help-28

[fast peak]

row reduce "as usual" by treating m as a variable

and then look at the rref and check for which m it is solvable

[rose nymph]

Hi can you help me expand this example? This is about hypergroupoid

For any group G, if the hyperoperation is defined cosets, it generally yields a hypergroup

<@&286206848099549185>

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[torn jolt]

is this ok? is derivaties

[analog tundra]

Howd u cancel

[white smelt]

it only cancels once, how'd you cancel the other factor of (2-x)

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[torn jolt]

okay

give me a second

[torn jolt]

okay okay so that part is incorrect thanks for clarify

so what can i do, instead

[grim skiff]

What's the goal? Find g'(x)?

[torn jolt]

yeah to derivate

btw, thanks guys for answering*

yeah i was thinking about it

[grim skiff]

Just use quotient rule

[spice orchid]

they are equal

[grim skiff]

Are they? The terms are swapped

[spice orchid]

a^2 = (-a)^2

[torn jolt]

btw man can you see my solution, and tell me what´s wrong?

[spice orchid]

this

[torn jolt]

but the part of converting (x-2)^2 to (2-x)(2-x) is ok?

[spice orchid]

yes

then factor the bottom

[torn jolt]

let me do it rq

[torn jolt]

i cant understand thsi

[spice orchid]

what is the common factor in 4 - 2x

[torn jolt]

i mean is 2 being 2(2-x)

[torn jolt]

this?

[spice orchid]

yes this

[torn jolt]

i got this at the moment

[spice orchid]

now you can cancel one of the 2-x in the top with the one in the bottom

[torn jolt]

i just dont want to fuck it haha
thanks ill do that

[torn jolt]

is this ok?

[spice orchid]

why did you cancel the 2 and not the 2-x

in the bottom

[torn jolt]

oh fk

i did the opossitive

[torn jolt]

sorry for so many question i have nobody else to asking to

[spice orchid]

thats correct but dont forget the 1/2

[white smelt]

you forgot the 1/2

[torn jolt]

I did it?

[spice orchid]

yes

[torn jolt]

Thanks dudes you the best

.close

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[torn jolt]

.reopen

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✅

[torn jolt]

Can I leave the 1/2 multiplying from above so as not to lose it and make it look magical later?

[spice orchid]

not sure what you mean by "from above"

[torn jolt]

i mean from 1/2 . d/dx... line

[torn jolt]

google translate sorry

[spice orchid]

yes what youve done here is fine

[torn jolt]

that's it

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[median nest]

More

[median nest]

Uhh i think i got the answer

I need some help confirming it

.close

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[dense solar]

a ball tossed to a height of 4 meters rebounds to 40% of its previous height. find the distance the ball has travelled when it strikes the ground for the fifth time.

Help

[silver crag]

whats the height after the first bounce?

[dense solar]

1.6 I think

I have actually no clue how to solve this

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fathom saddle]

Weird place for someone to drop a !status

[fathom saddle]

That's the correct height of the second bounce.

What's the height of the 3rd bounce?

[dense solar]

0.64, since 40% of 1.6 is 0.64?

[fathom saddle]

Exactly. That's the third bounce

And we can keep computing until we get the 5th

[dense solar]

So 0.4096 is the answer??

[silver crag]

no...

[dense solar]

Nvm

0.1024, and u add all right?

[fathom saddle]

Well the answer has to be at least 4, since the ball falls 4 meters on the first drop

[dense solar]

4 + 1.6 + 0.64 + 0.256 + 0.1024

[fathom saddle]

Then bounces up 1.6, then falls 1.6

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@dense solar Has your question been resolved?

[sage harbor]

4(0.4)^5?

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[stiff wagon]

Could someone proofread my work for this problem?

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[fathom cairn]

Hi

[fathom cairn]

If I want to derive this, how do I do it:

${d/dyln(y+1)}$

[glossy valve]

biyyaaaa

[fathom cairn]

uff

Thats pretty easier

[strange basalt]

chain rule

[fathom cairn]

okey d/dy 1 + y is 1

[strange basalt]

sorry?

oh ok

yeah

[fathom cairn]

but ln(x)?

[strange basalt]

sorry?

1 sec

[fathom cairn]

okey

[strange basalt]

differentiation of f(g(x)) = f'(x)g'(x)

[fathom cairn]

yes

[strange basalt]

if you have afunction within a function

first differentiate the outer function considering g(x) = y

then multiple it by g'(x)

so what did you get?

[fathom cairn]

Wait

The outer function is ln(x) right?

[strange basalt]

ln()

yes

[fathom cairn]

and the inner function 1+y

[strange basalt]

yep

[fathom cairn]

okey if we do the inner function we get 1

so v'(x)= 1

lets say g(x)= ln()

[strange basalt]

?

[strange basalt]

v?

[fathom cairn]

or f(x)

it doesn’t matter

[strange basalt]

f(g(x) ) = f'(x) g'(x)

fair

i thought we were going by the set convention would be easier to follow

[fathom cairn]

Okeyy

[strange basalt]

continue

[fathom cairn]

So we have f(g(x))= f'(x) * g'(x). That means we have to have f(x) and g(x). Lets say: f(x) is ln(x); g(x)= 1+y. So g'(x) would be 1 => g'(x)= 1

ln(x) is tje outer function

1+y the inner function

[strange basalt]

yes?

what is the differentiation of ln x

[fathom cairn]

Thats the point

I dont know

[strange basalt]

oh.

its 1/x

[fathom cairn]

How do I come to this solution

[strange basalt]

like ln (x) = 1/x

?

like how is f'(x) = 1/x where f(x) = ln x

thats your question?

[fathom cairn]

My question is How do I simply derive ln(x)? I need intermediate calculations to understand this

Its a new topic I began

At my own

Or on my own idk

gramma

[strange basalt]

by the deffination of derivative ig

but doing that would require more knowledge

so just learn some frequent functions derivatives

1 sec

[fathom cairn]

okey

[strange basalt]

have you done limits?

[fathom cairn]

yes at/on my own too xd

I understood it actually

[strange basalt]

also

[strange basalt]

oh great

and some series?

[fathom cairn]

no

[strange basalt]

oh ok

[fathom cairn]

Ohhhh that looks nice

I have to learn them

I know that e stays always the same

after derivation

[strange basalt]

i dont think you can solve derivative of ln(x) directly without series , so yeah dont use this for ln(x) , but you can try to find the derivative of other functions using this

like sin x

etc

[fathom cairn]

Yessss

[strange basalt]

you will get them , just practice some questions you will be through them in no time!

[fathom cairn]

I‘m familiar with that derivation

[strange basalt]

thats cool

[fathom cairn]

I have a math school book

and yk

[strange basalt]

this is what d/dx operator does to a function

[fathom cairn]

its pretty boring

and filled with low stuff

no limits

no chain rule

[strange basalt]

hm ic

[fathom cairn]

yea. But thank you. At first I let it but if I‘m advanced enough, I will hopefully understand it

[strange basalt]

https://www.blackpenredpen.com/_files/ugd/287ba5_b5b6cc959ca44e619bbc9b0ba20d69b1.pdf

[fathom cairn]

I like him

[strange basalt]

i even practiced from this when i first started

i did the 100 derivatives and was pretty confident after that ( had no problem solving any derivatives after it )

[fathom cairn]

With solutions?

[fathom cairn]

Ohhhh

I will do it

right nowww

[strange basalt]

just check his vid for solutions ( it has time stamps too in descriptions)

w good luck have fun

[fathom cairn]

okey

[fathom cairn]

Thank you

[strange basalt]

vid link should be in the pdf btw

yeah ofc

[fathom cairn]

I will look at it

[strange basalt]

lmk if you need any help

or well the server ( yeah ask the server idk what im talking about )

gl !

[fathom cairn]

okey thankss

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[sweet epoch]

i need help pls

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@sweet epoch Has your question been resolved?

[sweet epoch]

<@&286206848099549185>

[vale island]

C

Take a pen and start from the top of the graph

Lay it flat

[gritty rose]

look at what values the function can take on the y-axis
https://www.cuemath.com/calculus/domain-and-range-of-a-function/

[vale island]

And go down along the page

Take the fist point the pen touches the paper

For this question

It's 2

That's a maximum

Note it down

Then continue going down the page

Notice that the other point keeps going down the y axis

That means that it is going towards negative infinity

@sweet epoch

If you need more clarification I can forsure show you some mini tricks on how to understand and get it done better

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@sweet epoch Has your question been resolved?

[sweet epoch]

oh mini tricks would be nice if only u dont mind

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[torn jolt]

help

[torn jolt]

Could somebody help me with this one word problem

each backpack has 5 cats and each cat has 5 kittens and each kitten has 5 mice and each mice has 5 pieces of cheese

I got 3,125 but i dont think its right

[wild sleet]

what do you need to count though

we don't even know how many backpacks there is

[torn jolt]

theres 5 backpacks

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[torn jolt]

each one has 5 cats

and each 5 cats has 5 kittens

then 5 kittens have 5 mices

[wild sleet]

and there's no question at the end

[torn jolt]

there is

5 pieces of cheese

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[torn jolt]

There are 5 backpacks each 1 of the backpacks has 5 cats then 5 cats have 5 kittens then 5 kittens have 5 mices then 5 mices have 5 pieces of cheese thats the original question that was given to me

[wild sleet]

there's no question it's just data

i don;t think i can help with it either way

[quaint prawn]

A picture or screenshot is best

[quaint prawn]

There’s 10 dogs. Help

[torn jolt]

k

[torn jolt]

its alright

sorry for wasting your time

ill js figure it out somehow

[quaint prawn]

If you could post the actual question, we could help. The issue is there is no question in what you sent, just information.

[torn jolt]

the thing is

is that i dont have a picture nor a screenshot

bc it was writen on the board

in my classroom

[quaint prawn]

Okay, can you tell that you haven’t actually asked a question though?

If you forgot the question there’s nothing anyone can do

[torn jolt]

alr lemme do it again

There are 5 backpacks each 1 of the backpacks have 5 cats then 5 cats have 5 kittens then 5 kittens have 5mices then 5 mices have 5 pieces of cheese how much are all of it in each backpack.

<@&286206848099549185>

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[slate night]

Is this correct?

[dense vector]

no

wait

[slate night]

Where did i go wrong?

[dense vector]

let me check again

[iron cradle]

The first line seems wrong

Completing the square

Unless I didn’t read it correctly

[slate night]

It's completed correctly

[dense vector]

it's fine

[slate night]

At least that much I can be confident is correct

[dense vector]

I also thought completing the square is wrong..but it is perfect

[slate night]

@wide sundial

[dense vector]

I did not find any other mistakes as such.. your process is correct which is much more important

[slate night]

I finished it off

Maybe you can also have a look if you'd like

[spiral vigil]

please don't ping individual helpers, even if they've helped you in the past

[slate night]

ah alright mb

[iron cradle]

Yeah I thought the 27/4 was a 27/9

[slate night]

ig its correct then

thanks

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[heavy jetty]

Can someone help?

[quick cairn]

why did u set it equal to 0 ??

also u can't multiply by a variable unless u know if it's positive or negative

[heavy jetty]

oh i see

thx

.solve

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[slow sleet]

am i right with C.

<@&286206848099549185>

[gritty rose]

,tex .transformation rules

[glossy valve]

riemann

[gritty rose]

yes

[slow sleet]

thank you

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[hushed mountain]

hello

[glacial pasture]

👋

[hushed mountain]

I want to know how to integrate a function

simply like

the opposite of deriving it

for example i know how to do this:

Y=X^2
Y=2X

yk i think that's called deriving it

how can i do the opposite

[glacial pasture]

thats a very general question

[hushed mountain]

more specifically I'm trying to find the displacement from the velocity formula

[glacial pasture]

theres no 'one way fits all'

[hushed mountain]

so integrating isn't like deriving?

[fading narwhal]

In that case for example, instead of (multiplying) by the exponent (reduce) 1 from the exponent, now do opposite, (increase) the exponent by 1, then (divide) by the new exponent

[hushed mountain]

but i see them use that integration squiggly line thing, i used to know how to do all this perfectly but i forgot

[left bone]

integration has a lot of overhead - you should just find a course like khanacademy and review (or use wolfram if its a one off and you dont want to learn how it work)

[glacial pasture]

we could probably help with your specific velocity formula if youd like that

[hushed mountain]

okay one second

don't mind the question really

i just want to know how he did the thing

where he converted the V to X

x is displacement here btw

[left bone]

definite polynomial integral

[hushed mountain]

i know how to do the opposite that's it

[hushed mountain]

Im not sure i'm sorry

[left bone]

it wasnt a question

[hushed mountain]

oh lmao

[left bone]

he did a definite polynomial integral

[hushed mountain]

OHH

okay so how

[left bone]

well, like you remember the derivative rule for x^2 -> 2x?

[hushed mountain]

yes yes i do

[left bone]

bring the exponent down, then subtract one from the exponent?

[hushed mountain]

exactly

[left bone]

well if you want to reverse it, just do it in the opposite order

[hushed mountain]

okay but what about the squiggly integral lines?

[left bone]

(which is increasing the exponent by 1, then dividing by the exponent)

$\int f(x) , dx$ just means the integral of a function f?

[left bone]

not sure what your specific question is there

[hushed mountain]

ahh

wait so all i have to do is to reverse the derivative rule right?

[left bone]

I dont want to say yes to that, but the idea is generally right

there are a handful of caveats

[hushed mountain]

i see

well you answered the question that i wasn't able to google nor translate i think i'll be able to find the rest on my own now

thank you so much

for everyone that helped\

it's resolved you can close this if you'd like

[left bone]

you have to

.close

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[left bone]

oh i guess i can too

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[slow sleet]

this is my question

and i did this am i right with everything>

[spiral vigil]

yep good

[slow sleet]

okay ty

when it says "explain your reasoning" does that mean show your work

[slow sleet]

also do i have to put the plus sign after 8x or can i remove it?

[spiral vigil]

yeah exactly, what you wrote is perfect

[spiral vigil]

you'd need that plus sign (or steal the negative sign from -33)

oh but it wouldn't be 8x, it would just be 8

[slow sleet]

wait why?

[spiral vigil]

well it's descending powers right

start with x^2 then x^1 then x^0

[slow sleet]

oh ok yea i get it

thank you

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[void arch]

I don’t understand how x^3-1= (x-1)^3 in F3

[void arch]

Do I have to check this manually by subbing 0,1,2 or can I derive it algebraically?

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[warm harbor]

If I needed to find the MGF of a single variable in a mulitvariable joint pdf do I need to find the marginal first

[warm harbor]

so just looking at this work here which I know is messy

I cant just go from the joint MGF and say each respective variable for t is zero

like they are all going to be that way to matter what bc of the linearity property

I should have taken the marginal for x1 x2 and x3 and ran the expected value of each and then multiplied those together to get M ( t1 t2 t3)

Can someone confirm ?

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[fair walrus]

Unsure how to start

[torn jolt]

alright

so

what do you notice about the two vertical lines in the image @fair walrus

[fair walrus]

They are parallel

[torn jolt]

yeah

so what does that mean about the angles

70 and 2y

[fair walrus]

They are parallel

[torn jolt]

the lines are parallel

[fair walrus]

Yes

[torn jolt]

but because they are parallel

what does that make the 2 angles?

[full forum]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[torn jolt]

this channel isnt available

go above

this section is math help (occupied)

[fair walrus]

No worries

[torn jolt]

go to math help (available)

[torn jolt]

@fair walrus

[fair walrus]

Equal?

[torn jolt]

yeah

so what does that make y?

[fair walrus]

70

[torn jolt]

almost

70=2y

so what does y=?

[fair walrus]

Y=70

[torn jolt]

no because if you divide 2y by 2

you must also divide 70 by 2

resulting in 35=y

[fair walrus]

Oh okay

[torn jolt]

theres your answer

[fair walrus]

I didn’t know that

Thank you

[torn jolt]

make sure you keep it in mind

its very important for keeping the balance in an equation

.close if thats all you needed

[fair walrus]

Yes i agree

Thank you

.close

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[torn jolt]

np

[full forum]

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[torn jolt]

I used synthetic division and I’m stuck after this point

Instructions were to reduce to a quadratic and then factor

But I can’t get this to a quadratic

[forest widget]

syn looks ok
then try to find another factor (given your attempt you should see that x-9 isn’t one)

[torn jolt]

I thought grouping should work?

How do I find another factor when that method doesn’t work

[forest widget]

it’s highschool (middleschool?), if roots aren’t obvious it’s probably some integer in [-3, 3]

also grouping for cubics generally doesn’t work very well

[torn jolt]

Is there a way I can find the factors

The teacher only taught us quadratic formula, grouping, factoring

[forest widget]

introducing: guess and check

[torn jolt]

Completely forgot about that method

[forest widget]

works for 100% of the problems you’ll see pre uni when all else fails
(also rational root theorem)

[torn jolt]

I thought that’s only for quadratic equation?

I’m so lost

How does my teacher expect me to factor this

[forest widget]

who needs guess and check for quadratic when you can just blindly throw it into quadratic formula

it’s specifically for cubic and up

[torn jolt]

How

[forest widget]

if it is it’s a factor

it sounds really stupid but in highschool you generally have nice integer valued roots between -4 and 4

[torn jolt]

I don’t think I was taught that way to factor

In this lesson

[forest widget]

i mean, you more or less have to do the same here

“guess and syn div”

[torn jolt]

I could expand the equation by straight up doing this

[torn jolt]

is this viable?

why have i never heard of this before

[forest widget]

you can do it but it’s not generally viable because it’s slower than just guess and checking and in general you won’t be expected to apply grouping on anything that’s not a quadratic

[torn jolt]

Ok but this is really confusing

If I get a remainder like that is there anything I could do

Or did I screw up somewhere

I double checked like twice

Fuck

I just saw it

.close

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[desert cypress]

without any calculataion

how can i figure

the local

max and min

i see these examples

but

how do i figure

[forest widget]

you already have the critical points marked?

[desert cypress]

i dont get what u mean by critical

like vertex?

[forest widget]

local max local min and intercepts

[desert cypress]

i duno i looked at desmos

graphing

[forest widget]

just read them off desmos then

[desert cypress]

so

[forest widget]

those points aren’t marked at random

[desert cypress]

the one at -54 y

is local max?

[forest widget]

are there any points nearby that have higher y values

[desert cypress]

u mean lower?

[forest widget]

nope

[desert cypress]

then yea

(0.6)

where y is at 6

[forest widget]

so it’s not a local max is it

because it’s supposed to have higher y value than all nearby points

[desert cypress]

so

what would i say

[forest widget]

what do you call it when a point has smaller y value than nearby points

[desert cypress]

min

would (0,6) br local minumum

no

omg

im confused

.close

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@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[keen oasis]

their side reduce to half of the original one

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[royal temple]

Is the answer A?

coz max value of sin is 1 -> sub in and you get a - b

But, I dont think its that simple

Is it?

[drowsy zinc]

are you sure you want to maximise sin

b is positive

[sharp spire]

I might be wrong but the max value could be a+b
Because sin(x) could give you any value between -1 and 1. Therefore a-b*sin(x) could be anywhere in between a-b(1) [that’s what you’ve done]
or a-b(-1) which is a+b. As we know that a and b are positive numbers that should give you the maximum values?

Although I am not sure, so please have somebody else confirm it as well

[royal temple]

Ahh yeah, I see

I think you're correct

Coz yeah, a and b is >0

and a-b results in a negative b

!close

/close

fuck i forgot how to do this

.close

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[worldly wind]

need help with geometry problem. i know im supposed to use geometric mean but thats all i know. i dont even know how to apply it.

[undone vector]

Use similar triangles

[worldly wind]

yeah ik

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[torn jolt]

Can someone help me find the extrema for this function?

[torn jolt]

This is how far I've gotten

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[unborn quarry]

Hello. I think you sent your work for a different problem

[torn jolt]

LOL ur right

[torn jolt]

gimme a sec

this is the correct problem

the one I sent is correct but not the problem lmao

[unborn quarry]

anyway I don't know how to solve these

okno

[torn jolt]

😦

[unborn quarry]

no im just kidding xd

[torn jolt]

so help meee

[unborn quarry]

yeah I was checking

from I you know x=2yz

substitute that in II

you will be able to find z

then I think you can continue

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[full forum]

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[unique palm]

Is this correct? Im having trouble

pls ping if ur helping out

[unique palm]

<@&286206848099549185>

[obsidian agate]

Wsg bbg

What question

[strange ibex]

Can someone help me with this task pls:
Determine all integers n for which real numbers x,y exist in such a way that the following equations are satisfied:
x+y=n
x³+y³=n²

[unique palm]

all of em

[unique palm]

this channel is taken dude

go to another help channel thats free

[unique palm]

actually i fucked up that q

so it gave me a diff similar one

@obsidian agate

[obsidian agate]

I gotchu fam

41 is cot x

[unique palm]

thats the only one i got lol

[obsidian agate]

39 is - cosx

[unique palm]

how

[obsidian agate]

43 is 1 / sec^2

Call real quick

[unique palm]

i cant lol

my earphones are in use

[obsidian agate]

I’m on

Just go on phone

[unique palm]

phone mic is fucked 💀

[obsidian agate]

Or just listen to me

Idm

[unique palm]

cant u jsut explain on text like everyone else does 😭

[obsidian agate]

Beuhh

[unique palm]

literally everyone here explains on text

[obsidian agate]

I know but I don’t know how to use notation

[unique palm]

^ for powers

and uh

what else do ya need

[obsidian agate]

Dw

Cot x is cosx / sinx correct

[unique palm]

yeap

[obsidian agate]

So

(- cosx/sinx)* sinx

Is what you’re doing

Which is( -cosx*sinx)/sinx

Which is -cosx

That’s it

I should be doing my own homework right now sorry I gtg

[unique palm]

bruh

😭 bro came to help channel w/o doing his own shit

( ͡° ͜ʖ ͡°)

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[drifting cloud]

How to prove that function have inverse function?

[tepid prairie]

You must prove that every y has exactly one x

[drifting cloud]

I already find the inverse function, but this is second question in the task
First one is prove that it's have inverse function

[drifting cloud]

Horizontal line test?

[tepid prairie]

Yes

[drifting cloud]

How to do it without graph?

[tepid prairie]

If f(a) = f(b) implies that a must equal b then a function is one to one and then must pass the horizontal line test

[minor crater]

prove that it is bijective

[drifting cloud]

The function is sqrt(2x-1)
Then sqrt(2x-1) = sqrt(2y-1)

And few steps then x=y

So according to that f(x) is bijective, right?

[minor crater]

no

i mean

sqrt(2x-1) = sqrt(2y-1) implies x=y, but that's just proof that the function is injective

[drifting cloud]

So , i think i should prove that it's surjective also , since bijective is surjective and injective function

[brittle steeple]

or find an inverse

that would also work

[minor crater]

yeah that's probably easier

[drifting cloud]

Already do that+ It's say prove that its have inverse function then is second question find it

[drifting cloud]

So what about this

[brittle steeple]

yeah you would need to prove that it's injective and surjective

[drifting cloud]

So i should solve f(x) for x

And then f(3y/2 for example) and i should find that f(x) = y right?

Prove surjective:
sqrt(2x-1) = y
y²=2x-1
x=(y²+1)/2

f((y²+1)/2)=sqrt((y²+1)-1)
=sqrt(y²)=y
So f(x)=y

Prove injective :
sqrt(2x-1)=sqrt(2y-1)
.....some steps
x=y

Then f(x) have inverse function

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[torn jolt]

I don't understand this problem?

[full forum]

Please don't occupy multiple help channels.

[torn jolt]

No one was helping in the other channe

[full forum]

Please wait patiently, and do not interrupt other channels with your question. Helpers in this server are volunteers, and the server cannot guarantee that someone will be able to help you. By being impatient or begging, you will only turn potential helpers away.

In the meantime, please make sure your channel contains the original question, clearly describes what you have already tried, and states exactly what you are having trouble with. This increases your chances of getting a good response.

[quaint prawn]

Still do not open two channels, wait patiently

.close

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[torn jolt]

I just thought since you guys were at such a high level in math you'd have been able to help me with my geometry problem, my bad, sorry

[quaint prawn]

There are many help channels open, and we are all volunteers, sometimes you have to be patient to get help

[torn jolt]

Could you help me?

[gritty rose]

just wait in your other channel

[torn jolt]

my question is so easy for you guys, I'm sure it wouldn't take you long

[gritty rose]

.

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[torn jolt]

how would i get the final awnser and what ever i multiply all of them by how would i do get that

[spiral vigil]

the final answer is just combining like terms from the thing at the bottom, the
5x -6x -3 +9

[torn jolt]

.close

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[night bone]

Hey guys

[night bone]

I need to show:

$\lim_{n \to \infty} a_{n} = L$ and $\lim_{n \to \infty} b_{n} = M \Rightarrow \lim_{n \to \infty} a_{n}b_{n} = LM$

[glossy valve]

texaspb

[night bone]

But I am required to use the identity

$2a_{n}b_{n} = (a_{n} + b_{n})^{2} - a_{n}^{2} - b_{n}^{2}$

[glossy valve]

texaspb

[night bone]

how can I go about this?

I'm not getting it

[fast peak]

well do you know that lim f+g = lim f + lim g?

[night bone]

yes sir

[fast peak]

and lim f^2 = (lim f)^2 ?

[night bone]

yes sir

[fast peak]

well then just apply that

[night bone]

wait

just a minute

I'll do some scratching here

well thank you

I think that worked

lemme just write it in a cleaner way

yep!

thanks @fast peak

.close

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[worldly surge]

sum from n=0 to infinity of (n+3)/(sqrt(n^3+2n+8))

[worldly surge]

it diverges right?

[fathom saddle]

Right

[worldly surge]

by the lct since L=1

[fathom saddle]

Limit is 0 tho

[worldly surge]

and 1/sqrtn diverges

[fathom saddle]

Yeah that's the idea

[worldly surge]

but the test

(n+3)/(sqrt(n^3+2n+8)) / 1/sqrtn

[fathom saddle]

lct? Limit comparison with 1/√n?

Yep, perfect

[worldly surge]

its 1 right?

lim n->inf

[fathom saddle]

The limit comparison is yeah

[worldly surge]

therefore c>0

so both diverge

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[proper ocean]

I'm confused, in 8th grade

[proper ocean]

don't know how to figure out the slope

I know how to do y = mx + b but can't figure the slope out

[spice orchid]

stop trolling in the help channels

[proper ocean]

the y-intercept?

.close

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[kindred rampart]

Can someone help me with this calculus optimization word problem ?

[kindred rampart]

[full forum]

@kindred rampart Has your question been resolved?

[minor crater]

area = a*b

a*b = 2400

[kindred rampart]

yes

2400 = 3y(x)

?

[minor crater]

what's that

3y(x)

2(2*a + 4*b) = minimum

[kindred rampart]

oh yes

my fault

[minor crater]

get either a or b from this

[minor crater]

substitute here

find minimum by differntiation

and get the values for a and b

[azure burrow]

why are you multiplying it by 2 im kinda confused on this one

[minor crater]

perimeter

[azure burrow]

oh ok

[kindred rampart]

hmmm

[azure burrow]

hmm I'm still confused actually, why are we using the perimeter here? Since 3 sides have the same cost and one side doesnt wouldnt the perimeter not work

[minor crater]

ooh

oops

yes you are right here

[kindred rampart]

Wouldnt the perimiter be P = Y+Y+Y+X

P = 3y + x

so we use the area formula right?

we are given the area wich is 2400

[azure burrow]

Yeah we use the area formula as our constraint but I'm stuck on the objective formula

what I did was use the cost formula as our objective formula but I'm not sure if thats right

so I did C(x) = 3x + 4y,
2400 = xy
solved for y and then subsitiuded y

and then found the derivative

[kindred rampart]

where is the 3 and 4 from?

[azure burrow]

oh sorry

2x + 4y

[kindred rampart]

theres only 1 x tho

and 3 ys

since 3 of the sides are equal

[azure burrow]

Im using the cost function though, which is the total cost, C(x) equals 2x + 4y, 2x being 2$ per foot and 4y being 4$ per foot

and then we want to minimize our cost

[kindred rampart]

oh i never new there was a function for that

[azure burrow]

so we would find the minimum of that function I believe

so I got 40Sqrt(3) or sqrt(4800) which again im not 100% sure is right

I'm also learning optimization still

[kindred rampart]

mmm

[azure burrow]

I think it's right though

I had a similar problem

should probably get another person to check though

<@&286206848099549185>

[kindred rampart]

ok

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[shy valley]

Let $D = k[x]/(x^2)$, and $DD_D$ a $D$-$D$-bimodule. Is there a non trivial module endomorphism $\theta \in Hom{D-D}(D,D)$, I'm struggling to find one

[glossy valve]

ArtyLeAardvark

[plush egret]

This is probably not the place to ask this. I would try an advanced channel.

Is it algebra? I'm sorry I'd point to a channel but I don't recognize the topic.

there is #advanced-algebra

@shy valley

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[silent helm]

In a right angle triangle ABC, angleC=pi/2rad. Point E is on AC such that EC=2AE. Use complex humbers to prove that angleCBE + angleCBA = 3pi/4rad.

[silent helm]

idk how to start

however I think we need to use the trig notation

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[silent helm]

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[tribal flax]

Prove by induction that 5^2n - 1 is divisible by 24 for all positive integers n

[tribal flax]

,tex $5^{2n} -1$

ive proved the base case

i dont know how to equate 5^2n-1 to something divisible by 24 so that i can put (k+1) on that side

[glossy valve]

suds

[gritty rose]

Try factoring

But that wouldn't use induction

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@tribal flax Has your question been resolved?

[tribal flax]

the question has to use induction

<@&286206848099549185>

[white smelt]

when n = m + 1

$LHS = 5^{2m + 2} - 1 = 25(5^{2m}) - 1$

[glossy valve]

nalin

[white smelt]

using inductive hypothesis which stated that 5^2m - 1 = 24k => 5^2m = 24k + 1

[tribal flax]

wouldnt it be 24(5^2n) -1

[white smelt]

$25(5^{2m}) - 1 = 25(24k + 1) - 1 = 24(25k) + 24$

[glossy valve]

nalin

[white smelt]

which is divisible by 24

[white smelt]

no

[tribal flax]

sorry i just dont understand why its 25(5^2m) - 1

because 25 by any x value - 1 is not necessarily divisible by 24

e.g. 25 x 2 -1 = 49

[white smelt]

$5^{2m+2} - 1 = 5^{2m} \cdot 5^2 - 1 = 25(5^{2m}) - 1$

[glossy valve]

nalin

[tribal flax]

ohh

[white smelt]

you wouldnt get a 2 over there because it's 5^2m and 2 is not a power of 5

[tribal flax]

so the RHS is 25(5^2m) - 1

while LHS is my original one?

[white smelt]

what

[white smelt]

.

[tribal flax]

,tex $5^{2n} - 1 = 25(5^{2n}-1$

[glossy valve]

suds

[white smelt]

you have to show the result is true for n = m + 1, so the LHS is what i showed and we are supposed to arrive at the RHS of (24k)

[tribal flax]

because the equation has to work for the base case too

[white smelt]

what this makes no sense

[tribal flax]

im sorry im just struggling

[white smelt]

ok look let's go from the beginning

the base case was already established right

you did it for n = 1

right?

[tribal flax]

ive been taught that for the base case of whatever, you need to equate it to something that shows that its divisible by 24

yes

so then the RHS that shows its divisible by 24, you substitue k + 1 like you do with the LHS

[white smelt]

ok so since base case is done, next step of induction is to make the inductive hypothesis. for us, it would be

Assume $5^{2m} - 1 = 24k$

[glossy valve]

nalin

[white smelt]

this is our assumption

[tribal flax]

yes

[white smelt]

and the final step is showing the result for n = m + 1

[tribal flax]

yes

but what is k

[white smelt]

which would be to begin with $5^{2(m+1)} - 1$ and show that it comes down to some $24\alpha$

[glossy valve]

nalin

[white smelt]

any random integer, we just have to show it's divisible

if it's divisible then it is of the form 24k

[tribal flax]

ok

its just they usually put (m+1) on the RHS to show that it is divisible by 24

[white smelt]

wdym by put (m+1) on the RHS

[tribal flax]

because k doesnt necessarily mean that it is a multiple of 5^2(m-1) - 1

[white smelt]

i dont get what you're confuised about

[tribal flax]

ok give me a sec

im gonna bring the answers up and maybe you can explain?

[white smelt]

alright

[tribal flax]

this is what you did

i basically missed the lesson of induction and so ive been teaching it to myself via the notes

[white smelt]

yes, this is what I did

only difference that may have confused you is that I wrote m where these notes wrote k and I wrote k where they wrote m

but that's no difference in the math

[tribal flax]

why do they end up changes it to 24 x 5^2k + 24M

because its the base cae?

bro im gonna fail

thank you though

[white smelt]

they just want to show that the whole thing is 24(something)

[tribal flax]

the exam is tomorrow

[white smelt]

to show it is divisible by 24

[tribal flax]

yes thank you so much

[white smelt]

all the best for the exam :)

[tribal flax]

even if i didnt get it myself, i now know that theres other ways

thanks

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[glad whale]

does the -1 at the end do anything

[glad whale]

like i will show my work one sec

i feel like i did it right

but at the same time i kinda thing that -1 has to do something

like vertical shift down 1 i guess

[storm solstice]

like maybe 3,-1

and 5,0 you mean?

then ofc

[glad whale]

oh

thnxs]

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[grand yacht]

when is f'(x) negative

[lucid bolt]

when sin(theta) is in the 3rd or 4th quadrant?

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@lucid bolt Has your question been resolved?

[gritty rose]

Write this as an inequality for theta

Then set theta = x^2 - x and solve for x

[lucid bolt]

im confused

[gritty rose]

Well explain which part is confusing

Do you know what the word inequality means?

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@lucid bolt Has your question been resolved?

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[teal rover]

if i transform this to q.e. and it became x²-4x-12=0, why is my x equals to 6 and -2, why isn't it equals to 1? is my answer wrong?

[minor crater]

why should it be equal to 1?

[minor crater]

substitute x=1 in here. your sum won't be 1

[teal rover]

i think it should be equal to 1 because the number on the right side is 1, is it wrong?

[minor crater]

yes it is wrong

[teal rover]

why? so i can avoid it next time

[minor crater]

your task is to find the value of x that makes this equation hold, not look at the rhs and write down what's in there

[teal rover]

no no, my task is to transform the equation to q.e

i just want to check if my answer is correct, but how do i do that?

[minor crater]

my x equals to 6 and -2
huh? if you are supposed to transform, you don't have to find solutions, do you?

[teal rover]

quadratic formula? if i solve the x, how can i identify if my answer is correct?

[teal rover]

yes i don't need it, i just need satisfaction

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[knotty gale]

is this right?

[short crest]

!show

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[knotty gale]

derive top and bottom

top is f'(2) over 2x

then 3/4

[white smelt]

no, you have to use chain rule

so it's 5f'(2)

[knotty gale]

makes sense thank you

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[drowsy wyvern]

In any vector space V the span of any non-empty finite subset of
vectors S = {v�1, . . . , v�k } is a subspace of V.

[drowsy wyvern]

this is a proposition given in our notes, i just wanted to check if my understanding of this is correct

so suppose we have Vector Space of R2

let’s say i have the vector (1,1)

and say i have the vector (0,0) and both of them are in the set S. the span of S is the set of all the linear combinations of that set of vectors. so span of S would be a set containing a(1,1) + b(0,0) for any values of a and b in R

hence this span is a sub space of R2

is this right?

[nova basin]

Yes, it's a line

The x=y line

[drowsy wyvern]

ok thanks

sometimes these propositions are so hard to understand

especially when no examples are given and it’s kept abstract t

[nova basin]

And what would be spanned by (1,1) and (2,1) ?

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@drowsy wyvern Has your question been resolved?

[drowsy wyvern]

a different line?

[nova basin]

Does it have to be a line ?

[drowsy wyvern]

uh yeh idk?

@nova basin

[nova basin]

What's the span of (1,0) and (0,1) ?

[drowsy wyvern]

R2

[drowsy wyvern]

any point in R2 can be made as a linear combination of that so R2 is the span of that right?

[nova basin]

So why would this one be a line and not a plane ?

[drowsy wyvern]

not sure, how could i show that span of (1,1), (2,1) is a plane

[nova basin]

You have the formula for the span

Use it to show any vector is in the span

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