help-38

[full dock]

[whole coral]

Can't eliminate things as nicely as in other examples

[full dock]

arghh i got the common denominators with all of it and none of it looks pleasant

wait I can pick 0

[whole coral]

y in place of x it's so tempting to get them mixed up, I've already done that multiple times

[full dock]

reeeeee

okat

i got B = -3 if y=0

[whole coral]

Yep agree

[full dock]

so i think ill have to set up a system of eqs

if i pick y=1, -1, 2

[whole coral]

What happened to the y?

[full dock]

i can get an equation with 4 variables i think

[full dock]

where?

oh

oops

i forgor

[whole coral]

hehe

[full dock]

wait

nevermind i dont see it

haha which y

[whole coral]

See second to third line

Second had a y but I don't see how you'd cancel it, should be there I think

[full dock]

ohhhhhh

yeah i see

here comes the algebra

this is what i have

three eqs and i can solve for something like C and get 2 eqs

i think

[whole coral]

You can

But wait a moment

[full dock]

[whole coral]

Shouldn't the first one be equal to -11?

[full dock]

for y = -1?

[whole coral]

Yea

[full dock]

5(-1)^3 + 3(-1)^2 - 1

= -3 no?

[whole coral]

Oh, I read the line above it haha

Got mixed up

[full dock]

so im good 2 go?

[whole coral]

You are

[full dock]

yay

i know these tricks now how to take down this question

last time i endured hell and now i know

[whole coral]

Yep

[full dock]

hm

something is wrong

i cant sub in C = 9-D-2A into any y=-1 or y =1 equation

so i should find another value for y then

[whole coral]

you should be able to put that into the y = -1 equation you found, no? You got that from the y = 1 equation so won't be able to put it in there

[full dock]

ohhhhhh

thats y

yayyy

i didd itttt

i got nice looking numbers which means its probably right

[whole coral]

Awww, well done

What did you get?

[full dock]

hold on ill send

[whole coral]

,w partial fractions 5y^3 + y - 3)/(y^4 + y^2) wrt y

[solid kiln]

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[whole coral]

The A and B look good

[full dock]

what about the C and D

[whole coral]

hmmm, lemme look through it

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@full dock Has your question been resolved?

[whole coral]

Aha, found it think I did the same thing too when I tried it out

[whole coral]

the 2A's cancel out but then you forgot there was a D in the y = 1 equation, -2A - C + D = -3

@full dock

[full dock]

aaa

ojay

D = 3

then C = 4

yay

[whole coral]

Yep, better

Finally

[full dock]

so now i know A = 1, D = 3, B = -3, C = 4 now i can actually integrate

hhmmm

how do i deal with $3\int_{ }^{ }\frac{1}{y^{2}+1}dy$

[solid kiln]

water beam

[whole coral]

Looks very familiar to me

[full dock]

it would be familiar to me if it was a square root

but im not sure

[whole coral]

What would you think if it was a square root?

[full dock]

arctan

[whole coral]

[whole coral]

This one is the arctan one though

[full dock]

but

oh wait

it is

i just had a brainfart

[whole coral]

Hehe

[whole coral]

Happens

[full dock]

$\int_{ }^{ }\frac{5y^{3}+y-3}{y^{4}+y^{2}}dy=\ln\left|y\right|+\frac{3}{y}+2\ln\left|y^{2}+1\right|+3\tan^{-1}\left(y\right)+C$

hehe

[solid kiln]

water beam

[full dock]

i think thats correct

[whole coral]

,w int (5y^3 + y - 3)/(y^4 + y^2) wrt y

[solid kiln]

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Requested by chartbit

[whole coral]

It is

[full dock]

wooohooooo

thank u char

[whole coral]

Well done

[whole coral]

are you happy with everything?

[full dock]

ye

bai bai

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[mortal sparrow]

I need help with question 10

[orchid wagon]

,rccw

[hallow cliff]

!status

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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

[mortal sparrow]

1

[hallow cliff]

Do you know what a function with independent variable x means?

[mortal sparrow]

Nah can you explain

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[river merlin]

Am I on the right track?

Btw I used double angle formula idk if that’s right tho

[hallow cliff]

You have 6cos(2x)+8sin(2x)=0

Do you know how to combine them into one term by rearranging the equation?

[hallow cliff]

No, you are overcomplicating

[river merlin]

o

so dont use double angle?

[hallow cliff]

Try rearranging this equation to separate the trigonometric ratios and the constants

[hallow cliff]

Yes, don't use it

Hint: || try rearranging to get tan(2x) on one side||

[river merlin]

waot

how do i get tan2x?

sin/cos?

[hallow cliff]

6cos(2x)+8sin(2x)=0

6cos(2x)=-8sin(2x)

-6/8=tan(2x)

[hallow cliff]

Yes

[river merlin]

do i use double angle formula now?

or should i just completely ignore it

[hallow cliff]

Whatever you want

[hallow cliff]

But easiest is to just apply arctan on both sides here itself

arctan(-6/8)/2=x

[river merlin]

oh

wait is arctan just tan inverse?

[hallow cliff]

Yes

[river merlin]

ahhh

[hallow cliff]

But it's easier to type arctan instead of tan^-1

So I used it there

[river merlin]

ahhh okok

[hallow cliff]

But this is not between 0 to 180°

[river merlin]

right

do i use the argand diagram and reference angle?

[hallow cliff]

So add an appropriate angle that will make it between 0° and 180°

[river merlin]

ah yeah that

not what i said

so i guess just add 180

id get 161.56

[hallow cliff]

Yep, adding 90 also works since it's tan(2x)

[river merlin]

ahh

[river merlin]

so i sub this into the original equation?

[hallow cliff]

Yes

You need to find out which of the two are maximum and minimum

So check this angle and also the one where we added 90

[river merlin]

wait 2?

[hallow cliff]

We have 2 solutions

[river merlin]

ahhh

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@astral tangle Has your question been resolved?

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[forest egret]

what's the question

[crimson seal]

simplify

[forest egret]

let's focus on the numerator

[crimson seal]

(4x+2)/(x-4) + 1

[forest egret]

nice

now we need to combine them

we want them to have the same denominator

write 1 as (x-4)/(x-4) and combine them

[crimson seal]

(4x+2)/(x-4) + (x-4)/(x-4)

(5x-2)/(x-4)

[forest egret]

correct

try to do the same thing for the denominator

[crimson seal]

(5x-2)/(-2x+17)

tysm

I got the right answer

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[finite summit]

Guys 😭

[wraith hinge]

See, if one person is sitting near the door, the other 8 people will be able to sit at the table differently

[finite summit]

So (8-1)! ?

Oh

Ok so 40320?

[frail heron]

Did you submit it?

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@finite summit Has your question been resolved?

[finite summit]

Not yet

[finite summit]

Sorry i fell asleep 😭

[frail heron]

It’s okay

[finite summit]

Whats next?

[frail heron]

Red and blue count as one condition

[frail heron]

yeah…I hope this help you

[finite summit]

Sorry 😭 can you explain this

[frail heron]

First, choose someone to sit next to the door

Is it comprehensible?

Second, arrange the rest 8 people

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[frail heron]

Last but not least
clockwise and anticlockwise pose as the same pattern
For instance, ABCDEFGHI = IHGFEDCBA

.reopen

[finite summit]

Ohhh

.reopen

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✅

[frail heron]

Is it clear for you?

[finite summit]

Yes

[frail heron]

gl fam

[finite summit]

Thank you

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[hollow drift]

any fast ways i can use process of elimination to find th solution without having to solve?

[limpid sun]

it's a strict inequality so the boundaryt is not included

[hollow drift]

so b & d are out

[limpid sun]

and it's y less than f(x) so it's going to be below the curve rather than above it

if it were y > f(x) then the solution set would be above the curve

so that rules out which two?

[hollow drift]

b and d are automatically out consideringthe inequality is fx less than and not fx equal or less than

and b and d are not striped

so its either a or c

[limpid sun]

and it's not c because it's y < x^2-2x-3 and not y > x^2-2x-3

[hollow drift]

yep

[limpid sun]

less than => below, greater than => above

[hollow drift]

what abt this one

how can i use process of elimination for these questions if thats possible

[limpid sun]

that one isn't as easy

you do now it'll be a closed interval because it's a greater than or equal

so it can't be A or B because those are open intervals

but i don't know of an "easy trick" to decide between C and D

[hollow drift]

what are my altneratives

[limpid sun]

one thing you can do is choose a point inside the interval and see if the inequality holds

[hollow drift]

like (0,0)

?

[onyx smelt]

1

[limpid sun]

0 won't differentiate between C and D because 0 is in both of them

1 is only in C and not in D so 1 would be my go-to

also because 1 is easy to evaluate

[hollow drift]

ok yeah thanks

just 1 last thing i wanna know if my thought process is correct

heere its a positive leading coffiecient so c & d are out

and because the x coordinate of the vertex is negative it cant be B

therefore its a

[limpid sun]

yes that's sound

[hollow drift]

ok thanks a lot

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[fossil cobalt]

can someone explain

isnt the integral from 0 to 5 and 5 to 8

the same as 0 to 8

also here

isnt the area = definite intregal

i do not understand shit

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[fossil cobalt]

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[severe owl]

how does this work?

what are the steps

[fallen pecan]

what's 1 - 3/4?

[severe owl]

1/4

[fallen pecan]

yea now what's $$\pi - \frac{3\pi}{4}$$

[solid kiln]

shik

[severe owl]

I see what you did there, thank you

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[fallen pecan]

np

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[delicate lance]

guys did i do the right steps

[delicate lance]

how df do i show my work for this 😭

I dont get it

[delicate belfry]

The steps looks good.

[delicate lance]

Oh ok ty

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[alpine loom]

hi

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[devout dagger]

could someone please explain this to me like i was 5

[viscid flower]

how do you feel about a linear transformation

do you have a picture in your head of what that looks like?

@devout dagger

[devout dagger]

ive never tackled linear transformation

like i know how to get the determinant o a matrix

thats plain and simple

[devout dagger]

i imagine a square going flat

[viscid flower]

sure, or becoming some kinda parallelogram, right?

[devout dagger]

yeah

[viscid flower]

alright

so then all you really need to know here is a determinant is a way to express what happens to area under the linear transformation

[devout dagger]

so i can use the determinant to solve the problem?

[dull temple]

yes

[viscid flower]

yea

[dull temple]

determinant is a measure of how much area gets stretched (or squished) in a linear transformation

[viscid flower]

can you get the determinant of the matrix

[devout dagger]

yeah wait

[viscid flower]

hi hayley

[devout dagger]

-5

since D = ad-bc

[viscid flower]

so we drop the negative

[devout dagger]

its just 5?

[viscid flower]

hopefully that makes sense

[dull temple]

the determinant is -5

[viscid flower]

like, negative area isnt a thing

[devout dagger]

true

[dull temple]

so it scales area by -5x

[devout dagger]

and it also did say POSITIVE area

[viscid flower]

well, area is always positive

[devout dagger]

do i need to do anything else to the determinant to get the new area of the linear object

[viscid flower]

i guess unless you talked about signed area

[viscid flower]

determinant is in terms of a unit square

do you have a unit square?

i mean, i guess square isnt really being fair

the determinant tells you what the area will become if something has size one

[devout dagger]

its got an area of 2

so kinda?

[viscid flower]

right

so its not just the determinant

[devout dagger]

the sides are just root 2

[viscid flower]

say like

hmm i wanted to use linearity of the transform but i guess youve not covered that

[viscid flower]

we want to multiply the determinant by this

something with area one gets scaled up by determinant

so something with area 2 gets scaled up by determinant times 2

[devout dagger]

so 2*determinant?

which is 10?

[viscid flower]

yup

[devout dagger]

oh

ah that was correct

thanks

[viscid flower]

np

[devout dagger]

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[wraith hinge]

how do i evaluate this function

[fossil zodiac]

so u want h(-18) so start by plugging -18 into the function

[wraith hinge]

then what

[fossil zodiac]

so whats ur result

what did u get after plugging it in

[wraith hinge]

h(-18) = 14

[fossil zodiac]

k

[wraith hinge]

is that it?

[fossil zodiac]

yep

[wraith hinge]

oh okay, thanks

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[solar notch]

A leaky bucket picks up 20 litres of water from a well but drips out 1 litre every second from the bottom. If the bucket was lifted 5 metres from the surface of the water at a constant speed of 2m/s, how much work is done? Assume the bucket has negligible mass. So I'm mainly confused about how I would find the work for the leak/drip of 1 litre per second, do I break the the integral into a sum of multiple bounds and then calculate it, or do i subtract the the leak off the 20 litre then integral from 0 to 5? doing it the first way I get 855.05 J and doing the second way I'm getting 857.5 J

[granite surge]

dude, read the server rules and ask help the correct way

and dont just ping helpers its annoying

So there are multiple channels to tell you how

I dont know if I can help you I dont know the question

There is a high chance I wont know how to do it lol so unless you send it and I know how to help, I cant do anything

[lament reef]

go back to your own help channel and just ask the question instead of invading others'

[granite surge]

Thank you ❤️

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<@&286206848099549185>

[solar notch]

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[pseudo coral]

how can I find the maximal solutions without explictyl solving this ODE

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[simple jackal]

I want to calculate E[X^2], where X is a geometric distribution with parameter p. The textbook uses the Law of Total Expectation, so we can calculate E[X^2] = P(X=1)E[X^2 | X=1] + P(X>1)E[X^2 | X>1]. This setup is clear to me. I’m confused about the calculation of the term E[X^2 | X>1], specifically the highlighted equivalence

[simple jackal]

I think it might have to do with memory less property of geometric distribution, but not too sure, but this would only make sense to me if X^2 were geometric. Is X^2 geometric?

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[blazing geode]

I have a question

Given there’s a chain fixed and hanged on two walls

If the weight of it has to be put in consideration

Then the tension of each point on the chain is different

Why

hello I can solve your problem

No I can’t

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[wraith hinge]

no idea how to do this

[marsh forum]

try finding f(3)

[kindred pier]

The question is written kind of poorly

But basically you want to do what simp said

[wraith hinge]

$f(3)=(3)^2-4(3)+1$

[solid kiln]

wyldinwilliam

[marsh forum]

yup

[kindred pier]

The coordinate is just (x, f(x)), and you evaluate it at x=3

[wraith hinge]

-2

[marsh forum]

now , recall f(x)=y

[wraith hinge]

f(3)=-2

oh okay

that was it?

alright then lol

thanks

.close

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[kindred pier]

Almost

[wraith hinge]

.reopen

[trim jolt]

✅

[kindred pier]

You found f(3), but do you know the coordinates of the point now?

[wraith hinge]

(3,-2)?

[kindred pier]

yup

okay just wanted to be sure

but yeah, question was kind of badly worded

[wraith hinge]

alright then, yea the question's wording was hard to understand

.close

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[pulsar flume]

Not sure why it's outputting false does anyone know why?

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@pulsar flume Has your question been resolved?

[tranquil junco]

Maybe a syntax issue?

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@pulsar flume Has your question been resolved?

[pulsar flume]

Maybe, the syntax is pretty on point though and includes multiplication signs even where they would be extraneous, so I will try removing some of that to see if that resolves it.

I also tried removing the multiple character variable vo with just v, that did not fix it and ruled out the possibility of vo being the issue with multiple characters.

[simple haven]

So this equation is essentially: is it possible to throw a ball at a 60 degree angle and reach the point (11.5, 4)? Because this point sits lower than 60 degrees, it should be possible in principle.

https://www.wolframalpha.com/input?i=solve[{11.5+%3D%3D+v+t+cos(6π%2F18)%2C+4+%3D%3D+v+t+sin(6π%2F18)+-+4.9+t^2}%2C+{v%2Ct}]

So I also don't know why the calculator doesn't like it

[proper kernel]

try simplifying the equations manually then reentering them into the calculator
also what website are you using

[simple haven]

That's a screenshot from a TI calculator

[proper kernel]

how do you take screenshots on those

[simple haven]

Dunno, but I have a TI calculator and that's what the interface looks like

,w 60*180/pi

[solid kiln]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by omnipotententity

[simple haven]

,w sin(3437.75 deg)

[solid kiln]

Results provided by WolframAlpha

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

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[proper kernel]

it says DEG in the corner, whats this for

[simple haven]

^ I know the calculator says Deg in the corner

But perhaps it was changed after the calculation was attempted or something

?

[proper kernel]

theres no solutions if it was solved while the calculator was in radians

@pulsar flume try doing the calculation again after setting the calculator to degrees

[pulsar flume]

I believe the calculator is already in degrees.

[proper kernel]

thats not a "yes"

[pulsar flume]

The document settings indicate the mode to be in angle mode, it for sure is, just checked.

[proper kernel]

are you going to do this?

[pulsar flume]

From the official TI-Nspire discord:

Looks like I may have neglected the acceleration for my horizontal kinematic equation.

However that doesn't seem right either because the horizontal equation does not have the acceleration term because acceleration in the horizontal direction for projectile motion is zero.

[proper kernel]

neither of those answers are correct

you can place both of these equations through desmos and you get a more sensible answer

11.5 = v0 cos(60) + 9.8 * t is not how freefall works
it looks like theyre just modifying the equations until it gives you an answer

[proper kernel]

again you should try entering a different form of the equation

see if maybe its something off with how its entered in thats causing issues

because the equation does have issues and you can just find them

it really sounds like youre waiting for someone to find the answer for you
I dont have a TI-Nspire
the official discord just thought the ball has a rightward speed of 9.8 m/s

you cant just sit around as if the equation's haunted

[simple haven]

Instead of sin(60) and cos(60) try sqrt(3)/2 and 1/2 respectively @pulsar flume

[pulsar flume]

This worked, why did it work and how did you know it was these values?

Got it

When you simplify them

You must simplify the trig before plugging into a systems of equations for the TI-Nspire

Thank you everyone for your help. I really appericiate it!

[simple haven]

No, you should be able to use trig functions with the TI-Nspire systems of equations solver. This means that your calculator is probably interpreting these values as radians rather than degrees.

[pulsar flume]

That's weird, in Document Settings it is specified as angle, also, when evaluating it individually, it does output the values: sqrt(3)/2 and 1/2

[simple haven]

That is weird

On my calculator I can confirm it works as expected.

But I think you're using software, not a physical calculator, right?

[pulsar flume]

No, I am using the calculator, I took a picture using CX-Connect which is how I was able to get those screenshots

[simple haven]

Ah

Well, I'm not sure what is going on

If you put the calculator into radians mode and use π/3 instead of 60 does it work?

[pulsar flume]

No it does not, very weird.

[simple haven]

Well, I cannot speak to what precisely is going on here, but we've found at least a temporary work around

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[full dock]

I’m having trouble integrating 1/(e^(2x) - e^x)

[full dock]

I tried partial fractions and got:

something like 1 or -1/e^x I can’t remember

And the ended up with B/(u^2 + u) for the B denominator

Might’ve done something wrong but I’ll try again

[zinc ginkgo]

factor out a u

[full dock]

Doesn’t that just bring me back to the starting point with e^2x - e^x and I had to perform partial fractions

Do I have to do it again?

[zinc ginkgo]

you integrate the u integral

and partial fractions on that

[full dock]

oh

I was thinking of something like that when I saw the denominator but I thought I must’ve done something wrong if I have to partial fractions twice

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[green tusk]

hello! just had a quick clarification question i wanted to ask about this, so i already understand how to plot the points but something that came to my mind is if i start from the left (i was always told to read graphs from left to right) or from the lowest point where f(x) starts at (3,-4)

[green tusk]

or do i start from the line f(x) at (4,-4)

im honestly lost, i know u have to basically draw an imaginary line where both graphs are in between each other

so first i have 4+2 so the first point will be at (-4,6)?

if thats the case and i read it from left to right i understand now

my answer would be D?

or am i wrong

[dull temple]

yeah you got it

at like x = -5 the value of f(x) is undefined so that doesn't show up in our graph of f + g

[green tusk]

ok awesome, and to clarify my question do you always start left to right?

reading a graph

also one more question. Im watching this vid on function operations, for f-g i understand how he set it up

but my question is the answer, how come he changed the order of it

would 2x-x^2+9 be the same thing?

he has 2x+5-x^2-4
in my head i would just solve from left to right

2x+9-x^2

is another way i would have wrote it

im just curious if if there is a rule or smthing

he did the same thing when doing f times g

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[green tusk]

well i figured it out

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@delicate lance Has your question been resolved?

[delicate lance]

.close

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[real island]

I keep getting the standard deviation wrong

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Show your work, and if possible, explain where you are stuck.

[real island]

I cant show where im stuck

I can only show my asnwer

if I knew where I was stuck I would be getting this right

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[real island]

fuck no

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[dense panther]

need help in physics 3 and 4 plz

[left oriole]

,rotate

[left oriole]

for 3 did you try using conservation of momentum?

[dense panther]

No

LIKE Pi=Pf?

[left oriole]

yea
total momentum is conserved

(energy will not be since it's not an elastic collision)

[dense panther]

nah

how am i supposed to do that with a degree theta?

hello?

[left oriole]

well did you try doing it in terms of vectors first?

[dense panther]

no, i was not taught that

or to do that for this

[left oriole]

what were you taught?

[dense panther]

that formula in the image

XD

for 3)a

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[dense panther]

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[digital sonnet]

i need help on how to format this integral function

im not quite sure how to write it as an equation

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[orchid wadi]

For this problem:

[orchid wadi]

I don't understand why it is ALWAYS

consider this homogeneous linear system:

x + y = 0
x + y = 0

in a matrix, this looks like

1 1
1 1

this is obviously NOT linearly independent

so why DOES the answer claim that they are ALWAYS linearly independent?

$$
\begin{bmatrix}
1 & 1 \
1 & 1 \
\end{bmatrix}
\begin{bmatrix}
x \
y \
\end{bmatrix}

\begin{bmatrix}
0\
0\
\end{bmatrix}
$$

[solid kiln]

BigPenguin

[orchid wadi]

how is this NOT linearly independent???

[hallow cliff]

Thats one equation

Written twice

[orchid wadi]

lmfao

okay I see

so basically its lineraly independent

because you can't have a duplicate for system of equaitons

is that why?

[hallow cliff]

Yeah, its linearly independent if the equations you have are actually different

[orchid wadi]

yo I got another question

why is it that for a matrix N x M

the R is N times M

so if the matrix if 5 by 3

then it is R^15

[solid kiln]

smidgin

[hallow cliff]

So in your example, R^{3x5} is not the same as R^{15}

[orchid wadi]

I meant this problem

sorry, I should have sent the picture first haha

like the way I conceptualize a 3 x 5 matrix is that it takes a 5th dimensional vectors and converts it into a 3 dimensional vector

so where does R^15 come from???

[hallow cliff]

I think "the same as" here refers to the fact that there is a bijection between the two sets

More specifically, there is an isomorphism between R^{mxn} under addition and R^mn under addition

@orchid wadi

[orchid wadi]

uh

I don't know what bijection nor isomorphism means

😭

I don't think those words were in the textbook

could you teach it like you would teach it to a toddler haha

yo i'm here

I'm 100% focused

just cracked my knuckles

[hallow cliff]

Then they might have meant something else

[simple haven]

Essentially, isomorphism is a rather deep concept in mathematics, but what they mean at a surface level is essentially that two things look different but are actually the same.

[orchid wadi]

wait are those words important for linear algebra?

cuz if they are, I want to learn them!

[orchid wadi]

so like the set (1, 2) and (2, 1)?

[simple haven]

You'll probably run into the terms again

[orchid wadi]

wait but lokey I want to understand why this is, I only got it right by guessing LOL

[simple haven]

It's generally applied to more general structures. Like orientations of a cube vs permutations of 4 elements.

[orchid wadi]

got it

[orchid wadi]

wait but could you explain

[orchid wadi]

why the answer is 15?

[simple haven]

So a 3x5 matrix has 15 entries, each of which can be a real number.

[orchid wadi]

so 15 total combinations

15 total dimensions?

[simple haven]

So if we forget the matrix structure, and treat it as an ordered list of 15 numbers, we just get R^15

[orchid wadi]

if I recall, R^n means a space of all real numbers in N dimensions right?

[orchid wadi]

gotchya!

[orchid wadi]

oh, and if one of the columns was linearly dependent on the other, it would be 12?

[simple haven]

Well, again, we are forgetting the matrix structure. Linear dependence of columns is part of that structure that we're forgetting

[hallow cliff]

Forgetting the matrix structure and getting a list of 15 numbers (R^15) is the bijection part. The isomorphism part adds more "structure to it"

[orchid wadi]

gotchu

I HAVE ANOTHER QUESTION

[hallow cliff]

I only mentioned the isomorphism part because it is more true to the statement "the same as", but we don't know what they meant by it

[orchid wadi]

I am so sorry

forgive me

What does this E thingy mean?

its like EATING the P2

I know P2 is all polynomials with MAX 2 degree

[simple haven]

Element of

[orchid wadi]

got it

[orchid wadi]

oh, so like it "lives" in that subspace?

Like in the (1, 2) is E of coordinate plane?

[simple haven]

Yeah, it denotes set membership or other equivalent ideas.

[orchid wadi]

gotchu!

I will learn more of these sets things in abstract algebra right?

[simple haven]

Certainly.

[hallow cliff]

You might even learn it in your la course

[orchid wadi]

would you say it is better to go linear algebra (computation based) --> abstract linear algebra --> abstract algebra
or just computation based linear algebra --> directly to abstract algebra?

[hallow cliff]

Im surprised they asked a question like this to you without telling you what a bijection or isomorphism is

[simple haven]

Depends on what your end goal is

Are you after a math undergrad degree? If so then you'll run into your first proofs class eventually, but a proofs based linear algebra class might help transition you through it.

Because generally, but not always, abstract algebra is that first proofs class.

[orchid wadi]

my community college class is super wack

I spent the entire weekend speedrunning David C. Lay's Linear Algebra book (to comopensate for the college's bad teaching)

so I do have a stronger base than before, but I probably missed any specific definitions that were in teh book

[orchid wadi]

ohh, so abstract algebra with groups --> real analysis?

[simple haven]

Your college might do real analysis as the first proofs class.

It just depends, some colleges actually just have a class dedicated to proof techniques that's a prereq for every proof class.

[orchid wadi]

oh my state university has that yeah

I might sign up for it next quarter, IDK if I have the balls for it tho haha

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[summer ferry]

I think my equation is wrong, but im not sure where im going wrong
or im not sure how to use 2, because when i substitute to the equation i get 1/80

[zinc ginkgo]

that's not what you do to find the derivative of the inverse

and also not what you do to find the inverse value at 2

The inverse function is a function of $y$. Find $f^{-1}(y)$ when $y=2$

[solid kiln]

riemann

[summer ferry]

sorry are you referring to the implicit differntiation method?

It's worked for a similar inverse derivative problem i was working on, so i thought it would work for this as well

[zinc ginkgo]

well try finding $\frac{dx}{dy}$ after you find the inverse function at 2

[solid kiln]

riemann

[summer ferry]

so find the y value?

or is that the 2 reffering to y=2

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[junior willow]

can anyobdy help me understand what this q is asking

[forest egret]

is 255r+255g+0b wrong?

[junior willow]

yes

[forest egret]

weird

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[wraith hinge]

Can't proceed after this

[marsh forum]

,rotate

[marsh forum]

!status

[trim jolt]

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

[marsh forum]

!show

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Show your work, and if possible, explain where you are stuck.

[wraith hinge]

That's the work brother

I don't know how to proceed after that

[forest egret]

Take derivative

And set it to 0

[wraith hinge]

Um

I didn't understand anything with that😅

[vernal raptor]

hev you taught about maxima n minima?

have*

[wraith hinge]

Yes

[vernal raptor]

use that

that might help

or going through a rough way

A.M>= G.M yk?

[wraith hinge]

Yeah that's what written in ans

I didn't understand

[vernal raptor]

and?

ans.*?

[wraith hinge]

Yeah

[vernal raptor]

its a property

[wraith hinge]

Ok I will just watch leactur

[vernal raptor]

its just this porperty for types of question

mostly i will say if youre good in calc. use minima

[wraith hinge]

I didn't practice calculus much

I have to study that

Thanks anyeay

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[marsh forum]

$\frac{dy}{dx}=\frac{\left(y^2-2xy-x^2\right)}{y^2+2xy-x^{2\ }}$

[solid kiln]

Why am. I here

[marsh forum]

I started by cross multiplying

and then dividing the numerator and denominator by $y^2$

[solid kiln]

Why am. I here

[marsh forum]

I then subbed $x=uy$

[solid kiln]

Why am. I here

[marsh forum]

thus obtaining

$u+\frac{ydy}{dx}=\frac{\left(1+2u-u^2\right)}{\left(1-2u-u^2\right)}$

this is what that gave me

[solid kiln]

Why am. I here

[marsh forum]

now what?

[vernal raptor]

subtract the u to RHS

[marsh forum]

I thought of that

[vernal raptor]

and then cross multiply to cancel some terms

[marsh forum]

but that would introduce a u^3 term

[vernal raptor]

and then separate dy with terms of y and du with terms of u

[marsh forum]

which would make things really messy

[vernal raptor]

thats okay

it will even go till u^4

um no ig

nvm

wait lemme try

that is indeed actually messed up from start

[marsh forum]

huh, so it's just a messed up ODE?

[vernal raptor]

no wait

[vernal raptor]

dont we have -2xy up here or +?

for numerator is it -2xy or +2xy

[marsh forum]

ah, it's -2xy

[vernal raptor]

okay

[lusty delta]

ux = y

[marsh forum]

huh, ok

why not x=uy?

[lusty delta]

i've never done x = uy before but i assume judging by the image you sent it doesn't effectively reduce the ode

[vernal raptor]

y=ux????

[lusty delta]

in general, this is the well-studied "homogenous first-order differential equation"

which is defined as being of form y' = f(y/x)

[vernal raptor]

yes

yes yes ik

[lusty delta]

then why question marks

[vernal raptor]

i always use for y

no i was saying to @marsh forum

[marsh forum]

OK, I'll try that, thanks!

.close

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[marsh forum]

thanks both of you!

[trim jolt]

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[atomic musk]

There are 722 tickets. 38 of them are winning.

a) I bought 40 tickets. What’s the probability that I win 6 prizes?
b) I bought 20 tickets. What’s the probability that I win at least one prize.

[forest egret]

!status

[trim jolt]

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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

[atomic musk]

I don’t know where to begin

[light berry]

i fell like this is kind of subjective we cant assume 38/722 is base odds but we also cant say he is slightly unlucky/lucky neither can we say he was crazy lucky or unlucky our best bet is probably gonna be a converging infinite series that would give an approximation looking at the odds, but that would require a bit more complex math, i dont think this question is trying to tackle that though

[trim jolt]

@atomic musk Has your question been resolved?

[shrewd ridge]

you count all winning outcomes

38c6 × 684c34 covers everything

[trim jolt]

@atomic musk Has your question been resolved?

[chilly bobcat]

so, for a), out of the 40 tickets, 6 should be winning and 34 should be losing.
So, number of ways of choosing 6 winning tickets and 34 losing tickets = 38C6 * 684C34
Total number of ways of choosing 40 tickets = 722C40
So, probability of getting 6 winning tickets would be (38C6 * 684C34)/722C40

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[marsh forum]

Find the area enclosed by the figure $(y-arcsin(x))^2=x-x^2$

[solid kiln]

Why am. I here

[marsh forum]

How do I find both the point of intersection with the x axis

one is obviously 0

what about the other

[lusty delta]

do you need that?

[marsh forum]

Don't I?

[lusty delta]

i'd say you need the intersections between sqrt(x - x^2) and the x-axis

why?

square root both sides, accounting for plus-minus, and consider what you get

[marsh forum]

what about the arcsin term

[lusty delta]

did you do the last line here?

[marsh forum]

yeah, 0 and 1, right?

[lusty delta]

so do you see how to solve this problem?

[marsh forum]

no, the arcsin term is still troubling me

[lusty delta]

what do you get after square rooting both sides?

[marsh forum]

$(y-arcsin(x))=\sqrt{x-x^2}$

[solid kiln]

Why am. I here

[lusty delta]

almost

you need a plus-minus somewhere

or you can write this as two equations

[marsh forum]

ah, ok

[lusty delta]

writing this out as two separate equations (y in terms of x) will help you see

[marsh forum]

so $(y-arcsin(x))=\sqrt{x-x^2}$ and $(y-arcsin(x))=-\sqrt{x-x^2}$

[solid kiln]

Why am. I here

[lusty delta]

ye

and how do you find the area enclosed between two curves f(x) and g(x) ?

[marsh forum]

Let g(x)> f(x) on the interval over which the area is to be determined, then, it's $\int f(x)-g(x) dx$

[solid kiln]

Why am. I here

[hallow cliff]

Its the other way round

G is greater than f here

[tepid rock]

g - f, yeah

[marsh forum]

my bad

yeah, g(x)-f(x)

[lusty delta]

pretty nice

now, you can apply this principle here (after finding the points of intersection)

[marsh forum]

how

I'm still not sure I understand

[lusty delta]

first, do you agree that the area between these two curves is equal to the area enclosed by the original curve?

[marsh forum]

why would it be so?

[lusty delta]

since the two equations you have now are derived from the original expression

each equation defines only a portion of the original curve, but when put together, they define the entire curve

[marsh forum]

hmm, but both curves have an arsin component

which is what's troubling me

[lusty delta]

can you define f(x) and g(x) here?

using the "finding the area between two curves approach"

[marsh forum]

g(x) is either $(y-arcsin(x))=\sqrt{x-x^2}$ or $(y-arcsin(x))=-\sqrt{x-x^2}$ anf f(x) is the x axis

[lusty delta]

(as a slightly irrelevant but somewhat related note, this reasoning does give rise to other questions... but for this question in particular, it works)

[solid kiln]

Why am. I here

[lusty delta]

you express g(x) and f(x) in terms of x btw

[marsh forum]

then f(x)=0

*x=0

I mean y=0

shoot

[lusty delta]

oh i mean like

f(x) = smth in terms of x
g(x) = smth in terms of x

[lusty delta]

like the stuff you'd put into this integral

basically, f(x) = y and g(x) = y

(different y)

[marsh forum]

$\int_0^1 \sqrt{x-x^2}+arcsin(x)+\int_0^1 -\sqrt{x-x^2}+arcsin(x)$?

[solid kiln]

Why am. I here

[marsh forum]

so 2$\int_0^1 arcsin(x)$

[solid kiln]

Why am. I here

[marsh forum]

,w 2$\int_0^1 arcsin(x)$

[solid kiln]

Results provided by WolframAlpha

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Requested by physicsrocks

[marsh forum]

huh, but the answer is $\frac {\pi}{4}$

[solid kiln]

Why am. I here

[lyric nymph]

but why did you add them

[lyric nymph]

you are getting the area bounded between these 2 curves so you you should integrate this wrt x

what you did what integrating f+g wrt x

[marsh forum]

then what do I do?

[lyric nymph]

the same as here but - between the integrals instead of +

[marsh forum]

why?

so the answer is $2\int_0^1 \sqrt{x-x^2}$?

[solid kiln]

Why am. I here

[lusty delta]

you subtract because of the principle you posted here

[lyric nymph]

bc the curves that bound the area are $g(x)=\sqrt{x-x^2}+arcsinx$ and $f(x)=-\sqrt{x-x^2}+arcsinx$

[marsh forum]

ah, got it

Thanks!

.clsoe

.close

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[cedar sonnet]

I need help here

[trim thicket]

do u know the property that the diagonals of a rhobus bisect each otheer at rght angles

[cedar sonnet]

A little

[trim thicket]

us that property and angle sum property of triangle

[cedar sonnet]

UHM I can't really kinda get it, can you UHM use no. 1 as an example

[trim thicket]

anglle FIE = 90

also angle FEI + angle FIE + angle EFI =180

put in the given values and solve for x

[cedar sonnet]

Okay I'll try

UHM u may mean IEF and angle ife?

Thankss

.close

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[minor citrus]

am confused i use this formula for cylinders but is it only applied to regular shapes or what

[proper kernel]

when you multiply area x length, it extends the area upwards into 3D then finds its volume

so that formula works for C even if it doesnt look like a cylinder

area x length = volume is the formula for prisms

cylinders is a kind of prism but isnt the only one

[minor citrus]

ok

.close

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[robust swan]

Hello, I was wondering if anyone could explain to me how to figure out a Markov Chain's periodicity?

[digital bolt]

usually i just stare at it really hard and that suffices, but you could also take powers of the matrix and see if it becomes reducible if you had to

do you have an example

[robust swan]

Damn, I left my desk cuz I didn't think I'd get a response quickly

I know how to see if its reducible, but exact periodicity eludes me

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[robust swan]

.reopen

[trim jolt]

✅

[robust swan]

On this for example, how do I find the periodicity

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[native vigil]

Hello! I've been working on my own verse and I was wondering if you guys could help me with Cardinals. I've been trying to go beyond the concepts of infinity and using innacessable cardinals (and the cardinals above those such as weakly, strongly, ect). But my pea brain cannot comprehend it that easily so i'd love to discuss about it and ask professionals.

If I picked the wrong channel for this i'm sorry.

[wraith hinge]

tell us

[native vigil]

This is currently what i've got going on

https://docs.google.com/document/d/1tDk-yhD-B23eD7-BMEsVLqlUiwZEFM_TLn7mwX8xhyc/edit

I'd love to know what I did wrong and what I should replace that incorrect thing with.

[trim jolt]

@native vigil Has your question been resolved?

[native vigil]

<@&286206848099549185>

[trim jolt]

@native vigil Has your question been resolved?

[native vigil]

<@&286206848099549185>

[native vigil]

:/

[trim jolt]

@native vigil Has your question been resolved?

[trim jolt]

@native vigil Has your question been resolved?

[native vigil]

Screw this, i've been waiting for more than 8 fucking hours and so far nobody has responded with anything. EVERYBODY ELSE was getting help and my shit got ghosted, great fucking help said no one ever.

[frail heron]

I suggest that you move to the forum, at which doesn’t has time restrictions

[frail heron]

They bot won’t emerge and ask if your question is solved yet

[sullen ore]

I can help

Btw i found a small error in your document. Aleph 1 is <= the continuum.

[trim jolt]

@native vigil Has your question been resolved?

[simple haven]

@xeptorking when you ask about specific topics in higher level mathematics there are fewer people who are able to help. It's nothing personal, it's just how it is. I've had help channels open for several days before. Please be patient.

It also doesn't help that the question is very open ended and requires navigating away from discord to a Google docs link to even start.

Oh, he left.

Well, ok.

Saves me some trouble I guess.

.close

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[unborn estuary]

help

[unborn estuary]

me

please

are these right

[tepid hamlet]

note that for Q1 it is asking what is the domain of ANY polynomial function, not necessarily the ones given and well it is the same for all polynomials (-inf, inf) I think is the point they are trying to make, all polynomials are defined for all real numbers

[unborn estuary]

huh

so what should the answer be

[tepid hamlet]

just $(-\infty, \infty)$

[solid kiln]

Soosh

[unborn estuary]

oh ok

that’s it?

the answee

[tepid hamlet]

it's the same for ALL polynomials, which is what they're asking so no need to answer it separately for the example ones in a, b, c

[unborn estuary]

oh ok 😭 thanks so much

that makes sense

[tepid hamlet]

but yeah your work looks good 👍