help-28

[signal needle]

here on discord

[strong pawn]

i'm talking about typing formulas in the way that desmos.com does it, without caring about the latex formulas

Like, for example if I wanted to write x power of 2 I would just do x^2 and it would show up as latex formulated

[signal needle]

ok i don't have an idea

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[strong pawn]

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[glossy torrent]

Hello I have a question with the following procedure:

[glossy torrent]

How can you justifying "taking the integral on both sides"?

As far as I know, integrals are taken with respect to a specific variable

for two things to remain equal, you must do the same thing to them, i.e take the derivate with respect to the SAME variable on both sides

here the author seems to just "take an integral" with disregard for which variable he is taking it for

[gritty rose]

the integral on the left side is with respect to y, and the right side is with respect to x

if you have two functions, h(y) and g(x) that are equal everywhere, then you can make that substitution as long as you integrate with respect to their own variables

[glossy torrent]

but there is no statement that these functions are equal everywhere

would the equality come from $h(y)dy=g(x)dx$?

[glossy valve]

heka gigantes

[gritty rose]

yes

[glossy torrent]

I see

should it not be $h(y)=g(x)?$

[glossy valve]

heka gigantes

[gritty rose]

it's hand-wavy, but it's equivalent

[glossy torrent]

do you know the reason why?

Here is more context, in case it's useful:

[gritty rose]

i mean the explanation is probably out of scope for your class

[glossy torrent]

If you could point me towards the material, I would like to know, as it's been bothering me for a while now

I don't expect you to generate a whole mathematical proof, but It's just been weird that it is shoved under the rug for most courses

[gritty rose]

the main reason is you assume y is a function of x

More explicitly, $h(y) dy/dx = h(y(x)) y'(x) = g(x)$

[glossy valve]

riemann

[gritty rose]

Then $\int h(y(x)) y'(x) dy = \int h(u) du$ with u-substitution

[glossy valve]

riemann

[gritty rose]

Better explained here:
https://math.stackexchange.com/a/1275950

[glossy torrent]

Thank you so much

[gritty rose]

and here
https://math.stackexchange.com/a/182352

[glossy torrent]

YESS!

Thank you this is what I've been searching for

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[atomic vortex]

Can someone pls tell me where I messed up

[atomic vortex]

Apparently 2 of my answers here are incorrect

[gritty rose]

A should be step 3

[atomic vortex]

Oh its

C E A D B

[gritty rose]

step D comes after A because you multiply both sides by y

[atomic vortex]

got it

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[silk vine]

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[granite thorn]

Help Pls 🥲

[signal needle]

channel is occupied

[signal needle]

first simplify the left side by dividing num and denom by a-b

[granite thorn]

okay

For a^3-b^3 how to div by a-b?

[signal needle]

there's a formula

[granite thorn]

oh

What kind of formula?

Ahh okay I see

So it’ll be (a+b)^2/(a-b)^2

[signal needle]

no

[granite thorn]

hmm? Is it wrong

I thought a^3-b^3 div by a-b is a^2+2ab+b^2

[warm abyss]

It's a^2 + ab + b^2

[granite thorn]

Ahhh

I see

what should I do next hmm

[warm abyss]

What I did was expanding the denominator then

[granite thorn]

okk, I’ll try doing that

hmm i did that, i tried to cross mltiply and solve but i got (10a-13b)(13a-10b) = 0

I think im very wrong

[warm abyss]

So either 10a = 13b or the opposite

[granite thorn]

Yes

Ans is 23

Idk why

[signal needle]

if a=13 and b=10, it's 23.
if a=10 and b=13, it's 23.

so it's always 23

[granite thorn]

Ahh

[warm abyss]

What about a = 26 and b = 20

[granite thorn]

They said it’s relatively prime

Not sure what that means

[warm abyss]

Right

[granite thorn]

So.... it’s prime case by case?

[warm abyss]

There is no prime that devides both of them

[granite thorn]

Oh that’s what it meant?

[warm abyss]

Yes

So 26, 20 is invalid as 2 devides both of them

[granite thorn]

Ahh yes true

Okk thanks@@

[warm abyss]

Can you show how you did it? I used another method to get the same result

[granite thorn]

Ohh

I cross multiplied it

[warm abyss]

Ok, thx

[granite thorn]

Okayy

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[grim kestrel]

1/n

[grim kestrel]

i dont understand how we just leave it as 1

we kept 1 bc n increasese faster than ln(n) as n goes from 1 to inf

just delete ur messages plz

so it clears

bro

delete ur messages

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[fallen sonnet]

!hep

[fallen sonnet]

!help

Is my work and answer for this correct?

3% of £215,000
= (215,000 ÷ 100) x 3
= 2,150 x 3
= £6,450

6450 x 4 = 25,800

215,000 + 25,800 = 240,800

240,800 -> 241,000

Final Answer: The company's anticipated annual profit by the end of 2025 will be £241,000

@sharp vine

[signal needle]

nope

[fallen sonnet]

Tell me what's wrong

[toxic flower]

It’s increasing by 3% each year

You only took 3% from the first year

[fallen sonnet]

So the first year is 3% of 215,000 then the next year is 3% of 221,450

[toxic flower]

You need to use the formula a * (1+p)^t

Yes exactly

[fallen sonnet]

I don't know what on earth this is though

a * (1+p)^t

[toxic flower]

A = starting amount

[fallen sonnet]

So that question would take me way longer than I originally anticipated

[toxic flower]

P is percentage (in this case 0.03)

And t the years

Nah you can calculate it real quick

Way faster than writing down each year

It’s basically just 215000 * 1.03^4

[fallen sonnet]

This work is supposed to be for people 2 years ahead of me but I want to see if it's difficult.

[fallen sonnet]

That gives me

241984.39415

[toxic flower]

Sounds good I think

[stable heart]

if you want to work it out logically. you have the first year being 215000*1.03=221450, then you have a new profit for the next year, which is 221450*1.03=228093.5.... until you reach the desired year

[fallen sonnet]

Very confused about that formula though

[stable heart]

this general rule can then be retracted into that formula which was given

[fallen sonnet]

Wait, this just made it les confusing

[toxic flower]

Exactly what duh hello said

In reality 215000 * 1.03^4 is the same as

215000 * 1.03 * 1.03 * 1.03 * 1.03

[fallen sonnet]

At first glance, ^4 confused me but then I realized that 4's units is the years.

a (1+p)^T

[stable heart]

so now because this is very tedius for doing for example 1000 years, the formula makes your life much easier

[fallen sonnet]

215,000(1+0.03)^4

[stable heart]

(in this case the number would be very very large though )

[fallen sonnet]

Wait is this crorect

215,000(1+0.03)^4

[stable heart]

yep

[signal needle]

yes

[fallen sonnet]

215,000(1.03) ^ 4

Working out the power in an exam without calculators would be time consuming

[toxic flower]

You’re always gonna be allowed to use your calculator for that

[fallen sonnet]

Oh

Oh yeah it says you may use a calculator

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@fallen sonnet Has your question been resolved?

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[woven mango]

I was trying to solve this problem and I tried two methods, obtaining two different answers. If someome could explain where I went wrong that would be great.

[lament cloud]

when you factored the quadratic in the first solution, (3a-4)(a+1) = 3a^2 - a - 4

[woven mango]

ah whoops that was a copy error I mean to switch the + and negative so it reads 0=(3a+4)(a-1)

and a= 1, a=-4/3

[lament cloud]

so then because of the second rule you made the answer should be a=1

[woven mango]

ah ok so you can combine the rules

thanks!

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[stone flume]

How do we solve this? I have no idea

I see the (x^2+4) as the arc tan for integral but idk how to split it

<@&286206848099549185>

[rapid rain]

Simple fraction decomposition

Write 3/[(x+1)(x²+4)] = A/(x+1) + (Bx + C)/(x² + 4)

Find the values of A,B,C by the method of your choice (the most direct is multiplying both sides of the equation by the denominator and identify polynomial factors)

Integrating A/(x+1) is easy

Integrating Bx/(x² +4) is cool if you know that the derivative of x² +4 is 2x

And yes as you said integrating C/(x²+4) is done with u-substitution, and you will find arctan

Hope it helps @stone flume

[stone flume]

ohk

i will let u know if it works

[stone flume]

do i further split the Bx+C/(x^2+4) into bx/x^2+4 and (C/x^2+4)?

[rapid rain]

Yes

For integration purposes

[stone flume]

but i don't split it to find the A,B and C right?

[rapid rain]

It wont matter anyway

[rapid rain]

Since you multiply this equation by (x+1)(x²+4) to find the values of A,B,C

[stone flume]

i cannot solve it further

[rapid rain]

Let's try to solve it together then

[stone flume]

I did this

[rapid rain]

You forgor parentheses 💀

You have indeed A + B = 0

[stone flume]

shouldn't matter

[rapid rain]

It does

[stone flume]

4A+B=1

A+B=0

[rapid rain]

Not agreeing with the first equation. Where the hell does it come from ?

[stone flume]

those are the constants

wait it should 4A+B+C =1

cx=0 so c=0

cuz there is no x in the numerator

[rapid rain]

B is not appearing in the constant terms

This is why you should always multiply with parentheses xd

[stone flume]

lemme try again

[rapid rain]

3 = (A+B)x² + (B+C)x + 4A+C

A+B = 0
B + C = 0
4A+C = 3
=> A = -B = C = 3/5

[stone flume]

lemme try

so A=3/5 C=3/5

and B=-3/5

sryy

[rapid rain]

?????

This isn't your channel bruh 💀

[stone flume]

this is right ?

[rapid rain]

Yes

[stone flume]

I GOT IT

THANK YOU SOO SO MUCH!

appreciate it

@rapid rain

[rapid rain]

No problem :)

[stone flume]

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[torn jolt]

I know this is a transformation which includes a shift of three units up, but how can I know whether its horizontally or vertically dialated?

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@torn jolt Has your question been resolved?

[torn jolt]

Like how would I know the scale factor?

<@&286206848099549185>

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[ancient cairn]

I dont understand really what to do here.

[ancient cairn]

I know sin(A+B) = Sin(A)+Cos(B)

but

🤷‍♂️

[sand stone]

what are a and b

should it be A and B

[ancient cairn]

typo

[sand stone]

its not true then

[wicked condor]

thats not right

[ancient cairn]

thats probably why im getting this wrong then

[wicked condor]

sinAcosB + sinBcosA

i think

[ancient cairn]

yeah so I tried that

here

I think

but no work

[sand stone]

how so

[ancient cairn]

it said it was wrong

[sand stone]

show what you got

[ancient cairn]

I did

[sand stone]

you didnt simplify the inside

[ancient cairn]

....

right

[ancient cairn]

yeah it was right

I forgor

[ancient cairn]

I wrote that like 2 days ago

I forgot what do I do with this part outside?

[sand stone]

$16(\sin(47c)\sin(17c))$

[glossy valve]

dog.

[sand stone]

also make sure not to drop the c

[ancient cairn]

well its cos right?

[sand stone]

what is

the function which is summed

yeah

[ancient cairn]

ok so it would be like

?

[sand stone]

yes but you dropped the c

47c - 17c

47c + 17c

[ancient cairn]

theres no c here?

oh wait you mean add the c

right

ok cool

[sand stone]

dont add the c

look at the original function

16sin(47c)sin(17c)

its not added

it was there in the first place

[ancient cairn]

so its just 47?

?

oh sorry cos 17

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[ancient cairn]

still a bit confused

by a bit

I mean alot

said this was wrong

[sand stone]

didnt simplify again

[ancient cairn]

https://tenor.com/view/dh9511dh-head-banging-on-the-wall-gif-13355825

right

[ancient cairn]

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[charred shoal]

How would I rewrite this

[gritty rose]

what's psi_in mean

use this table
https://ethz.ch/content/dam/ethz/special-interest/baug/ibk/structural-mechanics-dam/education/identmeth/fourier.pdf

[vast shadow]

let thw whole function be x

the

[charred shoal]

I am trying to generalize it

I can express it as a convolution but, I was hoping there would be some neat trick using distribution theory that I just don't know.

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[plain plinth]

i know how to solve this

but i wanna ask how do you find the coordinates when you have a function?

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[candid musk]

you enter x and y

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[crystal moss]

Hi , basic exponential problem, over a fraction , I don’t understand why I can’t cancel out negative exponents under a fraction, i know I’m suppose to bring it up above but why doesn’t this work?

[crystal moss]

What’s that

A^4 and the a^-5

The fraction upside down

[stable heart]

this is how the exponent rule works. you cant just flip it around as it will not be equal anymore

[crystal moss]

Is that 2^3 was a negative power could you bring it up above to join the 2^5 power?

If

[stable heart]

if the 3 was negative instead then you would have $$\frac{2^5}{2^{-3}}=2^{5-(-3)}$$

[glossy valve]

Duh Hello

[stable heart]

you take the top exponent minus the bottom exponent

if the bottom exponent is negative then subtracting it from the top one will be the same as adding it to the top one

[crystal moss]

So you would get 2^2 power?

[stable heart]

nope

$5-(-3)=?$

[glossy valve]

Duh Hello

[crystal moss]

7

8

[stable heart]

yep

[crystal moss]

That’s so strange

[stable heart]

do you know what the definition of a negative exponent is?

[crystal moss]

1 over it

[stable heart]

exactly

[crystal moss]

Like a fraction

[stable heart]

so in this example we have that $$\frac{2^5}{2^{-3}}=\frac{2^5}{\frac{1}{2^3}}=$$

[glossy valve]

Duh Hello

[stable heart]

if we multiply both the top and bottom by $2^3$ then we have $$\frac{2^5\cdot 2^3}{\frac{1}{2^3}\cdot 2^3}=\frac{2^5\cdot 2^3}{1}=2^5\cdot2^3=2^8$$

[glossy valve]

Duh Hello

[crystal moss]

Ahh okay I see how that works, Also sorry in my picture the = was suppose to be a to the first power instead of a^5 at the end

Because I get confused sometimes in a fraction they cancel out the same base with exponents so I tried to do that

[stable heart]

if you just make sure to follow this rule correctly then you should be fine. just need to remember that if b is negative then you need to add it

[crystal moss]

Okay thanks a lot for helping me I really appreciate it.

Thanks a lot 🙏

[stable heart]

no worries

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[gaunt lynx]

hi

[gaunt lynx]

how do I prove this?

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[torn jolt]

Saw this on Wiki, not sure about the process of doing this

[torn jolt]

I understand I can take vector function A into vector c . function psi

But I don't know how the right hand side works

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[arctic jewel]

what are the steps to solving a parabola w/ vertex form?

[arctic jewel]

for instance, I have y=3(x+2)^2-5

have the vertex but when I went to check it on desmos, for the second point it had 0,7 and 4,7

but I got
x| a(x)

1| 3(1) | which equals 3

2| 3(2) | which equals 6

so from the vertex, (-2,-5) it should be change the x by one and go up 3, then change the x by one again and go up 6

should look like that?

can someone tell me where I messed up?

[hot herald]

x| a(x)

1| 3(1) | which equals 3

2| 3(2) | which equals 6
dunno where this is coming from

[arctic jewel]

is that not how you find your points?

[hot herald]

to find the y-coord where x=1,
you sub x=1 into 3(x+2)^2-5

[arctic jewel]

so y=22 at x=1?

[hot herald]

yes

[arctic jewel]

oh wait mb mb

I was confusing it with -1 ur right

oooh okay I get it now

[hot herald]

if you want to find the $x$-intercepts of $y=3(x+2)^2-5$ then you can set $y=0$ \
divide both sides of the equation by 3 to get
$$(x+2)^2 - \frac 53 = 0$$
and then factor as a difference of two squares

[glossy valve]

ℝamonov

[arctic jewel]

no no I don't want the x or the y intercept

I'm tryna find the points of the parabola

but you explained that alr

[arctic jewel]

this

it helped so I'm good now

thanks

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[north locust]

Anyone able to help?

[torn jolt]

there's a physics server in #old-network

[north locust]

Ty

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[lone path]

Find the value of Angel X

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[lone path]

Find x value

[sacred fog]

• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.

[void widget]

Show the full question in text

[lone path]

This is the full question

It's just
BC = AC
AF = FC

From the figure

Here is my work

[lone path]

.

[lone path]

.

[void widget]

Ok tell me how angle EBC is 49°

48*

Is it given?

[lone path]

Yes

[void widget]

Oh ok

[lone path]

Any thing in this original picture is given

He wnat to find X angel

[void widget]

Is all are right then

[lone path]

But for these red drawings, it is my work

[void widget]

AEBCF

You can take out angle x

Wait

(n-2)×180

Do you know this formula?

[lone path]

Yes

[void widget]

N is number of sides in a closed shape

AEBCF has 5 sides

You can take out Angle E

Draw a straight line

From E it will help you

Then take our the

Out*

This angle

And use some method in the other triangle where x is there you will get it

You can do it!!!

Do you need help?

[lone path]

I am wonder how did you find angel FEB

[void widget]

Yeah wait I am sending you

[lone path]

Until here every thing is ok

[void widget]

You have every angle

Then in this quadrilateral

Apply (n-2)×180

You will get FeB

Wait wait

My mistake

First I made this || line

[void widget]

Then I made another transversal perpendicular to that || kind

Line*

Which give me an idea for some angle

[lone path]

These are parallel lines?

[void widget]

Not all are ||

[void widget]

In this one is ||

[void widget]

I have made a perpendicular transversal in that || line

And I maded another parallel line from that transversal what is || to the line which I made at first

[lone path]

But how did you know that these 2 blue lines are parallel

[void widget]

Not the full line

Only this constructed one

[lone path]

Oh

[void widget]

And now I am thinking how to take out that x I have some ideas

But it is hard

[full forum]

@lone path Has your question been resolved?

[void widget]

I give up

My head is exploded

Not the full figure

I can't take it out

[lone path]

No problem bro

I appreciate your work

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[manic heron]

If one lets each columb denote x,y,z and p

[manic heron]

Why is it that it is y and p that needs to be parameterized to get some solutions?

I understand why p needs to be parameterized, since the first and the second row both contains it

But why does y need to be parameterized too? Why not x?

I.e, why is it that none-leading variables are the ones to be parameterized?

[clear lily]

because they can be anything if i remember correctly

something like that

but then again im not quite sure what your question is

[manic heron]

If I had to restate it, why is it that leading-variables are considered free, whilst none-leading variables have to be paramaterized?

[clear lily]

do you have the answer of the exercise

i think seeing it would help

[manic heron]

It's not a question from my textbook, rather a statement when explaining how to solve linear equations with infinitive many solutions.

It states "All none-leading elements in a reduced echeleon matrix must be paramaterized"

Translated from Swedish

[clear lily]

https://www.youtube.com/watch?v=Y8gB7nvtmrU

this should help

[manic heron]

Thank you once again, Gijs

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[rare zenith]

How would you prove $\frac{n^2}{n-1} \to \infty$ using the definition of tends to infinity

[glossy valve]

todadqa

[rapid rain]

Remember then the definition.
Let A > 0
You have to find N natural integer so that for every n > N, n²/(n-1) > A

[rare zenith]

Yes

[rare zenith]

struggling to pick an N

[visual thorn]

pleae

[rapid rain]

Channel already taken

#❓how-to-get-help @visual thorn

[rapid rain]

Well, how about just floor(A)

More precisely floor(A) + 2 because you don’t want the denominator to be 0

[rare zenith]

but then i can't see how

$\frac{n^2}{n-1} \geq floor(A)+2$

[glossy valve]

todadqa

[rare zenith]

if n>floor(A)+2

[rapid rain]

Yes

[rare zenith]

oh

is it because

$n-1 \geq floor(A)+1$

[glossy valve]

todadqa

[rare zenith]

no wait im still confused

[rapid rain]

You only need n > n-1

So n/(n-1) > 1

So n²/(n-1) > n > floor(A) + 2

[rare zenith]

ahhhh i see it now

so writing it as

n*(n/n-1)

is the key

tanks!!

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[torn jolt]

What did I do wrong

[torn jolt]

@sharp vine sup

[sharp vine]

maybe try to simplify it

u did

[torn jolt]

Is what I did correct

Should it be 13pi/4

[sharp vine]

u did

ye?

[torn jolt]

Huh

What was that

[torn jolt]

Yeah that’s what I did

Btw

Is the lower and upper sun the same

[sharp vine]

so it should be ok

[sharp vine]

nope

generally not

but in this case they are same

[torn jolt]

I think in this case that’s how the math is working out

Yeah

Yeah it’s not working

Idk why

Is there an error with my program

@sharp vine am I applying the formula right

[sharp vine]

I think so

[torn jolt]

The. What is up lol

@sharp vine what about pi over 8

What would the formula be there

Ex

N = 8

Not 4

This?

@sharp vine

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[past creek]

I graphed this equation and this seems like it should be the x value of the first limit but it seems I'm missing something

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@past creek Has your question been resolved?

[sharp vine]

asymptote of tan is x = pi/2
hence solve 5sin(x) = pi/2

[past creek]

So first I would divide by 5 to get
Sin(x)=pi/10

[past creek]

I'm not to sure what to do next. Could I use trigonometric equations to make it
x=archsin(pi/10)+2pi

[past creek]

<@&286206848099549185>

[scenic yew]

I mean, you're correct
You should probably show it to your teacher if your teacher didn't give an instruction that it should be entered in a fractional form

I mean if you entered pi/9 its the same thing that you entered but only in numbers

[past creek]

Yeah I just sent him an email because I'm pretty lost

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[balmy sphinx]

I am stuck at here

does 1/tan^2(x) become cos^2(x)/sin^2(x)

?

<@&286206848099549185>

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@balmy sphinx Has your question been resolved?

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[nova island]

For problem 8 (a) down there at the bottom that refers to 6 (a), it would still be an equivalence relation, right?

[rocky vale]

Yep

[nova island]

Okay for sure, thank you!

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[sullen birch]

Hello, can someone help me? I tried to evaluate this integral. However, in the final answer, there is indeterminate. I just want to ask if something’s wrong with my process that led to having that indeterminate? Or is my process for evaluating the integral, wrong? I’d greatly appreciate if u will check my work 😌😌😌😌

[swift fulcrum]

What's this part?

[sullen birch]

That’s for the integral with blue line

I took 3 out of the integral

[swift fulcrum]

I mean

What did you write for the denominator

[sullen birch]

Oh okk. I performed first completing the square, then i simplified it. I didnt show the process of completing the square so that i can shorten the process

I know that it’s factorable

[nocturne creek]

its 16, but it looks 11

[sullen birch]

But i tried completing the square so that i can arrive to the arcsin

[crude tapir]

@nocturne creek can you help me

[sullen birch]

Ohh ok that’s what he meant haha

[crude tapir]

Or arrundel

[sullen birch]

This is my channel

[crude tapir]

Oh sorry

Never mind

[sullen birch]

U should ask in the unoccupied channels

[nocturne creek]

shouldnt the last two terms have negative sign?

[sullen birch]

On the red one?

[nocturne creek]

no

the next line

[swift fulcrum]

Everything else looks fine, but I don't understand this part

Why dv?

[sullen birch]

Cause i already used u.. i performed substitution twice, so i used v, so that i wont be confused

[sullen birch]

Wait, sorry, where particular part in the black one?

[nocturne creek]

the black is you combining the answers for the red and blue right?

i mean wont these 2 terms be negative

[sullen birch]

Wait imma check

[nocturne creek]

Are you sure the question is correct 🥸

[sullen birch]

It’s positive because of here

[nocturne creek]

Oh okay

[nocturne creek]

But this

[dense oriole]

if you do the complete the sqaure then use the trigonometric intergral rules then this problem is straightforward

[sullen birch]

Yep i used completing the square so that i can arrive to arcsin

[sullen birch]

That’s what given to us 🥲

[nocturne creek]

well then the question is wrong?

[dense oriole]

can't you just now plug in pi and zerom from the blue link?
\

[nocturne creek]

this is undefined

(pi+3)/4 wont be in the domain of sin inv

[dense oriole]

oh I must have missed that pic

[sullen birch]

Here?

[nocturne creek]

wdym?

also one more thing ur doing is when u do a substitution ur not changing the bounds

[sullen birch]

I replied to this message

[sullen birch]

Im not changing the bounds in my process, but i just make sure to substitute back the u

At the final answer

[nocturne creek]

i know thats why it wont matter but still

[nocturne creek]

ive had question where they ask to evaluate an integration and it was from some random point to an infinite discontinuity which is doable with limits, but here they want you to go much further as in the inf disc is not at x=pi, its before that

[sullen birch]

will it be wrong to put “indeterminate” as my answer, given that the integral is definite? Hahahahaha

well it’s kinda ironic to have indeterminate answer in a definite integral (assuming that the given is correct) ?

[nocturne creek]

it could be that wanted u to integrate from 0 to 1

as in if it was their intention that you notice that pi is undefined

its also not defined at x=1 btw, but theres an inf disc and so u can still try to find out the integral

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[glossy mulch]

Hello!

Not sure

How the 6 turned into a 3

[dense sequoia]

since

the 16 turned into 8

the 6 turned into 3

they just shortened the fracture

from 6/(16 x 25) to 3/(8 x 25)

[glossy mulch]

Ahh!!

I see

Thanks!

[dense sequoia]

nw

[dense sequoia]

close the channel if youre done :)

[glossy mulch]

k

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[sinful sand]

part 1

doesn't work when I substitue 2n into my formula

only works when n is substituted

my summation formula is ∑(2r-1)²-∑(2r)²

with both upper limits of 2n

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[keen jungle]

Can anybody help me solve?

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[torn jolt]

for 1 i got x

[torn jolt]

in the answers at back of booklet, it doesnt state for answers for these questions

unsure

[balmy peak]

yea thats right

[wise widget]

You are absolutely right

[torn jolt]

alright thanks

and for 2

i got

x

unsure again

[balmy peak]

yea ur right

just plug into wolfram if you want to check

[torn jolt]

alright ez

ty

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[smoky wing]

Depends if x is positive

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[sacred stratus]

Quick question from discrete maths. I need to figure out whether this relation is reflexive, transitive, symmetric, anti symmetric and equivalent. My answer is yes to all but I dont know if that's correct.

[signal needle]

ok explain why each

[sacred stratus]

reflexive because n and m do the same thing, aka equal to each other so if n = m then n = n. It's more of an intuitive answer than a mathematical explanation

transistive because ix n = m and m = q then n = q

symmetric because equals sign is symmetric? n = m iff m = n

equivalent because reflexive transitive and symmetric

antisymmetric because if n = m and m = n then n = m

Idk how correct it is because we're dealing with n and m which are elements of Z x Z and not Z

[signal needle]

(n, m) is part of ZXZ, so that means n and m are from Z

[sacred stratus]

does it not mean that n is from Z X Z like (3, -1)

[summer echo]

-3 relates to 3 and 3 to -3 but -3 != 3

Not anti symmetric

[sacred stratus]

oooh

makes sense

Does that mean that this relation:

is also not antisymmetric? @summer echo

[summer echo]

Yes, because n is a divisor of -n

[sacred stratus]

because -9 R 9 and 9 R -9 but 9 != -9

[summer echo]

Yup

https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_relations.htm# this site explains it

[sacred stratus]

And finally is this one Transitive? My guess is no

because if u have X = {1} Y = {2} Z = {1,3}

X R Y and Y R Z but not X R Z

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[signal needle]

correct

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[keen moth]

Can someone explain how?

[onyx glen]

$\sin^2(x) + \cos^2(x) = 1$

[glossy valve]

Ann

[keen moth]

@onyx glen Just tested it and it works

thanks

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[atomic vortex]

How is my a2 wrong. h(x) = cosx/fx and the derivative of that should be h'(x) = (-sinx(f(x))-(cos(x)f'(x))/f^2(x) right?

[atomic vortex]

and then plug in pi/6

so (-sin(pi/6)f(pi/6)) - (cos(pi/6)f'(pi/6))/f^2(pi/6) = (-sin(pi/6)) - (cos(pi/6)f'(pi/6))/f(pi/6) ?

[hollow heart]

hello hi i have a question: six women and two men wait in a grocery store checkout line. determine the number of possible ways these customers can stand in line, given that A: the men do not stand together; B: the men do not stand on either end; C: the men do not stand together and do not stand on either end

[atomic vortex]

yo this channel is taken

😭

go to #help-0 or sum

I checked my answer with photomath and got the same as 2.84808

so what am I doing wrong

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@atomic vortex Has your question been resolved?

[atomic vortex]

😭😭

<@&286206848099549185>

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@atomic vortex Has your question been resolved?

[ember otter]

think you might be missing a negative sign when taking the derivative of f(x) in cosx/f(x) in the second terms of equations

https://www.derivative-calculator.net/ you should be able to verify it here

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[gritty rose]

are these related images?

[nocturne creek]

yes

[gritty rose]

[nocturne creek]

i know the answer to this is 0

and so the only option can be option A

but idk how to show option A ia 0

[gritty rose]

x = 1 - t. then f(x) = f(1 - t) = f(2 - x) = f(2 - (1 - t)) = f(t + 1)

damn hard problem

[nocturne creek]

okay i got it

.close

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[torn jolt]

Two cars leave towns 640km kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car? _ Kilometers per hour

[torn jolt]

<@&286206848099549185>

[sand belfry]

bruh

Just make it a system of equations

s=vt

[torn jolt]

@sand belfry wdym

im confused what is the answer

[hallow cedar]

distance = speed x time, call the sped of the slower car x

the faster car would therefore be x + 20

then you set up the 2 equations for the 2 cars

[torn jolt]

@hallow cedar what at the equations

[gritty rose]

Try it yourself

[torn jolt]

dude i dont know how to thats why im asking here

[hallow cedar]

use the formula distance = speed x time

[gritty rose]

Bo gave a hint. Try something with the hint

[torn jolt]

@hallow cedar so 640 = 20 x 4?

is that the equation

[hallow cedar]

no alright I'm going to make a diagram one second

[torn jolt]

okay

[torn jolt]

so...?

[hallow cedar]

think about it

look at all the hints I've given you

there's no use in me giving you everything, you won't learn that way

[torn jolt]

dude just tell me the equation im so confused

i dont understand a thing on that diagram

[hallow cedar]

what don't you understand on that diagram

[torn jolt]

idk what u want me to do

makes 0 sense

[hallow cedar]

I've set up the final equation

the pink distance + gold distnace = 640

find the pink and gold distance

[torn jolt]

how

[hallow cedar]

using distnace = speed x time

[torn jolt]

okay im so confused just tell me the equation

i do not understand whatsoever

[hallow cedar]

I'm not going to give you the equation

you know how to do it

[torn jolt]

bro no i dont

[hallow cedar]

yes you do

[torn jolt]

thats why im asking

[hallow cedar]

no you're asking because you just want the answer

you don't want to learn

[torn jolt]

so is it x + 20 = distance

i dont know man

[hallow cedar]

the speed is in units km/h
the time is in units h

the speed x the time would be km/h x h = km , aka distance

[torn jolt]

what

[hallow cedar]

no, that's the speed

[torn jolt]

4h + x = distance

dude i do not know i swear

[hallow cedar]

+?

[torn jolt]

please just tell me the equation

[hallow cedar]

I have distance = speed x time

ok let's go through the pink distance together

what's the speed of the pink car

[torn jolt]

sure

@hallow cedar x + 20

[hallow cedar]

yes

what's the time it takse for it to meet the gold car

[torn jolt]

4h

[hallow cedar]

right, so if distance is the speed multiplied by the time, what's the distance that the pink car travels equal to

[torn jolt]

80h+x?

[hallow cedar]

not quite

4(x+20)

[torn jolt]

okay

so now what

[hallow cedar]

also you don't need to include h that just represents hours

[hallow cedar]

what do you think

[torn jolt]

k

[torn jolt]

no clue, thats why im asking

maybe solve

[hallow cedar]

look at the diagram

[torn jolt]

we need to find the other distance

[hallow cedar]

yes

you can do that yourself

I'll check your work

[torn jolt]

x times 4?

or what

[hallow cedar]

yeah

that's written it as 4x

[torn jolt]

4x

yea

[hallow cedar]

ok so we have both the distances

now what do we do

[torn jolt]

multiply?

[hallow cedar]

why?

[torn jolt]

dunno

[hallow cedar]

then don't say it

[torn jolt]

okay

so what do we do

[hallow cedar]

have at hink

[torn jolt]

?

[hallow cedar]

have a think*

[torn jolt]

add?

its either add or divide

[hallow cedar]

why add

[torn jolt]

im not sure

[hallow cedar]

explain your reasoning

[torn jolt]

i have no reasoning

just a guess cuz i got no clue

[hallow cedar]

why are you saying then

you have barely thought about it

have a think

[torn jolt]

probably add because you combine the distances?

[hallow cedar]

why do we combine the distances

[torn jolt]

do get the final answer

to*

[hallow cedar]

well everything we do is to get the final answer

how does this help us get the final answer

[torn jolt]

man i got no clue

[hallow cedar]

you do man

you're rushing

[torn jolt]

i sure do not

[hallow cedar]

I am 100% sure you can figure this out

[torn jolt]

its multiply to find the total distance

@hallow cedar

[hallow cedar]

hm?

[torn jolt]

???

[hallow cedar]

I do not understand what you said

it doesn't make sense

could you rephrease

[torn jolt]

you multiply to find the total difference

[hallow cedar]

we aren't multiplying though

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[vast yew]

Hello! I need to do an Epsilon-Delta Proof of this Limit:

[vast yew]

$ f(x) = 3x^2 − 7x + 2, a = 1 and ε = 0.02 $

The problem is that I've never done any proofs and I don't have pretty much any idea on how to proceed

More clear like this

[cloud shore]

What's the question exactly

[vast yew]

Give me a sec

1. In the following cases calculate limx→a f(x) and given the ε calculate δ according to the definition of the limit, and
   do the limit proof with that epsilon.

[gritty rose]

https://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm

second example

here, your L = f(a) = 3 - 7 + 2

[vast yew]

Wow interesting step by step

I am gonna give it a try with that

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[oblique pier]

x^2-4xy+y^2=4
I ended up with dy/dx(-2x+y) = -1(x+2y) not sure what to do from here

[gritty rose]

are you supposed to isolate dy/dx ?

[oblique pier]

yea

[gritty rose]

let z = dy/dx and re-write your equation

then solve for z.

[upbeat bay]

is it z=-1(x+2y)/-2x+y ?

[gritty rose]

missing parentheses, but looks good

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[undone harness]

I need some help with this please

[undone harness]

I want to find d1,d2 and x

[hallow cedar]

I think you might've missed some information

because the line labelled x could be shifted , which would change d2 but not any of the info given

[undone harness]

maybe im missing something

i know how to solve the problem but i have problems with the distances betwen AB and BC

[hallow cedar]

.

well I could tlel you how to AB

I'll give you a hint, use sin = o/h twice

[undone harness]

the total distance is 5m/sin20° right?

[hallow cedar]

yes

[undone harness]

but how do i use that again, i don't see it

[hallow cedar]

lets say the point where alpha = 20 degrees is O

so AB is 5/sin 20

and AO - BO = AB

what's BO

[undone harness]

ohhhhh 4m/sin20

tysm

i think I can work with that to get more info, ty!

[hallow cedar]

np 🙂

[undone harness]

.close

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[waxen beacon]

in a system of two congruences where both moduli are even, but one remainder is even and the other is odd, does this always mean no solution exists?

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@waxen beacon Has your question been resolved?

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@waxen beacon Has your question been resolved?

[signal needle]

yes

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