help-0

[stark yew]

,w int 1/(6x - 3) dx

[ocean seal]

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[stark yew]

,w int 1/(2x - 1) dx

[ocean seal]

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[alpine valve]

this is a diff problem but what would I do next

,rotate

[stark yew]

I'm gonna have to review partial fractions before i can do this : |

[hot pagoda]

is the ² in (x+1)² under + C supposed to be there?

[alpine valve]

uhhhh

yes

idk

I think that's how my teacher taught it

[hot pagoda]

i dont think so, that'd become a denominator (x-7)(x+1)(x+1)² if you condense it back

yields (x-7)(x+1)³

[hot pagoda]

ah my bad, it is indeed supposed to be there

[alpine valve]

ohh ok

how would I find b value

[stark yew]

okay so the thing about this is they're the same integral but from different families. look! they're translated. that's just a +C. so both (1/6)ln|6x-3| and (1/6)ln|2x-1| are valid answers.

[alpine valve]

so it is dependent on c value

[stark yew]

yes.

[alpine valve]

okkk ty

[stark yew]

now, you know A and C. choose any convenient value for x and use the computed values of A and C and isolate B.

[stark yew]

same drill as above for this one

[alpine valve]

what's it mean convenient value?

[stark yew]

whatever makes life easier

[alpine valve]

would b=-1?

[stark yew]

your computed values for A is wrong

[alpine valve]

o

[stark yew]

let's get the right values first

[alpine valve]

ok

is my partial fraction wrong

[stark yew]

the factorization is correct

my sincere apologies. the value for A is correct: 2.

and so is it for C.

now let's choose a convenient value for x

let's say x=0

then -5 = A -7B - 7C = 2 - 7B - 14 => B = -1

so the integral becomes
$$ \int \frac{2, dx}{x-7} - \frac{dx}{x+1} + \frac{2, dx}{(x+1)^2} $$

[ocean seal]

waris

[alpine valve]

so b=-1?

[stark yew]

indeed

[alpine valve]

oooo ok

lemme try to solve

[stark yew]

this evaluates to
$$ 2\ln\mid x - 7\mid - \ln\mid x+1 \mid - \frac{2}{x+1} + C $$

[ocean seal]

waris

[stark yew]

let's check our answer

,w int (x^2 + 12x - 5)/((x+1)(x^2 - 6x - 7)) dx

[ocean seal]

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[stark yew]

wunderbar : D

[stark yew]

perfekt !

let's tackle the remaining one now

[alpine valve]

o there's 2 more lol

[stark yew]

: |

aaanyway

[alpine valve]

is okkk u don't have to help me

[stark yew]

$$ \int \left( \frac{1}{x+2} + \frac{2}{x-1} + \frac{4}{(x-1)^2}\right) , dx $$

[ocean seal]

waris

[alpine valve]

eh?

[stark yew]

this is simple enough to evaluate now ..

[alpine valve]

which is this one

[stark yew]

the one i replied to

[alpine valve]

oh that was notes

that one is finished already

[stark yew]

oh

well send the other two integrals

it's 4am and i've already opened my notebook : |

[alpine valve]

okok

3 more actually

[stark yew]

: |

very well

bring em on !

[alpine valve]

I haven't started yet

[stark yew]

the first one should be simple enough

[alpine valve]

yes

[stark yew]

or maybe not : |

okay yea it's simple

[alpine valve]

im working it rn

[stark yew]

me too

[alpine valve]

b=-1

a=5?

[stark yew]

$$ \int \left( \frac{5}{x+3} - \frac{1}{x+1} \right) , dx $$

[ocean seal]

waris

[stark yew]

which evaluates to
$$ 5\ln \mid x+3 \mid - \ln \mid x+1 \mid + C$$

[ocean seal]

waris

[stark yew]

i don't like the look of the second one

[alpine valve]

yes that's what I got too

[stark yew]

the second one becomes
$$ \int \left( \frac{1}u - \frac{1}{u-1} \right) , du $$
where $u = \cos x$

[ocean seal]

waris

[alpine valve]

wait why

[stark yew]

u = cos x
du = -sin x dx

[alpine valve]

do I need partial fraction

[stark yew]

then $$ \frac{\sin x}{\cos x(\cos x - 1)} = \frac{-1}{u(u-1)} $$

[ocean seal]

waris

[stark yew]

^ now you do

[alpine valve]

couldn't I do it without putting them as u first

[stark yew]

of course, but life would be a little harder that way

[stark yew]

so now
$$ \frac{-1}{u(u-1)} = \frac{1}u - \frac{1}{u-1} $$

[ocean seal]

waris

[stark yew]

integrating which and substituting $u = \cos x$ then gives
$$\int \frac{\sin x}{\cos x(\cos x - 1)} = \ln \mid \cos x \mid - \ln \mid \cos x - 1\mid + C $$

[ocean seal]

waris

[stark yew]

i don't know about you but i think the result is quite beautiful

ready for the third one?

c'mon! it's past four and i really wanna sleep

[alpine valve]

sorryy

yeah

[stark yew]

so for the third one ..

if the degree of the numerator is greater than the degree of the denominator, you perform long division and then decompose the obtained fraction into partial fractions

performing long division on $\frac{x^3}{x^2-1}$ gives
$$ x + \frac{x}{x^2-1} $$

[ocean seal]

waris

[alpine valve]

wait

I think I messed up on second one somewhere

sorry

uh

would the b value be sin1

[alpine valve]

I'm sorry

[stark yew]

wdym?

[alpine valve]

sorry I'm struggling

[stark yew]

$u = \cos x$\newline
$du = -\sin x , dx$

[ocean seal]

waris

[stark yew]

<@&268886789983436800>

[alpine valve]

why find du tho?

[stark yew]

you can't integrate with respect to u if you have dx

you must convert dx to something in terms of du in order to be able to integrate wrt u

[alpine valve]

but partial fraction

[stark yew]

what about it?

the catch is that you can't have two variables; you must convert all expressions into expressions of a single variable

[alpine valve]

like if it's sinx/u(u-1) can't I just

[stark yew]

so you must have either u or x. you can't have both.

[alpine valve]

separate

OHHHHH

I forgot sinx has x

🗿

[alpine valve]

sorry sorry

wait so

[stark yew]

$u = \cos x$\newline
$du = -\sin x, dx \implies dx = -\frac{du}{\sin x}$

[ocean seal]

waris

[alpine valve]

so it's like doing u sub

without integrating

[stark yew]

i'm not sure what you mean

[alpine valve]

it's ok I think I got it

-sinxdx cancel out dx and the numerator

[stark yew]

$\frac{\sin x}{\cos x(\cos x -1)} , dx \newline = - \frac{\sin x}{\cos x(\cos x -1)} \frac{du}{\sin x} \newline = - \frac{1}{\cos x (\cos x - 1)} du \newline = - \frac{du}{u(u-1)}$

[alpine valve]

👍

and then do partial fraction

[ocean seal]

waris

[stark yew]

indeed

[alpine valve]

and u=0, 1

[stark yew]

precisely

[alpine valve]

a=1, b=-1

[stark yew]

yes

[alpine valve]

would I plug u in again

after integrating

[stark yew]

at the end, yes

[alpine valve]

okok I got it

sorry took me forever

[stark yew]

ready for the third one?

[alpine valve]

yes

[stark yew]

alright !

if the degree of the numerator is greater than the degree of the denominator, you perform long division and then decompose the obtained fraction into partial fractions

you know how to perform a polynomial long division, yes? @alpine valve

[alpine valve]

kinda forgot

💀

[stark yew]

time for a refresher then

watch this video and ping me when you're done: https://youtu.be/Ns8pa77f91M

waits

[alpine valve]

,rotate

[alpine valve]

like this?

[stark yew]

indeed !

[alpine valve]

okok

[stark yew]

this is what it'd become as a result of the long division

[alpine valve]

yes

[stark yew]

so far so good?

[alpine valve]

yup

wait

could I separate

[stark yew]

time to decompose the second term into partial fractions

[alpine valve]

like

int(xdx) + int((x)/(x^2 - 1)dx)

[stark yew]

yes

[alpine valve]

RLY

[stark yew]

yes

[alpine valve]

yay

[stark yew]

because $\frac{x^3}{x^2-1} = x + \frac{x}{x^2-1}$

they're equal

[alpine valve]

yes yes

[ocean seal]

waris

[alpine valve]

but

nvm

[stark yew]

ergo, integrating one is equivalent to integrating the other

after partial fraction decomposition, the whole thing would become
$$ x + \frac{0.5}{x+1} + \frac{0.5}{x-1} $$

[alpine valve]

I think I understand

[ocean seal]

waris

[stark yew]

go ahead, integrate !

are you done yet?

[alpine valve]

[stark yew]

das ist richtig !

well done !

now i'll go sleep

[alpine valve]

thank u sm

I rly rly appreciate it

[stark yew]

Please close the channel with .close if your question has been resolved.

[alpine valve]

good night

.close

[lone heart]

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[deep hollow]

Oh

[grizzled saffron]

I'm a first year engineering student, straight out of alevels, fresh
Can you please explain in a way i understand

Thank you

[marsh rapids]

Q1) this is a property called the linearity of the integral

$\int \sum a_i f_i(x) dx = \sum a_i \int f_i(x) dx$

[ocean seal]

Bezier

[marsh rapids]

as you said, when things are finite it works well. Infinite sums get tricky and then you need more complicated theorems

[marsh rapids]

Q2) what about n=r ? Do you still have 0 ?

[grizzled saffron]

If n=r then that big expression which i equated to zero is undefined

[marsh rapids]

so compute it differently, so that it is defined

[grizzled saffron]

OHH okay okay
How do you assume i approach this? You can give me a hint and I'll try to figure it out on my own

[marsh rapids]

compute that special case differently, going back to the last step where you didn't do anything illegal for n=r

[grizzled saffron]

So upto here it's fine right

[marsh rapids]

except when n = r

don't you dare divide by 0

[grizzled saffron]

Okay so basically even the fraction at the top would be illegal

I'm correct upto here then

[marsh rapids]

hence you find the last line where you can plug in n = r and see what it becomes in that case

[grizzled saffron]

Okay so the way i computed the integral is wrong?
Okay I'm super confused now sorry😭

because n=r is gonna be an issue as soon as i take that integral

[marsh rapids]

you can split the sum into two different computations

a sum for r in {0, ..., 2n} \ {n} and a "sum" over {n}

[grizzled saffron]

A sum for r and a sum over n..
could u write it in latex

okok
I'll figure it out

[marsh rapids]

$\sum_{r=0}^{n-1} a_r + \sum_{r=n+1}^{2n} a_r + a_n$

[ocean seal]

Bezier

[grizzled saffron]

okay
Thank youu
That makes a lot of sense

[marsh rapids]

a sum of 0s and a special term

[marsh rapids]

at some point you'll get familiar with summing over sets, rather than just ranges

[lone heart]

@grizzled saffron Has your question been resolved?

[grizzled saffron]

Alright this is awesome

I'm at the very end now
How do i remove the r in (2n,r) cuz I'm assuming I'd have to give the answer all in terms of n

[round geyser]

i dont think you can take the (2n C r) out of the sum

r is being incremented in the sum, so (2n C r) isnt a constant

[grizzled saffron]

Oh okay
How do u suppose i use that final expression to calculate, say F(3)

What's r going to be

[round geyser]

r goes from 0 to 6

[grizzled saffron]

OOOOO

[marsh rapids]

2nCr doesn't leave the sum, so you end up with ||2nCn pi / 4^n||

[grizzled saffron]

OHHHHHHHHHH

I UNDERSTAND

Damn

You're smart

Thanks

Wow, maths really is brainfood
I love it

.close

[lone heart]

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[clever harness]

how do i get the equation for f here?

to do the integral

[sharp gate]

You can’t

It doesn’t give you the equation

[clever harness]

so what do i do??

[sharp gate]

You gotta use process of elimination. There are some options you can immediately eliminate

[clever harness]

ye i can eliminate c d e

[junior vigil]

Mean Value Theorem

[clever harness]

but there has to be a way to actually do this problem other than process of elimination

[junior vigil]

that is all I will say

:)

and note the question is asking about average rate of change not average value

[clever harness]

oh i just noticed that

so i dont have to do any type of integration in this problem?

[sharp gate]

No like I said you use process of elimination

There is no function to integrate

It’s out of a and b. I’d draw a line from (-2,f(-2)) and (4,f(4)) , and then draw tangent lines to points A and B to see which it is

[clever harness]

ah yea i see

i got it

it was B

.close

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[cyan void]

Why is variable moved to the left in this equation

[barren portal]

what is the orginal problem?

solve 45x=-675? or

where did you begin? 375=45x-300?

[cyan void]

75x + 375 = 120x - 300

That was originally problem

Than I get down to 375=45x-300 but I don’t understand why variable goes left

[barren portal]

@cyan void

375=45x-300, This is what you have

now your goal is to make x as the subject

add 300 both sides?

[barren portal]

the above step is wrong, you will get 45x= 675 not 45x = -675

[cyan void]

Oh thanks

I understand now

[lone heart]

@cyan void Has your question been resolved?

[lone heart]

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[undone hornet]

Not sure if my proof is right

[undone hornet]

I think its good

but I am not sure

this is the one to one proof

<@&286206848099549185>

[lone heart]

@undone hornet Has your question been resolved?

[undone hornet]

.close

[lone heart]

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[heady creek]

sum of the first 5 numbers: 1/81, 1/54, 1/36....

[lone heart]

@heady creek Has your question been resolved?

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@heady creek Has your question been resolved?

[heady creek]

.close

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[junior warren]

could anyone help me figure out how to do this question

im not sure how to use the expected value here

i know that for each r E(x) is the r'th derivative evaluated at 0 (which i assume is the coefficient) but not entirely sure how to use that here

[soft ruin]

P(X=0)=0.15,P(X=1)=0.85

[junior warren]

could you explain the P(X=0)

i got the X=1

[soft ruin]

it can only be 0 and 1

so 1-0.85 is what you want

[junior warren]

oh it can only be 0 and 1?

but isnt r infinite

oh i guess it just defined it as the two

[soft ruin]

the generating function have hinted you that

[junior warren]

so then i assume that means the coefficient in front of e^0t is also 0.15?

[soft ruin]

correct

[junior warren]

ok i see

makes sense

thanks

.close

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[shut crest]

Do I know you

[lusty hearth]

3 is the product of the second number of both binomials

[shut crest]

Bro

[lusty hearth]

so u see how it has 5x^2

[shut crest]

Why was I pinged

Unless Ik you

[lusty hearth]

that comes from multiplying 5x and x

you can do the same thing with 3

so 3 is equal to 3 times what

so square is 1

for a at least

you know FOIL right?

[shut crest]

I ain’t forget this

[lusty hearth]

so since you have (5x+1)(x+3) now foil it to get the middle number

ye

thats good

[lone heart]

@fickle vigil Has your question been resolved?

[lone heart]

@fickle vigil Has your question been resolved?

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[languid bolt]

don't occupy multiple channels, close one of them.

[alpine sable]

.close

[lone heart]

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[acoustic geyser]

Sorry I couldn’t find the other channel so I thought it closed automatically

[lone heart]

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[forest glacier]

how to differentiate $\sqrt{x-1}$

[ocean seal]

N1x1T4

[languid bolt]

sqrt(x - 1) = (x - 1)^1/2

and chain rule it

[lone heart]

@forest glacier Has your question been resolved?

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[native cloud]

Hello

[native cloud]

What does A, A^2, A^3 mean here?

[lone heart]

@native cloud Has your question been resolved?

[native cloud]

.close

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[mint cosmos]

I don't understand what i'm doing wrong

[vale wigeon]

show your work

[mint cosmos]

ye just a se c

[vale wigeon]

you've gone haywire in general + i don't see where the 3x and -4 terms actually even come into play...

[mint cosmos]

oh

[vale wigeon]

why kx^2-4x^2 instead of (k-4)x^2? why keep them as two separate terms and set yourself up for this confusion???

[mint cosmos]

but how would you minus through a bracket

[vale wigeon]

as your next step you would bring down the 3x to get (k-4)x^2 + 3x

then subtract from it (k-4)x^2 + (2k-8)x

get 3x + (8-2k)x which simplifies to (11-2k)x

[mint cosmos]

ok ty, it works out now because i forgot to add the 3x - 4

[mint cosmos]

though still don't quite understand this

so

[vale wigeon]

3x + (8-2k)x = (3 + 8 - 2k)x

[mint cosmos]

ah so you're saying this would be easier to work with

okk

ty

[vale wigeon]

yes

[mint cosmos]

.close

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[spice mantle]

hello

[spice mantle]

I have a question about linear transformation

[vale wigeon]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[spice mantle]

translate: The matrix T: ℝ3 → ℝ2 given by T(x, y, z) = (x + y, x + z), with respect to the bases A = {(1, 0, 0), (0, 1, 0) , (0, 0, 1)} and B = {(1, 1), (0, 1)}, will be of order 2x3 and will have the elements:

How can I calculate this?

[vale wigeon]

ok so this is about finding the matrix of a linear map

do you know how to do that in general?

[spice mantle]

No, my classes are not very good!

but I know how to do the transformation I just don't know how to find the matrix

[vale wigeon]

well ok

so the idea behind matrices is that to know what a linear map does, you only need to know what it does to a basis

and here that's the input basis, A

so can you work out T(1,0,0), T(0,1,0) and T(0,0,1) for me?

[spice mantle]

yes! 1 second

T(1,0,0) = (1,1)

T(0,1,0) = (1,0)

T(0,0,1) = (0,1)

[spice mantle]

here

[vale wigeon]

yeah ok so

now put these as columns into a matrix

in the same order

[spice mantle]

[11]
[10]
[01]

like this?

[vale wigeon]

no

you put them as rows, i told you to put them as columns

also, separate the entries with spaces

otherwise 2 ones can't be told apart from an eleven

[spice mantle]

okay

[ 1 1 ] [ 1 0] [ 0 1]

like this?

[vale wigeon]

no...

write it on paper

[spice mantle]

okay

[spice mantle]

like this?

[vale wigeon]

yes

[spice mantle]

🥹

[spice mantle]

how did 1 become -1 ?

[spice mantle]

here

[vale wigeon]

what

oh

oh fuck sorry

i didn't see

[spice mantle]

[vale wigeon]

i thought B was also the standard basis

i misread

this means you will need to express all these values of T in terms of B, and the columns will be the coordinates in that basis.

[spice mantle]

how i can make this?

[vale wigeon]

T(1,0,0) = (1,1) = 1 (1,1) + 0 (0,1) so the first col is (1, 0)

T(0,1,0) = (1, 0) = (1,1) - (0,1) = 1 (1,1) + -1 (0,1)

[spice mantle]

why? (1,1) - (0,1) ?

[vale wigeon]

yes

[spice mantle]

why do you subtract?

[vale wigeon]

i am expressing the vector (1,0) in the basis B

[spice mantle]

Could you explain this account in more detail?
where did you get that -1 from?

[vale wigeon]

subtracting something means adding it with a -1 coefficient

a - b = a + (-b) = a + (-1)*b

[spice mantle]

How did you know to put the -1 there?

[lone heart]

@spice mantle Has your question been resolved?

[vale wigeon]

idk what else to tell you sorry

[spice mantle]

okay, thank you for try help me : )

[lone heart]

@spice mantle Has your question been resolved?

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[obsidian shell]

How do I remove the inside area of the triangular prism using double integrals, thanks for the help

[obsidian shell]

i can list all of the values used in desmos

z=-0.00000964821x^{4}+0.00215211x^{3}-0.152445x^{2}+3.96793x+0.381383 {-0.50010827695276y+60.968<z<120}{0<y<121.9096}
{triangle}((0,121.9096,0),(0,0,60.968),(0,121.9096,60.968))
z=-0.50010827695276y+60.968{0<x<120}{0<y<121,9096}
y=121.9096{0<x<120}{0<z<60.968}

[lone heart]

@obsidian shell Has your question been resolved?

[obsidian shell]

<@&286206848099549185>

<@&286206848099549185> please

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@obsidian shell Has your question been resolved?

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[covert island]

hello

[covert island]

i need help is this question solving part-

It x/a + y/b = a ^ 2 + b ^ 2 and x/(a ^ 2) + y/(b ^ 2) = a + b , then x is equal to ?

Options are 1) a 2) a² 3) a³ 4)a⁴

im in 10th grade Studying in SSC board in India so pls provide solution according to my understanding

It's probably better if I provide it's pic

[latent jolt]

try to put x = a

then x = a ² , ...

we have the answer easily by replacing but this is certainly not the right method

[covert island]

i dont understand

can u show me the steps to the solution so i can understand?

[lone heart]

@covert island Has your question been resolved?

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[green magnet]

what is this:

[worn fox]

https://www.cuemath.com/n-choose-k-formula/

[green magnet]

Combinatorics?

[worn fox]

?

[vale wigeon]

it is a combinatorics thing, yeah

(most likely)

but the name is "choose" or "combinations"

[green magnet]

i see

so this is like 17C2?

[vale wigeon]

yes

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[alpine sable]

u can use graph

[pale kestrel]

dont calculators come with manuals

if not, there will be an online one if you lookup your model name

[alpine sable]

u just look for intersections

[vale wigeon]

read the manual for your calculator.

[vapid steppe]

graph the two sides of the equation and look for where they intersect

[vale wigeon]

google, usually.

or you could take a picture of your calculator and we could tell you the model number.

bc you need that

[lone heart]

@alpine sable Has your question been resolved?

[ocean whale]

If this is your calculator, look up the manual for that calculator

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[rotund crater]

why this search reference angle if not is necessary?

[ocean whale]

Because I'm assuming the mini table gives the values in the first quadrant

So you would find the reference angle, and use the table

[gray isle]

its useful if you can't remember the full unit circle

if you know your unit circle, you can jump to the end result without having to go through that work

[rotund crater]

thx

.close

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[gray jetty]

I am extremely confused on how to do this proof

[gray jetty]

ive been trying for a while

@alpine sable this is taken

[alpine sable]

\let\l\lambda so you have [
(-1)^n (\l -\l_1)(\l -\l_2)\dots(\l-\l_n)
]

[alpine sable]

is this ok with u

[gray jetty]

yeah i saw that on the internet, but i dont understand that step

sorry if im being stupid,

why cam you factor out the -1

[vale crag]

you take out -1 from each factor

and there's n factors

[alpine sable]

i mean why not, you take it out from each one of them

[vale crag]

idk where you're going with that tbf

I don't even see what they leave you to prove in this question, they literally explain everything

[gray jetty]

i mean i dont know

i still didnt get it

so

[gray jetty]

is the next step to distribute the -1

[hallow cargo]

hi

i needed help with 1 question

[vale crag]

god why is everybody coming here

[vale crag]

#❓how-to-get-help

this channel is already occupied

[hallow cargo]

it says help0 is my channel

so sorry about that

[vale crag]

yeah it's just an example picture

otherwise everybody would have the 0 channel

[vale crag]

what don't you get then ?

[gray jetty]

legitimately i do not get any o fthe hint

[vale crag]

det(A - lambda I) is a polyomial in lambda, fine with that ?

[gray jetty]

yes

like that comes from the expansion of the characteristic polynomial right

[alpine sable]

\let\l\lambda
yeah sorry left for a bit, but [
\m\det{A-\l I} = (-1)^n(\l -\l_1)(\l -\l_2)\dots(\l-\l_n)
]
which can be obtained by expanding the determinant along the diagonal from the permutation definition of det. Now like u said, you can distribute in the sign for each of the terms

afterwards, i think it should be pretty clear no?

[gray jetty]

no im sorry, im genuinely still confued

confused*

[alpine sable]

you can substitute in lambda = 0 and just simplify

[vale crag]

I'm also confused by this question to be fair

[gray jetty]

idk ik the hint should help, i went to tutoring too for this class and my tutor couldnt really help me

[gray jetty]

then you get like

youre just multiplying lambdas ? fter that?

[alpine sable]

yeah and u get get det(A) = lambda1...

its just that i think there is nothing else thats fancy unless im mistaken

[gray jetty]

just like this?

[alpine sable]

ok u mada lambda =0 but why is it still there inside the det

but yeah that should really be it

[gray jetty]

oh yeah right

[alpine sable]

i feel like this was less about u not knowing what to do and more so you overcomplicating it by thinking it would be something much more insane

[gray jetty]

yes

I mean like i dont know why this would be something i had to prove if all i had to do was expand the problem and substitute a 0

[vale crag]

¯_(ツ)_/¯

[alpine sable]

yeah like they really just gave it all to you in their hint haha

it's just that all the text jargon bloat made you think it's much harder subconsciously

[gray jetty]

in my life i. never thought id have this many problems with linear algebra

can i ask more qs

[alpine sable]

it's advised to open a new channel after finishing the original question (in the eyes of a subset of the helpers here)

[gray jetty]

like close then reopen?

[alpine sable]

edited

[gray jetty]

ok ty

.close

[lone heart]

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[junior relic]

Can someone pls help me with number 16

[toxic estuary]

We can proof ABC and ADB similar and AA criteria

Angle b and d are rights so they are equal (given)

Angle a is common

We know that sides of similar tri are in same ratio

So ab/ac==ad/ab

ab^2 == ac.ad or x^2==pz

Other 2 can be solved using same steps but for bc dc

[lone heart]

@junior relic Has your question been resolved?

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[inland marsh]

Is this true?

[inland marsh]

$if (x=y/z), then (z=y/x)$

[ocean seal]

Villiam

[stark crater]

Consider x=0

[prime badge]

unless x=0, yes

[inland marsh]

So, this is true unless x and/or z is 0?

[prime badge]

yes

[inland marsh]

aight thanks

.close

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[lone heart]

@finite vigil Has your question been resolved?

[lone heart]

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[uncut rapids]

Hello, I've to find the value of

[uncut rapids]

I tried to split with ln property

I tried to split again
-666 -> 666 : -666 -> 0 / 0 -> 666

I'm not sure of what i'm doing

[tacit arch]

is that an odd function

[uncut rapids]

Yes

wait uh

[tacit arch]

,w is log[(1+exp(arctan(x)))/(1+exp(-arctan(x)))] an odd function

[ocean seal]

Results provided by WolframAlpha

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

Requested by rie.mann

[uncut rapids]

yes

It's an odd

ff :c

[tacit arch]

,calc log((1+exp(atan(1.23)))/(1+exp(-atan(1.23))))

[uncut rapids]

I tried to compute some points

and it works

[ocean seal]

Result:

0.88817377437768

[tacit arch]

,calc log((1+exp(atan(-1.23)))/(1+exp(-atan(-1.23))))

[ocean seal]

Result:

-0.88817377437768

[tacit arch]

yea i think wolfie's wrong here

but you should prove it algebraically

[tacit arch]

did you here?

[uncut rapids]

Wdym

[tacit arch]

prove the function is odd using algebra

f(-x) = -f(x)

for all x

[uncut rapids]

Oh no I jsut checked it on wolfram alpha

So I've to prove it ?

[tacit arch]

you should yes

[uncut rapids]

ABout the property of odd functions on integrals

[tacit arch]

that too yes

but you need to show the integrand is odd to apply it

[uncut rapids]

It means that

Minus on the right side ?

I checked by myself

Thanks for your help

.close

[lone heart]

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[thick night]

I need help with the algorithm or how to find the shape of a polygon based on radius information. I have a piece of hardware that gives me 1000 points of radius for a shape and I want to draw that shape in a program

[mortal trellis]

is radius the correct word you want to use here?

[thick night]

yes. It's a shape tracing device that gives out the radius from the center of the shape in hundreths of a mm

so I have the radius from the center, 1000 times in a pattern from bottom around in a circle

[full canopy]

Sounds like polar would work really well here

Is it based on radius angle or does the program give x y coords?

[thick night]

its single number per read spot. I wish it was x,y because then I could do that with logic

the output I'm working with is just semicolon separated numbers in hundreths of a mm

[full canopy]

So what do those numbers represent? Radial lengths?

[thick night]

yes

[prime badge]

yeah just convert from polar

[full canopy]

You would need to know the angle of these points, is it safe to assume that the machine simply moves by 1/1000 rotation as it calculates the lengths?

[thick night]

yes, and it starts at 90º down from the center

it moves left from there

[full canopy]

Yeah polar here for sure

[thick night]

so I'm trying to read what polar is, but I will admit I am terrible when it comes to math so I'm not understanding it straight away

[prime badge]

for each number, x = radius × cos(1.5pi − (n*pi)/500)

[full canopy]

y = radius x sin(same angle)

[prime badge]

n is which number it is

[thick night]

ok and the sin/cos would be based off the angle and that would start at 90 and work slowly up? or does that formula calculate the angle in it?

my working knowledge of angles is still at SOHCAHTOA levels. not helpless but not strong

[full canopy]

That formula has the angle in it

[thick night]

ok

so I'll try to plug those in and loop through my input and see if I undertstood it properly

very much appreciated

[full canopy]

Yessir

[thick night]

what get's put into (same angle)

it's the stuff in the paranthesis above, I think I understand that part better the more I look at it

.close

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[vale wolf]

hiya, I'm currently working on part B but I don't really understand why the answer for x from cosine has 2 values, 39.2 and 140.8. I got 39.2 from cos^-1(1/5) but I can't find 140.8. Thank you so much.

[subtle birch]

$\cos\left(2x\right)=2\cos^{2}x-1$

[ocean seal]

B-eard

[subtle birch]

$\cos\left(\pi-x\right)=-\cos\left(x\right)$

[ocean seal]

B-eard

[vale wolf]

so do i not do inverse cos?

[lone heart]

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[thin hull]

You forgot about symmetries. The range of $cos^{-1}$ is $[0, \pi)$. However, what is your domain for 2x?

[ocean seal]

chencking

[thin hull]

.close

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[desert cairn]

An amount of chlorine is added to a swimming pool that contains pure water. The concentration of chlorine, c, in the pool at t hours is given by
c(t) = 2t/2+ t where c is measured in milligrams per litre. What happens to the concentration of chlorine in the pool during the 3rd hour

[tacit arch]

!status

[lone heart]

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

[desert cairn]

1

[tacit arch]

c(t) = concentration of chlorine

where t is hours

the question asks for the 3rd hour

[lone heart]

@desert cairn Has your question been resolved?

[desert cairn]

No

[lone heart]

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as this action is irreversible, and this channel may abruptly lock.

[lone heart]

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[small breach]

Hi ive just finished my personal statement, can anyone take a look at it

[tacit arch]

sir this is a wendys

[worn fox]

Not the purpose of these channels, try #discussion

[obtuse needle]

Hi guys, can someone help me with this question? It's on Map scale and ratio which this question includes dimensions so here is the question :

The scale of a map is 1:1000. What are the actual dimensions of a rectangle which appears as 4cm by 3cm on the map? What is the area on the map in cm^2? What is the actual area in m^2? <@&286206848099549185>

[tacit arch]

!15m

[lone heart]

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

[obtuse needle]

I don't think so man 💀

[tacit arch]

what part of that is confusing

[obtuse needle]

I mean I have half of the answer but I am confused for real

I don't have the final answer

Nor I am understanding the workout

[worn fox]

Not your channel btw

[obtuse needle]

Which channel do I go to 💀

[worn fox]

Math help available

[lone heart]

@small breach Has your question been resolved?

[worn fox]

.close

[lone heart]

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[worn fox]

OP went to discussion

[lone heart]

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[dawn quail]

Do I understand this correctly?

[ivory pivot]

yes

[worn fox]

If by any size you mean you can dot any two vectors of the same size then yes

[ivory pivot]

wdym with 3x3?

[worn fox]

Cross product is only defined in 3 dimensions (atleast at this level)

[ivory pivot]

ohh

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[lusty sigil]

How to differentiate 2^lnx ?

[tacit arch]

,tex .log rules

[ocean seal]

riemann

[tacit arch]

oh wait

[lusty sigil]

Why use log?

[tacit arch]

use $a^b = e^{b \ln(a)}$

[ocean seal]

riemann

[lusty sigil]

Is that a rule?

“So i can write it in my notes”

[tacit arch]

it follows from $e^{\ln(x)} = x$ for all $x>0$

[ocean seal]

riemann

[tacit arch]

and power rule here

[lusty sigil]

Ok i know this

[lusty sigil]

But this doesnt make sense?

[tacit arch]

why

[tacit arch]

did you see power rule here?

[strange meadow]

Yes it does e^x is the inverse of ln

[lusty sigil]

Yesss

[lusty sigil]

I knowwww

Ok ill memorize it

OK I GOT IT THANKS

[tardy stag]

$a^b = \lp e^{\ln(a)}\rp^b = e^{\ln(a)\cdot b} = e^{b\ln(a)}$

[ocean seal]

Haylsune Miku

[lusty sigil]

Thank uuuuuu

[desert cairn]

An amount of chlorine is added to a swimming pool that contains pure water. The concentration of chlorine, c, in the pool at t hours is given by c(t) = 2t/2+ t where c is measured in milligrams per litre. What happens to the concentration of chlorine in the pool during the 3rd hour

[tacit arch]

you need to stop spamming everywhere

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[wispy trellis]

I have a question regarding limits to infinity. How do I know when to divide out vs. l'hopital's rule?

[wispy trellis]

I know that l'hopital's rule only applies to indeterminate forms like inf/inf or 0/0 but I've seen problems where this is the case and using l'hopital's rule results in an invalid solution

[tardy stag]

that should be valid

do you have an example?

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[clever harness]

can i get some help with this

[clever harness]

farthest ive gotten is 1/p*dp/dt=k

idk where to go from here

where does the s come from here?

and also how did they get the lnP(t)-lnP(t0) on the left

shouldnt it be dt at the end of each integral?

did they change it to s to avoid confusion with the bounds?

[vale crag]

yes exactly

it's just to not reuse t

[clever harness]

ah ok

what about the ln on the left?

and i think i kind of understand how they got the bounds but could you explain it to me

[vale crag]

you have a chain rule opportunity inside the integral

P**'** * 1/P

that looks a whole lot like the derivative of ln(P)

or just do a u-sub if you know about it

[clever harness]

i dont understand

[vale crag]

you should prolly revise your integration skills a little bit then

it's the bread and butter of differential equations

shows up all the time

[rose pasture]

for this question in particular, where you have to calculate some value and not prove things, i think it suffices to use the known statement:

$$y'=ky\Leftrightarrow y=c\cdot \text{e}^{kx}$$

[ocean seal]

Ab

[clever harness]

yea i know that equation

[rose pasture]

then do some stuff with the bacteria doubling every 24 hours to find the constants

[clever harness]

also i understand what you did here i think

[rose pasture]

well the equation $dP/dt = kP$ looks similar, no? if you are (already) aware...

[clever harness]

yes but i need to solve for k

[ocean seal]

Ab

[rose pasture]

well since you want your value to double, maybe trying to convert the base to 2 is a good idea?

try doing that. then you might need to think about that it doubles every 24 hour

[clever harness]

how did they get the bounds

[clever harness]

idk what you mean with this

[rose pasture]

these two things might be handy $\text{e}=2^{\log_2(e)}$. and $(a^b)^x=a^{bx}$.

[clever harness]

what is exp here?

[rose pasture]

oh that's the proof... exp is just the exponential function, i.e. taking e to the power of the value

[ocean seal]

Ab

[rose pasture]

... i need some sleep. i am making sloppy mistakes... someone else can probably help you if you need it.

[clever harness]

all g

[clever harness]

can you help me a bit here

[tacit arch]

did you do this?

on here

[clever harness]

ye i did it the other way

not u sub

[tacit arch]

what are you stuck on then

[clever harness]

cuz i got P'/P which was ln(P) right

uhh

one sec

wait one sec

when they do this

they did it to get this right

[tacit arch]

ln(P) does not equal P' / P

[clever harness]

derivative of ln(p)

[tacit arch]

oh

then yes

[clever harness]

ye

[tacit arch]

what is "did it" mean

[clever harness]

multiply by P(t0)

[tacit arch]

to get from the top to the bottom, they multiplied by P(t0)

[clever harness]

oh yea mb

thats what i meant

but my question is why did they do that

[tacit arch]

to solve for P(t)

[clever harness]

but the question is asking for k

[tacit arch]

yes

getting P(t) doesn't mean you're done. you use the remaining information to solve for k

[clever harness]

how did they get the 24k here

e^24k

[clever harness]

^

[tacit arch]

doubles means multiplying by 2

t0 + 24 means 24 hours after t0

[clever harness]

yea

i still dont know where the e^24k came from

[tacit arch]

they plugged in t = t0 + 24

[tacit arch]

show the entire solution you have. are you skipping steps?

[tacit arch]

yea you gotta read every line

[clever harness]

alr i got it now

.close

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[crimson quail]

how do you do 12 o and p?

[tawdry urchin]

what is 6 in terms of 2 and 3 and 5

[crimson quail]

2^2 + 2

how do i apply the ^-3

is the answer
(2^2+2)^-3

?

[tawdry urchin]

can you multiply two numbers to get 6?

[crimson quail]

oh shoot

2x3

[tawdry urchin]

ayo no cussin

[crimson quail]

oh fr

mb

[tawdry urchin]

lol bro acc changed it

[crimson quail]

wait so whats the answer

is it 1/(2x3)^3

[tawdry urchin]

yeah

[crimson quail]

okay thanks

[tawdry urchin]

can you do p

[crimson quail]

lemme try

bc before i was sticking with1 number for some reaosn

2^2 x (2x5)^2

?

[tawdry urchin]

i would combine further

2^4 * 5^2

but yeah

gj

[crimson quail]

oh yeah

after u exapnd it

thanks man

.close

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[alpine sable]

Hi!; I need to do this by hand but I don't know how to do the process and I'm a bit stuck, I have a quiz tomorrow

[ocean whale]

Having 37, 53, 16, and 74 degrees in a unit circle chart is wild

That's the first time I've seen something like that

But you should know 45, 30, and 60 since those are actually the common ones you use

[alpine sable]

It's actually a example, my square is 0 degrees to 315 degrees

[alpine sable]

I don't know how to do the process by hand

[ocean whale]

What exactly does it look like?

[alpine sable]

Let me show you

This is a partner's work, I'm trying to understand and do it by myself

@ocean whale

[ocean whale]

So what exactly are you having trouble with?

[alpine sable]

I don't know how to find the sen cos etc of each degree like the way my partner did, since I didn't assist that class

And I don't understand it

[ocean whale]

https://www.youtube.com/watch?v=57VrEiEPD1I&ab_channel=TheOrganicChemistryTutor
Up to like the 7:30 is useful

[alpine sable]

Thank you

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@alpine sable Has your question been resolved?

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[olive oar]

How do I do (a), I have this sketch of E

[olive oar]

this is my attempt

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@olive oar Has your question been resolved?

[olive oar]

<@&286206848099549185>

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[rugged bough]

can anyone help me with my algebra 1 homewokr

[rugged bough]

i dont get this at all

and im struggling

so

its only 12 questions

[remote heron]

you should ask one at a time

if possible

[rugged bough]

okat thats fine take ur time

i just dont get this at all

ignore my answers that i put there

their all wrong

😭

[remote heron]

? they dont look wrong

only the last one

[rugged bough]

what would the last one be then

[remote heron]

none of those look right

[rugged bough]

thats whqat im sayingg

[remote heron]

I guess if you had to say itd be never negative

I guess they are saying like

okay this functions models the height

[remote heron]

we are choosing that height cant be negative

[rugged bough]

it worked

[remote heron]

because it doesnt make sense

[rugged bough]

thank you

[remote heron]

np

[rugged bough]

can you help me with the rest?

[remote heron]

my suggestion although this sounds crazy is to close this channel then open a new channel with the new question

itll make it easier for people to help you