help-0

[undone cliff]

.close

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[dim matrix]

I don't understand how the terms are derived here. If (1-a) was taken common here, how it turned (1-a^2) (underlined with red)

[half epoch]

Typo?

[vale wigeon]

i think they meant (1-a)^2

the subsequent lines indicate as such as well

[dim matrix]

but the term was turned to 1 (blue)

[vale wigeon]

they took a factor of (1-a) from the forst column and from the second column

each one scales the determinant by (1-a)

so (1-a)(1-a)

[half epoch]

I think they call the determinant multilinear because of that. A keyword to google if you’d like

$det(cA) = c^n det(A)$ for an nxn A

[ocean seal]

Learath2

[dim matrix]

Okay thanks @vale wigeon @half epoch , I'm trying to solve it again. I'll ask if I face a problem.

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[dim matrix]

.reopen

[lone heart]

✅

[dim matrix]

@vale wigeon How taking (1-a) common from c1 turned a^2-a to -a ?

[vale wigeon]

a^2 - a = a(a-1) = (-a)(1-a)

[dim matrix]

okay

.close

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[sick jewel]

I can't figure how to get h. I use the laws of logarithm but I can't seem to figure it out. I can't remove the k from the equation

[lone heart]

@sick jewel Has your question been resolved?

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[next chasm]

Uhh how do I write this in Latex

[plain flame]

$\lim_0 \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^(1/5)}{cosh(sinx) - e^((x^2)/2)}$

[ocean seal]

Gijs

[next chasm]

oh right thanks

[plain flame]

lim_ 0?

[next chasm]

oh i googled limit command

it gave that

x -> 0

not just 0

also (1/5) is supposed to be a power, idk where i messed up

is there a seperate command in latex to declare a power, or do I just use ^

[ocean seal]

Davit

[lone heart]

Channel closed

Closed due to the original message being deleted

[next chasm]

now i deleted the fucking problem

$\lim_0 \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^(1/5)}{cosh(sinx) - e^((x^2)/2)}$

[ocean seal]

Davit

[plain flame]

lim x to 0?

[next chasm]

yes

im trying to figure latex out lol

$\lim_0 \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^0.2}{cosh(sinx) - e^((x^2)/2)}$

[ocean seal]

Davit

[plain flame]

$\lim_{x\to 0} \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^{\frac{1}{5}}\cosh{(\sin{(x)} - e^{\frac{x^2}{2}}}$

[next chasm]

yea this

also 1/5 is power

idk how to fix that

$\lim_{x\to 0} \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^{1/5}}{cosh(sinx) - e^{(x^2)/2}}$

[ocean seal]

Davit

[next chasm]

nvm did it

[ocean seal]

Gijs

$\lim_{x\to 0} \frac{cos(sinh(\frac{x}{sqrt(5)})) - (1-\frac{x^2}{2})^{\frac{1}{5}}\cosh{(\sin{(x)} - e^{\frac{x^2}{2}}}$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 394938706760302592.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[next chasm]

Anyways

heres the problem

$\lim_{x\to 0} \frac{cos(sinh(\frac{x}{\sqrt(5)})) - (1-\frac{x^2}{2})^{1/5}}{cosh(sinx) - e^{(x^2)/2}}$

My question is regarding cos(sinh(x/sqrt(5)) and cosh(sinx)

do i expand whats inside at first, so x/sqrt(5) and sinx

or do i expand cos(sinh(x/sqrt(5)) based on sinh(x/sqrt(5))

[ocean seal]

Davit

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[next chasm]

Evaluate the Limit
$\lim_{x\to 0} \frac{cos(sinh(\frac{x}{\sqrt(5)})) - (1-\frac{x^2}{2})^{1/5}}{cosh(sinx) - e^{(x^2)/2}}$

[ocean seal]

Davit

[next chasm]

I found the values for cos(sinh(x/sqrt(5)) and cosh(sinx), if somebody can help me find the value for (1-x^2/2)^(1/5) that would be nice

<@&286206848099549185>

[lone heart]

@next chasm Has your question been resolved?

[next chasm]

$\lim_{x\to 0} \frac{1 - \frac{x^2}{10} - \frac{x^4}{200} - (1-\frac{x^2}{2})^{1/5}}{1 + \frac{x^2}{2} - \frac{x^4}{8} - e^{(x^2)/2}}$

[ocean seal]

Davit

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@next chasm Has your question been resolved?

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[amber wigeon]

how do i find the lenght DE

i have tried to find out how to do it, but i get wrong all the times

similarity

[viral pagoda]

Yea

So corresponding sides proportional

8.5/DF

[viral pagoda]

=6/dr

De*

=6/10

[amber wigeon]

ahhhhhhhh

understood

thats the thing ive been getting wrong when im trynna figure it out

i took x/x insted og the corresponding sides

[viral pagoda]

.close then

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@amber wigeon Has your question been resolved?

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[strong rain]

Hello

[strong rain]

Got a basic derivative question here

For the function y(x), is y’(x) the same as dy/dx for derivstives? They are just different notations?

[pliant cedar]

yes just different notations

[strong rain]

Ah ok and how do u read them? In y’(x) is it the derivstive of y of x?

But for dy/dx u read it just dee y dee x ?

[pliant cedar]

yes dy/dx is "dee y by dee x"

y'(x) is "y prime of x"

[strong rain]

Ah yeah right

And btw

For d/dx is it just derivative?

For eg d/dx (x)

Is just derivative of x ?

[pliant cedar]

d/dx is "dee by dee x", u r supposed to put something in front of it for this to make sense,
like dy/dx is "dee y by dee x", and it is the derivative of y with respect to x

[strong rain]

Yeah for dee by dee x i saw it used with constants

Like d/dx (2)

[pliant cedar]

thats the same thing as d2/dx

[strong rain]

Ahh

Then what did u mean by something in front of it?

[pliant cedar]

like u put a 2 in front of the d

d2

or whatever function it is that u want to differentiate

u write in front of that d

df/dx

[strong rain]

Ohhh okay. So d/dx is the same as d’ ?

[pliant cedar]

is the derivative of the function f wrt x

[pliant cedar]

well no

d/dx on its own doesnt make sense

[strong rain]

D’ on its own is also just derivative no?

U need something in front

Like d’ (something)

[pliant cedar]

can u give an example?

[strong rain]

Well for eg here

D/dx c

Is the same as dc/dx as u said

And also the same as d’ (c) ?

[pliant cedar]

no

say f(x) = c

where c is a constant

then d/dx f(x) = df(x)/dx = df/dx = dc/dx = f'(x) = 0

[strong rain]

Ahhh

So for the prime thing

Its like y prime with respect to x

And u can substitute y with d

[pliant cedar]

u dont substitute y with d, i dont understand what u mean

u dont write d'

[strong rain]

Like f’ (x) = 0

Is not the same as d’ (x) = 0?

[pliant cedar]

unless u have a function that is called d

[strong rain]

Ohhh

Ok so for prime

U only attach the ‘ to the function f y g h etc

[pliant cedar]

if u have a function f, then its derivative wrt x is denoted f'

[strong rain]

So if its g(x)

[pliant cedar]

yes

[strong rain]

Then derivative is g’(x)

[pliant cedar]

yes

[strong rain]

Okay i see thanks, i thought the prime thing was just another general notation for derivative

Like d/dx

[strong rain]

In this case as u said, is d/dx g(x)

[pliant cedar]

yeah

[strong rain]

Okay tbanks! Sorry for my confusion

Thank u very much!

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[formal spruce]

$a{n+2}=2a{n+1}-a_n$

[ocean seal]

LeL-wyamihere

[formal spruce]

I still can't get this right

I need to find this

[plain flame]

$a_{n+2}=2a_{n+1}-a_n$

[ocean seal]

Gijs

[formal spruce]

$a{5}+a{2}$

[ocean seal]

LeL-wyamihere

[formal spruce]

And a1=a2=1

I literally can't get it

[tacit arch]

compute a3 and a4 to get a5

[formal spruce]

i tried

But it just tells me its wrong

[tacit arch]

show your work

[formal spruce]

I ve done stuff in a notepad wait

[wild trail]

Dude you just asked this minutes ago

[formal spruce]

Ye but idk man

It tells me i'm wrong

Idk where i went wrong

I ve done all the others questions right thanks to u

[wild trail]

What does the answer say?

[tacit arch]

yea we can't correct your work if you don't show your work

[formal spruce]

WAIT i found it

thx anyway

yall made me look thru my stuff lmao found out i fked a4

.close

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[hard garden]

The image of a linear transformation can be viewed like surjective function right?

[tacit arch]

no

[alpine sable]

no

[weary wyvern]

The image is not a function

[hard garden]

What is it then

[plain flame]

youre comparing two different objects

[weary wyvern]

A set

[plain flame]

the image of a linear transformation is a set

[hard garden]

Doesnt it mean that for every b element of V' there exists a from V such that fi(a) =b?

[weary wyvern]

What's "it"

[ruby current]

every function is surjective onto its image

[hard garden]

Thanks. That's what i was hoping to hear

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@hard garden Has your question been resolved?

[lone heart]

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[chrome gust]

can someone tell me the rule? How did he he got to -6t -6?

[plain flare]

How to solve this..

The Q says give ur answer in exact values

her's the Answer

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@chrome gust Has your question been resolved?

[chrome gust]

<@&286206848099549185>

[tacit arch]

$1 \ge 6|t+1|=|6t+6|$

[ocean seal]

riemann

[chrome gust]

lol u literally just can 1/|t+1| * 6?

just the under part

|t+1|

?

[tacit arch]

$\frac{a}{b} \ge c$ and multiply both sides by $b$

[ocean seal]

riemann

[tacit arch]

the sign won't change if $b>0$, which is the case here

[ocean seal]

riemann

[chrome gust]

aaaaaah lol thanks

.close

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[alpine sable]

I found that

[alpine sable]

the equation for this is basically

(10-2x)(8-2x)(x)

which simplifies down to

(x^2 - 9x + 20)(x) > 0

since it's the equation for volume so it can't be negative

so owhat i concluded is x > 0

but then

i tried to solve that god forbidden quadratic and i got

and now I don't know if I am doing something wrong

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

actually yes

i solved it

ty for asking AI

🫡

.close

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[woeful wind]

what is cos2x all squared, so (cos2x)^2

[vale wigeon]

cos^2(2x)...?

was there anything that you wanted to do with this expression

[woeful wind]

its finding the area in a polar expression

i need to integrate 0.5(1 + cos2x)^2

[vale wigeon]

right

http://xyproblem.info/

anyway, you might want to rewrite cos^2(2x) as (1 + cos(4x))/2

[woeful wind]

thats what i was looking for as it said something similar to that in the ms

did you just use double angle formula?

thank you for your help ive done it

.end

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[lost rock]

Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Please provide an explanation and proof.

[lone heart]

Please don't occupy multiple help channels.

@lost rock Has your question been resolved?

[hollow sparrow]

1. calculate the volume of the pyramid A
   V = L²H/3
2. divide the volume of pyramid B by the volume of pyramid A
   multiply by 100 to get the percentage

[sly mantle]

@lost rock pls only use 1 channel. also dont just ask for a full answer. post what you tried

[lost rock]

ok

can u help me on the other channel n i close this one

[lost rock]

tyyy

[lost rock]

i have another question i need help w

Ellis is painting wooden fenceposts before putting them in his yard. They are each 5 feet tall and have a diameter of 1 foot. There are 10 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 10 fenceposts? Use 3.14 for π, and round your answer to the nearest hundredth. Provide an explanation and proof for your answer to receive full credit.

[hollow sparrow]

the surface of the cylinder(which is wooden fenceposts) is :
2πR² + 2πRH

diameter = 2R

[lost rock]

how did u know it is a cylinder?

n it says diamete is 1ft?????

[hollow sparrow]

It is known that a wooden fencepost is a cylinder

[lost rock]

ohhh ok

[hollow sparrow]

since the diameter equal to 1 foot so the radius equal to 1/2 foot (R = 1/2)

H = 5 feet

se just plug them in 2πR² + 2πRH

[lost rock]

wait so wat do i plug in for r

[lost rock]

2?

[hollow sparrow]

1/2 for R
5 for H

[lost rock]

ohhh ok

so like this 2π(1/2)² + 2π(1/2)(5)

[hollow sparrow]

yeah

[lost rock]

ok

17.2787595947 is the answer

n 17.28 is the answer to the question

since i round to the nearest hunderedth

so wat is 2r?

[hollow sparrow]

2r is the diameter of the base of the cylinder which is 1 foot

[lost rock]

how

it said it is 1ft

what is the r

[hollow sparrow]

the diameter is 2 time the radius

[hollow sparrow]

radius of the base of the cylinder

[lost rock]

oh

so now i need to multiply 17.2787595947 by 10

since their is 10 fenceposts

[hollow sparrow]

yes

[lost rock]

i jus looked back to the question n it said to use 3.14 as pi

so i got the answer 172.2

is that right?

WAIT

[lost rock]

is it asking for volume or surface area

[hollow sparrow]

surface area of course

[lost rock]

omg

i think u gave me the formula for volume

[hollow sparrow]

you can't paint inside the wooden fenceposts

[hollow sparrow]

nope

[lost rock]

the surface area formula is 4(pi)(r)^2

oh wait

srry

nvm

i waas lookin at the sphere one

srry

[hollow sparrow]

np

[lost rock]

but i still don get how its a cylender

[hollow sparrow]

since they give you the diameter

and pi and the height

it's must be a cylinder

[lost rock]

oh ok

so now that i found the answer

how do i phrase it n my complete sentence answer?

[lost rock]

do i say ellis needs 172.2ft of paint to paint all 10 of the fenceposts?

[hollow sparrow]

i'm not sure if ft² describe how much paint ellis needs

but ellis need to paint 172.2 ft² (area)

[lost rock]

ok

[lost rock]

ty

[hollow sparrow]

anytime

[lost rock]

thats it right?

[lost rock]

u helped sm i rlly apreaciate it ima close this now. 😊

[hollow sparrow]

glad that help

[lost rock]

.close

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[plush badger]

Wouldn't the integral of 3A dt be 3A * t + C since we're integrating with respect to t?

[plush badger]

so would a solution be 3At + 7?

[tacit arch]

try plugging that into the differential equation

Might help to write A(t) instead of just A

[plush badger]

wdym

[tacit arch]

stop spamming everywhere

read #❓how-to-get-help

delete your messages

[tacit arch]

you're proposing 3At+7 as a solution to A?

[plush badger]

I suppose, but it looks wrong

but I'm not sure where the flaw in my thinking is

[tacit arch]

A is a function of t. so when you integrate A(t), you don't simply multiply A(t) by t to get the antiderivative

that's like saying if f(x) = sin(x) and you integrate f(x) dx to get f(x) x = xsin(x)

have you heard of separation of variables?

[plush badger]

yes, sort of

I know of separable equations

or at least how to check for them

is that the same thing?

[tacit arch]

yes

use those techniques and solve for A here

https://tutorial.math.lamar.edu/classes/de/separable.aspx

[plush badger]

oh I see. Thanks so much!

.close

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Please don't occupy multiple help channels.

[quick karma]

,rotate

[quick karma]

So for 2(a), expand 3(11+8x) and then add 14x

there's really nothing different, just that one extra step of adding that outside term that's not in the brackets when you're done expanding

[lone heart]

@alpine sable Has your question been resolved?

[quick karma]

yes

it's literally bedmas

multiply out before addition

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[ember sky]

can someone help explain how the derivative of this was done?

[hollow sparrow]

product rule derivative

$\frac{d(f(x) g(x))}{dx} =f(x)' g(x) + g(x)' f(x)$

[ocean seal]

Mehdi_Moulati

[ember sky]

ohh

ok i understand

so f(x)= -ax and g(x)= the exp?

[hollow sparrow]

yes

[ember sky]

thank u very much

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[strange tiger]

dx{(x^2-3x+2)(2x^3+1)} please help me compute the derivative

[ocean seal]

Mehdi_Moulati

[hollow sparrow]

like this ?

[strange tiger]

yea

[hollow sparrow]

use the product rule derivation

or expand then derivate

[strange tiger]

2x-3 2x3 +1 + x2 3x + 2 (6x2?

this new topic for me please explain

[hollow sparrow]

expand : (x² - 3x + 2)(2x³ + 1)

then derivate it

[strange tiger]

f(x) = (x^2 - 3x + 2)(2x^3 + 1) ya?

[ocean seal]

Mehdi_Moulati

[hollow sparrow]

now derivate : 2x^5 -6x^4 +4x^3 + x² -3x + 1

( 2x^5 -6x^4 +4x^3 + x² -3x + 1 )' = ?

[strange tiger]

10x^4 -24x^3 +12x^2 + 2x -3

yea?

im wrong?

[hollow sparrow]

correct

,w (2x^5 -6x^4 +4x^3 + x² -3x + 1)'

[ocean seal]

Results provided by WolframAlpha

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Requested by Mehdi_Moulati#1210

[strange tiger]

whats next

[hollow sparrow]

that's it

[strange tiger]

its derivative 10 x 3 24 x 3?

theres no simplify

[hollow sparrow]

yes

[strange tiger]

how to make it factor

[hollow sparrow]

no need to

[strange tiger]

it says here in module i need to answer factor

[icy ruin]

s

anyone know how to make this type of shape using these functions

[lone heart]

Please read #❓how-to-get-help

[strange tiger]

do i need to use it factorial

@hollow sparrow

cus it say it need

[hollow sparrow]

if that so the product rule derivation is better

[strange tiger]

do i repeat?

in 2x^5 -6x^4 +4x^3 + x² -3x + 1

[strange tiger]

maybe this is answer

i am to not strong math

[lone heart]

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[lone heart]

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[manic fern]

didnt really understand this

its basic algerba but I dont understand algerba in any way shape or form

[limpid spade]

Found it

[manic fern]

💀

[vale remnant]

there has to be more info

[limpid spade]

Yes

Has to be an equation

[vale remnant]

show the full question

[manic fern]

well, its the gravitational field equation

yknow?

G*M/R

[limpid spade]

No

[manic fern]

I just filled in G and m with random numbers

and was wondering if there was a way to get r

[limpid spade]

GmM/r^2

Plug in a random number for M and Force then too

Otherwise u have 3 unknowns

[manic fern]

yeah

ok tysm

[limpid spade]

F=(GmM)/r^2

What would u try first to solve for r

[manic fern]

I would try

Getting the mass

because G is always constand

its 6.67x10^-11 m/s^2

smthing like that

[limpid spade]

Huh

Didn't u plug in random values for the other unknowns u just have to solve for r

[manic fern]

yeah

I think I missed up

ty tho

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[dark fern]

is this logic correct?

[dark fern]

for explaining why logarthimic laws relate to exponential laws

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[spare fern]

hey

[spare fern]

how would I find the range of this function?

[dense plover]

range is the possible y outcomes of the graph

so what would be an inequality that represents what y there can be

[spare fern]

y >= 0

[dense plover]

yeah

[spare fern]

so it would be (0, infinity)?

[dense plover]

it would be [0, inf)

"[" means 0 is a possibility

[spare fern]

oh I see

[dense plover]

"[" or "]" is like <= or >=

[spare fern]

thanks for helping out

[dense plover]

yw

[spare fern]

.close

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[tranquil ermine]

hello

[tranquil ermine]

im stuck on this question

could someone show me how you would solve it?

<@&286206848099549185>

[lone heart]

@tranquil ermine Has your question been resolved?

[tranquil ermine]

<@&286206848099549185>

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@tranquil ermine Has your question been resolved?

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[dark ibex]

How do i prove this

[dark ibex]

trigonometric identites

[median oar]

what have you tried

[dark ibex]

idk what to do

[lone heart]

@dark ibex Has your question been resolved?

[median oar]

i mean

try cross multiplying

[next glade]

anyone know how to optimise surface area and volume for a truncated cone/ frustum

how to optimise surface area and volume for a truncated cone/ frustum

[dark ibex]

.close

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[cloud sparrow]

simple question i just forgot how to get inverses

[faint sage]

did you find what the linear function is?

[cloud sparrow]

No I'm not sure actually

[faint sage]

For that you need the y-intercept and the slope

Can you get that from the table?

[cloud sparrow]

oh wait yeah i can do that i just realized it was linear lmao

slope is 1/3

[faint sage]

are you finding the slope of f(x)? because slope is rise/run or change in f(x) over change in x

[cloud sparrow]

yeah the slope is 1/3 right?

oh

had my variables flipped sorry

it's 3

[faint sage]

exactly

[cloud sparrow]

3x-3 = f(x)

[faint sage]

and y-intercept is what f(x) is when x=0

[cloud sparrow]

yep

[faint sage]

which is?

[cloud sparrow]

-3

[cloud sparrow]

ya

[faint sage]

whats f(0) from the table

?

[cloud sparrow]

-3

oh wait nvm

[cloud sparrow]

DX

XD

yeah

+1

[faint sage]

alright cool so f(x)=3x+1

f-1(13) is asking us what value of x makes f(x)=13

so just plug in 13 for f(x) and solve for x

[cloud sparrow]

right

f(13)=40

[faint sage]

dont replace x with 13; replace f(x) with 13

so you'd get f(x)=3x+1 -> 13 = 3x+1

[cloud sparrow]

ok x=4

[faint sage]

theres the inverse^

you can check that f(4)=13, which means its right

[cloud sparrow]

ah ok

also what's the difference between odd and even degree polynomials again

above x^3

[faint sage]

A function f is odd if f(-x)=-f(x) and even if f(-x)=f(x)

[cloud sparrow]

ah oh thx!

[lone heart]

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[empty plover]

if we move on a circle on earth, do we experience coriolis force

[lone heart]

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[quartz acorn]

Can anyone solve the following integral?

[quartz acorn]

$$ \int_0^\infty x^{a-1}\exp\left(-\beta x^2 - \gamma x - \delta x^\eta\right) dx$$

[ocean seal]

Stadius

[quartz acorn]

I've tried everything I can think of but can't work it out except for some special cases. I know that there are a several special cases in which it reduces to 3.462.1 of Gradshteyn and Ryzhik (e.g. when eta=2 or eta=1, or when delta=0)

I have a feeling that differentiating under the integral sign (e.g. 'Feyman's integral trick' is the answer here, but I can't quite crack it

Any solutions or suggestions welcome

[lone heart]

@quartz acorn Has your question been resolved?

[lone heart]

@quartz acorn Has your question been resolved?

[lone heart]

@quartz acorn Has your question been resolved?

[lone heart]

@quartz acorn Has your question been resolved?

[tawny stratus]

@quartz acorn You've been waiting a few hours- ping helpers.

<@&286206848099549185>

[slim spire]

,w \int_0^\infty x^(a-1)exp(-bx^2-cx-dx^e)dx

[tawny stratus]

<@&286206848099549185> @quartz acorn Still needs help!

[slim spire]

@quartz acorn Where did you encounter this integral?

[quartz acorn]

In a paper I'm reviewing. The authors resort to numerical methods, but I'm sure there must be some special function out there that contains this as a special case, though I can't find one.
My only real lead is the link to the parabolic cylinder function via Gradshteyn & Ryzhik 3.462.1

[slim spire]

Is it from CERN by any chance? lol

[quartz acorn]

🤐

[tawny stratus]

<@&286206848099549185>

[mortal trellis]

try the advanced channels or stackexchange or something. but if this is from a paper you are reviewing then these help channels are not exactly the best place

[lone heart]

@quartz acorn Has your question been resolved?

[lone heart]

@quartz acorn Has your question been resolved?

[rocky grove]

!help

[lone heart]

Please read #❓how-to-get-help

[quartz acorn]

Do you have a translation?

[tawny stratus]

<@&286206848099549185> <@&286206848099549185> <@&286206848099549185> <@&286206848099549185>

<@&286206848099549185>

[quick stream]

what!

you mention us 5 times!

[rocky grove]

@quartz acorn you could try posting this in #multivariable-calculus or in #calculus

[lone heart]

Please read #❓how-to-get-help

[rocky grove]

Please read #❓how-to-get-help

[lone heart]

@quartz acorn Has your question been resolved?

[tacit bobcat]

!help

[lone heart]

Please read #❓how-to-get-help

[last pewter]

do u kco for a positive minus negitive??

<@&286206848099549185>

[quick stream]

what?

[woven ivy]

Nİ

[lone heart]

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[noble ermine]

is f(x)= 1 considered a function or does it need to have a variable beside it for it to be a function?

[long axle]

It’s a function

More specifically a constant function

[noble ermine]

oh ok

Thank you

[long axle]

U can read more about it here https://www.cuemath.com/calculus/constant-functions/

[alpine sable]

It's a function where every value of x will give you 1

So it is definitely not injective, but a function it sure is

[noble ermine]

Thank you

.close

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[noble ermine]

.reopen

[lone heart]

✅

[noble ermine]

.close

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[honest roost]

Can someone tell me how I have to do this?

[alpine sable]

have you tried anything

[safe crypt]

If you know AP, what else can you work out

[honest roost]

OP=6a+8b

[safe crypt]

what do you reckon BP would be then?

[honest roost]

BP=6a+2b

[safe crypt]

what about AB?

[honest roost]

AB=-4a+6b

[safe crypt]

can you work out PQ from this? Sorry, I'm a lil high so slow to type

sorry OQ

either would probably help tho

[honest roost]

For that I would need the ratio but it should be something like OQ=4a+ratio*(-4a+6b)

[safe crypt]

So can you express AQ and BQ in terms of the other sides?

(hint, you know OQ + OP, OA + AQ, OB + BQ, AP-AQ, BP - PQ

The trick to the problem is, since OQ is shared, you can work out what AQ is pretty easily, and from there you can work out BQ from OP

[honest roost]

I cant imagine a way to express OQ without knowing the ratio

[safe crypt]

Did you get up to here?

[honest roost]

how do you get QP?

IS QP just 1/2OP

[safe crypt]

QP isn't used yet, I just shared the relevant bit

nah

oh, you mean in this bit, sorry

these are the first observations

the directions might be wrong btw

[honest roost]

But for all of these I would need the ratio to express OQ

[safe crypt]

check my working, but does this work?

[honest roost]

I get would you are writing there but I dont get how to find the ratio of AQ:QB from this

[safe crypt]

So you've got 4a + AQ = OQ, 6b + QB = OQ right?

so therefore 4a + AQ = 6b + QB?

[honest roost]

yes

[lone heart]

@honest roost Has your question been resolved?

[safe crypt]

sorry dude, the answer is legit long as fuck to do, but it's just -> what info do I know -> what can I work out from that

you can work out AB, OX, etc etc and you eventually get there

[honest roost]

.close

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[pastel swift]

I have tried it and almost got an answer

Then I realised that I looked at the distance between B and C not B and X

<@&286206848099549185>

.cloes

.close

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[vocal tapir]

how do I solve 25^(log/125/8)

[vocal tapir]

125 as subscript to log

I got to 5^2(log/5^3/8)

[tacit arch]

$25^{\log_{125}(8)}$ ?

[ocean seal]

riemann

[vocal tapir]

yeah

[hazy plank]

calculator probably

[vocal tapir]

gives 4

but I want to solve it manually

oh well

[hazy plank]

hm

[vocal tapir]

it becomes this

then this

[hazy plank]

125^x = 8

hm im not familiar with that type of log simplification

maybe its (5)^3x = 2^3

yeah

so you get 5^x=2

ah

i se now

[vocal tapir]

this multiplies log

this divides log

that's where 3/3 comes from and becomes 1

becomes

[hazy plank]

5^log_5(x) = x right?

[vocal tapir]

so 4

[hazy plank]

yes

[vocal tapir]

.close

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[glacial zinc]

guys, I have a box that is 50mmx80mmx20mm how many mililiters it can hold?

[glacial zinc]

1L = 1000x1000x1000mm right?

so....

[limpid turret]

I don't think this is the correct definition

[vocal cape]

it is not

[glacial zinc]

halp?

[limpid turret]

Figure out the actual definition of a liter

Start there

[glacial zinc]

1L = 1000000 cubic milimiter

oh

so 1L = 100mm x 100mm x 100mm

right?

[vocal cape]

yep

[glacial zinc]

nice

[keen mason]

no

[glacial zinc]

so, if I have 50x80x20 I'd have 80000mm^3

[keen mason]

1 liter is 1 dm^3

[vocal cape]

he corrected himself

[keen mason]

ya

i saw

[glacial zinc]

So

1L = 1000000 m^3 and 1000ml

[keen mason]

woah

[vocal cape]

1L = 1000000 MM^3*

[glacial zinc]

I'm stuck

._.

[vocal cape]

this was correct

now, according to your problem, you have 80000mm^3

[glacial zinc]

can I go like this?
1L = 1000000mm^2
? = 80000mm^2

and find how much of a liter it is?!?!

[vocal cape]

80000mm^3

[glacial zinc]

0,08L !! 😄

[vocal cape]

that's correct

[glacial zinc]

now to mls.... 80 ml

❤️ thanks!!

[vocal cape]

consider you are working in ^3

[glacial zinc]

thats so small amount

I thought I'd need a glass of water to fill it

but turns out its less than half of a glass 😮

[vocal cape]

great work 🙂

[glacial zinc]

thanks mate, I'll round up for a 100ml for safety

cya!

mr bot I'm done, thanks

.close

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[exotic sundial]

x^(x+2)=(x+1)^x, theoream binomial, help, please!!!

[limpid turret]

what

[exotic sundial]

x^(x+2)=(x+1)^x

[limpid turret]

$x^{x+2}=(x+1)^x$

[ocean seal]

SWR

[limpid turret]

Is this what you are writing?

[exotic sundial]

yes

[limpid turret]

And what are you trying to find?

[exotic sundial]

x=???

[limpid turret]

And you're trying to find it using binomial theorem?

[exotic sundial]

YES

How would it be??

[limpid turret]

what a weird problem

Well, if you're using binomial theorem, I guess you gotta assume x is an integer

[keen mason]

u sure u cant just solve it nromally

[exotic sundial]

In this video he explains how the binomial theorem is, but I don't know what to do after expressing (x+1)^x raised to x.
https://en.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/v/binomial-theorem

Help!!!

[limpid turret]

Where did you get the problem from?

Who gave you the problem?

[limpid spade]

We can find one solution via taylor series.

[exotic sundial]

I found it on the Internet

taylor series??

[limpid turret]

Did it say to use binomial theorem where you found it?

[exotic sundial]

yes

[limpid turret]

Weird, because the solution doesn't really work with binomial..

[exotic sundial]

So how is it???

[limpid spade]

Use this

Using the first order we can get an integer solution.

Which is just 1

So x^(x+2)=1

Solve for x

[exotic sundial]

How is it done, I don't understand?

My teacher told me it's something like this:

But, then what is done afterwards?

Please, help!!!

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[languid igloo]

Hi, given the height of a cone and its half angle, how can I get the radius of its base? I.e, I have the blue info and want the red one.

[hollow shale]

Draw a right triangle with h, θ, and r/2.

[last ether]

Not r/2

just r

[fallen verge]

yeah make a trig equation

[languid igloo]

So, I can use trigonometric rules to get it?
I'll have to read about it because my memory is a bit lossy haha

[fallen verge]

tan theta= ?

[languid igloo]

tan(Θ) = r / h
h * tan(Θ) = r

Right?

[fallen verge]

yup

[languid igloo]

Thanks

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[alpine sable]

How can I solve sin(pi/12) by hand?

[fallen verge]

half angle formula

[minor needle]

not this

$\DoubleCos$

[ocean seal]

Modus

[minor needle]

3rd line

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@alpine sable Has your question been resolved?

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[distant lichen]

my final answer is close but doesnt exactly match

[fallen verge]

plug in x=0

[molten pivot]

Yeah looks good

[fallen verge]

the y intercept is not always at C

[molten pivot]

But what is a y intercept?

[fallen verge]

when x=0

so it hits the y axis

,w define y axis

[ocean seal]

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[molten pivot]

It was a rhetorical question

[fallen verge]

,w define y intercept

[ocean seal]

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[distant lichen]

i plugged in x=0 and got c = -1/2

[fallen verge]

????

you have your function already as like y=f(x)

plug in f(0) and find y

[distant lichen]

ohhhh

i see

so its -12 got it thanks

how do i close

/close

.close

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[weary void]

is this true

[delicate jacinth]

yes

definition of log

[weary void]

thx

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[quasi gull]

I am working on a complex problem where i try to optimizing a algorithem to generate the next sequence. It look something like this:

a = ArthSeq([a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12]) = v0, v1, v2, v3, v4, v5, v6, ...
b = ArthSeq([b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12])= v0, v2, v4, v6, ...

Where the following formula been used to generate the next sequence.

b1 =     1*a1
b2 =     2*a2  +    1*a3
b3 =     4*a3  +    4*a4  +    1*a5
b4 =     8*a4  +   12*a5  +    6*a6  +    1*a7
b5 =    16*a5  +   32*a6  +   24*a7  +    8*a8  +   1*a9
b6 =    32*a6  +   80*a7  +   80*a8  +   40*a9  +  10*a10 +  1*a11
b7 =    64*a7  +  192*a8  +  240*a9  +  160*a10 +  60*a11 + 12*a12
b8 =   128*a8  +  448*a9  +  672*a10 +  560*a11 + 280*a12
b9 =   256*a9  + 1024*a10 + 1792*a11 + 1792*a12 
b10 =  512*a10 + 2304*a11 + 4608*a12
b11 = 1024*a11 + 5120*a12
b12 = 2048*a12

The integer constants[1] in the above formula are been generated like this. Where x and y are >= 0:

$\binom{x}{y}2^{x - y}$

https://cdn.discordapp.com/attachments/856211862592684063/858609099230019604/119917984419545088.png

Does anyone have a intuition where this theory comes from? Does anyone have seen this structure before? Any lead that i could understand this better would be really welcome!

Reference:
[1] http://oeis.org/A038207

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@quasi gull Has your question been resolved?

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@quasi gull Has your question been resolved?

[merry depot]

that's a term from the binomial expansion of (2+1)^x
no idea what you're doing though.

[quasi gull]

@merry depot Well its a long story, i doing a long research on prime factorisation. I stumbled on this while I did a side project with a team on arithmetic sequences.

What your basically looking at is that i can convert one arithmetic sequence to the next arithmetic sequence that can generate al even values.

When i did analyzation i manage to extract this information. But i have no idea what kind of relationships i am looking at. I am just hoping that anyone is familiar with this and can tell there experience.

But i will look into your binomial expansion. Thanks at least for your thoughts!

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@quasi gull Has your question been resolved?

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@quasi gull Has your question been resolved?

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@quasi gull Has your question been resolved?

[flint harness]

Guys I need help with a equation in absolute value the question is written in black a = 1 over 2 and b equals 3 over 4

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[alpine sable]

The 4th one is confusinf

Can any1 explain it

Or “it is wat it is”

do you not understand what the property means

or why the property is true?

Yh

[alpine sable]

Idk that for all of em doe

How did dey even come up with dese laws

Wat if dey jus made it all of em randomly and put= sign in b/w

[pseudo ice]

https://tenor.com/view/tim-micallef-tim-micallef-tim-and-friends-sportsnet-gif-25847065

For e.g. the first one, let $z = \log_{a}(xy)$

[alpine sable]

Mhm

[pseudo ice]

Then $a^{z} = xy$

[ocean seal]

chartbit

chartbit

[alpine sable]

basically a logarithm of a number with a given base can be written as a fraction with two logarithms with the same base.

[pseudo ice]

But then $x = a^{\log_{a}(x)}$ and similarly $y = a^{\log_{a}(y)}$

[ocean seal]

chartbit

[pseudo ice]

So you get $xy = a^{\log_{a}(x)} a^{\log_{a}(y)} = a^{\log_{a}(x) + \log_{a}(y)}$

[ocean seal]

chartbit

[pseudo ice]

(by power rules)

So then $z = \log_{a}(x) + \log_{a}(y)$ as well

[ocean seal]

chartbit

[pseudo ice]

The other ones can be proved similarly, they're "trivial and left to the reader"

Hahah but really, does the above all make sense?

[alpine sable]

Lemme try consume dis all hol up

[alpine sable]

Why did you break xy

[pseudo ice]

Because that way we could get x and y in terms of logs, but you agree that the line is true?

[pseudo ice]

they get put back together here btw

[alpine sable]

Wat do dey mean

[pseudo ice]

Hang on, where did that even come from? Is there like a preceding line to that?

[pseudo ice]

Oh, that's to the power rather than multiplied!

[alpine sable]

Yh

What is loga(x)

[pseudo ice]

Remember that $y = \log_{a}(x)$ iff $x = a^{y}$

[ocean seal]

chartbit

[pseudo ice]

So that's me just putting in the y on the LHS into the RHS

[pseudo ice]

Logarithm base a of x, you're somewhat familiar with logarithms and why they exist yea?

[alpine sable]

X is the result and a is the base and ^log a x means a is base and x is result so..

All IKnow is dis

Meh .close

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[rigid plover]

hey can someone explain me bpt theorem of triangles'

[vale wigeon]

"bpt theorem"?

[worldly lotus]

thale's theorem i think

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@rigid plover Has your question been resolved?

[umbral pulsar]

If you are asking for Thales Theorem then,

if PQ || YZ
then,
XP/XY = XQ/XZ = PQ/YZ

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[tired linden]

Why is this wrong?

-1,5x+9=2,5x-7
-1,5x+2=2,5x
2=4x
0,5=x

[wary stream]

What did you do with the 7?

Add or subtract on both sides?

[tired linden]

Oh my god haha

add

[wary stream]

Do you see the mistake now?

[tired linden]

Yes, thank you very much!

[wary stream]

.close
If you are done with the channel

[tired linden]

.close

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[weak field]

△ABC is inscribed in a circle with center O. Let P ,Q be points on AB,AC such that
P Q passes through O. If M,N are the midpoints of BQ and CP , prove that ∠MON =
∠BAC.

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[austere viper]

Hello! I am new tot his channel. Tomorrow I'll have a math exam, I need some help with 4 exercises. It is related to matrices and decompositions. Can someone help me with those, please?

This is the first question!

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[viral pine]

good mornin USAAA

[viral pine]

is this how im supposed to be using long division?

like so far

have I made any mistake

[ruby current]

channel is occupied, please post in an available channel under the available category

[viral pine]

get uut

[ruby current]

should probably write that you're subtracting 2x^2 - 8x rather than just - 8x

otherwise that's good

[viral pine]

alrighty

what should be the next course of action?

it should be dividing the 1 by the x right

[ruby current]

no

make sure you keep the order correct

8x + 1 rather than 1 + 8x

you must check whether the leading term of x - 4 divides the leading term of 1 + 8x, which is 8x not 1

[viral pine]

alrighty I get it now

thanks!

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[inner path]

how to prove that (n²+1)/n^6+2n^4 is irreducible ? I don't know how to do I try with congruence and bezout theorem to prove that (n²+1)u + (n^6+2n^4)v = 1 but it don't work

[inner path]

$(n²+1)²/n^{6}+2n^{4}$

[ocean seal]

phoestaclies

[inner path]

yes sorry i had forgot the ² in the n²

(n²+1)²

[ocean seal]

chartbit

[inner path]

the second $\frac{(n^2 + 1)^{2}}{n^{6} + 2n^{4}}$

[ocean seal]

phoestaclies

[inner path]

sorry not very good in latex 🙂

[pseudo ice]

Well now you learned something new in $\LaTeX$

[ocean seal]

chartbit

[pseudo ice]

Me no remember irreducibility of fractions of polynomials tho

[inner path]

ah

[pseudo ice]

Wait where are you working over?