math-help

[soft stag]

Is this allowed?

[ember kernel]

Yes

Thanks to the commutative property of multiplication, a•b = b•a can be simplified to ab without ambiguity
Therefore, h•Q•(1/2) can be simplified to hQ/2

[soft stag]

Thank you very much! Thats a big help for me

[steady tide]

what type of math are you doing 👀

that is a very important fact

[soft stag]

My last math lesson was like 6 years ago and i need to catch up because i didnt need any math during my whole bachelor

Just forgot everything

[soft stag]

well good that i know it now. Just creating a basic rn to learn more via youtube etc

[cyan night]

looks like a big ass congruence modulo problem

[atomic dagger]

Hi! I don’t understand why we say that the derivative of cos(x) is -sin(x) but here the derivative of cos phi is -(phi)’ * sin(phi)? Why isn’t it just -sin(phi) ?

[cinder yacht]

phi is a function tho

if u want, (x)' = 1

so actually derivative of cos(x) is - (x) ' * sin(x) = - sin(x)

[ember kernel]

Yeah that's chain rule

Technically speaking, (sin(x))' = cos(x) * x', not just cos(x)

But since x is mostly used as the variable we differentiate with respect to, it leads to x' = dx/dx = 1, as Coly mentioned

Here, it's not the case

[frank echo]

Borrow $200000 at 3% p.a. Compounding monthly. If your equal monthly repayments are $3000, how long will it take to pay off the loan?

mind helping me with this?

[left knoll]

The question should have the duration the amount borrowed is compounded, ….. compounding monthly for 3/4/5 years

[frank echo]

yeh ty

[naive cape]

anyone familiar with latex plzz I have to submit it in 3 hours

[last echo]

shudnt it be c?

[static stream]

it should be c

[frank echo]

On a velocity time graph, when is the acceleration of the particle 0

?

[static stream]

when the line is parallel to the x axis

[fluid summit]

phi is a function

[glossy latch]

Even the derivative of cos(x) is -sin(x)dx, but we generally divide dx on both sides to get dy/dx

[robust kraken]

The acceleration will be zero when the velocity remains a constant; when the velocity-time graph takes the form of a straight line parallel to X-axis

[patent rain]

slope is 0

acceleration always slope of velocity vs time

[frank echo]

thank you

[vivid hearth]

how to solve this?

[frank echo]

could some help rq

[fluid summit]

[cos(x)]' = -sin(x)

-sin(a) = m

(...)

[fair harbor]

You want the solution or help with understanding?

[quaint imp]

solution first

then understanding

so if its a solution and i get it, i dont need understanding then

[fair harbor]

-4y + 3x = 8 = -4y = -3x + 8 = y = -4/(-3x + 8) = y = 3/4 x - 2

you basicly isolate the y on the left side

in this question, m will be 3/4 and b will be -2

[quaint imp]

so in the end -4y = -3x + 8 = y = -4(-3x + 8) = y = 3/4 x - 2 will be the answer

[fair harbor]

The question asks you to put -4y + 3x = 8 in the order y = mx + b, so the dsolution is y = 3/4 x - 2

It's the equation of a straight line

put that in the graphic calculator and you will see a straigh line intersecting the Y axis in the position (0, -2) and with positive growth

[quaint imp]

ohhh

so what what wud i put as the final answer

[fair harbor]

this

[quaint imp]

the whole thing

[fair harbor]

So that the teacher wont know you just copied the ending solution

[quaint imp]

but an online calculator says its (-4y+3x)+(-3x)=8+(-3x)

@fair harbor

[fair harbor]

Yeah, that's not wrong, it's what we did, but showing the in between steps

It's also incomplete and not what you want

[quaint imp]

oh ok

[fair harbor]

For example, if you have y+x = 5, if you want to "put the x on the other side", in reality you need to do this; y+x -x = 5 -x so that the x's on the left side negate each other

That's what the calculator you are using is showing

But usually we omit thoes setps since they are usually so elementary we don't really need to write them everytime

[quaint imp]

lol we need to

[fair harbor]

Sorry, didn't see you had the middle school role

So go ahead and write them, the logic is the same

And you will get the same result

[quaint imp]

im in highschool

forgot to change

there

can u write the steps

@fair harbor

Im kinda confused

[outer pond]

I am stuck on this question
Any help is appreciated 🙃

[fair harbor]

-4y + 3x = 8 =
-4y + 3x - 3x = 8 - 3x =
-4y = -3x + 8 =
(-4y)/-4 = -4/(-3x + 8) =
1y = -4/(-3x + 8) =
y = 3/4 x - 2

@quaint imp

[quaint imp]

omg

thx

[fair harbor]

pretty sure it's C)

[quaint imp]

at the end is that a multiplication or x

[outer pond]

can you tell/show me how you did it?

[fair harbor]

x

[quaint imp]

ok

so its 3/4x

[fair harbor]

replace sec(x) with 1 / cos(x) and tan(x)^2 with (sin(x) / cos(x))^2 and you should be able to follow from there

[outer pond]

@fair harborlet me try

[fair harbor]

What are the distance between each square?

[quaint imp]

1

@fair harbor

its 1 unit

The formula is y=mx+c

[fair harbor]

Line A: y = 4
Line B: x = -3

[quaint imp]

how

what r the steps

im so confused

[fair harbor]

Step 1, count the squares

[quaint imp]

ok

[fair harbor]

For either line the there is a value that doenst change

this means that the equation doesnt care about the variable that changes

For example

look at Line A

For anny x, y will always be 4

So the equation is y = 4

Same for Line B, but for x this time

[quaint imp]

but thats not an equation

ohhhh

wait....

i get it now

[fair harbor]

why not? You could write it like this if it helps you understand: y = 0*x + 4

[outer pond]

@fair harbor thanks buddy i actually did it

[fair harbor]

np mate

[quaint imp]

thanks @fair harbor

[red spruce]

( 3,1 ) substitute the value of y in second eq to get x and then get y from value of x

[outer pond]

Find the value of x and y by any method of your choice and the value of x and y will be the point where it intersects

[quaint imp]

so its (3,1)?

[red spruce]

solve it

[quaint imp]

hmm

lemme see

but how do i devide -1/3 on both sides

[red spruce]

dont divide, substitue y

[quaint imp]

with what

[outer pond]

substitute the value of y in the second equation and solve it

[red spruce]

1st eq is y= something in x js put this in firstequation in place of y in 2nd one

[quaint imp]

so substitute for anything?

[quaint imp]

what is eq

[red spruce]

equation

[quaint imp]

oh

so i can substitute y with any number

@red spruce

[red spruce]

wait

[outer pond]

no the value of y is given in first equation
substitute that value

[quaint imp]

yeah so I can substitute y with any value

[red spruce]

ur understanding of substitue is wrong

[quaint imp]

?

[red spruce]

in eq like these u gotta remain in boundary of question js use the value given and solve ez

[red spruce]

see the solution

[quaint imp]

what is that after the brackets

y=-1/3x +2
-2n+3y+3=0
-2n+3(-1/3x X 2)...

@red spruce

[red spruce]

bro u confused rn , read som theory pls

[red spruce]

from where did u got n

[quaint imp]

oops

i meant x

dw

[red spruce]

why u even doing that

[quaint imp]

Sorry wrong variable

[red spruce]

no like why solve it

[quaint imp]

anyways whats after that bracket

[red spruce]

u js need to put first one in second and solve

[red spruce]

• 3

[quaint imp]

bruh i dont get u what do u mean

[red spruce]

same

[quaint imp]

lol

this what i have so far

@red spruce

[red spruce]

yes now put x= 3 in eq 1

[quaint imp]

ok

i did

[red spruce]

and u get y= 1?

[quaint imp]

do i multiply the fraction by 3

[red spruce]

yes ofc

[quaint imp]

ok i got y=1

[red spruce]

this speed is slow man

[quaint imp]

so the answer is (3,1)

[red spruce]

yes

[quaint imp]

Bro i was confused

[red spruce]

about what

[quaint imp]

yeah the typing speed

[quaint imp]

this whole question and it takes time to type

[red spruce]

it is one of the basic question of linear alegbra

[quaint imp]

i just started to learn about it

[red spruce]

which grade are u in

[frail kindle]

Damn what a bad explanation

[red spruce]

?

[quaint imp]

who

*doesnt respond

@frail kindle

[quaint imp]

?

[frail kindle]

To solve any problem of point of intersection, u have to clear one of the variables, for example y. Leave y aside example y=x+2, then replace that y in the other equation example 3x+2y=-3 replace 3x+2(x+2)=-3, so you get the value of x. Once you get x you can get y, those two values are your (x,y) intersection point.

[quaint imp]

ohhhhh

thats better

if u were here listening to the explanation this whole time y didnt u help

[frail kindle]

Hahah, i was studying xd

[quaint imp]

bruh

[sterile birch]

Would anyone be able to help me out on this?

Really grinding my gears rn

https://tenor.com/view/gon-hunterx-hunter-anime-huh-wtf-gif-10137967

[sterile birch]

nvm

I got it

[cyan night]

chain rule i think

chain rule + product rule

maybe u missed chain rule

[left knoll]

I was seeing a solution to a Trigonometry problem.
(sinA)^2 + (secA)^2 = (sinA)^2 + (cosA)^2 + 1
Is it actually mathematically correct?

The question was
Prove that (sinA)^2 + (secA)^2 = 2

[glass matrix]

can sum1 explain Bearings to me pls 🙂

[subtle sluice]

Hi guys. Is there a Math Lord here i can dm?

[cyan night]

not me

[sharp ferry]

are you sure this was the question ?

[left knoll]

Yeah

[sharp ferry]

but if you put A=60° then it becomes (√3/2)^2 +(2)^2 which is clearly not 2

so this cant be an identity

[left knoll]

Yeah, the question is probably wrong.

[subtle sluice]

How do you find the quadrant of t?

Say for example 9pi/4

If the reference number is pi/4, then...

[cyan night]

quadrant I

the unit circle is 2pi radians

divided into 4 quadrants

each quadrant is pi/2 radians

[subtle sluice]

Yes

[cyan night]

uh yes

so whats your concer

n

[subtle sluice]

How is it QI?

[cyan night]

because pi/4 is in between 0 and pi/2

[subtle sluice]

Yes but what if it's 31pi/6

[cyan night]

you take the reference angle

keep subtracting 2pi

until its 0 =< x =< 2pi

[subtle sluice]

oh no ㅠㅠ

Is there a faster way to do that?

[cyan night]

hm i dont think so

but i dont think it would take too long, right?

31pi/6 - 12pi/6 = 19pi/6 - 12pi/6 = 7pi/6

which reference's angle is pi/6

forget that

just until 7pi/6, and when you are required to find the trig ratios (sin cos tan) then use pi/6

[subtle sluice]

Or just use 4pi+(7pi/6)

[cyan night]

uh yeah

31pi/6 = 4pi + (7pi/6)

[subtle sluice]

But what if it's negative

Like -54pi/3

Scratch that

-41pi/4

[cyan night]

my method is that i do the same thing

i subtract 2pi until it fits the unit circle

then when it ends up with a negative angle

i take 2pi to subtract

for example

-pi/6

is the same as 2pi-pi/6 = 11pi/6

[subtle sluice]

Okie okie wait a sec

[cyan night]

aight

[subtle sluice]

Okay i think i found my problem

Thanks for the help bro <3

[left knoll]

So i just imagine how is it look like if i^i. And the result is at the image, can anyone can explain why i^i = 0,2078...

[ember kernel]

Just type i^i into youtube and watch the recommended demonstration videos

I think that'd be better than any textual explanation

[lime junco]

Help me please

[granite nexus]

Help me

[ember kernel]

a)
T0 = 1
T1 = 3 * T0
T2 = 3 * T1 = 3 * (3 * T0) = 3² * T0
T3 = 3 * T2 = 3 * (3 * T1) = 3 * (3 * (3 * T0)) = 3³ * T0

Therefore, without any calculation, you can observe that Tn = T0 * 3^n.
Since T0 = 1, you get your exponential form : Tn = 3^n

b) Oops, I accidentally did it in (a). You just need to plug 1, 2 and 3 in the formula.

c) Now, instead of having T(n+1) = 3 * Tn, we have U(n+1) = 3 * Un - 1 (because we remove one bacteria after it reproduced the day before)

d) Replace U(n+1) by 3 Un - 1 and you get the equation 3 Un - 1 - a = 3 Un - 3a (yeah I also distributed the 3 on the right hand side)
From that equation (simplify the 3 Un on both sides and rearrange the remaining terms), you get 2a = 1, which means a = 1/2

I did it in a rush so don't hesitate to ping if you see something wrong, but anyway the general thinking process is there and that's what matters the most

[ember kernel]

I'm willing to, but can't if you give us nothing to work with 🤷

[lime junco]

thank you!! @ember kernel

[muted flare]

yo

does someone think it is possible if someone can simplify this:

[fast saffron]

Hey, the second term becomes 1 since cosec(x) is just the reciprocal of sin(x). For the first term, since there a cos^2(x) in the denominator, we can write sin^2(x) in the numerator as 1-cos^2(x) (since sin^2(x) + cos^2(x) = 1).

Separate the two terms in the numerator, we'll get sec^2(x) - 1. So, the final answer would be sec^2(x).

[raven silo]

very special integral

arises from the calculation of the energy radiated by a black body

can anyone solve it ?

[tropic bear]

can someone tell me the answer and the reason for it ?

[ember kernel]

Unsolvable with our basic functions. I typed it in Wolfram Alpha and the result contains complex functions

[cyan night]

do you know the formula for the perpendicular line?

[chilly moth]

is it the reciprocal of the slope

[cyan night]

reciprocal and different sign

which means when they multiply it is equal to -1

so the slope of the perpendicular is -3/2

[chilly moth]

oh so -3/2= to the slope of 0, -12 and x, 0?

[cyan night]

so it has a slope of -3/2

and it intersects point Q at (0,-12) which has 0 x value right?

0 x value meaning its the yintercept

so it has y-intercept of -12 (the same of the original graph), right?

right jamal

jamal

[chilly moth]

yes

[cyan night]

so whats the equation of that line?

[chilly moth]

y=-3/2x-12

but how do i find x

[cyan night]

then point (x,0) right

whats the y value of (x,0)?

0 right

plug 0 into that equation

to find x

jamal

plug y = 0 in

sorry if i was unclear

[ember kernel]

(c) and (d) make no sense (why would getting close to a give us f(b) ???)

we can't do (b) since we don't know if f is defined for values before a

Therefore, it only leaves us with (a), which makes sense when you think about it (when x tends to a, f(x) tends to f(a))

[cyan night]

DIDNT I JUST HELP YOU

what

[chilly moth]

The graph of y=⅔ x - 12 intersects the y-axis at
Q (0, -12) and is perpendicular to a line joining Q to the point P ( x , 0). Find x

[ember kernel]

The dude spent some of his time trying to help you. Least you must do is acknowledge his answer and, if you haven't understood everything from the explanation, ask more questions or be honest (say his explanation is unclear). Here, you're just ghosting him :/

[cinder yacht]

XDD

[ember kernel]

Anyway, here are the big steps :

• Slope of first line = m'
• Slope of perpendicular = m = -1/m'
• The perpendicular line (let's name it f) can be expressed as y=mx+p. You know m and you know that Q belongs to f. Therefore plug in (x,y) = (0,-12) and solve for p
• Once you've got p, you know the expression of f : y=mx+p
• You know that P belongs to f, so plug in (x,y) = (x,0) and solve for x
• Done

If you struggle with my explanation, please ask questions. Don't just copy your question again --'

[raven silo]

yup

[autumn robin]

does anyone have any tips for find interquartile range?

[spare pendant]

whats that

[tropic bear]

so the answer is 3a and 4d....? i understood y you didn't go for f(b) in the 3rd question BUT i didn't get how u decided it was right continuous (a+) instead of left continuous(a-) and if i am right the same logic is used in both the questions

[cinder ibex]

It is right continuos because f(x) is only defined in the right of a, in [a, b]

So a+ and not a-

[cinder ibex]

So 3a and 4d because in question 4 f is only defined in the left of b, since it is [a,b]

[tropic bear]

why is f(x) defined on the right of a and not on left tho ?

[cinder ibex]

Imagine f is something like these, it dsnt make sense to study for a- because f is only defined in [a, b]

If u had f defined [0,b] and considering that a is bigger than 0 and smaller than b then it would make sense to study for a+ and a-

But if the function isnt defined at the left of a it dsnt make sense to make the limit to the left

This is not the case in ur question assuming it is related to what u are studying this might be helpful it says it exists the limit on the above cases and in the below it dsnt exist limit

[tropic bear]

ok got that...thank you for anwering my questions...it means a lot :))

[cinder ibex]

No problem : )

[glacial summit]

Can anyone please help me simplify this equation?
Dunno, why I can’t do it🙁

[polar heron]

take common 1/ (1-4x^2)^2 from the denominator of the first term, then it will cancel with the denominator of the second term. then simplify both numerator and denominator and you will get (1+4x^2) common in both which will get cancelled, and left with 4/(1+4x^2).

[sharp inlet]

hey, could someone please help me simplify this?

[sharp ferry]

is the answer just A?

[sharp inlet]

im not shure, sorry im rly bad at this stuff

[sharp ferry]

try drawing venn diagrams i got my answer using that

[sharp inlet]

ty very much, ill try my best

[sharp ferry]

here now u just need to find the

common part

in both

[plush quest]

hello

can anyone help me solving this?

[sharp inlet]

ok thanks for your time 🙂

[glacial summit]

At first use (a+b)^2 formula. Then multiply the equation by 2. Then use 2(cosA)^2 and 4(cosA)^3 formulas

[lime junco]

Can elaborate your answer to part c? I don't get it where Un came from

[ember kernel]

Since Un is the number of bacteria after we removed one, I just defined Un = Tn - 1

[glacial dust]

@ember kernel heelp how did that became 18(4t2-1)

do i have to find gcf then divide them but how am i supposed to get 18

do i have to multiply 4tcube to 6?

[ember kernel]

In the left brackets, 3 was factored out and multiplied to the 6 in the middle of the expression

Also you forgot to use brackets in the first two lines of your answer

And (second line) it's u = 4t³ - 3t, not y = ...
Otherwise your expression y = u⁶ (just on the right) makes no sense since you never define u

[glacial dust]

we multiplied 6 to the exponent of 12 which is t3

?

but what about the 3t which is inside the parenthesis as well

[ember kernel]

You didn't get it

Give me 2 mi.

[glacial dust]

ya ya sure take your time

[ember kernel]

Always remember that log_a (b) is the exponent you need to apply to a to get b

Since you're looking for the value of an exponent, it is relevant to use logarithms

[strong widget]

8i =(x+2i)(y+2i)+1 ……..help plz

[weary arrow]

B

[atomic dagger]

thanks for the answer and sorry for answering late!!

i'm not sure if i can ask physics questions here, but I was wondering if anyone could tell me what differential equations are for ? from my understanding, they are equations which have functions as solutions. And so in one of my lessons, we have the "differential equation of the movement of oscillation" but i don't understand why. I understand how we calculated it, just not what's it used for.

[ember kernel]

Differential equations are equations (thanks captain obvious) that :

• have a function or set of functions as a solution
• make use of the derivatives/partial derivatives of the solution-function in the expression of the equation

Quick 1D example : y'(x) - 3y(x) = 0 is a differential equation (because of the y'), which has y(x) = exp(3x) as the solution
2D example (more difficult) : (df/dx) + 3 (d²f/dy²) = f(x,y) * exp(2y)

Differential equations often arise in physics stuff (fluid simulations, heat diffusion, wave propagation), and we mostly need to solve them numerically due to their difficulty. However, some equations can be solved via calculus (just like the example I gave you)

We almost never come up with them or invent them ; most of the time they appear by themselves in physics problems, so we can't do much but try to solve them to get to the results we want

[atomic dagger]

i see, thank you very much !!

[ember kernel]

No problemo :D

To find the minimum of a function, you need to :

• find the values where its gradient is 0
• at these values, identify whether the function is a max, a min or a saddle point

Here, you need to do the same, but the "function" you want to minimize is a gradient.
Therefore, you'll have to work with the gradient's gradient, which is the second derivative, and see for which values it is = 0

||(The answer I gave you is only valid for one-variable functions. If you're dealing with multiple-variable functions, you won't use a second derivative but the Hessian Matrix). Ignore this remark if the function you're working with has only one variable||

No problemo :D

Function increasing <=> Derivative > 0

(ax + b/x²)' = (ax)' + (b/x²)' = (ax)' + (b x^(-2))' = a - 2b/x³

a - 2b/x³ > 0 <===> 1 > -2b/(ax³)

Now, you want to multiply by x³ to make it appear on the upper side of the fraction.
BUT since you're dealing with two different cases :

• If x³ > 0 (which means x > 0), nothing special happens
• If x³ < 0 (which means x < 0), you have to switch the inequality sign from > to <

Depends

Yes if x³ < 0

No if x³ > 0

You need to treat both cases separately

Also, it's but my humble interpretation but I think you need to calculate these values in terms of a and b, without subbing any value for them

Ok

4 - 32/x³ > 0 then.
First let's divide by 4 to simplify the numbers
1 - 8/x³ > 0
From that, you get 1 > 8/x³
Now, let's make the x³ appear on the main line (in the upper side of the fraction) by multiplying both sides by x³

CASE 1 : x³ > 0 ===> no sign change

You get x³ > 8, which is true for x > 2

CASE 2 : x³ < 0 ===> sign change
(this is logical : take 3 > 2 as an example. If you multiplied both sides by -1 without changing the side, you'd end up with -3 > -2, which is painfully wrong)

You get x³ < 8, which is always true (since we're in the case x³<0, which means x<0 ===> x<0<8 is always true)
Therefore, the inequality is verified for any value of x < 0

CONCLUSION :
Reunite the results you got in both cases into a single answer :

4x + 16/x³ increases for x such that x<0 or x>2, which you can also write as x ∈ ] -∞ ; 0 [ ∪ ] 2 ; ∞ [

(The latter way of writing it is a more rigorous notation, but it expresses the same thing as "x<0 or x>2" . If you haven't learnt about it yet, just ignore it)

And you're done :)

No problemo :D

[cinder yacht]

and they're not thaaat weird

like if in real life you say smth like "the more money you have, the faster u'll earn money" that's maybe the equivalent in math of saying << f'(t) = f(t) >>where f(t) is the amount of money u have at the time t
so that's a Differential equation, where it says that the bigger f(t) is (AKA the more money u have), the bigger f'(t) is (AKA the faster money grows)

(and solving that "Differential equation" is figuring out what sort of function f could possibly have those properties. In this case, in math the solution is exponential (multiplied by a constant), irl we would also say "money growth is exponential" lol)

they translate things that we think about outside of math, like the relationship between a quantity and the speed at which it evolves

shit like that

[left knoll]

I'm looking at remainder theorem and I'm not sure why the +3 becomes a -3

[fast saffron]

Hey, the denominator should be in the form of (ax-b). So, write 2x+3 as 2x - (-3) to convert it into that form. Then b/a becomes -3/2.

[left knoll]

Ohhh

That makes sense

If the 3 was already in that form you don't multiply it by negative X right?

You just leave it as is?

[fast saffron]

not sure I got what you mean

[left knoll]

If the question was like this

Would the answer still be -3/2

Or 3/2

[fast saffron]

3/2. Since it's 2x-(3)

[mystic dune]

Does anyone know how to calculate the overall rate of increase of a set of numbers over some years?

[still briar]

does anyone know how to do this

[solemn vessel]

well to start

you can write an inequality for y

you can use the y values and the given equation for y to find two bounds for an x inequality

from those two u can get the third

[still briar]

is it like this. y=8?

[solemn vessel]

No, that’s not an inequality

you should first get familiar with the definition of an inequality before attempting that question

otherwise you won’t be able to solve it :p

[still briar]

thats why idk how to do

[solemn vessel]

well i told you where to start

first familiarize yourself with what an inequality is, then do the steps i mentioned

i could just give you the answer, but then you wouldn’t be learning !

[still briar]

ahh okay then. thanks btw

[solemn vessel]

Sure thing, if you want help once you’ve given it a shot, let me know and i’ll answer if i’m awake

[merry steppe]

?

[rain onyx]

Help!

[left knoll]

can anyone help me with these

[ember kernel]

Try to put 5 and 7 into roots of the same type

You've got roots of types 1/3 (cubic root) and 1/2 (square root)
Common denominator for those fractions: 6

Therefore your answer will be in a 1/6-type root

Now, you just need to find the equivalence between the 1/6-type root and the ones you have. You'll observe that :
7^⅓ = 7^(2/6) = (7²)^⅙ = 49^⅙
5^½ = 5^(3/6) = (5³)^⅙ = 125^⅙

Now, just multiply the two to get (49*125)^⅙

[ember kernel]

Oh god I've been thinking about this for 10 minutes before realising these are * and not decimal points

Factor 5^n out of everything (in both parts of the fraction, so they cancel each other out) and you'll be left with something that doesn't depend on n anymore

I can't believe your teacher really used .'s instead of *'s while writing on a computer. It made it so difficult to understand these were multiplication signs ;-;

[left knoll]

omgggg i thought they were decimal points lollllll

[left knoll]

lollll exactly it was difficult to understand

[left knoll]

woooooww u are smart!

thanks a lot for helping!!!

[thick pine]

Does anybody know LU decomposition (linear algebra)? https://en.wikipedia.org/wiki/LU_decomposition

[woven elbow]

Hi how would you graph f(x)=x^2(x-6)^3? Like what steps would u take to graph it only knowing the equation.

[ember kernel]

No problemo :D

[thick pine]

Start by finding intersections with the x axis

[strong widget]

Thank you soooooo much🥰

[woven elbow]

Yes so i know a zero would be 6 but thats all i know

[thick pine]

What about the other x^2?

[ember kernel]

Method 1
(Quick but imprecise)

Calculate f(x) for some values near x=0, sketch the points in a cartesian coordinates system and link them with a smooth curve (you know it's smooth and continuous since your function is a polynomial)

Method 2
(Long but precise)

• Calculate the y-intercept
• Calculate the roots of your polynomial
• Calculate for which values f'(x) > 0, = 0 and < 0
• For values such that f'(x) = 0, check if the points are minima, maxima or saddle points using f''(x)
• Calculate the turning points where f''(x) = 0
• Calculate vertical, horizontal asymptots (you won't have any since you've got a polynomial here)

Now, sketch all the special points you've calculated on a cartesian coordinates system. You could also add some additional points in-between for more precision.

Then, following the signs you calculated for f'(x) and the turning points you have sketched, draw your function by linking all the points with an "approriately-sloped" line

Method 1 will give you exact values for certain random points. It's almost only valid if you know for sure that the function is continus and does not present special characteristics (asymptots,...)

Method 2 will give you the exact values for the most interesting points (roots, y-intercept, extrema, turning points, asymptots). Furthermore, you'll get the exact form of the function (even if the scale might not be perfectly represented), which can be very useful depending on why you need to draw the function. That's the best option possible for hand-drawn quality graphs

[timber cosmos]

Can anyone give some hint to this problem

[ember kernel]

You might want to watch G. STRANG's lecture on the matter in his MIT 18.06 course, thoroughly accessible on YouTube

I highly recommend his playlist

[glacial dust]

quentin any tips for like being comfy to solving problems and building that confidence to solve questions these things are actually the ones stopping me to keep ongoing

[ember kernel]

Training, training, training.
Also, when you don't understand something, try your best not to skip it, but actually pay attention and ask around/search online. If you understand it once, you're good to go for a good while

[thick pine]

Yeah I've understood the concept but have problems with answering questions on my programming task

[ember kernel]

The answer is in the last line

But, besides multiplying the 3 terms in the brackets 6 times to themselves, idk what tips you could use to get the result

[frank echo]

https://media.discordapp.net/attachments/555699933752066049/852479138496249866/image1.jpg?width=503&height=670

can someone help me with 5 ii

[left knoll]

Hi guys

I need help with a subspaces problem

Idk if this is a subspace of R^4

It means
Where a>0 and b<0

[left knoll]

It's not a subspace 🙂

[plucky gale]

is there something wrong in the ques or hv i done something wrong? 😅
I cant figure out the language lol

[left knoll]

If the question was asking you which recorded amount of rainfall was the most frequent during the year, your answer would be 18, but in this case the question is asking you what the highest amount recorded in centimeters was for a single day. 38 is the highest recorded amount of max rainfall for the year and the one dot tells us that this number was recorded for only 1 day. That makes 38 the right answer.

Hopefully that made sense to you. It made a lot more sense in my head and apologies if i didnt express it well to you😂

[heady egret]

yo, does somebody know how to find the weight in newtons?

[ember kernel]

Mass * 9.81

[left knoll]

Solve it using unitary method

[quaint imp]

im guessing its 3.63

since if u convert 1kg to grams its 1000 then u devide 1000 by 4 its 250 u devide 14.50 by 4 its 3.63

@left knoll

[left knoll]

Thats right

[quaint imp]

yay

thx

[left knoll]

134 calculate the perimeter

[quaint imp]

?

@left knoll

[left knoll]

I got confused lol I edited

[quaint imp]

lol

ok

y 584

@left knoll

[left knoll]

Formula for perimeter of rect is 2l + 2b

L and b is the length and breadth

[quaint imp]

oh

wait...

breadth?

@left knoll

@left knoll

@ember kernel

Quentin it says in ur name u do math help...so i pinged u lol

[glacial dust]

I think its asking for the length/the hypo

[chrome dew]

breadth means width

[left knoll]

Calculate the area

[quaint imp]

i did its not giving me the right answer

[quaint imp]

oh

[glacial dust]

calculate the hypo

try it

[quaint imp]

hypo?

[chrome dew]

u need to find the area of the triangle nd then convert it into square feet

[glacial dust]

hypotenus

[quaint imp]

ik

[left knoll]

What was ur ans?

[quaint imp]

i did

[quaint imp]

hold on

[left knoll]

Yes dont forget this conversion

Meter to feet

[chrome dew]

here ig the answer should have been 134cm

[glacial dust]

how did u get it?

[chrome dew]

perimeter?

[ember kernel]

Yeah. I do help in math. When I decide to :D

[quaint imp]

lol apology in dms

[ember kernel]

Yeah, but I prefer to indicate that here as well. I only answer when I feel like doing so and have spare time. I always feel good getting pinged (because that means I'm doing an at least okay job), but that doesn't increase your chance of getting an answer from me

[quaint imp]

im so sorry @ember kernel I really didnt mean for u to get personal im sorry this is my fault😔 u always do a good job helping ppl out and me and everyone uderstand that u r busy also

[fair harbor]

use the pythagoras theorem

[quaint imp]

yep!

[fair harbor]

Well, you just need to calculate the volume of a sphere with radius of 0.4 cm

and the Volume of the cilinder with height 1.6cm and radius 0.4 cm

and... add them toghether

You dont have the formulas?

Thats to calculate the volume of the sphere

And you can use this for the volume of the cilinder: V = pi * radius^2 * height

[quaint imp]

ohh

ok thanks

I understand now

[fair harbor]

👍

[heady egret]

Thanks.

[ember kernel]

Dude there's no need to be that sorry you know

[lethal crown]

can someone give a hint about this problem please.

[weary arrow]

maybe this will help you on your way

[left knoll]

Hi

Can someone help me?

Why x1=-r-2s?

[reef veldt]

does anyone know any free resources online that cover continuity and differentiability from the basics?

[left knoll]

What happened to the 4

Why did it disappear

[eternal flicker]

it didn't disappear, the equation was divided by 4

xd

[cyan night]

think abiut odd and even functions

[faint lance]

Hello

[marble basin]

Hi

[faint lance]

I need help with maths

Help

[vestal spoke]

Do you want the value of this??

[faint lance]

No

I have to prove its 1/16

[vestal spoke]

U have to prove the whole thing is 1/16 right??

[faint lance]

Yeah

[vestal spoke]

Wait let me try

[cyan night]

the first term in brackets is half of the second term in brackets

i was about to use double angle but i thought it was dumb

[faint lance]

So what do I do after that

[cyan night]

im thinking with you

[quaint imp]

but u asked for one here too, I apologized in DMs and then u said to state it here too

[plucky gale]

hmmm...yea

[plucky gale]

haha i understood the mistake no worries thank you!

[cinder yacht]

= 1/4 ( cos 2pi/5 - 0.5) ( cos 4pi/5 - 0.5)
= 1/4 (cos 2pi/5 * cos 4pi/5 - (cos 2pi/5 + cos 4pi/5)/2 + 0.25)
= 1/4 ( [ cos 6pi/5 + cos 2pi/5] / 2 - [cos 2pi/5 + cos 4pi/5] /2) + 1/4 * 0.25
= 1/8 ( cos (2pi - 4pi/5) + cos 2pi/5 - cos 2pi/5 - cos 4pi/5) + 1/16
= 1/8 ( cos(4pi/5) - cos (4pi/5)) + 1/16
= 0 + 1/16
= 1/16

I used cos 120= cos 240 = 0.5,
and cos a * cos b = [ cos (b+a) + cos (b-a)] / 2 to go from line 2 to line 3

and cos (2pi-c) = cos ( c) to go from line 4 to line 5

[ember kernel]

No I just wanted to state to everyone that pinging me won't help anyone get an answer more quickly.
You don't need to apologise publicly for sending messages to me.
You don't even need to apologise for sending messages to me.
Please stop repeatedly apologising for so little

[hearty tapir]

I have a function like this: f(x) = f(x+1) + 2.How to find the true relation f between two sets?

[cinder yacht]

do u know if f is continuous?

seems to me like f(x) = g(x) - 2x where g is a 1-periodic function

[hearty tapir]

Honestly, I don't know anything about functions like this.For instance, how did you reach this result about this function?

[cinder yacht]

well , f(x+1) = f(x) - 2
so everytime X goes up by 1, Y goes up by exactly -2 (aka goes down by 2)

so u draw something random on the interval [0,1) for example, then u replicate that drawing on [1,2) + translating it downwards by 2

etc

anyway I saw the answer by imagining a graph

u didn't study periodic functions?

and what sets do u mean exactly? R->R or N->N?

cause would be much easier if it's N->N (if x are integers)

[fair harbor]

gonna need more information about the question if you want to get help

[fair harbor]

From looking at that, the sistem is possible but undetermined

x2 and x4 are the variables that we can't determine

the group of possible solutions are in function of the missing varialbes, and assuming that x2 = r and x4 = s,

you just need to solve the equation system

fuck let me do this in paper it's easyer to explain then over text

1 sec i'll post the steps

[hearty tapir]

Not yet..

[hearty tapir]

Lets say N => N, to understand easily

[cinder yacht]

but what does the question say tho

[fair harbor]

@left knoll, this is the solution explained in steps

[cinder yacht]

if it's N=>N then f(n+1) = f(n) - 2, AKA for every integer n f(n+1) - f(n) = -2
that's an arithmetic sequence of common difference -2

[fair harbor]

Sorry for grammar erros in advance, my main lang is not english

[cinder yacht]

so f(n) = f(0) + n * (-2)
so f(n) = f(0) -2n

and you can arbitrarily choose any f(0) you want

actually this works even if it's N=>R *
but the problem is R=>R

[hearty tapir]

Hmm, you mean functions like this treat like they're actually sequences?

[cinder yacht]

i mean functions that go from N to R

are literally sequences

f(n) = Un basically lol

so i assume ur question initially implied R->R ?

[hearty tapir]

Yes

[cinder yacht]

do u know what a periodic function is?

and is it said that f is continuous or no?

[hearty tapir]

Not really

[hearty tapir]

It's not given

[cinder yacht]

https://mathworld.wolfram.com/PeriodicFunction.html

it's weird that you get this exercice.. without knowing what a periodic function. Unless they gave you some information about f other than "f(x) = f(x+1) + 2"?

[cinder yacht]

this was the answer btw

[cinder yacht]

and the proof is :
we know that f(x) = f(x+1) + 2
so f(x) + 2x = f(x+1) + 2 + 2x
so f(x) + 2x = f(x+1) + 2(x+1)
so by naming g(x) = f(x)+2x, we have :
g(x) = g(x+1) for every x in R
so g is a periodic function, 1 being a period of g
so in general f(x) = g(x) - 2x where g is... (same as line above)

[hearty tapir]

Ugh don't question it. Our education system is not that good so unfortunetly we can encounter problems like this at the beginning of functions, which is veery nonsense...

[cinder yacht]

this is a difficult problem for that stage

lol

like I'd expect this problem in

university

definitely not just after discovering what a function is

[hearty tapir]

I'd better to study periodic functions after making a lot of process in functions (i just started to study functions in real meaning after all..). Maybe i can understand better after studying them.

[cinder yacht]

periodic functions are just functions that repeat themselves regularly, but yes that's for later

[hearty tapir]

Really 😄?

[cinder yacht]

u should ignore this problem for now I guess

[cinder yacht]

in my opinion yes

[hearty tapir]

Yes, of course

[cinder yacht]

for me it was easy cause I did exercices like this before, but for high-school me I would've found it hard and it would've taken me a lot of time

[hearty tapir]

I see

Thanks a lot friend 👍

[cinder yacht]

try to draw (or analyze the monotony of) f(x) = sqrt ( 10x/(x+1) ) for x in [0;10]
deduce from that the different intervals of X:
-where 0<=f(x)<1 : that's where [f(x)] = 0
-where 1<=f(x)<2 : that's where [f(x)] = 1
-where 2<=f(x)<3 : that's where [f(x)] = 2
-where 3<=f(x)<4 : that's where [f(x)] = 3
once you find out all the values of [f(x)] for x in [0;10], you can just compute the integral

[raven cobalt]

PLZZ GIVE COMPLETE ANSWER

[ember kernel]

He gave you 70% of the answer tho

[opal warren]

any tips to solve logarithm questions ( linaer and exponential)

[slim juniper]

For 3b, how do you know when to use integral by substitution

[hasty owl]

How do you know if something is a minimum or a maximum point? Eg, the point (3,1) is a minimum, but the point (-4,47) is a maximum. How can you tell?

And this is for a parabola and not a cubic, so there's only one answer

[slim juniper]

the bigger number is the max, and smaller number is the min

[hasty owl]

but how could you tell that from looking at say, the point (3,1)?

Like, how do you know it's a positive or negative parabola from looking at the point?

Or would you look at the original equation?

or the x value, or y value?

[slim juniper]

if the original equation is negative, then negative parabola. the point (3,1) tells us that when x is at 3, y is at 1, when we;re trying to find min or max, we're looking at the y-value

does that make sense?

[hasty owl]

yes, thank you

[lime junco]

Help me please ;-;

[cinder yacht]

I guess that when the primitive isn't obvious, and ur dealing with a fraction, u can substitute the denominator by U

[cinder yacht]

but that stuff I read made no sense

u can't tell how the parabola is just from one point

u need for example to look at the equation : is f(x) = ax^2 + bx + c :

• the sign of "a" determines whether the parabola has a minimum, or whether it has a maximum
• x=-b/(2a) is the X where Y is maximal or minimal [that can be proven if u studied derivation]
  -to get the value of that maximal/minimal Y, u compute y = f(-b/(2a)) =...

[cinder yacht]

in a parabola ur not supposed to have a maximum AND a minimum, u typically only have one of those, unless X is restrained in a bounded interval

[left knoll]

help 🥲

[plucky gale]

hey i was wondering what type of calculator will i need for the SAT exam? like a simple + - x / one will do or do i need anymore functions?
(i dont have any knowledge of calculators since in my country we dont need it for any exam)

[slim juniper]

well, in some of my problems, it's the numerator that's being substituted by u

[quaint imp]

oh I was confused

[patent rain]

any calculator works

but if u were to get a graphing calculator get the ti nspire

its way better than ti 84

[plucky gale]

ah all right thank you!

[atomic dagger]

hi! I'm trying to find the limit as n-> infinite here. They say the answer is 3/2 but I just don't understand (I thought it was infinite). Could someone help me ?

[left knoll]

i m stuck plz help

[sharp ferry]

this is a very famous question you can find a lot of video solutions on youtube

i remember i saw the exact same question once

https://youtu.be/9IUVbwPFwKI?t=410

[sharp ferry]

at this time stamp the solution starts

[ember kernel]

The two expressions are the same, I just distributed the sqrt(x+1) to get to it

If you look closely, the second expression, with x tending to inf, results as "inf - inf", which is an undefined form

You can look up on the internet how to solve a inf-inf form, but uf I recall correctly you need to multiply these two terms a-b by their conjugate a+b

[left knoll]

thankyou soo much! you saved mee

[astral berry]

Answer is E and idk how

For 14

[cinder yacht]

-tu multiplies en haut et en bas par le "conjugué" du numérateur (aka [ (n+3)^(1/2) + n^(1/2)]) pour utiliser l'identité remarquable (a-b)(a+b) = a^2 - b^2

• le (n+1)^(-1/2) en bas devient (n+1)^(1/2) en hautq
  -après toutes ces transformations, tu factorises partout par n^1/2 (numérateur et dénominateur), tu les simplifies, et tu fais tendre n vers +inf

faster if u studied equivalence in sequences

[cinder yacht]

2^7-1-7

to form a new color, you just need a subset of the set color {red, blue,..} : there are 2^7 of those
except that the 1 empty subset (aka no color) and the 7 subsets containing just one color aren't viable, so u subtract 1 and 7
so that's 2^7-1-7

maybe "combination" is better vocabulary than "subset" depending on how this stuff was taught to u

[atomic dagger]

merci de m'avoir répondue!

[tepid spade]

Bonjour, je suis un jeune étudiant et je ne comprends pas vraiment les fonctions, (les images des nombres)

[random flame]

Heyo I need help with Q15c, so if anyone wants to help pls ping me, and thanks in advance!!

[quaint magnet]

you use the combination formula n(c)r = n1/r!(n-r)!

so with the no restrictions there are 10 cd's and the number of selection is 5 so it becomes:

10
C
5

using the formula it will be:
10c5 = 10!/4! (10-4)!

for B however we take the number of jazz cd's (3) and subtract it by the total amount (10) so it becomes (7)

and we do the same

7
C
3

im not really good at explaining nor am i sure about this certain equation but the basic idea is to get the amount of combinations

hope this helps in anyway!

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

the video uses a different equation but both explain the same idea

[left knoll]

Hi guys

I need n value

Can someone help me?

[inland oracle]

Translation:
b) find the characterization of the subspaces that generate the vectors u1, u2, u3 and u4.

[amber bluff]

(fog)(x)=3x-4

g(x)=x-4

what is f(x)?

can you help me with this question

i found an answer but i'm not sure

[ember kernel]

f(x) = 3x + 8

Therefore f(g(x)) = 3g(x) + 8 = 3(x-4)+8 = 3x-12+8 = 3x - 4

[vocal juniper]

What does this exactly mean?

[quaint magnet]

correct me if im wrong but this is physics isnt it?

[vocal juniper]

It's from physics but I thought vector space is a concept in math ..

[amber bluff]

i think so

[amber bluff]

yes

[quaint magnet]

it may be linear transformation but im not too sure

[vocal juniper]

So that any number of R^n can be transformed to R^n?

[quaint magnet]

i dont really understand it myself but ill link something that may help
https://textbooks.math.gatech.edu/ila/linear-transformations.html
(the example in the picture is included in the last page)

mb wrong example

[vocal juniper]

thanks!

[quaint magnet]

no problem, if im incorrect about anything please do correct me!

[cinder yacht]

I dont think the second case is correct

you just surely take that one favoritr jazz CD, so u just need to choose the 4 others among the 9 remaining
so that would be (9 choose 4)

[cinder yacht]

for 15c,
-either u take exactly 4 classical CDS :
then u just need to pick the 5th CD among the 6 other choices
so that's (6 choose 5) = 5
-either u take exactly 3 classical CDS:
in that case u first need to pick which classical CDS you take : (4 choose 3) = 4
then you pick which 2 other CDS you take among the 6 other choices : (6 choose 2)

so the final answer is : 5 + 4 * (6 choose 2)
which is 65

[quaint magnet]

Oh my bad, thanks for correcting me

[cinder yacht]

it means that F takes a vector in n dimensions as argument, and returns a vector in n dimensions

an example for n = 3 is, let's say, the transformation F(u) = 2u where u is a 3d vector
so F would be the function that "doubles" the size of the vector lol, AKA stretches it

but you can imagine allll sorts of functions F

to sum up : F is a function from the set R^n to the set R^n
R^n is the set of n-dimensional vectors (so for example, R^3 is the set of 3D vectors, AKA "irl space" kinda i guess lol)

[ember kernel]

@quaint magnet is wrong. This notation just means that we define F to be a function that takes a vector of length n as an input, and returns a vector of length n as the output.

This is pure mathematics btw

[vocal juniper]

So if i plug n numbers into F, i can/will get n numbers out?

[cinder yacht]

write that (blabla)^X as exp(x * ln(blabla))
and write (nx+1)/(nx-1) as 1 + 2 /(nx-1)

[quaint magnet]

Again, thank you for correcting me. I did not know much into the subject but wanted to help in someway.
Shouldnt have dug my head into something i dont purely know and im sorry for that but overall glad that they got the help they needed

[ember kernel]

Np man. That's nice to offer help anyway. But yeah maths can be tough to those who haven't been introduced to some specific concepts

[cinder yacht]

seems to me like that subspace is the 2-dimensional subspace generated just by (u1, u2), so in other words by (-1,0,1) and (0,-1,-1)
aka a subspace where z=y-x
But idk what you mean by characterization

[ember kernel]

You won't get n real numbers out, but you will get one vector of length n

[cinder yacht]

kind-of...
u could have for example, for n=4
F(0,2,3,2) = (666,69,666,69)

or if V is a velocity vector, and V0 is a constant velocity vector, and n=3,you could have F defined as :
F(V) = V+V0

u can view the vector as n different numbers, and vice versa, it depends on how that "F" is used

[quaint magnet]

So these return arrays or matrixes in someway?

[cinder yacht]

what u shared here is too general for me to be able to explain what kind of F

[ember kernel]

Nope, just an array :)

[cinder yacht]

oh

[quaint magnet]

Oh thats p neat

[cinder yacht]

arrays are different from matrices for them?

in my mind it's the same thing

[ember kernel]

A matrix would be R with m*n as """exponent"""

[quaint magnet]

So its an N array of R I suppose?

[cinder yacht]

ah they say array for vector?

[vocal juniper]

Do you know what divergence is?

[ember kernel]

R^n just describes a space of arrays

[cinder yacht]

yeah

[vocal juniper]

that's what i'm trying to understand

[cinder yacht]

but divergence is a R^n -> R function if i recall

[quaint magnet]

Ohh ok i get it, thank you

[vocal juniper]

I don't think so

[cinder yacht]

It takes a vector and returns a number no?

[ember kernel]

It is

[cinder yacht]

div(E) is a number, where E is a vector

so it's R^3 -> R

[ember kernel]

Curl is R3 -> R3
Diverg. is R3 -> R
Gradient is R -> R3

[vocal juniper]

oh no, you are right. But for an F: R^n --> R^n

[cinder yacht]

Curl what's that in French?

rotationnel

[ember kernel]

Rotationnel

[cinder yacht]

okok

and Laplacien R->R

i didnt study physics for 1.5 year im starting to forget this stuff

[quaint magnet]

So this function takes R^N amounts of arrays and returns R^N amounts of array?
But why would we need to return the same array?

[cinder yacht]

it doesn't return the same array

the screenshots u sent were wrong

[ember kernel]

Think Laplacian is R3 -> R, might be wrong

[cinder yacht]

that was just one example of an F

(the F that doesn't change anything to the vector, AKA the identity function)

[cinder yacht]

ah I think there are both

scalar Laplacien and vector one

im glad I don't study that anymore

[ember kernel]

No, it takes one n-item-long array, and returns one n-item-long array

[quaint magnet]

Oh ok

Glad to learn something new

And thank you all!

[ember kernel]

Just think of it as any function you've ever dealt with before, except it doesn't use x as the input, but (x,y,z, ...)

[vocal juniper]

so can you say that the R on the left is the domain?

[ember kernel]

The R^n on the left is indeed the domain :)

And the one on the right is the codomain

[cinder yacht]

the codomain*

[ember kernel]

But the original pitcure you sent didn't specify any expression for F, so you just need to treat as any arbitrary function that could exist and deal with arrays coming from the vector space R^n

[cinder yacht]

range is Im(f) I guess

[vocal juniper]

alright, thanks a lot!

[cinder yacht]

in physics R^n more often represents "space vectors" than "arrays" (even tho ik those are basically the same things), so maybe not talk abt the array thing too much

[ember kernel]

Thanks for correcting

[cinder yacht]

i mean physics isn't very mathematically precise ukno

[ember kernel]

R^n is indeed a vector space. But it contains vectors/arrays

That's how I meant to explain it at least

[cinder yacht]

nvm im just a bit confused abt the English terms cuz i studied it in French

[maiden sigil]

im confused on this topic on geometry

[ember kernel]

Slope = (difference in y)/(difference in x)

Example : the slope of the line that goes through P = (-4,17) and Q = (1, -3) is :
(Py - Qy)/(Px - Qx) = (17 - (-3)) / (-4 - 1) = 20 / (-5) = -4

Two lines are parallel if they have the same slope

[opal pivot]

when we are to find the standard deviation of a number set, but aren't told whether it is for the population or sample, do we always assume they ask for population standard deviation unless told otherwise?

[left knoll]

idk how to go about this problem like how do i test for addition or multiplication

[cinder yacht]

u didn't study Dot products did you?

and orthogonal vector spaces

cause if u did u can prove it in 1 line

if not u need to:
-mention its a subset of R4
-show that [0 0 0 0] is in that set

• set lambda in R, [a b c d] in that set and [a' b' c' d'] in that set. Prove that the vector (lambda * [à b c d] + [a' b' c' d']) is also in the set (AKA that its coordinates verify the set's equation)

or actually u can just say that it's the Null space of the linear map f : [a b c d] ->a+b-c-d = D * [a b c d] where D is the 4x4 diagonal matrix whose 4 diagonal coefficients are 1, 1, -1 and - 1

that makes it a vector space

[naive lagoon]

Prove these three things for the set -

[small canyon]

is f-1(x) continuous on r?

[cinder yacht]

if f(x) is continuous yes

[small canyon]

this is all the information that's given (Q18)

will it be e^x?

[ember kernel]

e^x is continuous on R

Since you don't know what f(x) is, you can't be 100% sur that f-1(x) is continuous tho

Since mathematicians always take into account the "worst case scenario", that means we treat f-1(x) as "not continuous on R" as long as we don't prove the opposite (which we can't since f(x) could be any possible function that exists)

@small canyon

[small canyon]

thanks alot :))

[ember kernel]

np man !

[left knoll]

i did but honestly its such a clusterfuck to understand atm, i was aware of the 3 rules but didnt know how to implement them, thanks a lot

[cinder yacht]

don't worry it takes time to get used to it

[cyan night]

why do they use vectors to represent points on the argand plane but not the cartesian plane

why are there vectors even

[cinder yacht]

well vectors cover more ground I guess?

like if u want to translate a point A on the argand plane by a translation vector u = 2+3i

you can deduce a point B from that translation (so that the vector AB = u)

would it make sense for you to use a point to represent 2+3i?

vectors can represent all points (cause every vector OM represents the point M, where O is the origin of the coordinate system) and more (things like the translation vector u that I talked about)
while points can't represent all vectors that well (it wouldn't make that much sense to represent the previous 2+3i with a point in the plane)

so interpreting complex numbers as vectors does have a point

(and even beyond that, linear algebra is all about vector spaces... You will see that for example, a function continuous on [0;1] is a vector. A polynomial is a vector. A sequence is a vector. The notion of vectors is very general)

while we rarely talk about points in linear algebra

[cyan night]

for example you plot a point 3+i on the complex plane, and you represent its modulus as a vector.. why dont you use a line segment?

its just the distance from that point to the origin why do they use vectors

[cinder yacht]

it's not distance :o

otherwise 3+i would be the same as -3-i

that's not at all 2 things we wanna mix up

and we don't actually represent its modulus as a vector

we represent its modulus as the norm (length) of the vector, but we also represent the direction and orientation of the vector

[wooden elbow]

:o

[cyan night]

isnt the distance calculated via pythagorean?

i meant the sqrt (a^2+b^2)

this is what im asking

why does it have direction

(represented by the arrow tip?)

[ember kernel]

Historicallly, complex numbers come from the R2 plane, to which has been added a specific, commutative R2->R2 multiplication (R2 has no "general" multiplication operation, and dot product is not considered multiplication since it's R2->R).
The specific multiplication operation is :
(a,b) * (cd) = (ac - bd, ad + bc)

Then shorter notation conventions were applied :
(1,0) would be denoted as 1
(0,1) would be denoted as i

That leads to eg. (2,5) = 2 (1,0) + 5 (0,1) being denoted as 2 + 5i

You can also check that i² = i * i = -1 and that a * b = (a,0) * (b,0) = (ab, 0) = ab

Since the complex plane comes from the R2 plane (with a multiplication operation and notation conventions as their only difference), it could make some sense to use vectors to represent them. However, complex numbers represent ... well ... numbers, and I therefore advise you represent them as points

But that doesn't matter that much. In linear algebra, physics, etc., we also represent points in R^n with vectors anyway, and don't make a whole deal about it

[ember kernel]

A complex' modulus, however, cannot be represented by a vector, as it is a real number (it belongs to R)
But if you want to represent it graphically anyway, the only conventional ways to do so I can think about are :

• Write it at the middle of a segment that links the origin (0) to the desired complex number (z), with an arrow tip on both tips of the segment
• Or just the same as before but without the arrow tips ; either because you're lazy or because you need to represent several modulus in your sketch, which would be overloaded if you drew all the arrow tips as well

[cyan night]

i think it was a misuse of words by me, the "complex' modulus" was what i referred to the graphical representation

but why are there arrow tips anyway?

[ember kernel]

Because that's how we represent distance

[cyan night]

why is it not like that on the cartesian plane

[ember kernel]

Well we also represent distance this way in R2

Never with a vector

Always with a segment with optional arrow tips on both sides

If you draw a square, how would you represent its side length ?

You'll most likely just write c next to one of the sides, or draw a double-arrow parallel to the side and then mark a c next to it

But I'm almost sure you've never ever seen a one-tip arrow represent it (besides in lower grades, where maths is not rigorous)

@cyan night

[cyan night]

because i learnt in khan academy sal keeps saying its a vector

like this one

so whats it called if not a vector?

[ember kernel]

What is "it" : modulus or complex number ?

[cyan night]

the graphical representation

the arrow itself

not any number specifically

[ember kernel]

Yeah the arrow is a vector

[cyan night]

yeah thats what i was wondering about, why is it a vector

[ember kernel]

But what really matters is what it represents

[cyan night]

its length is the modulus of the number

[ember kernel]

Then it's wrong

[cyan night]

🤔

[ember kernel]

You can't represent a modulus (in C) or a distance (in Rn) by a vector

I think you misunderstood

The vector actually represents the complex number

[cyan night]

oh

but the vector indicates continuity right..??

is it like a ray

[ember kernel]

Continuity... of what ?

[cyan night]

i thought the arrow tip of the vector indicates that the vector keeps going

[ember kernel]

No

The arrow tips is meant to say two things :

• "Here, it's the head (end) of the vector, not its tail"
• "The vector stops exactly at the tip of the arrow tip"

We usually make use of dashed points to represent that something keeps going

[cyan night]

ohh okk thank you

[cinder yacht]

why wouldn't it? why reduce the rich information of a complex number a+ib (the information a and the information b) to the poor information of its modulus (only 1 information remains : sqrt(a^2+b^2))?

then I'd ask you why not represent every complex number with just its Real axis and ignoring the imaginary axis?

we want our representation of the complex number to tell us as much as possible about the complex number

a vector does it greatly, just by looki g at the vector u can tell what complex number it represents

[cinder yacht]

no we represent distance + direction with vectors

[wooden elbow]

We can say magnitude ?

[cinder yacht]

ohh no at all xD

[cinder yacht]

yea magnitude

im not on point in terms of the English translation of what I learnt

also he was saying distance so I was saying that too, that's a fine way to view magnitude

[wooden elbow]

Distance is always in positive I guess

[cinder yacht]

magnitude is always positive

[wooden elbow]

Oh yea

But we can add direction

[cinder yacht]

to?

[cyan night]

so the arrow is used to represent the direction (the argument of the complex number)?

[cinder yacht]

ehmm it tells u whether its "towards the left" or "towards the right" for example

[cyan night]

but why are there no vectors in the cartesian plane?

[cinder yacht]

so the angle of a horizontal arrow pointing right is 0° (compared to the x axis)
while the angle of a horizontal arrow pointing left is 180°

if we didn't see where the arrow was pointing we can't tell what's the argument

[wooden elbow]

Sorry not add

[cinder yacht]

there are

idk what u mean

maybe u didn't study it yet but there are

[cyan night]

oh hm

[cinder yacht]

for example if u draw 2 random points À and B, the vector AB is drawn by drawing the segment AB and adding an arrow head on the B side

[wooden elbow]

Always there are in Cartesian plane

[cyan night]

i mean what will change when its a segment instead

of a vector

[cinder yacht]

represent the complex number (as a vector)

+1

and represent -1

then remove the arrow heads

can u tell them apart? +1 and -1?

don't they look exactly the same if u take away the arrow heads?

[wooden elbow]

https://youtu.be/U5XpIctSZYU

@cyan night

[cyan night]

okk ill watch it after school

[wooden elbow]

It explains all the questions you are asking

[cyan night]

wait dont they have different ending points?

[wooden elbow]

Np

[cinder yacht]

u can define vectors without even defining starting and ending points tbh

for example 3i can represent any vector (arrow) going up +3 towards the y axis

u can draw the arrow anywhere and it'll still represent 3i, itll still be the same vector

[cyan night]

wdym by "draw the arrow anywhere"?

[cinder yacht]

ofc if u wanna represent 3i with a point A, then u can just put your A at coordinates (0,3), u don't NECESSARILY need an arrow for that it's fine

u don't even need to draw a segment if ur goal is to represent a complex number with a POINT

[cinder yacht]

choose anywhere to start ur arrow, doesn't have to be in the origin of the plane

it's like if I have 1$ in my pocket, or if u have 1$ in ur pocket, we're still gonna call it a 1$ coin regardless of where it is

same with vectors, we can represent the arrow "3i" wherever u put it in the plane

[cyan night]

but 3 is normally interpreted as the modulus (the distance from 0,0) so shouldnt it be from the origin

[cinder yacht]

however we often prefer to start the arrow from the origin so that the arrow representation of the complex number and the point representation of the same complex number sort-of agree

[ember kernel]

Indeed. What I meant was "you can't represent distance (and only distance) with a one-sided arrow"

[cinder yacht]

modulus doesn't mean distance from (0,0)

modulus of a vector that starts at (0,0) sure that's the distance from (0,0), but in general modulus is just the ""size"" of the arrow

[cyan night]

oh

[cinder yacht]

modulus of a complex number z
= the distance of a POINT REPRESENTATION of z, from (0,0)
= the magnitude (size) of a VECTOR REPRESENTATION OF Z, wherever u draw ur arrow

[cyan night]

it can be interpreted as both??

[cinder yacht]

yeah

u can interpret a complex number as a point in the plane, or as a vector in the plane

for example in some problems u'll see them saying stuff like : "let A(1+2i) and B(3+4i) be 2 points in the complex plane, and let u(-1-i) be a vector in the plane"

or shit like that

[cyan night]

u(-1-i) be a vector on the plane means it has modulus 1?

[cinder yacht]

I think u'll understand more with exercises

[cinder yacht]

no it's modulus is : sqrt[ (-1)^2 + (-1)^2] = sqrt[2]

[cyan night]

wait thats the point

me brain just broke

[cinder yacht]

it's weird to study vectors representing complex numbers when u didn't know about vectors in the usual Cartesian plane

[cyan night]

how do you draw u on the complex plane

[cinder yacht]

what u can do for u (-1-i) is :
-u choose any random starting point of ur arrow
-by moving 1 to the left (cause the x coordinate of u is -1) and 1 to the bottom (cause the y coordinate of u is also -1), you deduce the ending point of ur arrow
-so now that u know where the starting and ending point, u just draw the arrow

often u'll see ppl choosing the starting point of the vector u to be O, the origin of the plane, but that's not necessary

I think maybe try to understand whzt vectors are in the normal cartesian plane first

before studying them in complex numbers

[cyan night]

if the starting point is O then doesnt that mean the u is the number -1-i itself

[cinder yacht]

if the starting point is O, then u is the vector OA where A is the point representation of the number -1-i

[cyan night]

ah ok ty

[hazy blaze]

Hey does anyone know how they got to r 15/7 and s 10/7? I just don't get it

[cinder yacht]

(line I) + 2 * (line II) gives you 7r = 15 so r = 15/7

and you use for example line III to deduce what s is (now that you know what r is)

[hazy blaze]

Tyvm

[minor valve]

does anyone have a google classroom for math or anything

[fossil token]

Minimize 𝑧 = 12𝑥 + 18𝑦, subject to 4𝑥 + 𝑦 ≥ 4, 𝑥 + 3𝑦 ≥ 6, 𝑥 + 𝑦 ≥ 3, 𝑥 ≥ 0, 𝑦 ≥ 0.

Can someone help please?

[small canyon]

plot the graph for this and find the feasible region with the constraints given, y>3 wil be parallel to x axis at y 3. then find the corner points of the region and put it in the objective z. @fossil token

[atomic dagger]

does anyone know how the first epxression gives, after integration, the second expression?

[cinder yacht]

integral of w'(t)dt from 0 to t
is w(t) - w(0)

and integral of alpha*dt from 0 to t
is alpha * t

[thick pine]

Can somebody help me with this question?

[glacial dust]

find the x when the area is 400

how can i do that can someone help 😦

[turbid swallow]

Area = ½ * base * height (half a rectangle)
next fill in what you know
400 = ½ * x * 2x
400 = x²
||20=x||

[glacial dust]

nvm i got it thank for trying to help

[sharp night]

If i am trying to find the local extrema of a funcion using the 2nd and 3rd derivative test, if the stationary point is odd when I add it to the 3rd derivative, then the function does not have a local extrema in that point

Right?

I hope my sentence makes sense

Trying to find the extrema of: f(x)=x^(4)-6x^(2)+8x-3

[potent pond]

hi

should I send you my solution private ?

[small canyon]

is tan-1x domain (-infinity, infinity) or [-in,in.]

[left knoll]

Sorry

i cant delete

Why

[thick pine]

Successful attack though lol

[limpid juniper]

can anyone please help me with this? ive tried to set up a factored form equation for it but i sense im not getting the degree of the function or the orders for the zeros right.

[mild nebula]

Hello can someone help me with my homework in math or teach me through call would gladly appreciate it

it's about performance task sequences

[thick pine]

Nobody an idea? 😦

[thick pine]

For a), create a table:

iteration # | 1 | 2 | 3 | ... | n
------------+---+---+---+-----+----
# add. dots | 1 | 3 | 5 | ... | ?

For b), create a formula for all needed dots (you can use the same table as in a) to get there)

[mild nebula]

I honestly still don't get it but thanks for the reply-

[thick pine]

Okay so for the 2nd iteration you get 3 additional dots. For the 3rd you get 5 additional ones. right?

[mild nebula]

Yeah..

[thick pine]

Do you have an idea how to put that in a formula?

[mild nebula]

I don't.

[thick pine]

ok 1 sec

[thick pine]

Does this help?

Sorry for my bad handwriting I hope you can read it

[mild nebula]

I can read it but-

3+3+1 = 2 . 3 +4

What's that? -

[thick pine]

A multiplication sign lol

3+3+1 = 2*3+1

Do you understand? 😁

[mild nebula]

You're going to struggle- I still don't get it..

[thick pine]

Haha okay so you have 3 for the right side, 3 for above and 1 extra for the corner.

So that's 2x3 dots for the two sides plus the additional one in the corner. In math language 2x3+1 dots. right?

What part do you not understand?

[mild nebula]

This is embarassing everything-

[thick pine]

Do you understand the question?

Or, if you don't understand the question, do you understand the situation presented here?

[mild nebula]

I don't.

[next valley]

https://media.discordapp.net/attachments/913594609949610034/913594681378627594/IMG_1357.jpg

Can someone please help with this

[hazy halo]

@small canyon open braces

[hazy halo]

.

[left knoll]

look at the roots and what number it is at the root. eg at -1 its is x^3 etc