two points with same x coordinate

[left knoll]

Yes it's a function because x isn't repeating

HA?

It is a function tho :0

[cyan night]

it isnt a valid function

so we could say it isnt a function since no function exists in order to satisfy that

[left knoll]

Hold up, you're talking about the first one right?

[cyan night]

so what im saying here is u see the stripped vertical line that passes through some points? those points have the same x coordinate

[cyan night]

the not a function ones

[left knoll]

Ahhh

Okay

[left knoll]

I see it now

[cyan night]

so using this graph

for example, we input x = 7

we get y = 5

but we also get y = -5

the ones i circled

[left knoll]

Ahhhh

Ye yes

[cyan night]

whenever 2 points have the same x-coordinate, they create a verticle line, and with that, the function is invalid

[left knoll]

Yess

[cyan night]

ya

[left knoll]

I understand all this I'm just sleepy at this point sorry 😭😭😭

[cyan night]

maybe u can sleep and continue tomorrow

[left knoll]

Ahh I car

Can't

Lmao

I have school tmr and it's only 4 pm

But I understand what you're saying dw

You're good at teaching

ahh another question, i hate this lmao,

Express the edge length of a cube as a function of the cube's diagonal length d.
Then express the surface area and volume of the cube as a function of the diagonal length.

[left knoll]

Literally never took this stuff 😩

[dusty goblet]

does anybody know how can i solve this?

actually, the expression is this

i can't even find a calculator that can solve this, even using differential equations aa

[weary arrow]

are you sure this can be solved?

[hushed flax]

anyone?

[thorn reef]

C. i guess

2 triangles CAB and DAC are similar since ACB^ = CDA^ and they share CAB^.
-> AB/AC = AC/AD = 8 / 3 -> AB = 64 / 3 -> DB = 55/3. Correct me if i'm wrong

[hushed flax]

no no

its right

[dusty goblet]

hmm this was given by my teacher, she could have made a mistake, i can't see how this can be solved either

[weary arrow]

I think it might be, even an online calculator like Wolfram Alpha cannot give a good answer to this, maybe she accidentally put 2x instead of 2 f.ex.

[obsidian sage]

i always use this one to solve integrals

https://www.integral-calculator.com/

[dusty goblet]

i found this but... i don't understand this at all lol, and it's supposed to be an exact differential equation, which it isn't, so i'll assume she typed something wrong. thanks anyways!

[left knoll]

Help :(

[cyan night]

Sorrry I went studying physics zay

[cyan night]

Do similarly, you should know the relationships between the diagonal and the edge length, or the diagonal and the cube length

[left knoll]

:D BLUEEEE

[cyan night]

I am not quite sure about 3D shapes yet u can give it a search

Hi

[left knoll]

Oof physics

[left knoll]

I don't know the relationships

[cyan night]

Search it up

Idk either I’m not good with 3D shapes

[left knoll]

ahh ok

[cyan night]

Let the edge length be x, the problem requires us to express x as a function of d

So x=f(d) = Seth

[cyan night]

Sth

What are the relationships zay

[left knoll]

Because this is a cube, it's helpful to remember that the value of the diagonal of one face is the same length for the other five faces. Additionally, the length of one edge will be the same length of all the cube's other edges.

thats what i got

[cyan night]

Search relationship between diagonal and edge of cube

There’s actually a way using Pythagorean twice to find it but I’m kinda lazy

[left knoll]

A diagonal of a cube is a segment joining two points that are not the endpoints of an edge. ... The final edge is perpendicular in particular to the longest diagonal of the previous cube, and these two segments form the two sides of a right triangle having the longest diagonal of the new cube as its hypotenuse.

okay so we have a hyp

which means imma repeat what we did last time right?

[cyan night]

Have I figured out relationship yet

It should be expressed in variables

Draw it out and follow their directions

[left knoll]

nah it's not showing up the edge of the cube

[cyan night]

Draw it out zay draw the cube and diagonal out

[left knoll]

diagonal = 3 sqrt * x

i did draw it out

😩

[cyan night]

Sqrt of 3* x?

Yes correct

Now u have it then make it a function with d as input and x as output

For question 2 do similarly it instead of the edge, it’s the entire volume, if u know how to calculate the volume of a cube then u are able to find the relationship between the edge and the cube and hence the diagonal and the cube as u previously found how the edge and the diagonal relates

[left knoll]

ahhh okay

[cyan night]

Bye I go to sleep now it’s 12 am

I will help you tmr if u need help

[left knoll]

okayyy

thank u sm

[olive trail]

Hey could anyone please help with this

[dark sorrel]

Put all of the information in a system of equations, then you will have three variables and three equations.

[inland oracle]

how i can do it??

[left knoll]

<@&717391911132069929>

xD

[azure lion]

is it wrong if i rearrange 3x+4 as 4/3 and insert that? i didnt get zero. so what should i do

[obsidian skiff]

Don’t take 4/3

You have to take -4/3

Because 3x+4 = 0
So x = -4/3

Take this x value and substitute it into f(x). You should get zero. And then when you do conclude the
“Therefore (3x+4) is a factor of f(x)

Hope that helps

[ember kernel]

Agreed

To get the other factor, there is a shortcut :
you know that f(x) = 6x² + 5x - 4 = (3x+4)(ax+b) = 3a x² + (3b + 4a) x + 4b

Therefore, that means that 3a = 6 (the coefficient of x²) and 4b = -4 (the coefficient of the independent term)

That gives you a = 2, b = -1 ➡️ the other factor is (ax+b) = (2x-1)

[azure lion]

ty to both yall

[obsidian skiff]

Are you doing A2 maths @azure lion ?

[leaden field]

anyone know how to approach this?

[edgy hinge]

can anyone help me with this

prove a=b=0

[atomic cipher]

Is anyone here familiar with markov chains/stochastic processes?

[peak gale]

Do you know anything about a,b?

[edgy hinge]

A sqrt 2 + b sqrt 3 = 0

[cyan night]

domain?

wait

why would it have domain

lol

[edgy hinge]

ok so we got

and we have to prove a=b=0

[cyan night]

ok

whats ur approach

i think ill do it this way

a sqrr 2 + b sqrt 3 = 0

=> a sqrt 2 = -b sqrt 3

=> -a sqrt 6/3 = b

=> a sqrt 2 + -a sqrt 6/3 = 0

=> -a sqrt 6 + 3 a sqrt 2)/3 = 0

=> - a sqrt 6 + 3a sqrt 2 = 0

=> a sqrt 6 = 3a sqrt 2

and 3 sqrt 2 is not equal to sqrt 6 => a = 0 => b = 0

[ember kernel]

To get the solution a = b = 0, we HAVE to assume a and b are integers

[cyan night]

uhh yeah i figuered that out

[ember kernel]

You said it didn't have a domain tho

[cyan night]

i mean why would the problem give us domain

[cyan night]

is this correct?

i doubt it lol

[edgy hinge]

yes it is

[cyan night]

ok

@ember kernel sorry for the ping but in a non-linear slope (velocity/time graph) that represents motion, does the secant line of any particular point represent its instantaneous change in velocity?

i cant do calculus yet so may this work

[ember kernel]

Every parameter MUST have a domain. Most of the time we just assume it is the real set, but that's not always the case

[cyan night]

but this time they said that prove a = b = 0 why would they give us the domain

of a and b

[ember kernel]

Because you have :

[ember kernel]

If a and b are real, this equation has infinite possibilities of solution: (0; 0), (sqrt{3}; -sqrt{2}), ...

[cyan night]

oh

ok

[ember kernel]

Since the question tells us that the only solution is (0; 0), that means a and b are assumed to be whole numbers

[cyan night]

can u help me out a bit

or is it the tangent line

IDK I DONT GET IT

[ember kernel]

Instantaneous => tangent

[cyan night]

THANK YOU SIR

[ember kernel]

np

[cyan night]

its calculus right

[ember kernel]

It is

It's related to derivatives

[cyan night]

aw man

is there any other way to find instantaneous change

ig i can only work with linear slopes when solving instantaneous velocity

[ember kernel]

How are you asked to find the instantaneous acceleration (= difference of velocity) ?

Graphically or using derivatives (if you know what this is) ?

[cyan night]

i was just questioning it wasnt a question

i mean i was just wondering

[ember kernel]

At your level, you must either use Calculus for a precise answer (for any x of the function and using the derivative of the function itself), or solve graphically to get only an approximation of the actual acceleration (for only one value of x and using the graph of the function)

[cyan night]

wdym at my level

my level is 0 aaaa

[ember kernel]

Middle school

[cyan night]

but i dont have calculus at my level yet

[ember kernel]

Then just use the graph

[cyan night]

ok

[ember kernel]

Draw the tangent at the x-value you want, measure its slope, and that's the instantaneous acceleration (= difference of velocity)

[cyan night]

yes

thank you

[ember kernel]

np!

[left knoll]

@cyan night bii was right yesterday, also we went way too deep into the questions (not bii) because it so easy😭😭

[cyan night]

How

[cyan night]

I was just explaining the concepts

And how is she right

[left knoll]

Ye ye we actually didn't need to know much about the concepts

She made me feel so silly hahaa

Wait I'll voice recording cause it's too long

I will eat first

[cyan night]

Ok

The thing about math is that it’s important to thoroughly get what’s behind the equations, the functions. Not only it makes you more versatile, you would be able to find mathematics interesting.

[left knoll]

Yes yes , we're going deeper don't worry

Ahh I might not have time to explain

Sorry :(

I'll try

[cyan night]

I’ll go to sleep now sorry zay

Good luck

Knight can help u @left knoll

[left knoll]

@cyan night

Oops

I just saw ur sleep message

Oops

Sorry

Idk I must've been high last night 😩

Not literally

I wasn't saying you're wrong blue!

[cyan night]

ok

[vernal finch]

How is this wrong? I did (20-0)*28 +(40-20)(53) + (60-40) * 64 + (80-60) * 50 + (100-80)(44)

[cyan night]

its a miles per hour not miles per second

ya gotta convert the mi/hr to mi/s

and also u should keep in mind the actuality, whether if its asctually ppossible to get 4780 miles in 100 seconds lol

[olive trail]

Hey so I was able to get the first two solutions but can someone explain how to get the second two please?

[white maple]

anyone here familiar with latex?

[ember kernel]

What's the question ?

[white maple]

sorry, i solved it already!

[random flame]

Hi can someone help me solve Q3ai? Ping if you do and thanks in advance! :D

[white plover]

hello, if x maps to themselves that means f(x)=x so you have to solve the equation x=5x/(3-2x)

[raven arch]

you can replace the x's with y's and make x the subject. So, you would have x = 5y/3-2y. then you'd multiply both sides (by 3-2y) to get x(3-2y) = 5y. Expand the brackets --> 3x-2xy = 5y. Add 2xy to both sides --> 3x = 5y + 2xy. Factor out y --> 3x = y(5+2x). Divide by 2x+5 (it looks better in the solution but 5+2x is the same) to get --> 3x/ 2x+5 = y. Then just replace y with f^-1. That's my way of doing it.

[solid mesa]

hey i solved it, I'll send you the work in dm

[random flame]

Thank you!!

[random flame]

Ooo aight thanks :D

[solid mesa]

it's really easy it just requires a lot of work

the idea is literally just using the theorem of integrating rational functions, u swapping and integration by parts

the last 2 you have to use it at least 13 times, its ridiculous

this integral is fucking dreadful

very boring

[random flame]

Hi can someone help me with this question? I have to solve it, and I’m not sure where I went wrong. Ping if you’re interested to help, and thanks in advance!!

[dusty goblet]

tytytytytytyty

[dusty goblet]

you can write e^(2x) as e^(x²), use t= e^x and you have a quadratic function, t²+4t-4=0, solve it and you will get the value of t, swap back to e^x and do ln to get the x value

[random flame]

Thanks so much!!

[maiden crag]

Exactly

[cyan night]

@ember kernel the slope of tangent line in a non linear graph indicates whether the object's velocity increases or decreases right (acceleration)?

like compared to the previous line of tangent

when dealing with instantaneous

v

[azure lion]

can someone explain how there is squared and cubed when inserting x=0

[pastel helm]

Just expand the brackets of f(x)

[formal heart]

Can someone help i dont really understand what this question is asking me

the answer to the question is 0.68, 0.6823 but I dont understand the process to get it

[formal heart]

nevermind

i got it

[tidal stone]

Any maths nerds who can help me out pls

Pls

@pastel helm

@formal heart

Can someone help out with q4

@here

[ruby tinsel]

I think it would depend on the distance he needs to travel. If it usually took an hour, he would take double the time to arrive, which is two hours. Do you have the distance?

[tidal stone]

Yes i figured it out. I was lacking on it haha

Thnx though

[leaden field]

here again

does someone know how to approach this q?

[mystic dune]

I need help

[cyan night]

with what

[mystic dune]

Statistics

[cyan night]

nevermind

[mystic dune]

lmao

[vernal finch]

How is this wrong?

I did 10(35+39+65)

[lofty arch]

They're probably using n = 3 to mean 3 different subintervals

So that'd be [10,20], [20,30], [30,40]

wait no that's exactly what you've done

[ancient prawn]

how do you find the domain of this function using algebra?

[cyan night]

you cant take the sqrt of a negative number

so x^2 -2x+5>= 0

so the minimum value of x would be when x^2-2x+5 = 0

and solve using quadratic formula or whatever method you prerfer

[ancient prawn]

I see

Would you happen to know how this would apply to a trig function?

[lofty arch]

the denominator can't be 0, so we need to choose x such that 1 ≠ sin(x)

[ancient prawn]

mm yes ok I see that

[lofty arch]

You also have to take into account that sin(x) is periodic, and will be equal to 1 many times as well

[cyan night]

Just remember that the denominator of a fraction can’t b e 0 and u can’t take negative roots

[ancient prawn]

So would I use logarithms here?

[cyan night]

Trig function or quadratic

[ancient prawn]

trig

[cyan night]

I dunno hehe

[ancient prawn]

:(

[cyan night]

I’m only middle school I’m about to take alg2

I’ll help you when I can

[ancient prawn]

I see, I'm reviewing a lot of old material and it's hardly comming back

[wraith pilot]

@ancient prawn u can use mathway

https://www.mathway.com/Trigonometry

finds everything fro u

[ancient prawn]

yea but the steps and methods of how to get their arent shown

its just the answer

[wraith pilot]

oh

what do uneed help with

[ancient prawn]

im trying to figure out how to calculate the domain of this trig function

I understand so far that sinx ≠ 1

so that you don't divide by 0

[pastel helm]

Maybe you can use general solution of sinx=siny?
Then x is not equal to nPi +(-1)^n Pi/2

[lofty arch]

sin(x) = 1 when x = pi/2

but sin(x) is 2pi periodic

so sin(pi/2 + 2pi) = 1 as well

same with + 4pi, +6pi ..., as well as -2pi, -4pi ...

[lofty arch]

this second line is 50% right in what x can't be equal to

[pastel helm]

I thought it'd be covered if n is an integer.Then what is the domain?

[lofty arch]

pi/2 + 2pi*n, where n is an integer

I should've been more clear sorry, yours is still correct but it could be simplified more

[pastel helm]

Ah right.this one is more clear too.I was just overdoing it

[cyan night]

pythagorean

take sqrt of 20^2-10^2

which is sqrt 300

which is D,

[low orchid]

ty

[left knoll]

How do I prove that 2^n + 2^n+2 is divisible by 5?

[weary arrow]

Double check that the math checks out

[left knoll]

thank u

[maiden sigil]

I dont understand this part of geometry can I get help on understanding.

[steel plover]

yo guys quick question

what's the reciprocal of 16/x^-12

[median wigeon]

idk

[muted ridge]

uhhhh x^-12/16 ?

1 / (16 * x^12)

[steel plover]

ah thank you

[royal marsh]

My book says the answer is e^x/(e^x+1) + C. Idk how they got to that answer, any help?

[median wigeon]

nope sorry

[pastel helm]

Yours is correct.maybe your book gave wrong answer

[peak coyote]

If anyone’s taking honors calc please help me with this nightmare of a question 😭

[median wigeon]

bro goodluck 🤣 im sorry i cant even read that correctly

[blissful zinc]

https://cdn.discordapp.com/attachments/854413728938590268/884920278713528360/Screen_Shot_2021-09-07_at_5.56.43_PM.png my teacher never told us this part can someone explain

[still flower]

This is using the program MATLAB. I have done no work this semester and have a project due in 3 days. so just trying to learn the basics now. Anyone know why I'm getting this error?

[median wigeon]

no 😔

[obsidian skiff]

can some one please help me integrate this. (need some knowledge and application of trig identities)

[lofty arch]

What exactly are you trying to do?

[still flower]

this is the first task, context is we are doing stuff to do with cryptopgraphy. I wasn't sure what to do about the uint8 stuff

[lofty arch]

Bisecting is cutting something until two equal parts, so UY=YV, then you can solve for x and find UV from UV=UY+YV

[lofty arch]

Are you writing a function?

[still flower]

yea cus i need to be able to copy and paste this function to use in future tasks

[lofty arch]

Let me dm you

[knotty totem]

for anyone that does financial math, how do you derive the maximum of a constant rebalanced strategy in a two asset model? In terms of the number of periods n?

[digital snow]

can someone help me with this question. My answer doesnt seem to be any of the options. (disregard option 1 being chosen)

i got (-5/x+5) +1

[dreamy depot]

can anyone help me with this?

[digital snow]

i have gotten the answer it is option a tyty

[summer jacinth]

Is it Option B 0.10; 0.09 rounded off to 0.10

[grand lodge]

Hello, this isn't really school related but I need expertise of someone studying curves and such in math or cs
I'm looking for an algorithm/formula, similar to bezier curves, that would allow me to interpolate not only the 3D position, but also direction
From what I found so far I want to get a manifold, where for any point on the curve, I'll be able to get that point's basis vectors (2 are technically enough, the 3rd can be derived as it's tangent to the first 2, and it's direction is not important in my case)
Standard bezier only gives me a single basis vector (from the derivative)
I've tried to find or derive something of my own, with no greater success, if you have any clue that may help me lmk 🙂

[cobalt mural]

hello! can someone show me how to do this problem?

[spark gyro]

can someone help me with this? please :(

[steep swan]

i could be dumb but isnt the rate of drainage 100 gallons/minute

sorry mate this question confused the everloving hell out of me

[hollow socket]

only if speed is constant, if is full weight over the bottom is higher son it pushes with more force the water and rate of drainage is higher

[hollow socket]

just do the derivate of the volume ecuation and then evalute it on the times indicated 5 and 20

derivative of 3000 *( 1- t/30)^2, do first the square parentesis (a+b)^2 and then do the derivative d/dt

[hollow socket]

you need to increment the mean by 2, you have 5 days, if you just put 52, the mean will stil same, if you want it to be 1 point higher you need to increment by one, for each day !! if you want it to go from 52 to 54, same as incrementing the mean by 2, you need to add 2 for each day, so 5 days*2, thats 10, now the actual mean is 52, at the 5th day first you need to keep it same so you need 52 and the add 10 to that to increment it from 52 to 62,

[ember kernel]

Total of customers (cst) after the 4th day = 52 cst/day * 4 days = 208 cst

A goal average of 54 cst over 5 days requires a total of 54cst/day * 5 days = 270 cst

The difference of total cst between the end of the 5th day and the 4th day is 270 - 208 = 62. Therefore, there must be 62 customers on the 5th day to get an average of 54cst/day

[cobalt mural]

ooo thank you!!

[waxen storm]

guys can someone explain this solution to me

its basically finding the area of a triangle using determinant

but i cant understand the second step

like how did it become 0 0 2

[left knoll]

can someone tell me how did we do the binomial approximation over here

[dark sorrel]

If you add one row to another row in a matrix, the determinant of that matrix wont change. Here the first row was added to the last

[waxen storm]

ohhhh

got it thanks!

[late thunder]

what do i do here?

[supple forum]

hai anyone know how to do these two questions 💔

[late thunder]

for "5",
find the distance bet'n P and R or P and Q..
and as it is a rhombus, the distance from P to Q and R to S OR P to R and Q to S would be equal, use the distance formula for S

[small canyon]

hey, can someone explain me how do i solve the 40th question, ik the formula of angle bw two lines, but I am not able to solve it correctly after many attempts

[summer jacinth]

Did you get the point of intersection (0,0) and (1,1)? Then you just get the tangents and angle done

[summer jacinth]

3pi/4

[solid mesa]

nvm, realized that wasn't the question deleted a post explaining something else

[solid anvil]

find the area of a kite shaped piece of land having unequal adjacent sides of length 120 m and 160 m and the bisector diagonal 200 m

every side of kite is adjacent :/

to each other

[left knoll]

ab=bc=120m
ad=dc=160m
bd bisects ac at o
BD=200m

@solid anvil

[solid anvil]

ik upto that then dont know 🥲

[left knoll]

im sending wait..

[solid anvil]

i need ao and ac

and thats not right angle or angle not given

[left knoll]

actually you dont, just wait bro..

in triangleABD

(AB)² + (AD)² = (BD)²

ie. 120² + 160² = 200²

=> TriangleABD is right angled at A
=> Similarly, Triangle BCD is right angled at C

[solid anvil]

uhh wait lemme have a look

wait how is that right angle ?

[left knoll]

find area of ABD or BCD using formula

1/2 * base * height

multiply the area by two

[left knoll]

converse of pythagoras theorem

[solid anvil]

how ?

not given or stated

[left knoll]

we have to find it bro, that is the whole point 😑

[solid anvil]

but how is it a right angled ?

[left knoll]

do you know pythagoras theorem?

[solid anvil]

upto my grade

[left knoll]

its just a basic one bro

[solid anvil]

how 😭

[left knoll]

ur in which grade?

[solid anvil]

10th

[left knoll]

which country??

[solid anvil]

Nepal

[left knoll]

ohk

[solid anvil]

how is that right angle ?

[left knoll]

CONVERSE OF PYHTAGORAS THEOREM!

[solid anvil]

explain 😑

[left knoll]

wait im sending a pic from my book..

[solid anvil]

jesus christ no wait i understand since base and perpendicular add upto the hypotenuse it is a right angle

i ignored that i was just looking at the figure

right or wrong @left knoll

?

[left knoll]

its correct
that is what is written here..

[solid anvil]

uhh but i gotta find the length of ao

ac

[left knoll]

its not needed..

[solid anvil]

area of kite is 1/2 d1 x d2 ?

[left knoll]

its not necesary to use that

[solid anvil]

:o

how

[left knoll]

you have 2 rt angled triangles

[solid anvil]

1/2 b x h

1/2 bxh

ad them

right ?

[left knoll]

yes!

[solid anvil]

yay so easy who is this idiot that doesnt know how to solve this

[left knoll]

understood na?

[solid anvil]

yes

[solid anvil]

<@&717391911132069929>

woah you guys quick thx

change pas

probs hacked

change pas

[low venture]

Hey is someone familiar with statistic tests like anova and ttest?

[cinder arch]

i can help you if you want

[cinder arch]

I made a complete file explain how to do t-test and anova because I took statistics last year

[winged coyote]

i currently have a d in calculus how do i study in general for math

[steep swan]

create a cheat sheet -- basically a single sheet of all the formulas that you've learnt

one thing that i noticed with math is that when solving people dont write down their given information & end up going back and forth between the question and their solving & get distracted

if you'e doing calc I i can tutor you in it -- i did pretty well when i was in year 11

[winged coyote]

ok thanks if im ever stuck on a topic ill make sure to reach out

[steep swan]

feel free to dm me or tag me -- i probably wont see it otherwise

[winged coyote]

okok appreciate the help

[sour sequoia]

@ember kernel Can anyone please give me an idea of what to do?

[ember kernel]

I'll be honest with you ; I'm not in a state where I can answer you right now. I'll give it a try when I wake up. Thanks for the ping and the trust tho

[sour sequoia]

@ember kernel No problem, when ever you get a chance to answer just ping back at me please so i know to check, Thank you!

[small canyon]

this is where im getting stuck

[summer jacinth]

@small canyon Brother take two cases. Use (0,0) in one case and take out the angle and then (1, 1) In another case.

@small canyon Or just simply make the graph of the two over each other and you will see for yourself

[small canyon]

aight got it now, thanks alot 🙂

[fiery widget]

how would I do this?

[opal rock]

So how do you solve

[cyan night]

yes

make -22y = -20y-2y

then factorize

@opal rock

[cyan night]

u know how to calc area of trapezium?

[fiery widget]

yup

[opal rock]

Thank you

[cyan night]

total of 2 bases * height * 1/2

total of bases = xm + (x+10)m

= (2x+10)m

(2x+10)m * 2xm*1/2 =50

2 and 1/2 cancel out

(2x+10)m * xm = 50

i think

[fiery widget]

the m stands for meters and isnt another variable

but thank you so far im following

[cyan night]

ok

so

lets not

use m

[fiery widget]

ahaha okay

[cyan night]

(2x+10 * 2x)/2 = 50 ye?

so (2x+10)*2x = 100

distribute

4x^2 + 20x = 100

4x^2 + 20x - 100 = 0

4 (x^2 + 5x - 25) = 0

x^2 + 5x - 25 = 0

heres how ill do it wait

brb

[fiery widget]

okay np thank you

[cyan night]

u can use the quadratic formula or this way

so x^2 + 5x - 25 = x^2+5x+25/4 - 125/4 = 0

sorry 5/2^2 = 25/4

so

(x+5/2)^2 = 125/4

x+5/2 = sqrt.125/2

sqrt. 125 is sqrt.5*5

-5/2 from each side

hm wait

ill send u a picture wait

[fiery widget]

okay thanks

[cyan night]

try using quadratic formula

[cyan night]

for this

[fiery widget]

okay sure

[cyan night]

i got the height of the trapezium is 5(sqrt. 5 - 1)/2

🤔

theres an extra /2

[fiery widget]

yea i get that too

OH

[cyan night]

hm?

[fiery widget]

its because x = 5(sqrt. 5 - 1)/2

[cyan night]

ye

[fiery widget]

and cause the height is 2x

[cyan night]

yes yes

u got it

👏

[fiery widget]

we times by two and get rid of it

[cyan night]

congrats

yes

[fiery widget]

thank you so much

[cyan night]

what were u struggling in the beginning again

i can give advice

[fiery widget]

it was just trying to re-arrange the equation to the normal ax^2+bx+c

[cyan night]

well yeah using the formula for trapezium

u can make it an equation with 1 variable

[fiery widget]

yea thats what i was having trouble with

i find it hard having a /2 with a variable and my brain just freezes so i have no clue what to do

[cyan night]

the /2 cancels with the 2x

always try to simplify

[swift ridge]

Hello guys

[cyan night]

think about input and output

1 input can only produce 1 output

[left knoll]

i have dyscalculia

literally dont understand antthing

[cyan night]

okay so here

in a function

theres an input and an output

for example y = 3x

input x, get a y

and for everyone x u input, u can only get 1 y

1 result of y

u cannot get 2 results of y because it makes no sense

here u see that there is the input -6

but it outputs 2 results, which is impossible

therefore it isnt a function

[covert anchor]

what do i do

never seen a sin^2 before

or a cos^2

[cyan night]

sin^2+cos^2 = 1

sin^2 pi/4 + cos^2 pi/4 = (sin^2+cos^2)* pi/4

very easy

[hollow escarp]

This is false

[cyan night]

yes

[hollow escarp]

I mean , the answer for sure is 1

but Sin^2+cos^2 = 1 is false

[cyan night]

Ok

[hollow escarp]

Sin^2(x) + Cos^2 (x) = 1 , x can be an angle.

[cyan night]

yeahhh

[hollow escarp]

but you cannot write it as (Sin^2+Cos^2)*x

[cyan night]

tru

[hollow escarp]

If thats the case , the result would be ! * pi/4 = pi/4

[cyan night]

ye that isnt right

[hollow escarp]

so, that's not how it's done.

[cyan night]

nvm

oik

[hollow escarp]

as long as both angles in sine and cosine function is the same , answer remains 1

[cyan night]

but i thought it only works in right triangles

and its the law of cosines for nonr ight

[hollow escarp]

😅 I suggest you go through the concept once again. It's better if you clear it up and go forward or it might end up causing some problems later

[cyan night]

i need help

[cyan night]

sin^2+cos^2 = 1 works for every triangle?

[hollow escarp]

it's about angles and not triangles

[cyan night]

Ok

[hollow escarp]

It's gonna sound even more confusing if I type it out here. please try to watch a couple of videos online . I'm sure there will be many videos available in your native language

[cyan night]

Ok

[hollow escarp]

for every angle x, Sin^2(x) + Cos^2 (x) = 1

[cyan night]

Ok

thanks

[muted ridge]

you can prove it through the right triangl

triangle

[cyan night]

yes

[muted ridge]

using Pythagoras theorem

[cyan night]

i didnt know it works for all triangle

i know

[muted ridge]

it works for all angle it's not about triangle

[cyan night]

ok

yo vietnam

chaof

[muted ridge]

oh

I don't think Vietnamese is allowed here

should be in the non-english chat

[cyan night]

ok

[muted ridge]

but how old are you?

[cyan night]

why

no dont ban me pls

[muted ridge]

I'm not a mod

if suitable we can study together

[cyan night]

look at my role

probably not heh 😓

[muted ridge]

ah

well glad to help you

I'm in grade 12

[cyan night]

alright

[muted ridge]

feel free to ask anything needed

[cyan night]

okok

do u take the ib

[muted ridge]

just dm through discord

[cyan night]

do u take ib

[covert anchor]

Guys so who do i follow lol

[cyan night]

him

lol

[muted ridge]

what do you mean?

[covert anchor]

Is this still false ?

[muted ridge]

it's true

[cyan night]

but with an ngle lol

true with an angle

(u cant square 2 functions and add them)

[steep swan]

has the trig question been solved? if not i can help

[ember kernel]

It's TOTALLY false

[ember kernel]

Nope

The real identity is cos²(x) + sin²(x) = 1

It's important to have an angle associated with trigonometric functions, because otherwise you could end up with non-sense such as cos²(pi) + sin²(pi/2) = 1, which is utterly wrong

[muted ridge]

yeah I didn't notice that

[vapid osprey]

Find all the points belonging to the line that contains the points (0.2) and (-1.0) and whose distance to the point (1.2) is equal to the square root of 5.

I determined the reduced equation of the line => y=2x+2 . How can I find the distance to the point (1,2) = sqrt5 ? help

[ember kernel]

Use the equation of a circle of radius sqrt(5) and of center (1,2)

If I'm correct, it's just (x-1)²+(y-2)²=(sqrt(5))²

Then, you have a system of two equations :
y = 2x + 2
(x-1)²+(y-2)²=5

Due to the square, it's likely that you get 2 solutions

[vapid osprey]

thank you friend !!

[ember kernel]

Ok so you know that vector addition works such that ab + bc = ac

Therefore, you can simplify P1P2 + P2P3 + ... + P{k-1}Pk into P1Pk

Therefore, you have vector P1Pk = -Pk, which is Pk - P1 = -Pk, which finally gives you 2 Pk - P1 = 0 and Pk = (P1)/2

[lapis yoke]

pls help me

[steep swan]

what's the question? graph the function or just solve

bc if it's just solving then the solution set is -3<x<-2/3

[sour sequoia]

Sorry for replying late , I dont understand how you get "-Pk"

[agile trench]

you have too see when [3x + 2 > 0 and x + 3 < 0] or [3x + 2 > 0 and x + 3 < 0]

[mystic dune]

I need help

Question 120

[fervent tide]

try to think about what median and mean mean. Try to think about what would happen to the mean and median of the data set if you added to it just one more company, that happened to have a growth of 100,000%
|| The answer is that most companies have negative growth, but there are a few rockets that absolutely explode in value, which hardly affects the median, but even just one such company can pull up the mean significantly ||

[random flame]

Hi can someone help me with Q5a? For some reason I got y=-2x-1 as my ans. The textbook ans is y=-2x :/

[surreal basin]

2x+y-5=0

[random flame]

Thanks I already solved it :)

[snow bough]

How do we do this question?

[upper parrot]

Equation manipulation. Anything that happens to the x-variable will shift the graph over by b units. Shifts to the right if -b and left for positive. A coefficient next to the function means the magnitude the graph grows or shrinks by. The y outpust grows if a>1 and shrinks if y<1. Anything that happens outside the function is how much the graph shifts vertically. Up c units if c is positive and down if c is negative. All you have to do is compare this graph with the parent function which in this case is just tan(x). I hope this helps and this might not be exactly right since I havent dealt with this stuff since algebra 2. Correct me if I'm wrong on anything

[ember kernel]

I just use ab = b - a with a and b vectors of length n

Pk is just an undefined vector, the value of which we're trying to find

Therefore, OPk = Pk - O = Pk (because O is just the vector [0,0,...0] )

And PkO = O - Pk = -Pk (the opposite of the coordinates of point Pk)

[daring sable]

is outer radius + inner radius = total radius?

[ember kernel]

I have no context, but I'd say outer radius = total radius when if you're talking about hollow cylinders

[lost breach]

Hello ! I would like to know how to be sure of the coherence of this :
(1) : ln(Y) = f(x) + e
(2) : Y = f(x) exp(e)

I am reading a paper on econometrics but I find it strange, because if (2) is true, then :
ln(Y) = ln( f(x) exp(e) )
<=> ln(Y) = ln(f(x)) + e (2.1)

The only way to resolve this would then be to confront (2.1) and (1) :
ln(f(x)) + e = f(x) + e
<=> ln(f(x)) = f(x)
Which is... impossible ?

[weary arrow]

Y = exp(f(x) + e)

You take the exp of both sides of the equation, so the entire right side will be in the exponent (sorry if my English is unclear, not sure how to translate this)

[lost breach]

Oh ok I will try this thank you !

[wicked pollen]

someone can help me with this task😅

[sharp ferry]

seee first look at the last term and the first term

and all the terms are perfect squares right

so you discard n^3 and now look at the last term and think of the last term and the number on the top of the sigma sign

i think this would be enough hintt now u should be able to figure it out :<

[left knoll]

hiii um i feel kinda embarrassed to ask but do u know what the answer is for this? im not good with math :((

[ember kernel]

Functions are input- and output-based

I'm sure one of the first things you've learnt about functions is that you CAN'T have two different outputs for a single input

That's exactly what (b) does ; assigning a single input (4) to several outputs (0,1,2 and 3)

That means it isn't a function

(a) and (c), however, follow that "single output per input" rule. Therefore, they are indeed functions

@left knoll Does it help ?

[left knoll]

YES thank u so much

[ember kernel]

You're welcome !

[hardy falcon]

So stumped idk where to start after setting up A=1/2 bh (in this triangle A=1/2s^2)

[hollow socket]

imagine its a sqaure, s·s = A --> s·x·s·x = A*(1-0.64), x is the (1-percentatge), you can translate it to your triangle easly modifying this

there are 2 x becuase you decrease both sides

[hardy falcon]

Sorry, what is “x” again?

[hollow socket]

if is 30% x is 1-0.3

[hardy falcon]

Yes, ok.

This was the book’s answer

[hollow socket]

in a square case of 10 value side A=100. if you decrease it 64% A=36, so sqrt(36) is 6, 6 is the value of the side, now they have been decresed 40%, 10*(1-0.4)=6

[hardy falcon]

But book says x = .80 meaning there is a 20% decrease in “s”, what don’t understand is the process of how they got that… 😦

[hollow socket]

sorry, i wrong understand, it says that the new area is 64% of the original, not the original decreased by 64%

A=s·s, if you want Area to be less then A·0.64 = 0.64·s·s, but you need to decrease both sides equally

[hardy falcon]

So the new triangle is smaller than the original triangle, 36% smaller

[hollow socket]

yes

imagine its a sqaure, s·s = A --> s·x·s·x = A*(1-0.36), x is the (1-percentatge), you can translate it to your triangle easly modifying this
t

[hardy falcon]

Thanks so much!

[hollow socket]

your welcome

remember, its a square, so for triangle you need to /2

[wicked pollen]

thanks a lot i solved it

[cyan night]

is geometric series just a way to summationally express an exponential function

[ember kernel]

No, they have an exponent in common but are different in many ways

[cyan night]

i find similarity since the problems i encountered seem real familiar

[ember kernel]

An exponential function is continuous and works with real numbers, while a series is discrete as it only works with integers as indexes

[cyan night]

wait what

the index could be 1.05 or something right

in series

like this

[ember kernel]

The index is used in the exponent

Like this :

[cyan night]

wa

[ember kernel]

The index is i

[cyan night]

oh

but if i express it under total = a (1-r^n)/(1-r) the index is 1.05

[ember kernel]

r = 1.05, but is not the index

[cyan night]

hmm yeah

[ember kernel]

You don't believe me

[cyan night]

what

i am curious

true the exponential growth is 1.05^10

[ember kernel]

The index is "i", and is just a temporary variable that is assigned integer values one after the other

[cyan night]

so you're saying we cant have fractional exponents right

[ember kernel]

1.05 is 1 + the rate of the growth

[cyan night]

in geometric series

[cyan night]

ye

[ember kernel]

Well you could, but not using the index only

Example :

[cyan night]

im not really used to sigma notations

[ember kernel]

The index itself is an integer, so if you want a fractional exponent, you need to make it a fraction yourself

[cyan night]

😕

[ember kernel]

Basically, it's just a simplified notation of :

[cyan night]

why could it only be an integer

[cyan night]

could the index be a non integer but still remain ratio

[ember kernel]

No

Imagine the sequence :

[ember kernel]

with u0 = 0 and u1 = 1

[cyan night]

ok

[ember kernel]

You'd get :

[cyan night]

ooof

[ember kernel]

Ok, do you agree with that ? (n is the index here btw)

[cyan night]

😕

i guess im going to try fractional indexes in the calculator and try to identify if there is common ratio

thanks btw

[ember kernel]

Just remember : exponents in exponential sequences/series CAN be fractional, but indexes CAN'T

And the rate 1.05 is totally different from the index

[cyan night]

wait arent exponents and indexes same thing

[ember kernel]

No

[cyan night]

oh

[ember kernel]

Check this

"i" is the index

however "i/2" is the exponent

[cyan night]

oh

uhh

[ember kernel]

?

[cyan night]

index means power right

[ember kernel]

Exponent = power

[cyan night]

oh

how do u define index then

[ember kernel]

Index is just the name of the temporary variable

[cyan night]

ok thanks

[ember kernel]

Have a good look at this

"i" is the index here. In the first term, we give the value i = 0, then in the second term we make it i = 1, then i = 2 in the third term, ..., until i = n in the last term

[cyan night]

is it n or n-1

[ember kernel]

n, you can see that in the last term

That's what a generic series is : a sum of terms which only differ by the value of the index

[cyan night]

okkk i get it now thanks

[ember kernel]

np

[sharp night]

How would you calculate the side of the square if you know that the radius of the circle is 2?

[modest compass]

Is that the only info the question gives?

[sharp night]

"A square is inscribed in a semicircle with a radius of 2 cm. Calculate the area of the square in centimetres"

[scarlet carbon]

it will be (side of square )^2 =2/root 5, i am not that sure but ...

[sharp night]

And also, the answer should be 3.2cm^2 (probably rounded), I just have no idea how to get there

[scarlet carbon]

ayo i will send my guess in a photo you can approximately judge yourself >

[left knoll]

Can someone please explain to me how

Equals

It literally just looks like the 1/2 disappears

I feel so stupid lol

[sharp night]

ill send it in a sec

[left knoll]

Alright.

I know that if you expand it, it's gives you the same thing. My question is,

If you start with the first one, how do you get it to the second one?

I tried factoring but I couldn't get it.

[sharp night]

I hope you can read my handwriting

basically you expand it and make a single fraction out of it

then you can rewrite the numerator using (a+b)^2 = a^2 + 2ab +b^2

Rewrite the denominator from 16x^6 into (4x^3)^2

[left knoll]

Okay one sec

[left knoll]

What is that factoring method called again? I completely forgot it.

The one where you get 16x^12 + 8x^6 + 1 into (4x^6+1)^2

[sharp night]

No idea how it's called, probably something like factoring it into a square or something like that

[left knoll]

Alright, thank you!

It would have made the integral literally impossible without doing that

[sharp night]

I can't do integrals, I don't even know what they are xdddd

[left knoll]

Well you'll be in good shape then haha it's been forever since I've done algebra

Been in algebra*

[cunning shore]

Can someone help me to find the T here?

🥺

[left knoll]

Linear Algebra?

[cunning shore]

tranpose matrices

maybe

[left knoll]

No I mean is that the class

[cunning shore]

ouh yes its linear algebra

[last echo]

Solve this using the (a+b)²=a²+b²+2ab

[left knoll]

Oh, I've never seen that before. Thank you for this.

[last echo]

Oh okay, np :)

[sharp night]

Yea.. it was a lot easier than I thought

[thorny plover]

anyone know this please?

[small remnant]

621.19m/s

[left knoll]

hello

i made a mistake but i don’t know where

[ember kernel]

I mistook your S's for 5's and almost had a heart attack

[random flame]

Hi can someone help me with Q6a? The ans is (0,-7) but I’ve been getting (0,8) instead

This is my working btw

[green root]

i guess you've gotta use point A for the perpendicular, not the midpoint, as it says "the perpendicular ..... at the point A", your working for gradient is fine, just that the point you substituted to form the equation is incorrect

I guess you're using midpoint cuz you learnt about the perpendicular bisector? But in this case the perpendicular line isn't a perpendicular bisector, so the midpoint is not a point of the line, instead it passes through point A

[random flame]

Ah alright I got it thank you so so much!!

Eyo me again QwQ
I need help with Q3a, been asking everywhere but I can’t understand the explanations-

Behold my confusion scribbles, also just ignore the sketch it’s completely wrong

[green root]

It's right angle at Q so you would get something like this, R could be any point on the line x = 7 as we dont know k yet, but since Q is a right angle, you can try to find equation PQ and equation QR and equate them, they would be perpendicular, so you got the gradient of QR there, just gotta solve for k

[green root]

just to confirm is k = -9?

[random flame]

Yes it is

Man you saved my life thank you-

Ima just try to understand it first

[random flame]

So I got y=2x+2 and y=-1/2x-5 1/2

Erm

How do I sub in the values?

R is (7, k)

And k is y

[green root]

ok so for equation QR you have to form an equation using point R so you get the k in your equation, and from my diagram you can see Q is an intersection point right?

I think there are other ways to do but i'll try to explain my method

[random flame]

Oh hold on I'm an idiot

Wait lemme calculate first-

Okay nvm I'm stuck-

[green root]

yea yea try it, and by equate, sorry i didn't make it clear, I mean equation both y equations, and substitute the x-coordinate of R in

oh

[random flame]

Idk what I’m doing-

[green root]

ok let's understand what's happening here first, so

the trick here is to try to find something common between these lines, we gotta need line PQ to find QR as we have all the info for PQ right?

first we form line PQ

and then we form line QR by using the coordinates of R

and are you able to obtain the gradient?

[random flame]

Yeah

[green root]

ok then i'll skip the part of finding gradients

so now we have two equations, PQ: y = 2x + 2, and QR: y = -1/2 + 7/2 + k

i used gradient -1/2 and R(7, k) to form eqn QR

and now what's common between two lines? can you see it?

[random flame]

Erm

[green root]

do they intersect somewhere

[random flame]

2x+2=-1/2x +7/2 +k ?

[random flame]

Erm maybe?

[green root]

yes and do you know what it means when we write this?

it means that they have a same y value

[random flame]

Yeah

[green root]

yes so at which point do they have the same y value? it is Q right?

as that's the intersection point

[random flame]

Ah yeah

[green root]

in other words, both lines contain the point Q

yea yea

so we take the x coordinate of Q

[green root]

and sub into here

[random flame]

OHHHH

THAT MAKES SO MUCH SENSE-

THANK YOU

[green root]

no problemmm

[random flame]

OH MY GOSH I WAS STUCK HERE FOR HOURS-

[green root]

and u got it now yayyyy

[random flame]

I'm forever grateful

Legit

Thank you