help-0

[mint hedge]

Just need help understanding what it’s saying lol

[worn fox]

What exactly is troubling you

[mint hedge]

Just the wording

[wary stream]

Do you know what the graph of -x^3 looks like?

[mint hedge]

The wording of the explanation to be exact, I wanted to see if someone can explain it

yes I know what it looks like! It’s the wording part

[wary stream]

So as x approaches negative infinity, and where does the graph approach, for the domain?

[mint hedge]

indeed

[wary stream]

It was a question for you to answer

What happens to the domain of the function as x approaches negative infinity?

[mint hedge]

It would make the domain all real #'s

OHHH

close

.close

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[alpine sable]

I am a bit confused on how I should calculate theta here

[alpine sable]

especially since there is no reference triangle

[wary stream]

You have x and y coordinates

Do you know the trig ratios?

[alpine sable]

sine cosine tan?

[wary stream]

Yes

Do you know them in terms of x, y, and r?

[alpine sable]

no i dont sorry

[alpine sable]

thank you! So to calculate theta i could do

sin of -2(sqrt/2)
------------
3

[wary stream]

Not exactly

Because you need r

You have coordinates, given as an x, y pair

[alpine sable]

sorry, forgot to mention r is 1 since we're dealing with unit circles

[wary stream]

Which one has x and y?

[wary stream]

Then that's fine too

[alpine sable]

wdym?

[wary stream]

Which trig function has x and y

[alpine sable]

tangent

oh so I could also do

tan y/x

if i dont have r

[wary stream]

Yes

[alpine sable]

thats useful to know

thanks!!

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[fleet quail]

$(x^2)/7 -(7y^2)/42 =1$

[fleet quail]

how do i simplify this equation into this one

$x^2/7-y^2/6=1$

[ocean seal]

KunoTheSumo

KunoTheSumo

[normal ingot]

$\frac{x^2}{7}-\frac{7y^2}{42}=1$

[fleet quail]

I'm assuming I can just divide the 42 by 7 but i need some clarification cause I feel like id need to divide everything by 7

[ocean seal]

lirmirit

[normal ingot]

then for $\frac{7y^2}{42}=\frac{7y^2}{7\times 6}$

[ocean seal]

lirmirit

[normal ingot]

the 7 can be cancelled out

so we get $\frac{y^2}{6}$

[ocean seal]

lirmirit

[fleet quail]

ok thanks

.close

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[quaint otter]

Find the equation to the circle which passes through the points A (10,-2) and B (27,-19) and has its centre on the line X-15=0. How do I find it?? help would be much appreciated

[vernal thunder]

Is it possible to graph it

[quaint otter]

I get this because y is 15 but i dont know what to do next

[vernal thunder]

Graph as in graph the points

@quaint otter try and find the midpoint of the y values presented

[quaint otter]

like this?

[quaint otter]

-2 and -19?

[vernal thunder]

Check point b

[vernal thunder]

Yes. Find the middle

[quaint otter]

-10.5?

[vernal thunder]

Yes

Now assemble the equation, and check your solution

We forgot r

[quaint otter]

got it

[vernal thunder]

For r take the distance between the midpoint and point a or point b

And square it

You might need to find the midpoint of the x values as well

,w midpoint formula

[ocean seal]

Results provided by WolframAlpha

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

Requested by % Openglobe %#3085

[fleet quail]

Is the problem saying the center is on x=15?? and A and B are both points on the arc?

[quaint otter]

How? sorry I dont understand

[vernal thunder]

Oh wait

[quaint otter]

center is on the x-15=0 line

[vernal thunder]

X value is already revealed

No need to find the midpoint

[vernal thunder]

First, plot the center point

On the graph

Then use the distance formula

[quaint otter]

I dont know the center

[vernal thunder]

The center is (15, midpoint of y values)

In this case (15, -10.5)

[quaint otter]

ahh ok

[vernal thunder]

The x value was given, the y value was through midpoint formula

[quaint otter]

one sec

[vernal thunder]

Something’s not right

How’s the center at x=15

And it’s given heh

Wait a second

[quaint otter]

[vernal thunder]

AB does not pass through the midpoint

[quaint otter]

A and B are just points in the circle

[vernal thunder]

This is gonna take some thought

[lean depot]

Hi Openglobe, I think you're making a mistake here. Not all lines through a circle pass through the center.

I think I can lend you a hand Sofia

[vernal thunder]

I now realize that

[lean depot]

This was a great start

Indeed the y-coordinate of the center will be 15

[abstract fractal]

y coordinate?

[lean depot]

So we want to work out what h and r will be, right?

[vernal thunder]

It’s a typo

[lean depot]

Whoops! x-coordinate :)

[quaint otter]

ok ok 🙂

[lean depot]

We know that (10, -2) and (27, -19) are on the circle

[quaint otter]

right

[lean depot]

So can you tell me, what does it mean for a point to be on the circle, in terms of the equation you have?

[vernal thunder]

@quaint otter try and find the radius first

SHIT WRONG IDEA

[lean depot]

Openglobe, would you mind just letting sofia think for a moment?

[quaint otter]

both have same distance to the radius?

[vernal thunder]

Imma leave

[lean depot]

That's correct, but I want you to think specifically about this equation:

https://media.discordapp.net/attachments/490557019623915520/999471917180395620/unknown.png

[vernal thunder]

Just take it from here

[quaint otter]

Your help was appreciated! thanks

[lean depot]

Why does this equation describe a circle? Because the equation holds for some point (x,y) exactly when that point lies on the circle

So what does it mean to say that (10, -2) is on the circle?

[quaint otter]

theyre both equal to r squared

[lean depot]

Sorry this isn't right

[quaint otter]

hmm

[lean depot]

Let me tell you what it means

[lean depot]

When we put x = 10 and y = -2 into this equation, we get the same number on the left and right hand side

So what it means for (10, -2) to be on the circle is that the equation is correct for x = 10 and y = -2

Do you agree with that?

[quaint otter]

sorry where are we putting it?

[vernal thunder]

@lean depot I found the answer. Literally found it by desmos tweaking

[lean depot]

You gave us this equation at the start:

[quaint otter]

I dont know if its dumb question I'm a bit lost

[lean depot]

https://media.discordapp.net/attachments/490557019623915520/999471917180395620/unknown.png

No, it's a good question

That's cool Openglobe, but I'm trying to get Sofia to understand this

[quaint otter]

I already got the answer I just have to know how to get to it

[lean depot]

So I'm just gonna ask, how did you come up with this equation?

[quaint otter]

15 instead of k

[lean depot]

Right OK

[quaint otter]

because of the graph

[lean depot]

So what does this equation mean? Can you tell me what it represents?

[quaint otter]

So k,h is the centre coordinates

[lean depot]

OK, I see that

but let me be even more specific

[quaint otter]

oki

[lean depot]

We have a circle with centre (k, h) and radius r

What does this equation mean for the circle? What does it have to do with the circle?

[quaint otter]

yes thats all i know

[lean depot]

Yup I'm right there with you

[quaint otter]

The thing i know is that when I'm given the centre and the radius i can graph the circle

[lean depot]

OK, so that's fine.

So I want to tell you what this equation means specifically

It means this:

A point (x,y) lies on the circle exactly when (x - k)^2 + (y - h)^2 is equal to r^2

So we agree that the question states that k = 15, right?

Now let me ask you

[quaint otter]

ooh ok

[lean depot]

Given that we know that (10, -2) also lies on the circle, what can we say?

[quaint otter]

right

[quaint otter]

we could say (10,-15)^2+(-2,-h)^2=r^2?

risky

[lean depot]

Eh, I'm not sure what (10, -15)^2 means?

Do you mean just (10 - 15)^2?

[quaint otter]

I wondered if it was just replacing x and y with 10 and -2

[lean depot]

Yes indeed you are replacing x and y with 10 and -2

So you did indeed mean (10 - 15) rather than (10, -15).

[quaint otter]

ahh yes sorry yes i meant that

[lean depot]

Great stuff!

So notice something about this:

(10 -15)^2+(-2-h)^2=r^2
This is now an equation with only h and r in it.

This is quite handy!

I want you to simplify this a bit first. Do you think you can do that?

[quaint otter]

ohh let me guess do i make a system?

[lean depot]

Yes that's right!

So okay, we have two unknowns

So we need two equations, right?

How do we get another equation so we can solve for the unknowns?

[quaint otter]

yes

with the other point

[lean depot]

That's exactly right

[quaint otter]

gimme a sec please ill write it

[lean depot]

Yeah no problem! Go ahead

Feel free to ping me if you need a hand with this part

[quaint otter]

Thank you! It would be solving this system for h and r right?

[lean depot]

Yes! Great job

How do you think you should go about solving this?

[quaint otter]

solve for r then replace the r with that?

[lean depot]

Mm, I think it might be hard to solve for r without solving for h

[quaint otter]

mm youre right

[lean depot]

Do you remember the two ways to solve systems – elimination and substitution?

Well there's technically a third one.

I think it should be called "equality"

So the thing on top is saying that (something) = r^2

And the thing on the bottom is saying that (something else) = r^2

Now this definitely means that (something) = (something else), right?

[quaint otter]

true

[lean depot]

I think if you observe this, and do some expansion and simplification, you will be able to solve this!

[quaint otter]

ohh okay!

Ill operate then

[lean depot]

OK, good luck!

[quaint otter]

Ok I got both values!

@lean depot very nice!! Thank you so much I was so lost you actually helped me understand very patient too

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[spare fern]

.close

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[autumn latch]

hello! I'm struggling to find resources to explain how the 2n and 1 in the summation is being pulled out by multiplying by n/5. is there a specific formula I should be looking at to understand that portion? thanks!

[remote heron]

is it a dumb question of what the ; is doing here

@autumn latch

[autumn latch]

i'm more confused how the 2n and 1 in the parenthesis gets pulled out to become 2n^2/5 + n/5

[remote heron]

its not pulled out

[autumn latch]

is that just a specific property when i = 0?

[remote heron]

i havent checked but my guess is they split into imaginary and real sums

then used a formula on sum(2n+1)

[autumn latch]

is the 10i imaginary while the 2n and 1 are real sums?

[remote heron]

yea

so $\sum(2n-10i+1) = \sum(2n+1) -10 \sum i$

[ocean seal]

jan Niku

[remote heron]

you can see 10 sum(i) still in the second line

so id check what 2sum(n) + sum(1) is

[jagged imp]

uh the i isn't imaginary, to be clear.

[remote heron]

oh

well

oh

yea

[autumn latch]

lmao

[jagged imp]

its the "dummy variable" for the sum

[remote heron]

well it doesnt matter here

dummy variable or not

this is still whats happening

[autumn latch]

that makes sense

how should i go about figuring out wut sum(2n + 1) is tho?

[remote heron]

split it

$\sum _0 ^{\sfrac n 5} (2n+1) = 2n \sum _0 ^{\sfrac n 5} (1) + \sum _0 ^{\sfrac n 5} (1)$

[ocean seal]

jan Niku

[remote heron]

right, i is the dummy

so you can pull n out too

[autumn latch]

and just to be clear, both of those would be n/5 correct?

[remote heron]

yea

i mean assuming this whole time n/5 is an integer

[autumn latch]

that makes perfect sense thank u so much for the help ❤️

.close

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[remote heron]

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[lone heart]

Please don't occupy multiple help channels.

[wary stream]

You don't need to close your channel and open a new one if no one helps you

[wary stream]

And is this a test?

[lusty ice]

No

[lone heart]

@lusty ice Has your question been resolved?

[lone heart]

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[rare gale]

the first two are definitely true

[alpine sable]

which one is a false statement c or d

n y

[rare gale]

c/d have some amount of subjectivity \ opinion but i would say d is easier for anyone to agree with

so my guess is c, but kind of bad question because it's really more about personal preference and what the code requires 🤷‍♂️

[alpine sable]

why would d be more agreeable than c

cuz i tested on code its possible to make an inf for loop on python

but then for d the prof slides say this

[rare gale]

well for loop is just a very natural way to traverse a variable

its similar to say sigma notation in math

[alpine sable]

true

thats y i also believe its c

bro.

how is 2 wrong..

2 gives an error wtf

.close

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[carmine harbor]

How do I convert this to 5^k+1

[novel night]

Write 6 as (5+1), and then distribute the 5^k into that sum.

[median oar]

Do you see you can factor out 5^k

[carmine harbor]

Oh lol

And then 5^k(5)

Is 5^k+1

Ty fam

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[livid sail]

someone please tell me how i’m wrong

[livid sail]

someone please tell me how i’m wrong

[vale wigeon]

impossible to tell without seeing your work

[vale wigeon]

let's see...

ah

cos(x-y) = cos(x)cos(y) + sin(x)sin(y).

[livid sail]

REALLY

what the heck am i doing

it’s really that simple

@vale wigeon thank you i appreciate this server so much

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[wheat crystal]

i need to find measure of the angle labelled "?"

uhh im not sure how to do this

[last ether]

arccos

[wheat crystal]

how does that work

[last ether]

arccosine is inverse cosine

[wheat crystal]

so 8/12 is cos right

[last ether]

Yeah

Take the inverse of that

[wheat crystal]

then do we just use calculator

for inverse

[last ether]

Yeah

arccos(8/12)

[wheat crystal]

ahh

alr

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[wheat crystal]

.close

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[tropic oasis]

how did my professor handle the 2dx?

i understand the rule involved with the 5,1 integrals

but the 5,1 integral of 2dx

i'm not sure what to do there or what he did

ohh i would get the net area?

4*2 = 8

[little drum]

yep \ $\int_1^5 2 dx = [2x]_1^5 = 2(5 - 1) = 8$

[ocean seal]

Arya

[tropic oasis]

aaa

so many rules

so one question

is every integral

even if it doesnt have the points of a,b

its all somehow correlated to the concept of net area/total area?

or is it only when a,b is specified

like it confuses me how integrals basically undoes something from a deriative standpoint

but then it also somehow ties into area?

[little drum]

Integral is basically like giving yourself a ... simpler function for how much area under the curve is covered as a function of 'x'

F(x) = int f(x) dx

Given the limits, you're only interested in evaluating the area under curve within particular bounds

[tropic oasis]

.close

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@winged slate Has your question been resolved?

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@winged slate Has your question been resolved?

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[vale fjord]

I had a quick question for SSA triangles

[vale fjord]

How do you determine if it has 0, 1, or 2 triangles given the side length as angle?

[copper stone]

do you have an example?

[vale fjord]

How would I determine if this has 1 triangle 2 triangles or 0 triangles?

I already found angle b = 240.99

[tame willow]

law of sines and cosines

@vale fjord

You should have notes

[vale fjord]

Yep I know how to use the two equations

However there was some way using the altitude I believe

[tame willow]

But you could just use law of sines and cosines

[vale fjord]

Is that easier than the altitude method?

.close

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[dusky igloo]

Is this written correctly?

[dusky igloo]

alright, thanks

[mortal trellis]

better the other way around if anything. z=a+bi in C

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[teal garnet]

Can someone help me calculate this derivative

[vale wigeon]

chain rule, no?

[teal garnet]

could you please show me?

[karmic rapids]

do you know the chain rule

[teal garnet]

yes

what's it gonna be? lnv times dv/dt?

[echo socket]

I'd start with viewing 1/V as V^(-1)

[teal garnet]

and then?

[echo socket]

Applying the power and chain rules yields that derivative of 1/V is -V^(-2)*dV/dt

[teal garnet]

Yeah makes sense. Thank you

[alpine sable]

Anyone have tips for functions?

Like plotting them

[lone heart]

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[teal garnet]

use desmos

[lone heart]

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[fallow valley]

Hi, is a normal operator under $\mathbb {R}$ also a hermitian operator?

[ocean seal]

Itamar

[lone heart]

@fallow valley Has your question been resolved?

[fallow valley]

<@&286206848099549185>

I think so, the definition I know is that if $f is an operator, f=f*$

[ocean seal]

Itamar

[fallow valley]

$f\circ f*=f*\circ f$

[ocean seal]

Itamar

[fallow valley]

Yeah, $If <\cdot,\cdot>$ is an inner product space, f operator, then $<f(u),v>=<u,f*(v)>$ and in matrices under $\mathbb{R}$ we'll get for a matrix A, $A*=A^t$

[ocean seal]

Itamar

[fallow valley]

Yeah

Ok so I found a counter example thanks for the help! if you take 2x2 matrix where 1,1,-1,1 are the values. It will be normal but not hermitian. What I meant was that all values were real

.close

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[alpine sable]

not sure what i did wrong

$\sum_{n=1}^\infty \left(\frac{1 \cdot 3 \cdot 5 \cdots (2n-1)}{2\cdot4\cdot6\cdots(2n)}\right)^3$

[ocean seal]

metnal

[alpine sable]

omg

im so dumb

it should be 2(n+1)-1 so 2n+1

😭

3/10 for that fucking stupid mistake....

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[white pike]

.open

What's the best way to prepare for my maths test, it's in 5 more days, anyone got any tips for me <3 ?

[alpine sable]

just keep practicing

just keep solving more problems related to the exam syllabus

[white pike]

Aight ty

what does this mean btw

why did they do 1/2

oh wiat

nvm

cause its triangle area x height i get it mbb

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[quasi rover]

Working on a larger problem, I got this as a part of an equation. Wasn't sure how to approach, so plugged numbers in. Got the Bernoulli Triangle sums [(1), 1, 3, 8, 20, 48]. I worked out that the sum permutation on the right -- if isolated -- form the fibonacci numbers.

[quasi rover]

whoops poor timing -- need to go -- please disregard

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[tidal zealot]

illegal maths?

[tidal zealot]

how did they simplify it?

i loie

i lie

[rigid smelt]

by multiplying the top and bottom by sqrt(2)

[tidal zealot]

im dumb

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[silent crane]

Heyhey, i have a question about how a vector formula comes to be
How does the first formula (proj(a onto b) =...) become the second one?

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[lost coral]

how do i solve the last question?

[lost coral]

.close

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[eager jackal]

I'm supposed to find the exact value of sin cos and tan of the angle and I'm not sure how to do it

[wary stream]

(-4, -5) are x, y coordinates. What's the horizontal distance?

[eager jackal]

wdym by horizontal distance

[wary stream]

The distance along the x axis

[eager jackal]

its unknown

[wary stream]

It's given

(-4, -5) are x, y coordinates

[eager jackal]

thats the point

not the distance

[wary stream]

What is the distance along the x axis you had to travel to get to that point?

[eager jackal]

oh -4

[wary stream]

Yes

What about the vertical distance, aka the distance along the y axis?

[eager jackal]

-5

[wary stream]

So you know the sides of that triangle

[eager jackal]

so how do i find the sin cos and tan of the angle i just find the angle of the triangle and add 180 to it?

[wary stream]

Do you know the ratios for sin, cos, tan?

In relation to that triangle

[eager jackal]

sin = o/h cos=a/h tan=o/a

[wary stream]

So if the angle theta is here, how would you make the ratios for each?

Then make it into quad 3

[eager jackal]

tan=-5/-4

[wary stream]

Yes

And use Pythagorean theorem to find hyp

[eager jackal]

-5 squared + -4squared = hyp

[wary stream]

Not quite

What's Pythagorean theorem?

[eager jackal]

a squared +b squared = hyp

[wary stream]

No

Not quite

[eager jackal]

oh its squared

so i need to do square root

[wary stream]

Yes

[eager jackal]

so then hyp = 6.32

so do i just add the angle of the triangle to 180 to find the sin cos and tan

[wary stream]

Yes

[eager jackal]

thanks

.close

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[tepid drum]

Hiii

[tepid drum]

I tried something but that didn't give any real roots

[last ether]

Two things you can do

[tepid drum]

First I got the derivative with respect to x

[last ether]

Find the absolute minimum and max

[tepid drum]

I got the value of sin

[last ether]

And use IVT

Or you can use sine-wrapping

[tepid drum]

And then I got the value of cos

So I got 2-sinx= 0

[last ether]

If you're learning calculus, then I would find absolute min and max and use IVT

[tepid drum]

So sinx=-2

[last ether]

buddy

[tepid drum]

Yes I am learning calc

But I want to know what's wrong with my method

[last ether]

You can use function behavior to skip using derivatives

[tepid drum]

Wdym

[last ether]

2x will have more of an influence on growth than cosine

Therefore, just take the limit as x approaches to negative infinity and the limit as x approaches positive infinity

Since 2x has more of an influence, you can visualize what the graph would look like

[tepid drum]

Thank you for giving me more than 1 method

But I want to know what's wrong with my method

Bc to me it seems correct

[noble sinew]

This make no sense

Why you setting it equal to 0?

[tepid drum]

Why

[last ether]

They're finding extrema

You can do that

[noble sinew]

What does that do

[last ether]

And you can use periodicity

[tepid drum]

Bc I differentiated both sides with respect to x

[noble sinew]

What does it do setting it equal to 0?

[last ether]

It just takes longer work

[noble sinew]

How does that help you prove anything?

[tepid drum]

Yes

Lemme continue

[noble sinew]

You can show its monotone

[tepid drum]

Now sinx= -3

-2&

[last ether]

You can find extrema since they occur periodically and then use IVT

[noble sinew]

I have no idea why you are solving for 0

[last ether]

But I would just use function behavior

[noble sinew]

(Seeing it also has no solution)

[tepid drum]

I want to prove that it has one real root so if I solve the equation and get the roots ill prove it

[noble sinew]

How is setting derivative equal to 0

[last ether]

The derivative doesn't equal to 0 ever

[weary wyvern]

Not a terrible idea to set the derivative to 0

[noble sinew]

Showing how many roots it has?

[last ether]

That only works if the derivative can equal to 0

[weary wyvern]

It gets you an idea of the function

[tepid drum]

Bro I have a question

[noble sinew]

And it doesn’t help at all still

It could be equal to 0 inf amount of times

And still only have 1 root

[tepid drum]

Now if I differenttiate both sides with respect to x now d/dx(0) = 0

So what is wrong

[noble sinew]

So again, I ask, what does this do?

Are you even reading anything I am saying?

What you are doing doesn’t prove anything

[last ether]

@tepid drum the problem with taht is that the derivative can never equal to 0, so it is hard to find any extrema that way.

[tepid drum]

The question wants me to prove that the equation has only 1 real root

[last ether]

They want to use IVT

[noble sinew]

And setting derivative equal to 0 does nothing

[tepid drum]

I get the roots and check if it has 1 real root then provedd

[weary wyvern]

Setting the derivative to 0 certainly helps

[last ether]

By finding a minimum and maximum and using IVT

[tepid drum]

You didn't lemme continue

[last ether]

But the problem is that the derivative will never equal to 0

[noble sinew]

Derivative could be equal to 0 inf times

[tepid drum]

I now get cos after I have the bus of sin man

[noble sinew]

And still only have 1 root

So how exactly?

[weary wyvern]

.

[noble sinew]

Still doesn’t prove anything

[tepid drum]

Bro wait lemme tell you what I reached

[noble sinew]

Like I have said to him 100 times

I’m saying it doesn’t do anything

[weary wyvern]

Right but it's not a bad idea

[tepid drum]

Can you check what I reached and tell me where I am wronggg

[weary wyvern]

And can give you insight for what to do

[noble sinew]

Setting derivative equal to 0

And thinking it proces smth

Is where you are wrong

[last ether]

The derivative cannot equal to 0

That's where you went wrong

[noble sinew]

Doing it in the first place and thinking it shows anything*

Is where he went wrong

[last ether]

Normally you can

[noble sinew]

You could have derivative have inf times be 0

[tepid drum]

Bro the equation is 2x+cosx= 0 so after differentiation both sides with respect to x I'll get 2-sinx= 0 now sinx= -2 And then cosx = +-rad(-3) and since all roots are complex then there is no real roots and this is wrong bc the question says that there is 1 real root now where is my mistake

[noble sinew]

Sbd still only 1 root

So No

[weary wyvern]

Wow this channel is toxic as hell

[noble sinew]

Doesn’t show anything

[last ether]

If you use that between an interval of a continuous function and find the minimum and maximum, you can state that there are roots if you use IVT, but only if the derivative can equal to 0

In this case, you cannot

So you have to use function behavior

[tepid drum]

It showed that there are no real roots

[noble sinew]

No it doesn’t

[tepid drum]

But my answer has a mistake

[noble sinew]

DERIVATIVE BEING 0 SHOWS NOTHING

I DONT KNOW HOW MANY TIMES I NEED TO SAY THIS

[last ether]

@tepid drum setting the derivative = 0 only shows the existence of a maximum and minimum, if any

Not roots

[tepid drum]

I used the derivative =0 to get the value of cosx

[noble sinew]

You think root=extrema?

Is that what this is?

[tepid drum]

Thus there are no real solutions to the equation bc in 2x-cosx cosx isnt realll

[noble sinew]

Does x=0 also have no solution?

Because taking derivative we get 1=0

Which has no solution

Do you maybe accept now you are wrong and will listen?

[last ether]

Buddy

Listen to Scape

[tepid drum]

Bro I am not saying that i am right

I am saying where is my mistake

[abstract fractal]

The value of cosx... where? Not at the root

[noble sinew]

And I told you?

10 times?

[tepid drum]

Ik that I have a mistake

[last ether]

The mistake is that the derivative can never equal to 0, so you can't use that method

[noble sinew]

I told you 10 times where the mistake was

And you just was like no

[tepid drum]

Ok you told me that getting derivative won't prove any thing

[noble sinew]

Setting it equal to 0 wont*

[abstract fractal]

What if it could? Setting the derivative to 0 gives the max/min, but I don't know how that relates to the roots

[tepid drum]

I used this derivative =0 to get the value of cosx which would prove things

[last ether]

Then yeah, you can use IVT on an interval to prove that roots exists

[noble sinew]

Again it sounds like you think extrema=roots

Which it most certainly isn’t

[abstract fractal]

Value of cosx where? At the extrema. There are no extrema though

[last ether]

There's none

So you gotta use function behavior for this

[tepid drum]

Now if sinx = -2 use the identity cos^2x +sin^2x = 1 and get the value of cosx

Thats what I did

[noble sinew]

Can we stop talking about taking derivative and solving for 0

[abstract fractal]

Value of cosx where? cosx doesn't just have a value, it's a function

[tepid drum]

After i did this I got no real values of cosx

[noble sinew]

You just accepted it was wrong

So can we move on?

[tepid drum]

It's wrong but show me where am I wrong I want the reason where I am wrong

[noble sinew]

.

Read this

[last ether]

Everything you did was wrong basically

[noble sinew]

A simpler example which clearly shows it makes 0 sense

[abstract fractal]

You've proven there is no relative max/min. That has nothing to do with the roots, though

No max/min on the reals, anyway

[last ether]

So you gotta use function behavior

[tepid drum]

I got cosx = +-rad(-3)

[noble sinew]

Did you read this?

[abstract fractal]

And that's not a real number, so there is no relative extrema. Again, that's not related to the roots

[noble sinew]

Simple yes/no @tepid drum

[tepid drum]

Ok now cosx= complex number so 2x+cosx is complex

It can't be real since cosx is not real

Doesn't that make sense

[noble sinew]

Come back when you want help

[abstract fractal]

It's complex at the extrema, but we don't care about the extrema

[noble sinew]

Because doesn’t sound like you want that

[tepid drum]

Yes i read what you said above

[noble sinew]

So agree derivative not being equal to 0 doesn’t mean original function doesn’t have a root?

[tepid drum]

I want to understand I don't just want to know the right answer

[noble sinew]

Simple yes/no

[tepid drum]

Btw I didn't say that

[noble sinew]

Simple yes/no

[tepid drum]

Yes

[noble sinew]

Okay so lets stop trying to set derivative equal to 0?

[tepid drum]

Why

[noble sinew]

Since that doesn’t show anything about roots

[tepid drum]

?

[noble sinew]

Like we just agreed?

[tepid drum]

Ok now I want to ask you a question

[noble sinew]

“Yes I understand why setting derivative equal to 0 doesn’t show anything from above example”

“Wait why don’t we do it now”?

You can’t have it both ways

[tepid drum]

If you have a number x + rad(-3) = 0 does that sound like x has a real root

[noble sinew]

Either you agree or you don’t

Why are you asking why?

When you just said “Yes”?

[abstract fractal]

Cosx is only √-3 at the extrema, which is irrelevant to the roots

[noble sinew]

So really sounds like you meant no here instead of yes, otherwise no idea why you ask “Why”

[tepid drum]

What you said was an idea in general but that doesn't mean that it is the case for every function

[noble sinew]

A counterexample shows we can’t do it

Because I just showed it doesn’t prove anything

[tepid drum]

Sometimes the derivative may be different than 0 and the function has no roots ??

[tepid drum]

But I proved it does after getting the value of cosx

[noble sinew]

No it doesn’t

[tepid drum]

Ohh

[noble sinew]

Again extrema is not same as root

Which is what f’(x)=0 gives

[abstract fractal]

Sometimes a function has a hole somewhere while also having an asymptote. Doesn't mean the two properties are related

[tepid drum]

Ok that's a reason

[noble sinew]

It gives extrema not roots

[tepid drum]

Now I understand where my mistake was

[noble sinew]

So can we agree soon that setting derivative equal to 0 doesn’t do anything?

[tepid drum]

Yes agreed

[noble sinew]

Even if derivative had roots it wouldn’t show anything

Agree with that also?

[tepid drum]

Yes bc it would just show values at extrema

Now I got the idea

So I should think in another way

[noble sinew]

(Also said that a couple of times that extrema is not root) but anyway moving on

Try showing its monotone

[tepid drum]

What is a monotone

[noble sinew]

Only increasing/decreasing

[tepid drum]

I heard that word before but I forgot what it means

Ohh

So I see if the slope is >0 or <0

Right ??

[noble sinew]

Check if derivative is >0 or <0 for all x

[tepid drum]

Increasing

[noble sinew]

Okay so if we can just find a value of x such that f(x) is less than 0

And greater than 0 of f(x)

It must also hit 0 (why)?

[tepid drum]

Bc when f(x)<0 Then it is below x-axis and if it is >0 then It is above it so to go from this value to that it should pass through x=0

Which is the x-axis

And also f(x) is defined when x=0

[noble sinew]

Have a theorem that says that?

[tepid drum]

Intermediate value theorem ?

[noble sinew]

Yes

[tepid drum]

Ok that would prove that there is at least 1 real root

But the question wants me to prove that there is exactly one real root

?

[abstract fractal]

You've already proven it's monotonic, right?

[tepid drum]

Yes

Ohh

Yes

I get it

[fresh parcel]

Bruh

[tepid drum]

Bro I am stupid

Idk man but I am In stupid mode rn

Anyways tysm all of you and sorry if I annoyed you

.close

[lone heart]

Channel closed

Closed by @tepid drum

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[clever summit]

I’m not very smart

I need an explanation

On why 9/33 is the correct answer

[languid bolt]

ok so

how many students participates in band

[clever summit]

33 total

[languid bolt]

how many students that participates in band also participates in track

[clever summit]

9

Wait

[languid bolt]

so 9/33

[clever summit]

That’s it

I’ve been looking at this formula

Holy

I didn’t need to do all that

What’s wrong with me

.close

[lone heart]

Channel closed

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[keen portal]

-10(cos4x)^2=-5cos8x-5, how can i generalise these equations

[languid bolt]

you can divide both sides by -5 first

and then use the rule

$$cos(2x) = cos^2(x) - sin^2(x)$$ i guess

[ocean seal]

MarveI

[languid bolt]

wait nvm, idk what generalisation means

[keen portal]

wait actually nevermind how do you just generalise the lhs of that: y=-10(cos4x)^2

[rigid smelt]

not sure what you meant by generalise

the equation -10(cos4x)^2=-5cos8x-5 is true

[keen portal]

Generalisation: what the transformations do to the function, and would the same apply to all functions of that type.

[rigid smelt]

so you want to describe what transformation had been done to go from y=cos^2(x) to y=-10cos^2(4x)?

[keen portal]

basically do this y=-10(cos4x)^2 and make it a(cosbx)^e

and describe what changing each letter does

[rigid smelt]

right

[keen portal]

hence transformations

[rigid smelt]

basically you want to describe how each parameters a, b and e changes the function

[keen portal]

yes

generalise it.

[rigid smelt]

well i suppose you can start taking one of the parameters as a constant first and then describe whether the graph is being rotated, stretched out or compressed, or translated compared to the graph of cos^2(x)

this should not be hard since you should be familiar with these transformation

for the exponent (parameter e) tho, you might need to do some calculus

[keen portal]

i think for e

it doesnt matter because my graph has to be sinusoidal so changing e makes it not sinusoidal unless it become ^1 which still works

any other changes makes it not work

so for e the only change that could occur would be e=1

[rigid smelt]

technically for e>=4, it is not sinusoidal anymore

iirc

[keen portal]

when e is 3 its not sinusoidal

only when e is equal to 1 or 2 it is sinusoidal

[rigid smelt]

actually no, i misremember

(cosx)^a is sinusoidal for even natural a

or well if you like to define sinusoidal as periodic

[keen portal]

yep periodic too

[rigid smelt]

so basically the thing is, for cos^2(x) and other similar functions, there is a double angle identity which can be used to rewrite the functions in terms of cos(2x)

but for any even power higher than that, it turns into an addition of sine and cosine

so technically, your function is still periodic

but it does not look like a sine wave

[keen portal]

yep

i need mine to look like a sine wave

[rigid smelt]

right, so that should restrict your power to being less than or equal to 2

[keen portal]

so e<=2 has to be made

[rigid smelt]

and that your power has to also be a natural number that is

[keen portal]

correct

cannot be decimals

[rigid smelt]

and the for the other parameters, they are just like how the coefficients a, b and c in af(bx)+c transform the function

which i hope you know

i guess you will want to compare this transformation to cos(x)

[keen portal]

yes a for amplitude, b for frequency, tehcnically c inside bracket for phase shift but there is none in this case and d for mean line

[rigid smelt]

well no

im talking about the general case given for any function f(x)

[keen portal]

hm?

[rigid smelt]

the easiest one to remember is the constant c, c translates the function up and down by c units
coefficient a represents a vertical scaling, basically compresses or stretches the function in the x-direction
and b represents the horizontal scaling

there is technically also the transformation of translating the function in the horizontal direction, but that is not need to describe the transformation here

this is what best represent your "generalisation"

so for example if you compare your function acos^2(bx) to cos(x), you will need to do some algebra first to rewrite cosine squared in terms of cosine first, then describe the transformation as mentioned above

you could also, compare the transformation to sin(x)

it would just differ by a phase change

[keen portal]

so do i describe what the transformations in my equation does like y=-10(cos4x)^2 eg the -10 does this, 4 does that, ^2 does this and then after that use this acos^2(bx+c)+d and from this i change the a value for example and state what that does, then b,c ,d

[rigid smelt]

yes

but again, you need to compare the transformation against another function of similar property

it would only makes sense then

[keen portal]

my function is this y=-10(cos4x)^2?

[rigid smelt]

for example, i would want to describe the transformation done to 2x^2-4x+7 compared to x^2

but not x^3

because x^3 is nowhere near similar to a quadratic function

[rigid smelt]

sure

[keen portal]

is the base equation just y=cosx^2 then

and then i add acos^2(bx+c)+d these transformations and describe what it does to the base of y=cosx^2

[rigid smelt]

sure

or it could even be cos(2x)

or cos(x)

or sin(x)

or even some as absurd as cos(pix)

[keen portal]

how do u describe the ^e transformation

how does ^2 differ to ^1 or ^3

[rigid smelt]

honestly, i dont know, it best describe by using derivatives

since changing the power of a function changes a lot of properties which the function has

[keen portal]

thats why i thought to keep it standard cos^2x since i dont know how to describe any changes above ^2

[rigid smelt]

for cos^n(x), there maybe a nice pattern to it, or not

[keen portal]

ill probably keep base equation cos^2x then

[rigid smelt]

sure

[keen portal]

but say changing ^e has to be <=2 otherwise it becomes not sinusoidal and also has to be natural numbers

thats all for the power transformation

since i cant describe the properties it changes

does that work

@rigid smelt

[rigid smelt]

sure

[keen portal]

i'll try and see if i come across any problems

do you mind if i contact you if that happens

[rigid smelt]

erm maybe you should just open a channel and someone can

im not very free currently

[keen portal]

okay thanks for ur help

[lone heart]

@keen portal Has your question been resolved?

[lone heart]

@keen portal Has your question been resolved?

[keen portal]

"coefficient a represents a vertical scaling, basically compresses or stretches the function in the x-direction" can i describe this as the graph dilates vertically by a scale factor of 10 or would that be incorrect.

[lone heart]

@keen portal Has your question been resolved?

[keen portal]

.close

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[keen python]

could I not calculate the limit like this ?

[mortal trellis]

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

I assume you meant a plus there?

[keen python]

ahhhhh

yeee....

thanks !

.close

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[keen python]

how can this limit be 0 ?

[keen python]

im getting 1 / 2017

[merry depot]

Why do you think it’s 0?

[keen python]

geogebra says so

[mortal trellis]

are you sure?

[keen python]

ye

[mortal trellis]

chances are you are probably using it incorrectly

[merry depot]

Is it actually 0 or “so small it’s effectively 0 for our calculator”

,w 1/2017

[ocean seal]

Results provided by WolframAlpha

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

Requested by Zybikron#5611

[keen python]

ah...

i had to show more numbers

in the settingsi only had 2 decimals

i was worried for real xD

thx !

[mortal trellis]

there are better tools to use for stuff like this

like wolframalpha

[keen python]

im used to geogebra from school

how can I show this ?

ive tried this but i dont know

I thought I could use squezee theorem (sandwich)

[analog basalt]

You might have more luck using l'Hôpital's rule

[keen python]

ahhh

i always forget

.........

its inf / inf

[analog basalt]

Exactly

[keen python]

but is my approach wrong ?

[analog basalt]

I don't think so, it seems correct

[keen python]

aghh with L'H so simple

didnt take 30 seconds

[analog basalt]

Just one to remember: using l'Hôpital you can show that $\lim_{n \to \infty} \frac{x^n}{e^x} = \lim_{n \to \infty} \frac{\ln(x)}{x^n} = 0$ for all $n \in \mathbb{N}$

[ocean seal]

Yuese

[keen python]

I see thx

if its > 1 then its divergent right ?

but im not sure if Ive done it correct

[real gazelle]

2/3 is not greater than 1

[lone heart]

@keen python Has your question been resolved?

[tacit arch]

,calc 2/3

[ocean seal]

Result:

0.66666666666667

[keen python]

hahaha

Ok i need to stop studying xD

thx too

.close

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[keen socket]

volume = pi integral (limits a,b ) y^2 dx

y^2=(f(x))^2 ???

partial fractions

u get -8/(x+1) -4/(x+1)^2+9/x

integrating that u get -8ln(x+1)+4/(x+1) + 9lnx

and then sub limits

[lone heart]

@dusky blaze Has your question been resolved?

[dusky blaze]

.close

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[cyan merlin]

okay so

[cyan merlin]

why is square root of negative numbers with an i? How is that possible? Why not undefined like ÷0

[raven rover]

i is used to represent these numbers because they’re called imaginary

It is undefined in the world of real numbers, but mathematicians long ago made a new type of math (world of numbers) called complex numbers to allow for i to exist

https://youtu.be/cUzklzVXJwo

This is an incredible video by Veritasium

It will likely interest you

[cyan merlin]

oh and one more thing

Are Sin A and Sin B same thing?

[raven rover]

Only if A = B + (some integer multiple of 2pi)

(And A and B are real numbers)

[cyan merlin]

.close

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[cyan merlin]

Thanks

[raven rover]

Np

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[earnest bridge]

i factored out the first fraction to see if that would make things easier but i don't know where to go from here

[wary stream]

Post that work

[wary stream]

So notice how the equivalent expression is just the factors

[earnest bridge]

yes

[wary stream]

You want to factor the second fraction so it cancels stuff out, correct?

[earnest bridge]

i think so, yes

[wary stream]

What in this fraction should be canceled out so you can get the equivalent expression?

[earnest bridge]

x+5 from top and bottom

[wary stream]

What else should be canceled out?

[earnest bridge]

I'm not sure... that's all i see

[wary stream]

In general, what is needed to be canceled out from that fraction?

Not things that you can see that can be simplified

[wary stream]

So I'm saying that the equivalent expression is (x + 2)/(x - 6). This is the first fraction, things need to get canceled out in both fractions to result the equivalent expression. The noticeable one that cancels is x + 5 since it's in that same fraction

So should the x + 2 get canceled?

[earnest bridge]

no, i believe not. i think that because it is in both expressions

but im not sure

[wary stream]

So this is what I'm asking. Say you have something like this, and you want a/d as the equivalent expression. You can easily see that the b's cancel

[earnest bridge]

yup

[wary stream]

And when you are multiplying fractions, if there is something in the numerator, and something in the denominator, it cancels out

Like this