help-0

[rain scaffold]

u just sub x

[ashen pulsar]

U replied to a bot dummy

[old sinew]

lel

[rain scaffold]

.close

[lone heart]

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[dawn quail]

Why do exponential functions need to have a base greater than 0?

[dawn quail]

Why can't we have f(x) = 0^x

f(10) = 0^10

(10,0)

[last ether]

What happens at 0^0

[dawn quail]

0

[last ether]

You sure?

What is 1^0

[dawn quail]

Ohh

1

[last ether]

Yeah you see 0^0 causes riots amongst people

Some say it's 0, some say it's 1

[dawn quail]

lol

[last ether]

I say "I don't give a shit make it an open circle"

So technically you can

Just at x = 0, you're gonna have a fire riot

It's a horizontal line in that case

[dawn quail]

OK so f(0) = 0^0
f(0) = 1
(0,1)

[last ether]

With no growth nor decay

[dawn quail]

that makes sense for exponential functions, they always hit the y axis at 1

but i don't understand why we can't use bases lower than 0, it's like forbidden for exponential functions?

f(x) = 0^x
f(3) = 0^3
f(3) = 0
(3,0)
x = 3, y = 0

but we don't draw (3,0) on exponential graphs

[last ether]

We can, but it'll enter the complex realm

[dawn quail]

Technically we could draw this coordinate and it would satisfy the equation?

[last ether]

So like (-1)^x

Have fun with that

[dawn quail]

Hmmm.. It just feels like exponential functions are locked into more strict rules that other functions don't have to deal with

[last ether]

I mean logarithms also go under some jank, stuff that's beyond my ken lol

[dawn quail]

Like you can do the math, it would satisfy the equation, but at the same time it won't tell you anything

[last ether]

I know that (-1)^x = cis(πx), which is a trig function

So you kinda get trigonometric stuff thrown in there

[dawn quail]

but you are using -1 for the unit circle, right?

what about f(x)=(-43)^x

[last ether]

Well uh

That's 43^x * (-1)^x

So 43^x cis(πx)

[dawn quail]

43^x * (-1)^x
I don't understand? can you explain how you separate 43^x and (-1)^x?

let's say f(3)=(-43)^3

[last ether]

$(ab)^x = a^xb^x$

[ocean seal]

Umbraleviathan

[dawn quail]

OK

I keep forgetting that

the negative symbol - can always be converted to (-1) at any point place or time in math?

[last ether]

Basically yeah

[last ether]

And it should work out either way

[dawn quail]

so long as you include the brackets around (-1)?

[last ether]

Yeah

[dawn quail]

wow

that is very good to know.. i don't think i have been taught that yet

and it's about time..

[last ether]

(-43)^3 = 43^3 • cis(3π) = 43^3 • -1

Oops

There fixed it lol

[dawn quail]

sorry im still wrapping my head around soh cah toa, cis is the opposite of cos?

[last ether]

cis is cosine + isine

[dawn quail]

sin, cos, tan
cis is related to cos

[last ether]

Cis is kinda like cosine

Cis is two trig functions in one

[dawn quail]

but flipped

[last ether]

https://en.m.wikipedia.org/wiki/Cis_(mathematics)

No

[dawn quail]

It's not one of these, is it?

i have only learned of these 6

is there another one after cis, the 7th?

actually it sounds like cis is advanced for me still

it talks about this https://en.m.wikipedia.org/wiki/Euler's_formula

but maybe i should know it already in pre-calculus..

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[lone heart]

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[sage pulsar]

i don't get this one can someone help me? need this for a enrolment test in unihttps://gyazo.com/18fac3c0e9866190ff646cf623788bb4

[ebon condor]

what part is confusing you

[old sinew]

isn't the Product Summation?

[ebon condor]

product and summation is two different things

product is multiplication

summation is addition

[old sinew]

i mean summation of products

by iteration

[ebon condor]

I dont know what that means

[sage pulsar]

Its just a part of math that i never had in school which i am unfamillier with im having a little enrolment test and im stuck here

[old sinew]

This Capital Pi over here, i mean

[ebon condor]

yeah it's product

$\prod_{variable = lower-bound}^{upper-bound}{expression}$

[old sinew]

my bad, products not summation

[ocean seal]

KurtDee

[ebon condor]

$\prod_{x=i}^{j}{f(x)}=f(i)f(i+1)...*f(j-1)*f(j)$

[ocean seal]

KurtDee

[sage pulsar]

how do i solve this

[ebon condor]

I just wrote out how to solve it

[sage pulsar]

this one

[ebon condor]

okay well

$f(n) = (\frac{2n-12}2)^{\frac 12}$

[ocean seal]

KurtDee

[ebon condor]

lower bound is 7, upper bound is 10

so just multiply f(n) for all values of n

[sage pulsar]

if n is 7 dosnt it equal to 0,5

or do i need to mutiple upper bound 10

[ebon condor]

uhhh what equals 0.5 specifically

1/2 power is the square root

[sage pulsar]

im sorry im lost rn

dont get it

[ebon condor]

okay

what is f(7)

f(7) = ((2*7-12)/2)^(1/2)

[sage pulsar]

just need to change 2n to 2*7 or not

[ebon condor]

yeah

[sage pulsar]

isnt it 1 then

[ebon condor]

yes

[sage pulsar]

what about the upper bound 10

do i do the same

[ebon condor]

you do the same for n= 7 through 10

and multiply them all together

[sage pulsar]

aaa

so 7 8 9 10

then mutiply

[ebon condor]

there are tricks to make this simple but in essence that's it

yes

$\prod_{n \in [7,8,9,10]} {f(n)}$

[ocean seal]

KurtDee

[ebon condor]

$=f(7)*f(8)*f(9)*f(10)$

[ocean seal]

KurtDee

[sage pulsar]

ok manageble i will try one second

4.89897948556

[ebon condor]

dont simplify

[sage pulsar]

4.9

[ebon condor]

that's none of your answers

[ebon condor]

this

[sage pulsar]

yes because they are shown in sqaure roots

[ebon condor]

yes...

[sage pulsar]

dosnt square 20 come close to it

[ebon condor]

so what's the number as a rational

dont guess

[sage pulsar]

2 square 6

[ebon condor]

seems right to .me

[sage pulsar]

thank you very much

[ebon condor]

$\sqrt{123*4}$

[ocean seal]

KurtDee

[ebon condor]

$=\sqrt{24}=2\sqrt{6}$

[ocean seal]

KurtDee

[sage pulsar]

.close

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[alpine sable]

when you enroll in a brilliant.org course are your answers marked by real teachers?

[lone heart]

@alpine sable Has your question been resolved?

[last ether]

That's not something we would know

[alpine sable]

www.google.com

[last ether]

So true

[alpine sable]

hello small man

[last ether]

Hasbulla

[alpine sable]

i love hasbulla

.close

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[hoary flare]

Okay so to explain the photos

The first photo is the graph I had to use

The seccond photo is the work I did for the general term so I got it

And the help I need is the third photo and I need help to understand how to do questions D and e

more specifically e

How would I explain the relationship between the y-intercept and the slope and graph to the formula 81=25+(8-1)8

essentially to sum it up, because all that is a lot to read and catch up on if someone is helping me lol

.close

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[alpine sable]

i think i need a full working out solution

[keen plinth]

plug the numbers in

[alpine sable]

im not too confident with exact values for trig

beside 30, 45, 60

[keen plinth]

look em up

https://en.wikipedia.org/wiki/Exact_trigonometric_values

[alpine sable]

👍

.close

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[neat sierra]

im not sure which condition is more restricting

to find C

then C^c

[ocean seal]

lord of crime

[neat sierra]

oh thats right

thanks

.close

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[fallen sierra]

hii i’m having a little trouble with my calculus homework and i’m not understanding how i’m supposed to use the dot product to answer the following question:

[vale wigeon]

do you know the definition of direction cosines

[fallen sierra]

yes and no? they’re in my notes from class but it’s just not making any sense to me

[slender gull]

Read your notes, see if the definition you've written makes any sense to you.

If you've already tried doing that, and still don't get it. Then note that direction cosines of a vector are the cosines of angles your vector makes with the coordinate axes.
That is, cos(alpha) for instance is the cosine of the angle alpha, which is the angle your vector makes with the x axis.

[vale wigeon]

show us your definition and tell us what part of it doesn't make sense

maybe we can explain

[vale wigeon]

ok

so tell us then

which part of this are you having trouble comprehending?

[fallen sierra]

wait yk now that I’ve read it over it makes sense but now I don’t understand how it’s suppose to help me with the problem

[slender gull]

Do you know what |a| means?

[fallen sierra]

magnitude of a?

[slender gull]

Sure but in terms of a_1, a_2 and a_3

[fallen sierra]

Uh nope

[slender gull]

What does the magnitude of a mean ?

[fallen sierra]

It like the length right

[slender gull]

Yes.

How'd you find the length of the vector given by say\
$\hat{i} + \hat{j}$

[ocean seal]

What the hell am I doing here?

[slender gull]

Just this for now.

[fallen sierra]

You square root them and then square each one then add them together?

[slender gull]

Exactly!

See you know, you know!

So how about\
$a_1 \hat{i} + a_2\hat{j} + a_3\hat{k}$

[ocean seal]

What the hell am I doing here?

[slender gull]

Same thing?

[fallen sierra]

but what would vector represent? Would they all be 1?

[slender gull]

no

They could be anything

[fallen sierra]

oh wait ok I think I sort of understand

[slender gull]

Yes, what do you understand?

[fallen sierra]

I know It can be anything and so basically your just pluggin it in? Right

Or?

am I wrong

[slender gull]

Plugging in where?

[fallen sierra]

the

expression

bc based on the notes

[slender gull]

Yes you have to put the values, definitely.

but you still don't know what |a| is

[fallen sierra]

oh

[slender gull]

You should know that the magnitude of the vector is equal to $\sqrt{a_1^2 + a_2^2 + a_3^2}$

[ocean seal]

What the hell am I doing here?

[slender gull]

Square them, add them, square root the result.

And now you can put values, and hopefully wrap the simplification?

However it's important that you UNDERSTAND, why we're doing this.

[fallen sierra]

there are values to the problem?

wait i’m confused

😭

[slender gull]

a_1, a_2 and a_3

That's all you've got.

[fallen sierra]

oh so no values

[slender gull]

Sub |a| in terms of that, and use tha value of cos(alpha) as shown in your notes.

No numerical values to play with, yes.

[fallen sierra]

ah ok

Is it something like this? Or am I getting confused?

[lone heart]

@fallen sierra Has your question been resolved?

[fallen sierra]

no 😔

oh i forgot to square

[fallen sierra]

<@&286206848099549185> pls help me

uh this is what i got

[fallen sierra]

this?

from adding or is that not how you add those

so the denominator stays the same for all of them?

[ocean seal]

lord of crime

[fallen sierra]

OHH

omg i’m so slow

wait so this would be it right

ok well i think i’m done thank you for the help : )

.close

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[serene flame]

very belated but okay thank you

[lone heart]

@serene flame Has your question been resolved?

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[fierce scarab]

I am trying to prove that if a function is affine (f(px + (p-1)x') = pf(x) + (p-1)f(x') where p is a member of [0,1]) its a linear function plus a constant (f(x) = g(x) + c where c is a real and two properties hold for g(x) 1. ag(x) = g(ax) 2. g(x) + g(x') = g(x + x'))

Im inclined to assume that f(x)=g(x) + c and prove the two conditions on g, however I'm not sure if adding that assumption would be changing the statement which I was proving

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@fierce scarab Has your question been resolved?

[lone heart]

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[hollow silo]

A retail shop accepts only cash or checks. Suppose that 65% of its customers carry cash, 34% carry checks, and 69% carry cash or checks (or both). What is the probability that a randomly chosen customer at the shop is carrying both cash and checks?

[lone heart]

@hollow silo Has your question been resolved?

[lone heart]

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[ornate condor]

hi guys

[ornate condor]

i have trouble with binomial formula

[keen plinth]

hi pizza boy

[ornate condor]

hey snow girl

[keen plinth]

back with more pizza?

[ornate condor]

yes

in my stomach lmao

[keen plinth]

mmm delectable

[ornate condor]

how do we binomial

[keen plinth]

his handwriting is horrible

[ornate condor]

well

its better than some~

[keen plinth]

wait ive got a name for this

[ornate condor]

aka

let me coin a term real quick

[keen plinth]

it's called the

Leibniz Rule

not to be confused with

Leibniz's Integral Rule

[ornate condor]

LOL

[ornate condor]

thats the first thing i saw n was reading

[keen plinth]

https://en.wikipedia.org/wiki/General_Leibniz_rule

[ornate condor]

yea ok

it looks

super weird but

hows it even related to binomial

[keen plinth]

it's like binomial

[ornate condor]

he was talking about

WHAT

NO

[keen plinth]

but it's with product rule

[ornate condor]

HOW

[keen plinth]

because binomial and product rule are very similar

[vale wigeon]

what happen

oh are we looking at product rule for higher-order derivatives

[ornate condor]

binomial scary

[keen plinth]

hi Ann 👋

[ornate condor]

D:

hii

[keen plinth]

we're just looking at Leibniz Product Rule

[vale wigeon]

yeah

product rule for higher-order derivatives

[keen plinth]

v similar to binomial

[ornate condor]

yea ask those 12 year olds to do this

[vale wigeon]

which bears some similarity to the binomial theorem

what 12 year olds

ok

[ornate condor]

they do binomials too

[vale wigeon]

let me say this again

WHAT IS THE ISSUE AT HAND?

[ornate condor]

yea i was

[keen plinth]

circle doesn't understand it

[ornate condor]

tryna understand this inequality

anw

imma just be

[vale wigeon]

that's an equality

[ornate condor]

readin up on leib inequ

[vale wigeon]

so you do not want it explained right now?

[ornate condor]

oops

close

eh

i mean

[keen plinth]

bye

[ornate condor]

ill read thru leib first

[ornate condor]

cya

ty u2

[lone heart]

@ornate condor Has your question been resolved?

[ornate condor]

ive been stuck here awhile

more specifically the

n n n+1
k-1 + k = k

atm i got

[ornate condor]

nvm

ok i get it but

is leibniz rule supposed to be trivial or smt

it took me awhile

like

idt it was even mentioned b4

trivial calculations -.-

[ornate condor]

.close

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[somber spoke]

How do u do q10

[gray isle]

start by drawing a diagram

[somber spoke]

I did

Something like this

But not sure how to advance from here

<@&286206848099549185>

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@somber spoke Has your question been resolved?

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[serene flame]

this is my taylor expansion of sqrt y

[serene flame]

when i plug it into desmos, with an upper bound of 100, it seems to closely follow the path of actual sqrt x

but after x = 2 it drops down really fast towards -infty

[keen plinth]

the radius of convergence is 1

when you expand sqrt x at 1 the radius of convergence is 1

[serene flame]

this means that after x = 1 it does not converge?

[keen plinth]

no it means for |x - 1|>1 it will not converge

[serene flame]

i understand

so, if i plug cosine taking care that it does not go below 0, into the series, it should converge, rght?

[keen plinth]

uh

sure

[serene flame]

okay thanks

.close

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[craggy kettle]

Can anybody help me with perfect square trinomial

[craggy kettle]

The equation is

8a³ - 125

I need the factor of it im tryna solve but im confused

[mortal trellis]

have you seen the factored form of x^3-y^3 ?

[grave island]

$a^3-a^b$

[ocean seal]

Mothy

[grave island]

= $(a-b)(a^2+ab+b^2)$

[ocean seal]

Mothy

[craggy kettle]

Ohh wait ok ty

.close

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[reef rock]

!help

[reef rock]

Is this correct?

[grave island]

well it doesnt say its parallel

[reef rock]

the arrows

represent its parallel

[grave island]

but assuming they r yes

[reef rock]

but the arrows

[grave island]

the arrows show that the lines extend

past the point they r drawn

[floral river]

The arrows represent that theyre rays

[grave island]

parallel lines r indicated by different arrows

[reef rock]

Arrows on lines are used to indicate that those lines are parallel. If there is more than one pair of parallel lines, additional arrow-heads will be used. So this picture shows that p is parallel to q and r is parallel to s.

[grave island]

like this

[reef rock]

According to the googles arrows in lines are parallel

My teacher said teh same

[grave island]

well u r correct

if u r going by what ur teacher said

[reef rock]

?

is this correct

[grave island]

ye

[reef rock]

and ima load up the lasto ne

Last one*

[grave island]

yea

[reef rock]

ty

[lone heart]

@reef rock Has your question been resolved?

[grave island]

what the heck do u still need help with

[reef rock]

Why are you getting so pissed

wait

In this question

Would this be good working

P = L + B + L + B
P = 4.2 + 9 + 4.2 + 9
P = 8.4 + 18
P = 26.4m

?

[grave island]

u could just say P = 2L+2B

but yes u can do it in 4 lines of working if u want

[reef rock]

Ok!#

.close

[lone heart]

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[high mural]

Question 8

I think it has something to do with the sum of infinity but i dont know whr to start

[alpine sable]

I think you can try an algebraic trick such as setting $u = \sqrt{4\sqrt{4\sqrt{4\hdots}}}$ but with cube roots

same for the denominator

[ocean seal]

Renegade

[alpine sable]

@high mural

[mortal trellis]

$\sqrt[3]{4}$ in latex btw

[ocean seal]

Denascite

[alpine sable]

ah I seee

didn't know that

$\sqrt[n]{a}$

[ocean seal]

Renegade

[mortal trellis]

notice that u "contains" itself in its expression

[alpine sable]

^

[mortal trellis]

you can use that to calculate u

then do the same thing for the denominator

[high mural]

So u is the first term and u^2 will the second?
Is that what u mean?

[alpine sable]

Set $u = \sqrt[3]{4\sqrt[3]{4\sqrt[3]{4\hdots}}}$. Then cube both sides and divide by $4$, notice that $u = \frac{u^3}{4}$

[ocean seal]

Renegade

[high mural]

I get what ur saying now but im still stuck

Its pretty late over whr i live so im braindead

[alpine sable]

Solve $u = \frac{u^3}{4}$

[ocean seal]

Renegade

[alpine sable]

$\implies u^2 = 4$

[ocean seal]

Renegade

[alpine sable]

we can clearly eliminate $u = 0$ and $u = -2$ for obvious reasons

[ocean seal]

Renegade

[high mural]

Ahh i see. Tq so much

.close

[lone heart]

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[quartz cave]

I do not understand the answer to this question

[alpine sable]

they solved the system of equations

[quartz cave]

Can you explain to me what the steps are?

It isnt immediately clear to me what happens

[alpine sable]

i think explaining that here is a bit too much u should look into gauss elimination

[quartz cave]

alright ill try it out

I thought

That with these matrices

You have a vector value that gets multiplied by the row it is in

But I dont see how for the values that they put in that it gets too an equivalent answer

[lone heart]

@quartz cave Has your question been resolved?

[lone heart]

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[hard patio]

did you try anything?

[slow osprey]

I did try smtg but I think I was going in circles

I kept erasing all my previous calculations

This is what I've been continuously attempting to do

I did figure out the first fraction makes 9/172

[proud basin]

yeah so you need a trick

[slow osprey]

trick?

[last ether]

Seems like you have to match terms

[proud basin]

continued fractions as they are called

lemme write it down on a piece of paper

keep reiterating until youve got it

[slow osprey]

hold on lemme try this real quick

[proud basin]

remember that the b’s have to match

[slow osprey]

is this

supposed to be trial and error or

[proud basin]

god knows

[slow hound]

im gonna be honest i doubt this has a solution

[proud basin]

it does

[slow hound]

a whole number solution

[proud basin]

yeah it doesnt

[slow hound]

im sure it has real solutions

[proud basin]

thats b

a is 1

[slow osprey]

what if a isn't supposed to be 1?

16^1/2=sqrt(16)

[frozen stump]

assuming b is a whole number, a must be 1

since the fraction next to a is always larger than 0 and smaller than 1

[lone heart]

@slow osprey Has your question been resolved?

[slow osprey]

should I try pinging helpers too?

<@&286206848099549185>

[lone heart]

@slow osprey Has your question been resolved?

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[median zinc]

$$\intd\frac{v^2}{2} = a\intdx$$

[ocean seal]

BryanChess99
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[median zinc]

$$\int d\frac{v^2}{2} = a\int dx$$

[ocean seal]

BryanChess99

[median zinc]

gives

$$\frac{v^2}{2} - \frac{v_0^2}{2} = a(x-x_0)$$

[ocean seal]

BryanChess99

[median zinc]

I was following an online video about this

how did they go from the first step to the second step with no integral bounds?

<@&286206848099549185>

[burnt ravine]

Quite confusing
It's like as if bounds are x and x0

or v and v0 for the left term

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[simple cave]

I am doing practice questions involving graphing functions and I don't understand the answers given.

[simple cave]

These are the questions

This is the graph

[blazing quartz]

How to find the values of y₀,y₁, y₂,y₃?

[simple cave]

And these are the given answers

I am confused about the range

It says to assume the graph goes beyond what is shown

In the graph, it looks like Y could keep going but it's hard to tell.

Apparently the range is -1.5 -> 1.5

How can I tell if it stops at 1.5 or keeps going beyond that?

The other question I have is that despite the domain being all real numbers, and the range of Y it says that there is no interval where the function remains constant

Wouldn't the function remain constant at x > 5?

Assuming that the range is limited to 1.5 and doesn't keep going up

The only way I can make sense of this is if it goes to 1.49999....and never quite reaches 1.5

That would make the range 1.5, and it would not be constant...But I have no idea how I'm suppose to know this with just the graph.

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[lone heart]

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[simple cave]

.reopen

[lone heart]

✅

[simple cave]

I think aquarius above messaged the same help channel at the same time, I have more information above that

[lone heart]

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[lone heart]

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[lucid citrus]

whats the difference between (-5^3) and -5^3? math teacher was talking about how the brackets matter and that the answers are different. (pretty sure one was 125 and the other was -125)

[minor needle]

in fact (-5^3) is the same thing as -5^3, I guess you mean (-5)^3 and -5^3, then there's a difference

[lucid citrus]

yeah

[minor needle]

because (-5)^3 (negative sign is inside the bracket) means we raise whole thing (with the sign!)

and -5^3 means we raise only 5 without a sign

well (-5)^3 = -5^3 in this case, but try with even power

[lucid citrus]

so -5^3 is just -5x5x5 and (-5)^3 is -5x-5x-5

[minor needle]

yep

[lucid citrus]

i see

ty

[lone heart]

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[alpine sable]

help pls how to simplify

[ornate condor]

um

[ornate condor]

4 ^log4(3) can be simplified to 3

[alpine sable]

i have no idea

[minor needle]

rule 3 and 7 basically

[alpine sable]

huh

[ornate condor]

idk to show it i always let it be some dummy var n whatnot

[alpine sable]

omg

ok

ig ot it

.close

[lone heart]

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[wise elbow]

I actually need help with the majority of questions on this homework

[ornate condor]

hey nice dp

[wise elbow]

dp?

[ornate condor]

display pic

Q has so many numbers hais

[wise elbow]

oh oh, thank you

<@&286206848099549185>

.close

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[mellow solar]

How does 15pi/4 equal 2pi + 7pi/4. I tried looking at the unit circle but I still do not see it how it works.

[worn fox]

do you see how $\frac{15}{4} = 2 + \frac{7}{4}$?

[ocean seal]

ΣAC

[mellow solar]

Oh

I see

that makes sense thanks

.close

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[mortal ibex]

.close

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[solar pollen]

i ended up getting 1/2(x^2 + 1)^1/2

how do you know if you are supposed to apply the chain rule here

i thinkt the correct answer is x/(x^2 + 1)^1/2

but im not sure where you get the x from

[atomic shore]

when you do the chain rule you first apply it on the "outer function" which in this case is the squareroot. then you apply it on whats within in this case x^2+1 and multiply it with the fist expression.

[mortal ibex]

It should be this

[solar pollen]

sorry, im still trying to understand it

i'll send you my steps and maybe that can make it easier

[mortal ibex]

you miss a factor, you have to derivate also x^2+1 and multiply

as Winus has said

[solar pollen]

wait that makes sense

but how do you know you are supposed to apply the chain rule

[mortal ibex]

because it is a composed function

[solar pollen]

wait because of the square root right?

oh that makes so much more sense

thank you so much

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[keen furnace]

I’m not very sure how I could solve for x

I can’t sub sinx to u right? As I can’t write sin2x in terms of u

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[rotund plank]

I’m curious about changing the limits of integration

[rotund plank]

Is it always valid to appeal to the formula you have for u in terms of x (say we’re using the standard variable notation)

Are there instances in which we would not be able to make this substitution and end up with the correct answer

If so what are the conditions (e.g does u have to be increasing/decreasing or something)

I feel like I’ve heard before you have to be careful but things I’m reading online seem to be saying otherwise, so any help is appreciated, it’s nice to have certainty with these things

In particular I suppose I remember examples of quadratic graphs where substitutions could go wrong, but I’m not sure if that’s because the substitutions just weren’t well-defined

E.g u = x^2 is unclear as to which branch x takes, but is it always fine in a case in which x has a clear formula

[last ether]

Wdym changing the limits

[lone heart]

@rotund plank Has your question been resolved?

[rotund plank]

Oh sorry for being unclear

When you make a u-substitution in a definite integral and you change over the limits of integration from being limits as inputs in terms of x to limits as inputs in terms of u

[last ether]

The bounds

Yes you change the x-bounds to u-bounds

[rotund plank]

Yeah

[last ether]

For any substitution you do

[rotund plank]

I’m curious about the details

I know it’s a requirement

[last ether]

The details are you change it, end of story

I don't know the real thought process but like

Logically, it makes sense

[rotund plank]

Well, for example the integral from -1 to 1 of x^2 - 1, with u = x^2

I’m curious if it’s fine as long as x is a function of u

[last ether]

You wouldn't do a u-sub

[rotund plank]

Because in that case the integral evaluates to 0

Yes but there’s no reason why you couldn’t

In theory at least if u-substitution is a clear-cut process

[last ether]

Well let's see

if u = x^2

Then 2x dx = du

So

Wel I see the issue now

[rotund plank]

Yeah the limits are the same

[last ether]

Actually no

That's fine

That just means that $\int_{-1}^{1}(x^2-1)dx = 0$

[ocean seal]

Umbraleviathan

[last ether]

They can be the same bound

That's not an issue

[rotund plank]

It’s not

[last ether]

No

Same bound just means 0

So I guess that's an easy way to say it's 0 lol

[rotund plank]

The integral is 2/3

[last ether]

Wait what

You sure?

[rotund plank]

I picked it because geometrically it’s non-zero

[last ether]

Hold on am I being dumb

[rotund plank]

And you can just do it directly and see it’s 2/3

[last ether]

,integrate (x^2-1) -1 to 1

Fuck I'm too lazy

[rotund plank]

It’s just 1/3 + 1 - (-1/3 + 1) = 2/3

[last ether]

$\int_{-1}^{1}(x^2-1)dx = -\frac{4}{3}$

[ocean seal]

Umbraleviathan

[last ether]

And then if I u-Sun

[rotund plank]

Oh yeah it’s 2/3 - 2 = -4/3 that’s my bad

Still same point

[last ether]

Hm yeah I guess u-subbing won't work

[rotund plank]

I think it might be because x is not a function of u

[last ether]

Well now I have the same fucking question

[rotund plank]

Since x = +/- sqrt(u) which isn’t well-defined

Not sure if that’s necessary and sufficient or just wrong though

Also wondering about increasing/decreasing stuff

[last ether]

I mean

Those should still work fine

From experience

Like let's say you have a always positive function 0 to -2

[rotund plank]

Idk it’s a bit murky to say for sure

[last ether]

And then u-sub will be something from 2 to 6 but the u-sub function will probably be always negative

But like

[rotund plank]

A simpler counter-example is just x^2 from -1 to 1

[last ether]

But yeah

Now I hate integration even more

[rotund plank]

Idk if the proof of integration by substitution is understandable or not

[lone heart]

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[rotund plank]

.reopen

[lone heart]

✅

[rotund plank]

If this channel closes and anybody has a clarification or anything please feel free to reopen it

[last ether]

Buddy you ruined u-subs for me

[rotund plank]

Truth hurts

[mortal trellis]

The proof in one dimension is just using fundamental theorem of calculus twice

[mortal trellis]

And yeah it's because of this

[lone heart]

@rotund plank Has your question been resolved?

[rotund plank]

Alright that doesn't sound too bad

[rotund plank]

Ok cool thanks

[lone heart]

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[dense sleet]

Point 𝑀 on side 𝐵𝐶 and point 𝑁 on side 𝐴𝐵 of triangle 𝐴𝐵𝐶 are chosen so that
holds <𝐵𝐴𝑀 = <𝑀𝐴𝐶 = <𝑁𝐶𝐵. Prove that 

[dense sleet]

I just need a hint

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@dense sleet Has your question been resolved?

[dense sleet]

<@&286206848099549185>

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@dense sleet Has your question been resolved?

[lone heart]

@dense sleet Has your question been resolved?

[lone heart]

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[spring harbor]

I did this, since the cdf is supposed to sum to 1 over the range

but i dont think we are supposed to use calculus so I think im on the wrong track

and also the "enter your answer as an exact fraction" implies to me that there shouldnt be a decimal, and im pretty sure 1/(35/8) isnt what theyre looking for

forgot this part of the question

.close

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[glacial ether]

Numba 8

[glacial ether]

I literally can’t seem to figure out how to solve it

[grave island]

do we know how to figure out area of circle

[glacial ether]

No

Idk how to find triangle height

[grave island]

knowing would help

[glacial ether]

That’s my issue

[grave island]

the height is given

its 3

[glacial ether]

No that’s my guess

[grave island]

what

nbm

[glacial ether]

When I first did it

[grave island]

u can use pytagg

we know its a equilateral

so we can split it into a right angle traingle

[glacial ether]

WhTs the hypotenuse

How find that

[grave island]

$\sqrt{6^2-3^2}$

[ocean seal]

Mothy

[grave island]

read the equation carefully

[glacial ether]

Alr

[grave island]

its an equilateral triangle

[glacial ether]

OH!!!!

Thx

[grave island]

which means all sides are equal

[glacial ether]

!close

/close

.close

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[calm willow]

can someone help

[calm willow]

idk how to solve this

i imagine two triangles

[abstract fractal]

You'd be right

[calm willow]

i have tried three times

i no longer care

its 2 points

i answered all the other questions

92 good enough

[abstract fractal]

Can you show your work?

[calm willow]

ill show u what i did the first time

fuck

2000/sin((180-17-160)deg)*sin(160deg)

ran out of tries

that didnt work

[abstract fractal]

Explain your answer

[lone heart]

@calm willow Has your question been resolved?

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[mental heart]

.help

[lone heart]

Commands:
clopen: .close, .reopen
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

Channel closed

Closed due to the original message being deleted

[abstract fractal]

#latex-testing

[mental heart]

Yes, sorry. Was trying to get familiar, but I think I can finally phrase my help question

[ocean seal]

ascii

[mental heart]

How would I re-arrange this formula to get t?

If delta d is 0.

[abstract fractal]

This channel is going to close since apparently the original message was deleted

[mental heart]

Let me just open a new one

.close

[abstract fractal]

It's already closed, you don't have to close it

[lone heart]

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[dawn quail]

I messed up here and trying to figure out what went wrong

i'm on the right track with exponents but base is wrong

[wary stream]

Post the exact question too

[dawn quail]

OK

[wary stream]

First, why is 15 in the denominator, if it started in the numerator?

[dawn quail]

My full attempt is here

[wary stream]

$-15 \neq \frac{1}{15}$

[ocean seal]

dldh06

[dawn quail]

I moved 15 from numerator to denominator because of the negative exponent but I think I see now, the negative exponent is only for the u, not 15u

15 is considered the base, u is the variable, ^-11 is the exponent, and with the three of these together it is called a term?

or is -15 the base?

[wary stream]

-15 = -1 * 15

[subtle delta]

You dont bring 15 down

[dawn quail]

yeah, i do remember negative symbol is just (-1). so what is (-1)(15) called when they are together? as -15

[wary stream]

Literally told them that if you read

[dawn quail]

the base or is there another word to use when symbol is included?

[subtle delta]

Avid, you can’t bring the base down. You can bring the exponent down though.

[wary stream]

A number, I guess. It can be referred as a base too if there's an exponent

[subtle delta]

I get why you would, but you can not

[dawn quail]

yes, i will fix this

i accidentally moved 15 with the u

[wary stream]

They know what to do, if you payed attention to the conversation

[dawn quail]

thanks.. i like to go through the vocabulary in my head as i work on math

[subtle delta]

Literally rule one I think states to be kind to the community 😊

calm down dude

everybodys tryjng to help eachother

you seemed passive aggressive as well

[wary stream]

And you didn't need to repeat everything that's been stated before

[subtle delta]

i didnt read it?

plus you were only saying -15 cant be brought down

[wary stream]

Hence, why I stated to read the conversation

[subtle delta]

if you were to explain to him/her why it’d be nice

whatever

good night or good morning whatever tiem it is for you

[wary stream]

I moved 15 from numerator to denominator because of the negative exponent but I think I see now, the negative exponent is only for the u, not 15u
They literally stated this themselves, they knew why it can't be brought down

Hence, why I didn't need to explain

[subtle delta]

.-.

[wary stream]

That looks fine

[dawn quail]

Yay!

Is there a function on your calculator that can find common factors of numbers?

with this example 15 and 6

[wary stream]

No there is not

[dawn quail]

i thought there was lcd or something

and i think allow these calculators for math exams, nothing too fancy

[wary stream]

There's GCD

[dawn quail]

GCD would show me that 3 is a common factor of 15 and 6?

[wary stream]

GCD = Greatest Common Divisor

[dawn quail]

oh

dang if i get two really huge numbers it would be handy to use this function in my calculator to find greatest common factor

GCF

[wary stream]

Yes

[dawn quail]

https://www.youtube.com/watch?v=0jsKOi9TY2s

TI-84 for math exams would be very nice, heh... (but just for this feature.. everything else would be considered cheating)

.close

[lone heart]

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[half island]

I am confused about this statistic eq.. if someone could explain it to me would be a great help 😅

[half island]

like I understanding that x bar is mean and we have variance square

also we are taking sigma but I am confused about that , in between and what does ~ mean in this context?

<@&286206848099549185>

[wary stream]

!15m

[lone heart]

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

[half island]

sorry didnt know the 15m rule

mb should have read #❓how-to-get-help more clearly ;-;

[wary stream]

Then you should read #❓how-to-get-help

And ~ refers to distribution so $X$ ~ $N(\mu, \sigma^2)$ means X follows the normal distribution with mean and variance

[naive valley]

worth mentioning that the assertion is false unless the X_i are independent

[ocean seal]

dldh06

[wary stream]

Well, that's annoying

[half island]

ohh thanks also one more stupid question.. X bar is mean of all observations right ? but then what is mu is here? arent both mean?

I think I probably should re read statistics xd

[naive valley]

Xbar is the sample mean of the N random variables, and it is itself a random variable

mu is the statistical mean of the underlying distribution, it is a number, not a random variable

[half island]

ahh

thanks I get the feel of it now :)

.close

[lone heart]

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[split slate]

My guess would be about 10, but the answers say ~11 m/s. How?

[split slate]

This is all the answers give

[rocky raven]

I got 10 too bro i dunno

[split slate]

ight, well

thanks for confirming

.close

[lone heart]

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[daring patrol]

First remove some x

[runic trench]

Cancel common factor

Can cancel more

[gray isle]

the first step was incorrect

[runic trench]

Yeah this is wrong lol

Factorize

Yes

Make both sides the same denominator

Can solve it from here ?

Bring 30x over and factorize

Yes

So it becomes x = 0 and x = 30

If it’s solved , .close

[gray isle]

note that x can't be 0 from the restrictions of the original equation

[lone heart]

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[gray isle]

division by 0

[lone heart]

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[steady frost]

How is this not correct

*close

.close

[lone heart]

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[native nebula]

Wait

[steady frost]

I got it. Silly mistake lmao

[native nebula]

Ohh ok then

Great 😃

@steady frost close the channel

[lone heart]

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[alpine sable]

do i just ignore the 2 in front

[wind yoke]

how did you get x and -3x in the first bracket?

[alpine sable]

from

$2x^{2}-10x+12=0$

[wind yoke]

tell me the qn

[ocean seal]

BabaEagle

[wind yoke]

ok

[alpine sable]

?

.close

[lone heart]

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[wind yoke]

Your answer is correct

[alpine sable]

ok thank u

[wind yoke]

the roots are same

I mean the roots are correcct

so i think we dont mind the 2

[lone heart]

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[alpine sable]

$-x^{2}-11x+12=0$

[ocean seal]

BabaEagle

[alpine sable]

how to factor this?

[tribal oxide]

u need to break -11 into two numbers whose sum is -11 and product is -12, think