help-38

[odd onyx]

find the derivative of that

[solid kiln]

Combustion

[frank merlin]

okay so simplify that first and then take the derivative

[jaunty scarab]

well, i'd start by going that ln(t^2)dt = 2ln|t|dt

[frank merlin]

yess that was my first step. so i just take the antiderivative and simplify it and then take the derivative?

[jaunty scarab]

i...guess...?

[frank merlin]

i got 2ln(e^x^2)-2ln(1) = 2x^2 -0 =4x..

what did i do wrong

its supossed to be 4x^3e^x^2

[odd onyx]

F is not equal to ln(t^2)

[frank merlin]

x ln x -x

[odd onyx]

$\int_{1}^{e^{x^{2}}}\ln\left(t^{2}\right)dt=F\left(e^{x^{2}}\right)-F\left(1\right) right?$

[solid kiln]

Combustion

[odd onyx]

take the derivative of that

[frank merlin]

i get 2x/e^^2 -1

[odd onyx]

??

$F\left(e^{x^{2}}\right)-F\left(1\right)$

[frank merlin]

derivative of ln is 1lx

[solid kiln]

Combustion

[frank merlin]

1/x

[odd onyx]

we don't take the derivative of ln

[odd onyx]

we're doing this

[frank merlin]

the derivative of F is just ln(t^2)

[odd onyx]

F isn't ln

F is the anti derivative of ln(t^2)

[odd onyx]

yep!

so

also you need the chain rule

to take the derivative of that

[frank merlin]

right

[frank merlin]

What did i do wrong?

[odd onyx]

,rotate

[odd onyx]

okay

so

[frank merlin]

i got 4x/e^x^2

[odd onyx]

$\frac{d}{dx}\left(F\left(e^{x^{2}}\right)-F\left(1\right)\right)\ $ isn't equal to $f\left(e^{x^{2}}\right)$

[solid kiln]

Combustion

[frank merlin]

but ln(1^2) just becomes 0

[odd onyx]

remember the chain rule $\frac{d}{dx}\left(f\left(g\left(x\right)\right)\right)=f'\left(g\left(x\right)\right)\cdot g'\left(x\right)$

[solid kiln]

Combustion

[frank merlin]

f(e^x^2)*2x

[odd onyx]

it's a constant anyways so it'll be 0 either way

[odd onyx]

yep

actually

you forgot the e^x^2

[frank merlin]

huh?

[odd onyx]

$g\left(x\right)=e^{x^{2}}\to g'\left(x\right)=2xe^{x^{2}}$

[solid kiln]

Combustion

[frank merlin]

okay i got 2xe^x^2 ln (e^x^2)

do i need to use product rule now/

?

[odd onyx]

xyz

we already differentiated

[frank merlin]

oh yeah mb brain is just not here rn

[odd onyx]

lol i feel you

[odd onyx]

by the way don't forget the other 2

[frank merlin]

which one?

[odd onyx]

remember the square exponent?

ln(t^2)

we made it 2ln(t)

[frank merlin]

oh yeah i forgot

yeah i got the right answer now. Thanks a lot!

[odd onyx]

[frank merlin]

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[abstract hazel]

I don't know where to go currently I have it set up as 2x^2(x-1)-5(x+1)

[naive dirge]

factor by grouping?

[abstract hazel]

wdym?

[naive dirge]

oh wait nvm

misread

[abstract hazel]

gotcha

[naive dirge]

probably could use a graphing calculator if allowed

[abstract hazel]

yeah I got a TI-84 but its but cheeks for this function

[naive dirge]

desmos maybe?

[abstract hazel]

true but I needa know how to solve it without desmos

<@&286206848099549185>

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@abstract hazel Has your question been resolved?

[abstract hazel]

nope

<@&286206848099549185>

[abstract hazel]

<@&286206848099549185>

[wraith hinge]

Factor by grouping

Gets you the zeros

Or use a graphing collator and it will tell u

The 0s

Then for rel minimums

Graph the function and use it to find minimums

Or derive solve for 0

And first derivative test

By hand

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[hardy beacon]

$$ \int \int y e^{xy} , dx,dy $$

[solid kiln]

vuviCa

[hardy beacon]

I did integration by parts

[edgy cedar]

is x a constant?

[hardy beacon]

yep since taking integral respec to y

[edgy cedar]

Show your work

[hardy beacon]

I am trying again

$$ \int \int y e^{xy} \ dx dy $$

This is the orginal form of my question

I take integral with respect to x

[solid kiln]

vuviCa

[wraith hinge]

Is this the whole question?

@hardy beacon ?

[hardy beacon]

Integrals are from 0 to 1 both of them

[wraith hinge]

Ok

So, you can integrate for x first

[hardy beacon]

I did u sub

[wraith hinge]

You don't need to do this

If you integrate by x

You'll get rid of the y

So you'll get effectively $e^{xy}$

[solid kiln]

Palahoo

[wraith hinge]

Did you understand?

@hardy beacon ?

[hardy beacon]

hmm

Isn't that $$ e^{xy} / y $$

[solid kiln]

vuviCa

[wraith hinge]

No, because there's an y on the left side of the e^(xy)

So them just cancel out

[hardy beacon]

hmmm

[wraith hinge]

And You get e^(xy)

[hardy beacon]

ok then I have to integrate it by dy

[wraith hinge]

Yes

$\int e^{xy} dy$

[solid kiln]

Palahoo

[wraith hinge]

$\int \frac{e^{xy}}{y}$

[solid kiln]

Palahoo

[hardy beacon]

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[covert oxide]

I tried it but was told I was incorrect

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[loud wasp]

i need to find the domain and range

[loud wasp]

i understand where the values 1/2 and 1 came from but i dont understand how you know wether it would be > or <

[cunning cairn]

if you were to say x > 1/2, try plugging that into the function, what would happen ?

lets say we chose x = 1

which is greater than 1/2

[loud wasp]

it would be negative

[cunning cairn]

(I am assuming you havent been introduced to the complex numbers yet)

[loud wasp]

and it has to posiitve

[cunning cairn]

yes so if you only work on the real numbers taking the square root of a negative number is a bit odd

you cant do it in the set of the real numbers

so our function f here can not be defined for x values smaller than 0.5

it has no defined result for such inputs

[loud wasp]

oookayy

[cunning cairn]

thats how you could think about it ig

[loud wasp]

tyyy

what about the range?

how do i know it should be >1 and not <1

[cunning cairn]

do you have a guess why its the way it is in this example ?

[loud wasp]

is it because 1 is being added?

[cunning cairn]

it plays a role

but you have to considers something else as well

what is your understanding of the range R of a function ?

[loud wasp]

all the possible y values in a graph

[cunning cairn]

yes and in context of the function its all the possible outputs of the function

so to figure out what the range is you would need to ask yourself what values the function can output. And if you take a close look at f you'll see that the smalles value is 1 , which is the case if you input x = 0.5. And for every x < 1/2 the output grows

since youll subtract less from 2 under the root and therefore have a larger value under the root making it a larger result

idk if I am missing something here but it seems liek you could limit the range as well

[loud wasp]

oh okayy

[cunning cairn]

the range should be y in [1, 1+sqrt(2) [

[loud wasp]

so it has to be >1 in this scenario

thank you so much!

[cunning cairn]

could be 1 as well

no problem

[loud wasp]

oh yes

right

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[void ice]

could someone assist me with part c please

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[void ice]

<@&286206848099549185>

so right

since f is injective then f(x) =f(y) ?

so x=y right

and g(u) = y?

since that's surjective

[void ice]

then

It’s g(u) = f(x)

?

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[whole coral]

You need to show this - you know that g comp f is bijective

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[deft crescent]

did part a

[deft crescent]

but part b is hard

i need to take the integral from point 0 to t of the original equation

correct

but how i do that is

confusing

im so fuckeddd

this is last problem

and i do NOT understand what to do from here

i dont have the slightest idea

[digital bison]

do you know how to integrate exponentials?

[deft crescent]

i mean

rieman summs i guess

could approximate

?

[digital bison]

$\int e^{kt}dt = \frac1k e^{kt}+C$

[solid kiln]

Zybikron

[deft crescent]

right yeah

so i solve for c value

[digital bison]

you have a definite integral, you don't nee dot solve for C

[deft crescent]

can you explain? what is the difference

between defineite and undefinite

i assume one is defined and one is not

what that means is not clear to me

lol

[zinc ginkgo]

https://socratic.org/questions/what-is-the-difference-between-a-definite-and-indefinite-integral

[deft crescent]

yeah

i just watched a youtube video

[zinc ginkgo]

Great

[deft crescent]

so the idea here

is to plug in my knowns

and simply evaluate my definite integral

i think

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[deft crescent]

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[manic flame]

Can someone help me with this anti derivative problem

[manic flame]

is a -2 btw

[worldly comet]

when integrating powers of x you add +1 to the exponent and divide by that new exponent value

[manic flame]

ok so 1/3 x^3

-3x

[worldly comet]

yes

then you use fundamental theorem of calculus

[manic flame]

okay now what?

f(b)-f(a)?

[worldly comet]

yes

[manic flame]

ok let me see

im left with 26/3

[worldly comet]

thats not it

[manic flame]

hmm

[worldly comet]

your f(a) is 8/3 - 3(2)

[manic flame]

well

this is what i have written down

for f(a)

[worldly comet]

oh shit thats a -2

[manic flame]

yes

[worldly comet]

I thought you meant that was the answer which I was doubting

uh lets see

[manic flame]

oh no the "a" is -2

[worldly comet]

now I got -10/3

[manic flame]

so did i get it right ?

[worldly comet]

yes, if that value you have on the prompt bar equates to -10/3 which it should

[manic flame]

wait

huh

i re did the math

can you show me the steps algebraically that you took to get 10/3

@worldly comet

[worldly comet]

1s

[manic flame]

i got 26/3

OHHHH

nvm

thank u daddy

♥️

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[manic flame]

I need help getting its definite intergrol

[nimble stone]

certainly is

try splitting the fraction

[manic flame]

splitting?

like working with the top then the bottem?

[lethal anvil]

$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$

[solid kiln]

MellowDramaLlama

[manic flame]

okay thats what I have

[nimble stone]

simplify it a bit

[manic flame]

hmmm

I have no idea it gets simpler

[nimble stone]

what is cos^2/cos^2

[manic flame]

1

[nimble stone]

what is 1/cos^2

[manic flame]

sec^2x

sec^2x+1?

[nimble stone]

bingo

[manic flame]

so i just get its anti derivite right?

[nimble stone]

yeah and evaluate

[manic flame]

soo

tanx + x

[nimble stone]

it appears to be so

[manic flame]

nice all i do now is f(b)-f(a)

right?

[nimble stone]

indeed

[manic flame]

hey quick question

so i know that i have to solve tan of pie/4

all i know is how to solve fro cos and sin tho

not tan, can you guide me

[nimble stone]

tan pi/4 should be quite memorable really

ig if you want to check it, do you know of the two trig triangles

or the unit circle

[manic flame]

yes

[nimble stone]

if you know what sin and cos are as you said, just do sin/cos

[manic flame]

pie/4 lands on the (square root of 2/2 , square root of 2/2 )

[nimble stone]

indeed

so tan=1

[manic flame]

ahhhhh

I will defenetly keep that in mind

so

the answer is 1 + Pie/4

[nimble stone]

seems so

[manic flame]

Chaaaaa dude

thanks papa

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[manic flame]

Can someone help me integrate

[manic flame]

[heavy lion]

what is 1 - sin^2x

[manic flame]

cos^x

[heavy lion]

yes

[manic flame]

sinx/cos^2x?

[heavy lion]

so now its $\int \frac{\sin x}{\cos^2 x}\dd x$

[solid kiln]

Bettim

[heavy lion]

right?

[manic flame]

yes

[heavy lion]

so

$\int \frac{\sin x}{\cos x} \times \frac{1}{\cos x} \dd x$

[manic flame]

💸

tan?

[solid kiln]

Bettim

[heavy lion]

right?

[manic flame]

oh yes

you expanded it

[heavy lion]

then $\int \tan x \sec x \dd x$

[solid kiln]

Bettim

[heavy lion]

right?

[manic flame]

ahhh

yes

[heavy lion]

thats it

it is secx +C

[manic flame]

ahhhh

how could i not see

u thought outrside the box and expanded it

I shall do the same

[heavy lion]

good luck

[manic flame]

thank you

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[wraith hinge]

What does the capital pi notation mean in this context?

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[little totem]

if anyone understand lodev raycasting tutorial(https://lodev.org/cgtutor/raycasting.html#Textured_Raycaster) i want to ask him about this
H: hitpoint of the ray on the wall. Its y-position is known to be mapY + (1 - stepY) / 2
yDist matches "(mapY + (1 - stepY) / 2 - posY)", this is the y coordinate of the Euclidean distance vector, in world coordinates. Here, (1 - stepY) / 2) is a correction term that is 0 or 1 based on positive or negative y direction, which is also used in the initialization of sideDistY.

[little totem]

<@&286206848099549185>

[golden vale]

@little totem bro you might find a server on #old-network

[little totem]

thank you

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[wise light]

Let α = (e1, e2, e3) and β = (e3, e2, e1). Here ei is the ith standard basis vector of R3.
Let T : R3 → R3 be given by T (x, y, z) = (2y, x + y + 2z, x + 3y + 4z).
(You may assume this map is linear.)
Compute Mβα(T ) and Pβ←α

[wise light]

for the matrix im getting
[2 0 4
3 8 10
7 14 22] I wanna verify if i did it right

anyone ?

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[real saddle]

I'm a little confused about whats going on here cause of the wording

it says to multiply the numerator by 10x but why is the right side of the numerator, -1/10, only multiplied by x

[silver furnace]

The 10x in the numerator cancels with 10 in the denominator leaving x

[real saddle]

ohhhh okay ty

i wish they covered that instead of glossing over it 😭

wait if that was the case shouldnt the left side be 1/x again?

[silver furnace]

Yes that’s an equivalent form, but the point of multiplying by 10x/10x is to end up with the same denominator on both terms allowing you to combine the fractions into one

10x/10x = 1 so 10x/10x * 1/x = 1/x

[real saddle]

alrighty i think i got it

ty

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[honest sinew]

I need help again

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@honest sinew Has your question been resolved?

[honest sinew]

no

<@&286206848099549185>

[fossil kraken]

What's a vertical asymptote?

Is that the next question?

[honest sinew]

Yes

I'm supposed to set the denominator equal to zero, but I'm not sure how to solve it

[fossil kraken]

$4x^2+4x = 0?$

[solid kiln]

G. Spark

[fossil kraken]

For x=0 the numerator also seem to go to zero. As there are xs in every term

Can we solve the denominator = 0?

Maybe we can get rid of the 4? Divide all by it?

$x^2+x = 0?$

[solid kiln]

G. Spark

[fossil kraken]

$x^2 = -x?$

Anything come to mind?
Or maybe use the quadratic formula?

$-x^2 = x?$

[solid kiln]

G. Spark

[fossil kraken]

$4x^2+4x = 0?$

[solid kiln]

G. Spark

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[honest sinew]

I've got it

Thank You @fossil kraken

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[remote island]

https://cdn.discordapp.com/attachments/711335261417504889/1181686001354149958/image.png?ex=6581f5d9&is=656f80d9&hm=2cd7631b38300382e8455c598a56df87a1961687c17007d663e1d58b31127eae&

[remote island]

The task is to say for what values of n the function is point symmetric to the origin

[rough grotto]

ok..symmetric to origin..hmm what does this phrase indicate about f(x)? is f(x) any special kind of function?

[remote island]

f(x) is this function

[rough grotto]

yes that is fine

but can you comment on f(x) by just going through the statement "function is point symmetric to the origin"

like what can we conclude on f(x) from this statement?

[remote island]

Nothing really

[rough grotto]

wait
do you know odd and even function?

[remote island]

Im sopposed to find the values of n that make the funktion odd

[rough grotto]

yes!

so basically symmetric about origin means f(x) is odd which is what I was looking from your end

but now try to solve for n using f(x) = -f(-x)

[remote island]

I dont really know where to go from here

[rough grotto]

2nd to 3rd line simplification doesn't seem to be right

just check once

[remote island]

Should be 4x^(n+1) - x^(2n+2)?

[glass night]

I have problem that I couldn't solve can you help me please

prove that R.H.S = L.H.S

[remote island]

ey man this is my channel to ask for help

[rough grotto]

#❓how-to-get-help

[rough grotto]

1st part is not right

think again

[glass night]

solve please

I want help

[rough grotto]

open a new channel

[glass night]

how ?

[remote island]

Ah I see now

I am here now

And dont know how to continue

[trim jolt]

@remote island Has your question been resolved?

[remote island]

This is what i did but I dont think its correct

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@remote island Has your question been resolved?

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@remote island Has your question been resolved?

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[green oak]

How would I find the angles between the rays from the origin?

[shy shell]

do you know any properties of the rays?

[green oak]

yes

we have x = |y| and the circle is just x^2 + y^2 = 1

[shy shell]

oh

in that case,

Can you form 2 equations from x = |y| ?

[green oak]

x = y and x = -y

[shy shell]

yes

Now, what is the slope of each one?

[green oak]

1

[shy shell]

and the other one?

[green oak]

-1

[shy shell]

Yes,

Now do you know the formula of tan theta = m2 - m1 /1+m1m2?

[green oak]

I need to find 2 values for theta

[shy shell]

$tan\theta = \frac{m_2 - m_1}{1+m_1m_2}$

[solid kiln]

Shockshwat

[green oak]

I need to get to pi/4 and 7pi/4

by manipulating the second equation using polar coordinates

[shy shell]

The angles between them?

[green oak]

no

thetha = pi/4 and theta = 7pi/4

So u see the imagine I posted

I need to find the area to the left of x = |y|

and to do that

I need to convert the given eqautions into polar form

so x^2 + y^2 = 1 just becomes r = 1

but no I need to find the thetas

idk how to find thos angles

[shy shell]

Your original question is to find the angle between the rays, why would you need to find the area

[green oak]

nah I phrased my original question wrong mb

[shy shell]

What is the original question ?

[green oak]

After drawing up a quick sketch of the shape, you realize that this would be better modeled in polar coordinates. Give equations for the boundary of the table in terms of r and θ.

The sketch I posted above

and the eqations are

x^2 + y^2 = 1

and

x = |y|

[shy shell]

Boundary of the table, do you mean the point of intersection of circle and line?

[green oak]

The tabletop’s shape R consists of everything within the curve x^2 + y^2 = 1 and to the left of the curve x = |y|.

[shy shell]

uh

in that case

you know this right?

[green oak]

yes

so one of our angles is theta = pi/4

now since we care about the area of the left side (the packman shape)

I need to get that entire other angle

[shy shell]

Why would you need the area when the question asks for the boundary of the table which should be the point of intersection of line and circle?

[green oak]

because I eventually need to use a double integral to find the area

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[devout furnace]

What is the PV here?

[boreal dome]

principal value

[devout furnace]

ok thanks

Also

Q_B is the joint law of the eigenvalues of a real symmetric random matrix with gaussian entries, and v is a probability measure, B is the ball around v in the space of measures, how do we integrate over this with respect to product lebesgue measure d\lambda?

I know from earlier in here we passed from haar measure to lebesgue measure via some magic (that I took from granted), is this somehow related?

or am i misreading their notion for what we're integrating over

nvm im stupid

l0l

\phi: R^n to M_1(R) injective, so we can recover preimage from whatever probability measure we have and work in R^n

.coose

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[jolly basin]

i need help finding the general term

for finding interval

the issue is that the denominator is not factorial so im not sure how you write a general term

since the denominator is 1 for both 1st and 2nd term

but you can't write the factorial on the top because then it either grows too fast or you'll end up with a negative factorial when you try to shift bounds

[blissful bison]

$1+\sum_{n=1}^{\infty }\frac{2^{n}x^{n}}{n}$

[solid kiln]

Joanna Angel

[blissful bison]

for investigating converghence radis etc, you do not need to inlue 1 isnide the sum

the convergence of a series is not affected by the finite number of terms in the series

it is also not hard to show that:

$x\in [-\frac{1}{2},\frac{1}{2})$

[solid kiln]

Joanna Angel

[blissful bison]

etc

[jolly basin]

ah so constants can be ignored for interval of convergence generally speaking?

[blissful bison]

yes

they only have meaning

if you want to fidn the sum

but if only convergence aspect, they are not important

[jolly basin]

alr thx

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[heady mesa]

which website i can draw coordinate plane?

[blissful hedge]

geoalgebra

geogebra*

[heady mesa]

thanks

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[slim lynx]

where tf do i get startred

slicing is a bitch

[austere cedar]

You're getting the volume of revolution of a circle

Know the equation of a circle?

Can you draw the curve, before revolving it?

[slim lynx]

yea i know equation of circle

[slim lynx]

even though its sliced

at height h?

@austere cedar

the radious i find by slicing it right and it results in a triangle?

idk where t ogo from there

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[viscid flower]

If we have some harmonic function f(u,v)

[viscid flower]

will all level curves approach a level curve of 0 at infinity?
I mean are we always able to join level curves f=C and f=D using a curve f=0 by letting f=0 join f=C and f=D at infinity

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[viscid flower]

I know we can make conclusions about the behavior of the level curves.

Like for example, a level curve cannot curve around and meet itself again, because then you'd pick up an extremum

and clearly level curves wont cross

Maybe it's helpful to ask more generally, if it appears visually that two level curves become arbitrarily close towards infinity, how do i show this?

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[viscid flower]

.reopen

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✅

[viscid flower]

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[urban tangle]

How do u find sin y and cos y?

[wraith hinge]

not sure if it is the easiest method, but you can use [
\m\tan{x-y} = \f{\m\tan x - \m\tan y}{1+\m\tan x \m\tan y}
]
for the first problem

[wraith hinge]

you can recover tan(x) and tan(y) easily

[urban tangle]

How?

[wraith hinge]

triangles

use Pythagorean theorem

remember sin(x), ... are all just ratios between sides of right triangles

\env{alignat*}{{2}
\m\sin\theta &= \f{\t{opp.}}{\t{hyp.}} & \q \m\csc\theta &= \f{\t{hyp.}}{\t{opp.}} \\
\m\cos\theta &= \f{\t{adj.}}{\t{hyp.}} & \q \m\sec\theta &= \f{\t{hyp.}}{\t{adj.}} \\
\m\tan\theta &= \f{\t{opp.}}{\t{adj.}} & \q \m\csc\theta &= \f{\t{adj.}}{\t{opp.}} 
}

[urban tangle]

But i need the values of sin and cos of x and y to solve the formulas

[wraith hinge]

cot(y) and cos(x) are enough for you to find that

[urban tangle]

How?

[wraith hinge]

Draw a triangle

ignore the minus sign for now

you have cos(x) = 2/3

[wraith hinge]

based on this, what does cos(x) correspond to

[urban tangle]

Adjacent over hypotenuse

[wraith hinge]

right

you want to find sin(x) but you're missing the opposite

[wraith hinge]

also idk why you're finding sin(x) I'd recommend just using this for simplicity sake

[wraith hinge]

so apply Pythagorean theorem [
c^2 = a^2 + b^2
]
where $c$ is the hypotenuse and $a$ and $b$ are the two other sides

[urban tangle]

So opposite is 1?

[wraith hinge]

no

[
a=\s{c^2 -b^2}
]

[wraith hinge]

this is how you are finding the opposite

[urban tangle]

Uh its sqrt of 5

[wraith hinge]

yeah

great

so your sin(x) is?

[urban tangle]

Sqrt5/3

[wraith hinge]

yeah great

but now observe that it says x is between pi and 3pi/2

sin(x) is negative during that interval

so chuck in a -

[urban tangle]

So its -sqrt5/3

[wraith hinge]

yeah

[urban tangle]

So if cot y is -7/6 , then is tan y=-6/7?

[wraith hinge]

yeah

[urban tangle]

How do i get sin y and cos y?

[wraith hinge]

same process

ignore the negative for now

[wraith hinge]

what does tany correspond to in here

[urban tangle]

Opposite over adjacent

[wraith hinge]

yeah

find the hypotenuse

[urban tangle]

Sqrt85?

[wraith hinge]

yeah

what are cosy and siny now

[urban tangle]

Cos y =7/sqrt.85
Sin y = 6/sqrt.85

[wraith hinge]

great

now y is between 3pi/2 and 2pi

cosy is positive there and Siny is negative

so chug a - in siny

[urban tangle]

Is this right?

[wraith hinge]

tanx should be positive

sinx is negative remember

negative/negative = positive

[urban tangle]

@wraith hinge

[wraith hinge]

yes

read what I said. You made a mistake

[urban tangle]

Ok

Just this last one

@wraith hinge

@wraith hinge ?

[wraith hinge]

Stop pinging me I'm here

[urban tangle]

Oh i thought u were gone

[wraith hinge]

P(x-y) isn't a full point. Did you forget a comma somewhere or is this supposed to represent the x aspect of the point?

[urban tangle]

Idk but it is a part with numbers 1 and 2 from before

[wraith hinge]

then I'm unsure on how to help

[urban tangle]

Ok ty

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[fervent drift]

there are specific formulas

to follow

[copper spade]

what are they i dont know

[fervent drift]

uhh

lets see

so

what do you know from the numbers given

what info can you get

[copper spade]

I got how much money he got after 5 and 6 years

[fervent drift]

thats given

but what can you get from that?

also, what type of interest is it?

[copper spade]

They gained that amount of money in 6 years

And it’s simple interest

[fervent drift]

what does simple interest mean

btw, ping me when u send a message, just so i remember to see

[copper spade]

I don’t know what simple interest means

[fervent drift]

simple interest means it increases by the same amount every year (depending on your starting amount)

for example

if i have $100, and i have 10% interest

yr 1: $110

yr 2: $120

yr 3: $130

[copper spade]

Ok I understand @fervent drift

So can u run me through how to answer it

[fervent drift]

give it a try first

do some thinking

every piece of information given will help you

why do you think they gave teo numbers

[copper spade]

Man my homework is due in 30 minutes and I have no clue about how to get how much money was deposited pls help

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[flat wing]

I’m trying to find the equation of the curve

[flat wing]

But can’t

[terse shore]

What’s the acc question

[flat wing]

Sorry it’s loading

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[ornate oasis]

So to start off with, here's a formula for temperature
$T = f(x,y,z) = 8x - 2y + z + 70$
With this function, we also have a tetrahedral solid region with the points:
$(1, 0, 0) , (0, 2, 0) , (0, 0, 2)$
I'm trying to use the given formula to find the average temperature over this region– and I'm really struggling with that I need someone that can go through the steps so I can understand plz

[solid kiln]

alani

[ornate oasis]

Here's a graph for visualization

I'm guessing, and correct me if I'm wrong, that we'd need something like $\int^{f(x)}{f(x)} \int^{f(y)}{f(y)} \int^{f(z)}0 (8x - 2y + z + 70) dz dy dx$ divided by $\int^{f(x)}{f(x)} \int^{f(y)}_{f(y)} \int^{f(z)}_0 1 dz dy dx$

[solid kiln]

alani

[ornate oasis]

To start off with, I need to find the z equation for the plane that connects these points, then the x and y equations, or are x and y just from 0 to 1 and 2?

any help is appreciated

[ornate oasis]

whoops, the points are actually (1, 0, 0) , (0, 2, 0) , (0, 0, 2)

looking at the visual rn

the other points I mentioned were from part a of the question, which I already solved

<@&286206848099549185> any help is appreciated

[trim jolt]

@ornate oasis Has your question been resolved?

[ornate oasis]

So I've broken down the question a bit
I got started with the cross product stuff
Technically took the points (1,0,0), (0,2,0), (0,0,2), and labled them Q, R, and P, then found vectors PQ and PR, then took the cross product using the formula I have memorized
$n = (u_2v_3 - u_3v_2)i - (u_1v_3 - u_3v_3)j + (u_1v_2 - u_2v_1)k$
I know there's an easier method than memorizing the formula, but this methods seems to work better for me, all I need to remember is 23, 13, and 12, and the rest comes to me

Either ways, found the formula $z = 2 - 2x - y$ and graphed it to confirm it intersects the points
Next the x's and y's and figuring out how to deal with this 4 dimension equation

[solid kiln]

alani

[ornate oasis]

Now that I think about it, I might be able to do it... but still would be nice to have someone check my work if possible and give advice

[ornate oasis]

$\int^{1}{0} \int^{-2x+2}{0} \int^{2-2x-y}_0 (8x - 2y + z + 70) dz dy dx$

[solid kiln]

alani

[ornate oasis]

,ask $\int^{1}{0} \int^{-2x+2}{0} \int^{2-2x-y}_0 (8x - 2y + z + 70) dz dy dx$

[solid kiln]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by hanzohalani

[ornate oasis]

${(\int^{1}{0} \int^{-2x+2}{0} \int^{2-2x-y}0 (8x - 2y + z + 70) dz dy dx)}/{(\int^{1}{0} \int^{-2x+2}_{0} \int^{2-2x-y}_0 (1) dz dy dx)}$

${(\int^{1}{0} \int^{-2x+2}{0} \int^{2-2x-y}0 (8x - 2y + z + 70) dz dy dx)}/{(\int^{1}{0} \int^{-2x+2}_{0} \int^{2-2x-y}_0 (1) dz dy dx)}$

[solid kiln]

alani

[ornate oasis]

,ask ${(\int^{1}{0} \int^{-2x+2}{0} \int^{2-2x-y}0 (8x - 2y + z + 70) dz dy dx)}/{(\int^{1}{0} \int^{-2x+2}_{0} \int^{2-2x-y}_0 (1) dz dy dx)}$

[solid kiln]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by hanzohalani

[ornate oasis]

,ask (143/3)/(2/3)

[solid kiln]

Results provided by WolframAlpha

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Requested by hanzohalani

[ornate oasis]

.close

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[wraith hinge]

How do I approximate cos(0.5) using Taylor series?

This is the problem I’m attempting to solve

[wintry stag]

What do you think the work you showed is doing

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

Approximating cos(0.5) using cos(x)’s Taylor series up to x^4 term

I’m not sure about the “error” part though

Need help on that

[wintry stag]

You should have a result somewhere in your notes about a Lagrange Remainder term, what did you do for that

Alternatively, I suppose it might just want you to punch it into a calculator and subtract from it the answer you got. That depends on the context of your class.

[wraith hinge]

The result here is what I got from a calculator

[wraith hinge]

In the context of my class, we discussed 2 methods to determine the error of an approximation

First one being the "alternating series approximation"

[solid kiln]

XO

[wraith hinge]

I am not sure I understand both these methods though

I'm inclined to use the first one in my case, would that be fine?

[wintry stag]

You should use the second one

Take the worst case scenario for f^(n+1)(z), in this case the easiest approximation is just 1

[wraith hinge]

But isn’t cosine’s Taylor series an alternating series?

[wintry stag]

You can use R_{5}(x) then if you like to improve the error since T_4 = T_5 in this case. This is the standard way Taylor Series are handled

[wraith hinge]

I used my notes to do this

But am still kinda confused

[wraith hinge]

What do you think?

[wintry stag]

I have no idea where you get a 7 from

[wraith hinge]

Oh shoot

Was reading my notes just copied that over

It’s 5

My bad

[wintry stag]

Ignoring the fancy language of the theorem. You have a Taylor series, it goes on "forever". The theorem says that if you stop at a certain point, like T_4. You can capture the most the rest of the series can be by looking at only the next term in the Taylor Series

[wraith hinge]

Yeah

[wintry stag]

Except now, instead of plugging in a value for your derivatives of f(x), you have some unknown value from the mean value theorem

So if this is intended to be a measurement of error, you take that to be a reasonable "worst case scenario"

[wraith hinge]

Right

[wintry stag]

In this case, |cos| and |sin| are bounded between 0 and 1, so just use the worst case scenario as 1

[wraith hinge]

The lower the term degree is, the bigger the error yielded?

[wintry stag]

you can clearly see that is the case here

[wraith hinge]

I’m not sure if I said that correctly

[wintry stag]

because (1/2)^n gets smaller as n gets larger

[wraith hinge]

Yeah

[wintry stag]

and as you take higher degrees, you divide by a larger factorial

[wraith hinge]

Yeah

So the error becomes smaller

Gradually

If you take more terms

Right?

[wintry stag]

Yes, but in this case, the error becomes smaller very quickly

because T_4 = T_5

So every step of a Taylor Approximation you get a second step for free

[wraith hinge]

Yeah I see

What should I change in my answer though?

[zinc ginkgo]

Where did you state the error

[wraith hinge]

Absolute value of f^(5)(z)/5! * (1/2)^5

I have no idea what I’m doing though

[zinc ginkgo]

The error should be a number

Find the maximum of the remainder and that'll be the error bound

[zinc ginkgo]

Reread what Jessica told you. She gave good hints

[wraith hinge]

I compute the error bounds, for z = 0, and z = 1/2?

[wraith hinge]

Alright

[solid kiln]

XO

[wraith hinge]

(For my approximation)

@zinc ginkgo

z is basically the fixed number for which cos(z) is equal to 1 (its upper bound, greatest value), right?

[wraith hinge]

@wintry stag Is this what you meant?

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@wraith hinge Has your question been resolved?

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@leaden panther Has your question been resolved?

[leaden panther]

How do I close this actually

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@leaden panther Has your question been resolved?

[fossil kraken]

If you don't need any help just type a dot followed by close

[fossil kraken]

If you don't need any help just type a dot followed by close without a space

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[north forge]

.close

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[sage anvil]

Logic problem: On a perfectly competitive market, margin (m) is 0. m=0. When there is a decrease in the competitiveness of a market, does the margin decrease or increase?

[sage anvil]

i need 100% expert to certify real answer pls

margin increases?

[edgy cedar]

This ain’t logic

Economics maybe

Imagine you initially have infinite buyers and sellers, and suddenly they all die and there’re only two shops left. What do you think would happen to the margin?

[full dock]

🤑

[sage anvil]

fr

dollar dollar bills yo

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[quick cloud]

I honestly have no clue where to even begin, I know to take get to the answer I first need to determine whether it is an unbiased estimator, to do so I need to calculate the E(X), but since the formula of f(x) is so (so me) complicated, I have no clue how to

[quick cloud]

Oh maybe this is too difficult for this thing, I am in university..

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@quick cloud Has your question been resolved?

[high heron]

It's not absolutely horrific

I'm still working through it

[quick cloud]

Oh thats very kind!

[high heron]

But I don't see any immediate way of doing it by not just integrating

[quick cloud]

Yeah I thinl integrating is the way to go, but how do you integrate that..

[high heron]

a correct u sub gets you to $A\int_0^\infty u^2e^{-u^2}$

[solid kiln]

Edward II

[high heron]

for A some constant I can't be bothered writing down

and then by parts u, ue^(-u^2)

[high heron]

probably easier to do several subs, but end result is the same

[quick cloud]

hmmm

I dont think Ill understand this soon, better wait until friday when the teacher explains

thank you tho!

.close

.closr

.close

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[wary sentinel]

HELP

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Please don't occupy multiple help channels.

[kindred pier]

Stick to one channel

.close

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[wary sentinel]

wheres my original

[kindred pier]

#help-34

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[cosmic jungle]

So I have this matrix A with four variables I need to solve. v1 and v2 are eigenvectors of A.

[cosmic jungle]

A\cdot\bar{v}\ =\lambda\cdot\bar{v}

[solid kiln]

OUP
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fossil kraken]

Yep. Looks as if that might do it.

[cosmic jungle]

I guess I kinda need to use this somehow

[fossil kraken]

Some people swap it round to A-lambda*I [x,y,z]^T= 0. Either way should work.

[cosmic jungle]

What :D

[fossil kraken]

$\begin{bmatrix}
a & b & 10\
c & d & 0\
-5 & 15 & -8
\end{bmatrix}
\begin{bmatrix}
1 & -1\
3 & 1\
4 & 2
\end{bmatrix} =
\lambda
\begin{bmatrix}
1 & -1\
3 & 1\
4 & 2
\end{bmatrix}$

[solid kiln]

G. Spark

[cosmic jungle]

how do I solve the lambda if I can't inverse the eigenvector matrix?

[fossil kraken]

Seems you will have six equations in 5 variables.
It might work.

Some prefer to write it

\left[\begin{bmatrix}
a & b & 10\
c & d & 0\
-5 & 15 & -8
\end{bmatrix} - \lambda
\begin{bmatrix}
1 & 0 & 0\
0 & 1 & 0\
0 & 0 & 1
\end{bmatrix}
\right]
\begin{bmatrix}
1 & -1\
3 & 1\
4 & 2
\end{bmatrix} =

\begin{bmatrix}
0 & 0\
0 & 0\
0 & 0
\end{bmatrix}

[solid kiln]

G. Spark
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fossil kraken]

But use what you are used to.

eek

$\begin{bmatrix}
a & b & 10\
c & d & 0\
-5 & 15 & -8
\end{bmatrix}
\begin{bmatrix}
1 & -1\
3 & 1\
4 & 2
\end{bmatrix} =
\lambda
\begin{bmatrix}
1 & -1\
3 & 1\
4 & 2
\end{bmatrix}$

[solid kiln]

G. Spark

[fossil kraken]

Not a winner?

[cosmic jungle]

my brains aint wrapping around this xd

[fossil kraken]

xd?

[cosmic jungle]

xd is the emotion "XD"

[fossil kraken]

"XD"?

Anyway, how's the problem?

Seems if you do the multiplication, you will get 6 simultaneous equations in 5 variables.

[cosmic jungle]

hmm, I mean I see what you did but I'm don't know what is the next step

oh wait,

[fossil kraken]

Since there are no variables in A for the bottom row of A, that row might get you lambda.

[cosmic jungle]

so one of the equations is a+b+10=1?

[fossil kraken]

a1 + b3 + 10 * 4 = lambda *1

Matrix multiplication.

[cosmic jungle]

ok wait let me just calculate real quick

[fossil kraken]

Wow, impressed if you can do that quickly. 🙂

[wintry stag]

You are assuming that those eigenvectors correspond to the same eigenvalue doing this.

[fossil kraken]

Not so far

No eigenvalues given.

[cosmic jungle]

$\left(\begin{array}{c}
a+3,b+40\
c+3,d\
8
\end{array}\right)$

[fossil kraken]

Are you seeing something that I have missed?

[solid kiln]

OUP

[cosmic jungle]

soooooooo the 8 is lambda aka eigenvalue?

[wintry stag]

This equation implicitly assumes they are part of the same eigenspace

[fossil kraken]

If this is pertinent to solution, perhaps you should take over. Be sure to talk at a level the poster needs.

[wintry stag]

It might or it might not, I'm not interested in taking over but that is a strong assumption that might cause problems down the road

[fossil kraken]

Simply not with you. Seems a simple problem. Likely a simple answer.
It's yours.

Enjoy

OUP meet JessicaK, JessicaK meet OUP.

BTW: Not sure lamda is 8.

[cosmic jungle]

oh wait, so I solve the lambdas from the equations, then I solve the variables with the lambdas I solved?

[fossil kraken]

Maybe you'll solve them at the same time as you will get equations in all combined.

@wintry stag is helping you now.

I guess I get
a * 1 + b * 3 + 10 * 4 = 1
1 * (-1) + b * 1 + 10 * 2 = -1
....

But the bottom line may let you solve for lamda as there are no other variables in it.

a * 1 + b * 3 + 10 * 4 = lambda * 1
1 * (-1) + b * 1 + 10 * 2 = lambda *(-1)
(-5) * 1 + 15 * 3 + -8 * 4 = lambda * 4
....

[cosmic jungle]

yeeeeeeeeeeeeeeeeeeeeeeah. I think I might get this tomorrow morning. It's like 3am here right now.

Thanks G. Spark a lot for trying to help me

[fossil kraken]

Sleep well. Try it in the morning. Good plan.

Get lambda from the bottom line

[cosmic jungle]

I will

[fossil kraken]

Solve for the others.

Don't forget to tell the bot to close

[cosmic jungle]

.close

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[wraith hinge]

I used the quadratic formula to find these numbers $-2 \pm 2i$, but now my question is how do I convert it to a factor. For example x=2 is (x-2), how would I do that for these imaginary numbers

[solid kiln]

Matt

[lethal anvil]

those are the factors, you just use it like you would in your example:

(x - (-2 - 2i))(x - (-2 + 2i) = 0
(x + 2 + 2i)(x + 2 - 2i) = 0
x^2 + 2x - 2ix + 2x + 4 - 4i + 2ix + 4i - 4i^2 = 0
x^2 + 4x + 4 + 4 = 0
x^2 + 4x + 8 = 0

So you can write it in factored form like this: (x + 2 + 2i)(x + 2 - 2i) = 0 You can internally factor out the 2 if you wish but not required

[wraith hinge]

oh so basically if i get imaginary factors i should put them in parentheses and subtract them from x and simplify from there

[lethal anvil]

yeah exactly

it's just like you would with a real factor

[wraith hinge]

ok ty!!!

.close

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[wary sentinel]

hel

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[drifting umbra]

i have a quick question

[drifting umbra]

If sin (x) = 12/13 , what could cos (x) be equal to?

i cannot understand

how to do this without calculator

if it is not on the unit circle i cannot find x from looking at it

[plucky grail]

draw a right angled triangle

[drifting umbra]

ohhhhhhhhhhhh

yeah

[plucky grail]

if sin(x) = opposite/hyp then you should be able to mark it

[drifting umbra]

im dumb

thank u

[plucky grail]

np

[drifting umbra]

/close

/close

.close

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[open fulcrum]

how do i tell

[open fulcrum]

hello

how am i supposed to calculate it from this image

i know what the golden ratio is but how do i find it here

?

[viscid flower]

I realized im dumb

well lemme think

[solid kiln]

jan Niku

[viscid flower]

was my original thought

but its not enough