help-23

[ruby musk]

if i square everything and then square root it

wouldnt it all just cancel out

okay so i would express the angle in terms of x

which would mean

btw how do you use the text edit thing

so it makes it more obvious

,rotate

[ruby musk]

this is what i got

and then would I just take cos ine inverse of the entire thing?

I took the dot product and got 1 + 5x^4 . 2/(1 + 3x)^2

because it is 1 * 1 + the A2 and B2 multiplied by each other right

okay

thank you so much for your help

,rotate

[ruby musk]

have a good day

[safe radish]

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[tribal inlet]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

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[quiet scaffold]

I dont know where to start

[safe radish]

@quiet scaffold Has your question been resolved?

[quiet scaffold]

<@&286206848099549185>

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[quiet scaffold]

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[edgy haven]

If m<JGH =79, calculate m<JIH

how can I find the angle JIH without knowing any of the lines.

[edgy haven]

huh?

what is cyclic quadrilateral

ohh

I know what you mean

wait lemme try it

so if do 180-79= 101?

thats it??

damn, i was too worried

mind telling me the other method? I'd like to know it maybe I'll use it for other questions if needed

this is the first and only question like this in the self check so I kinda dont know

[edgy haven]

mhm, I've never seen that way of solving

.close

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[autumn condor]

Can anyone tell me if i applied the chain rule correctly?

[autumn condor]

The answer is correct but I want to know if what i did is "legal" in math

[solid perch]

seems good

[silent token]

Seems fine to me

[solid perch]

you just simplified the 1/2 earlier on nothing wrong with that

[autumn condor]

The part im most curious about is if Im allowed to times the 1/2 by (14x+4)

[solid perch]

yeah

its just multiplication so its fine

[autumn condor]

ok thank you so much

.close

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[chrome parcel]

number 6

[chrome parcel]

i mean

#6

i thought it would be 1/5 because there's technically 10 socks but

idk

[torpid fable]

She could take 2 socks that come from different pairs

Think about what can happen after she picks the 1st sock

[buoyant shadow]

yeah you can do it in one step like that

if you treat it as taking one sock, then another

[sullen laurel]

Is there a solution to these two complex numbers?

[torpid fable]

#❓how-to-get-help

Also translate it

[safe radish]

@chrome parcel Has your question been resolved?

[chrome parcel]

so

what would it be

do i have to create a tree diagram?

the book says 1/9, but im not sure

[chrome parcel]

why are you posting this here? during my question?

[torpid fable]

U dont need a tree diagram

Just think about what happens when you take 1 sock out of the drawer. There are going to be 9 left and only 1 sock that will the corresponding sock to the 1st one you took out

[chrome parcel]

i think it's 1/90

but the book says 1/9

because

they need a matching pair, so after the second one, it's a 1/90

wait no

it's just 1/9

[chrome parcel]

solved

.close

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[urban cradle]

does anyone know what my teacher meant by writing "know" bottom right corner?

does he probs mean that we should know(have it memorized) the rule?

im tryna figure out why he wrote that

[shadow tapir]

most probably your teacher is telling you to remember the formula

the thing beside the "know" is like a mnemomic for the quotient rule

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[limpid mango]

hello i am a pupil at Second year average where can i get help for maths? for Engineering and calculation of √

[cobalt sinew]

huh

you can ask for help in these channels

or you can go to other channels for discussion

check #❓how-to-get-help

[limpid mango]

? why i need help

.close

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[safe radish]

@lean otter Has your question been resolved?

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[junior fable]

Need help with 8.

[cobalt sinew]

what does it says in the first?

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[junior fable]

Need help with 8

Or the bottom one

[cobalt sinew]

bro answer if u want help

or imma report you

if u do this one more time i swear

[junior fable]

Wdym

I answered

Oh it didnt send cuz my wifi buggin

Find the value of theta

[safe radish]

@junior fable Has your question been resolved?

[junior fable]

Bro idk whats happening and why stuff isnt sending

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[deft vigil]

Hi, I have a quick question about systems of homogenous linear differential equations
In my book it's stated that the set of homogenous solutions or the general solution, has to be linearly independent
but a few pages further, it's stated
that if the system of equations is linearly dependent in the first place, the solution will also be linearly dependent
does that mean that this linearly dependent set of solutions is a homogenous solution?

[safe radish]

@deft vigil Has your question been resolved?

[urban cradle]

i see, thanks

[safe radish]

@deft vigil Has your question been resolved?

[shut saddle]

no pretty sure for the homogeneous solution the system has to be independent, the whole thing with it being linear independent is so that you use this system to describe every actual homogenous solution of the equation, you can’t describe the entire set of solutions without the independence

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[tribal inlet]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[tribal inlet]

how?

ohh

nvm

[visual kraken]

If you don't need help anymore you should use .close to free the channel for someone else

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[lean otter]

Hey I tried asking this earlier but no one helped

[lean otter]

Would it be like 160?

[royal kiln]

hey so those two arcs are congruent

[lean otter]

im confused alot

[royal kiln]

CA and BD

you don't know what the angle is, but give it a symbol, like alpha

(the answer is obvious but I'm trying to show a logic train)

So lets say <AOC = <BOD = alpha

[lean otter]

160 ? still?

O, m∠AB = 20 degrees.

angle CDO is A

Pasting in the calculator doesn't work well on discord

And it doesn't help that I don't understand it

So it 160?

Damn

It's like 180 lmao

[granite idol]

aren't they just asking for mCD?

[lean otter]

Yeah

I don't understand what MCD is

It ain't mc donalds

[granite idol]

the measure of arc CD

[lean otter]

64

I aint the sharpest tool in the shed

[granite idol]

are you just guessing?

[lean otter]

No

[granite idol]

think about the problem

[lean otter]

Unsure

Yes

I don't know what mcd is

im so confused

IT may be 180

160

64

I don't know

So it's just the same as mab?

So it's still 20

Thats dumb

When will I use this info in the real world

So mCD is 20

atleast

?

I still dont understand how we got 20

[devout shale]

hopefully you can use problem solving skills and logical thinking on the daily

[lean otter]

thank you for trying to help me

Ah

But I aint got no circle in mine

[royal kiln]

.rotate

,rotate

[royal kiln]

"CPCTC" <--> "Congruent Parts of Congruent Triangles are Congruent"

oh shit, that's my car registration envelope

eh, I'll pay online

[lean otter]

This helped me alot

thank you

I now know why its 20

[royal kiln]

I know now why you try 😎

[lean otter]

I will use this knowledge when I build the teleporter in the future thank you

[royal kiln]

blech, nvrmnd

[royal kiln]

lol

[lean otter]

Thank you guys for helping me get thru the final exam

Ive passed geometry without knowing how the whole year

[royal kiln]

wat >:(

[lean otter]

just joking

[royal kiln]

this better not be from your final exam

[lean otter]

I learned alot from you guys

[royal kiln]

lol ok

[lean otter]

khan academy

I couldnt pass their stuff

They didnt help me learn

.close

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[unborn venture]

hi

[unborn venture]

i’m struggling with matricies

a lot

anyways i wrote this down and i wonder if im doing this right and what would be the next step

,rotate

[frigid locust]

Tbh i would interchange r2 and r1 first

Then make first digit of r2 and r3 zero

[granite idol]

and don't change into decimals

[frigid locust]

And then try to make 2nd digit of r3 zero

[unborn venture]

how did u think of that

[frigid locust]

6 , 2 , 8

2 times 3 is 6
2 times 4 is 8

Don't need to make it into 1 , just start

[unborn venture]

okay let me try this

[unborn venture]

usually the first step is to make it a leasing one

leading

it’s more different in this case?

[frigid locust]

Hmm?

U make it 1 cuz its easier because 1 times anything is anything

U already have 2 which is multiple of 6 and 8

[unborn venture]

yeah

so u would make that on top

the row 2 one

[frigid locust]

Yeah

[unborn venture]

what would u do next

make 6 zero

by how

2times 3 :6 so 6+-6

[frigid locust]

Yes

[unborn venture]

okok

[unborn venture]

and this for the bottom?

[frigid locust]

Yeah

See no fractions, clean work

[unborn venture]

ur right

okay for the first one

would u do those/

this

[frigid locust]

Why do u want to make it into a 1

[unborn venture]

to make it to row echolon form

[frigid locust]

u just want to find the answer , no?

[unborn venture]

well yeah

but

[frigid locust]

also theres no way u get -180

[unborn venture]

💀

wait one sec

-11

mb

[frigid locust]

i would make this into 0 now , but gotta think how to do that

[unborn venture]

hm

like this?

[frigid locust]

no then the 0 will cahnge

make the -4 into 1 first then it would be easier

by dividing with -4

btw u can turn that 2 in first row into 1 if u want cuz we are getting fractions sadly

hoped we wouldnt get any fractions

[unborn venture]

yeah i just checked the awnser and its fractions

okays let’s turn the top then

got this

[frigid locust]

now make the -4 into 1

this will help into making -3 into 0

[unborn venture]

i have no rations

equations

idk how to do it

wait

this one did it

[frigid locust]

hm?

make the -4 into 1 first

[unborn venture]

it made it a zero

yeah

i meant

one

ong

[frigid locust]

that doesnt work tho

[unborn venture]

omg

[frigid locust]

i mean

$\frac{-1}{4} R_{2}$

is what i was thinking

[flat frigate]

JustToPro

[unborn venture]

i’m h yeah

oh yeah

sm easier wth

[frigid locust]

that also works tho

[unborn venture]

okay

now we need the bottom a 0

[frigid locust]

yeah thats easy when r2 is 1

[unborn venture]

okie

imma do this

[frigid locust]

yeah its good

[unborn venture]

28 to a 1

times by 1/28 bottom?

[frigid locust]

yep

make the leading terms 1

[unborn venture]

bottom

okay cool

this row exholon?

[frigid locust]

how is that 0?

why is r2 2 times 0

that 0 is 1 ( ithink u made a mistake)

also yeah thats ur answer , change into x y and z

[unborn venture]

oh yeah

this the awnser

but wouldn’t one be 11/28 then

[frigid locust]

which 1?

[unborn venture]

like any

but at the bottom

a variable is 11/28

i feel that would be one of the awnsers as well

[frigid locust]

can u send ur answer

again

ill check why u are not getting -14/3 and are getting 11/28

[unborn venture]

,rotate

[frigid locust]

-7 - (-4) = -7 + 4 = -3 and not -28

-1/4 * -10 = 10/4 = 2.25

forgot to apply the row operation on the rest of the terms , only conveted the -3 into 0

@unborn venture ur mistakes ^^

[unborn venture]

omg

💀💀💀

one sec let me do

fox

[frigid locust]

correct then and check if u get correct answer

otherwise send ur working agian and ill chekc again

[unborn venture]

got this

,rotate

[unborn venture]

the 12.5 is supposed to be a 14

wait

it would be -3.5

idk

@frigid locust

[humble pilot]

how to solve this ques? i have gone crazy doin this

[frigid locust]

srry forgot about u D:

[frigid locust]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[humble pilot]

oh

[unborn venture]

it’s okay 💀💀

[frigid locust]

there should be no value for z

or maybe we made a mistake

[frigid locust]

u sure this the correct answer?

[unborn venture]

yeah

it it’s on the textbook

wait

just 4 mins

imma send the doing they did

[frigid locust]

ill check ur work again

found ur mistake !!

and then ur last term is
0 0 3/4 | -14/4
and then multiply it with 4/3
0 0 1 | -14/3

z = -14/3 and that matches with what im getting now

@unborn venture i did it , yay

we did it 👍

[unborn venture]

wait

i’m kinda confused

let me see

[frigid locust]

what are u confused about? ill help explain

[unborn venture]

i’m sure did the calculations wrong here

i

like for -3

right

[frigid locust]

,rccw

[frigid locust]

r3 + 3r2 is what u are trying to do

im guessing ur still here

[unborn venture]

yes

[frigid locust]

0 (from r3) + 3(0)(from r2) = 0

-3(from r3) + 3(1) (from r2) = -3 + 3 = 0

-3 (from r3) +3(5/4)(from r2) = -3 + 15/4 = (-12+15)/4 = 3/4

[unborn venture]

i got 4,5

4.5

[frigid locust]

-11(from r3) + 3(10/4)(from r2) = -11 + 30/4 = (-44+30)/4 = -14/4

4.5 is wrong , how did u get that

[frigid locust]

ig im smarter :p

[unborn venture]

u are 💀😭

[frigid locust]

write that again

and add another ) at the end

wait 0.75 is correct

[unborn venture]

i did it just didn’t show

[frigid locust]

u said u were getting 4.5 . 0.75 is equal to 3/4

[unborn venture]

yeha i changed it

mb

is -12.5 wrong

yeah this

[frigid locust]

yes

[unborn venture]

it is

it’s supposed to be -3.5

[frigid locust]

yeah

[unborn venture]

okay got it finally

tysm

would it have been the same awnser if i started by making the first a leading 1

[frigid locust]

yeah

[unborn venture]

okok

tysm fr

.close

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[stoic sage]

Can someone help me with question 4? I was thinking of doing it like what I have written so far for question 4 but it’s not right I think

[sour yew]

How did you ... reduce this fraction?

Am I seeing an assumption that the second and third coefficients form a geometric sequence ... but it should be the second and fourth?

$$\dfrac{T_3}{T_1}=\dfrac{T_6}{T_3}$$

I'm nervous about an off-by-one error (OBOE) here.

[flat frigate]

jolimath

[stoic sage]

thanks i got it now

[safe radish]

@stoic sage Has your question been resolved?

[safe radish]

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[hollow otter]

!status

[safe radish]

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

@fossil ledge Has your question been resolved?

[fossil ledge]

No

2

[safe radish]

@fossil ledge Has your question been resolved?

[fossil ledge]

Yes

[safe radish]

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[sour dome]

Help me with this inequalities question

.close

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[main frost]

oof

i was going to assist but alright

[sour dome]

If you can, then please 😁

[main frost]

so what im seeing that this is a modulus / abs value inequality yes?

[sour dome]

Yes

[main frost]

I'll just give you a clue and you can figure out the rest. So usually if both sides had modulus, i'd square them

[sour dome]

So take a square on both sides and solve them

[main frost]

yeah

[sour dome]

can I try solving it and show it you

[neat fable]

be careful of introducing extraneous solutions

[main frost]

Ohhh yeah right.

[safe radish]

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[sour dome]

I think I'm being stupid here

[sour dome]

😬

@main frost

[main frost]

hold on lemme see

mmm looks correct yeah

lemme check if there';s anything we might've missed.

m

should be correect

👍

you can put in numbers below or above 0 to test.

[sour dome]

ok

I have done inequalities question but I never did one where there is a modulus on both sides

[mortal thicket]

easiset way is to bring it all to one side

and draw the graph

[main frost]

you can do that, yes, but I think the question didnt want him to draw using graph

[sour dome]

Haven't used graphs, do you have any example like this question

[mortal thicket]

otherwsie u have 4 cases

[mortal thicket]

do u know how to draw absoulte value graph

[mortal thicket]

algebraically is a lot more tedious

[sour dome]

Lemme send an example of a question I did

[mortal thicket]

,rotate

[main frost]

WAIT

isnt ur question this

why did u right 2x-5 on RHS

[sour dome]

Do we change the position?

[neat fable]

huh, my answer was -3/7 < x < 7/3

[sour dome]

Can you please show the steps

[mortal thicket]

hes ur graph on desmos

[neat fable]

why are you all doing different questions

|2x + 5| > |2 - 5x|

[mortal thicket]

i meant hsi one

[main frost]

i got x<-3/7 and x>7/3

[neat fable]

is the original problem, right?

[mortal thicket]

yeah thats it

[sour dome]

Yes this is the original problem

so what is the answer 💀

[mortal thicket]

x<-3/7 and x>7/3

[sour dome]

can you please share the steps?

@mortal thicket

[mortal thicket]

do u wnat how i would do it or like full algebraically?

[sour dome]

this is the first time of me trying to do this double modulus question, so whichever method is more convinient

[mortal thicket]

try doing these types graphically if uc an

its just a lot faster

[sour dome]

This is how I do the questions btw

[mortal thicket]

ill show u how to make tehg raphs

its really easy for abolute values

[sour dome]

Thanks please show it

[main frost]

yay im corerect

[flat frigate]

misha

[neat fable]

then analyze the inequality again and test intervals

[mortal thicket]

see how long that is

[sour dome]

wow, thanks @neat fable @mortal thicket @main frost

[mortal thicket]

now u just fine which branch givees u the line and u find the x-int

[sour dome]

Ok thanks

[neat fable]

are your signs reversed

[mortal thicket]

i copied that fromt he toher guy

[neat fable]

,w |2x + 5| > |2 - 5x|

[flat frigate]

Results provided by WolframAlpha

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

Requested by misha.51

[neat fable]

…

[neat fable]

how,,

[sour dome]

ok this is confusing me 💀

[neat fable]

the correct answer is -3/7 < x < 7/3

[atomic pebble]

atp just split it into cases

[neat fable]

[atomic pebble]

yeah 😅

[neat fable]

still correct in the end

[atomic pebble]

you put the original equation in there?

or sorry inequality

[neat fable]

yes

[atomic pebble]

we're talking abt this right?

[sour dome]

Yep

[sour dome]

You are putting >=, its only >

[atomic pebble]

these can be a little confusing but since you have a simple line in absolute values

[atomic pebble]

yeah if its > then just (0, inf)

[atomic pebble]

its best to draw it

since its an easy line to draw ofc

and then see from the graph

[sour dome]

which app is this btw?

[atomic pebble]

oh, it's the classic photomath 😄

there it goes into cases and calculates from there

but to not do so much work just draw it

[atomic pebble]

here you're squaring both sides but you cant do that if both of them arent positive

so you're missing cases

[sour dome]

https://tenor.com/view/nouns-nounish-nounsdao-abacus-counting-gif-16562575250327679873

[neat fable]

are you saying both wolfram alpha and photomath are incorrect, and the problem should be interpreted differently

<@&286206848099549185> can someone please check our solutions

i myself am getting confused now

[atomic pebble]

well I put it in photomath and it gives me 0 to infinity

[neat fable]

because you changed the sign

[atomic pebble]

what sign

[neat fable]

inequality

[atomic pebble]

the >= ?

[neat fable]

yes

[atomic pebble]

even if you do just >

it'll be (0, inf) without 0

= just includes 0

[sour dome]

This is what I'm getting on photomath

[atomic pebble]

wolfram alpha also says the same thing

[neat fable]

you put the wrong inequality, again

[atomic pebble]

oh sorry yeah wait

wait no I didnt

[neat fable]

|2x + 5| > |2 - 5x|

[atomic pebble]

yeah

[sour dome]

I put >

[neat fable]

WHAT ARE YALL DOING 💀

[atomic pebble]

what's wrong?!

[neat fable]

are we not solving |2x + 5| > |2 - 5x|??????

[sour dome]

IDK I have my mids in 2 days 😭

[sour dome]

yeah that's exactly what I wrote there

[neat fable]

no that’s NOT what you wrote there

[atomic pebble]

oh 2 - 5x lemme see

[sour dome]

Wait what 💀

oh yeah

you are correct

[neat fable]

stop making remixes of the original question

[atomic pebble]

my bad I mixed up the terms

well then of course I assume your solution is correct.

[neat fable]

great so we concur

[atomic pebble]

I do apologise

[neat fable]

no problem

[atomic pebble]

🙂

[sour dome]

Yep @neat fable is correct
Here's your crown 👑 🛐

[neat fable]

💀ty

but did you understand the workings?

[sour dome]

Yes I did

Thanks a lot

This is a confirmed question from the upcoming exam, I have now secured 10 marks

hehe

[neat fable]

huh

so we just helped you cheat on an exam…?

[main frost]

PLOT TWIST OF THE CENTURY, and my bad, i think i didn t change sign for the inequlaity

Made a lil error

[neat fable]

oh no we are all getting banned from here

[sour dome]

Nah, I understood the thing, there will of course be more questions. The teacher just told us that this question is confirmed and there will be more questions adding up to 10

[neat fable]

uh ok

[sour dome]

so I understood the methodology

Now I can easily do the rest

[atomic pebble]

Might be best to just close

and goodluck

[sour dome]

🫡

.close

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[acoustic osprey]

hey there, I am minimizing the regularized least squares $f(x)=\frac{1}{2}\norm{Ax-b}{L^2(\Omega)}^2+\frac{\alpha}{2}\norm{x}{L^2(\Omega)}^2$. That I did just fine by doing basic steps (see the attached photo). Where I used the classic result from matrix calculus $\frac{\partial x^TBx}{\partial x}=2Bx$, where $B$ is a symmetric matrix, solving for $\hat{x}=(A^TA+\alpha I)^{-1}A^Tb$.

What I am struggling with is how would I go about solving the same problem is the regularized term is in the $H^1$-norm so $f(x)=\frac{1}{2}\norm{Ax-b}{2}^{2}+\frac{ \alpha}{2}\norm{\nabla x}^2{H^1(\Omega)}$ (last picture) I tried to to the same calculations but my matrix differentiation needs a little bit of brushing, any resources maybe? thanks

[flat frigate]

nani?

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[stoic sage]

How to get to the correct answer nC4 times 2^4?

[pseudo scroll]

1^(n - 4) = 1 for all n

so you don't have to worry about that

you can just use the laws of exponents $(xy)^n = x^ny^n$

[flat frigate]

Sadie Carnot (η > 1)

[stoic sage]

Oh okay thanks but how did they cancel out the X to get to 2^4 because that’s the correct answer given

[pseudo scroll]

They didn't "cancel" it

We're looking for the coefficient of x^4

That means you need the number that's multiplied with x^4

[stoic sage]

Oh yeah right

[stoic sage]

Thank you

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[dusky spruce]

Please can someone check my workings for this Greens function

[dusky spruce]

I'm pretty sure my residues are correct

$\theta(t)$ is Heaviside function btw

[flat frigate]

Jacob

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@dusky spruce Has your question been resolved?

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@dusky spruce Has your question been resolved?

[dusky spruce]

<@&286206848099549185>

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@dusky spruce Has your question been resolved?

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[rotund cobalt]

im trying to find the solution by sketching the slope field here and connecting the points but instead of 1/x, my slope field actually resembles a plot of x^3 since I did not really know there would be an asymptote at x=0. Do I have to solve the equation before plotting the solution using a slope field?

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@rotund cobalt Has your question been resolved?

[rotund cobalt]

<@&286206848099549185> bump

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[spice plank]

What does your course mean by a "phase diagram"? Usually (or at least in my experience) we only talk about phase diagrams for coupled systems of differential equations. It sounds like here they maybe just mean the slope field? But I want to check first before assuming it. @rotund cobalt

If we mean the slope field, you can look here: https://www.wolframalpha.com/input?i=x'%3Dx^2

And see the slope field if you scroll down a bit.

If you work from that slope field, then you can see x=0 is a critical point and is unstable because some curves (namely, those above x=0) leave the point (because they go to infinity).

When you see that x=0 is a critical point then you know your solutions cannot cross this line and therefore shouldn't look quite like x^3. In fact, I would say the solutions should look something like e^x because they go to infinity on the right, and converge to a finite value on the left, with no asymptote in-between (like you find with 1/x).

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[rotund cobalt]

yes its exactly this part that im struggling with. Why don't the solutions cross the critical point line?

[rotund cobalt]

also by phase diagram, it just means we draw a number line with all the critical point values and then classify each point as stable/unstable/semi-stable

tho that part i did get

i just had a q abt part b specifically

[spice plank]

No solutions to a differential equation can ever cross each other. The proof is not easy but the intuition is basically that, if two solutions cross then they would have the same point and derivative and just become the same solution. Anyway, solutions can't cross.

And here, if x=0 is a solution (which, critical points are basically constant solutions), then nothing can cross it.

[rotund cobalt]

how do you know that critical points are constant solutions? you set the derivative to zero to find them but what makes them a solution?

nvm i think i get it

Because you set the derivative to zero , x= the critical value becomes a constant solution.

thx for the help.

.close

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[fickle eagle]

Im struggling in a kid math, if i click a button, i have 10% of getting an apple, so if i click the button 12 times, whats the % of me getting exactly 2 apples?

[lean otter]

This can be solved with the binomial distribution, do you know the formula for this?

[fickle eagle]

No can i have the formula please

Thank you

[delicate patio]

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

[flat frigate]

joren

[delicate patio]

where

n = number of experiments
x = number of desired success
p = probability of getting success on a single experiment
q = 1 - p = probability of getting a failure in a single experiment

https://www.youtube.com/watch?v=rvg9oUHtX50

this video really helped me to understand it

[fickle eagle]

Thank you so much

[delicate patio]

My pleasure!

[fickle eagle]

Hi this maybe really dumb to ask but what if its 2 or more?

[delicate patio]

what do you mean?

Have you tried plugging in your values and cross referenced the result with the answer?

n is the number of experiments (button clicks): 12
x is the number of desired successes (getting exactly 2 apples): 2
p is the probability of success on a single experiment (getting an apple in one click): 0.1
q is the probability of failure on a single experiment: 1−p = 0.91−p = 0.9

you can adjust the values if your context changes, that would be no problem

$P(X = 2) = \binom{12}{2} (0.1)^2 (0.9)^{10}$

[flat frigate]

joren

[lean otter]

You can add P(X=2) + P(X=3) ... P(X=12) But that would be dumb and too much work. Instead calculate probability of the .. co event.. anti event .. idk what to call it

But essentially, in this case it's probability of less than 2 so P(X=0) or P(X=1)

And add those together

[fickle eagle]

I got the answer for the only previous question but is there way to calculate if the question ask for 2+

[fickle eagle]

So what if the question say ask the possibility of P(X=1000) out of 2000 attemps

[lean otter]

I think I explained this, but anyways

[fickle eagle]

More than 1000

[lean otter]

More than 1000 out of 2000 attemps? Damn that sounds like a lot of work

[fickle eagle]

Thats why i cant just adding up

[lean otter]

Well I don't know any shortcut for this, other than to use a tool to do it for you, like geogebra or python

[fickle eagle]

I got to show my work tho i cant just write down the answer

[lean otter]

Is your question really P(X>1000)?

[fickle eagle]

Yeah it is

Out of 2024 attempts

[lean otter]

Well dang

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[rough matrix]

Hi

[rough matrix]

Find the equivalent resistance of the following resistors in this circuit section.

How do i do this

[median vigil]

find the ones already in series or parallel, then replace them with an equivalent resistor and repeat

[jovial linden]

I'm too lazy to be explaining rn, now gn (if wrong srry)

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[rough matrix]

I think its drawn wrong

???

What is the correct answer? Is it 3.8

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@rough matrix Has your question been resolved?

[desert juniper]

You would start by computing the equivalent resistance on the rightmost branch, with the 4 and 6, which are in series.
You would follow with the ones in parallel of 9 an 8.
The results of both (i'm gonna call a and b) will be in parallel, so you get the equivalent c.
c and the one of 3 ohms are in series, so you get the equivalent d.
And last, the 20 and d are in parallel, so you get the equivalent total

Also, since Taco has copied two values wrong, his solution is wrong

[rough matrix]

What is correct answer?

[desert juniper]

we're not supposed to give you the answer. We're supposed to help you get the answer yourself

do you know the equivalent resistance of two in series?
do you know the equivalent resistance of two in parallel?

[rough matrix]

My answer key says 4.6 is that right?

[desert juniper]

im not getting that

[rough matrix]

Can u tell me what u get

Did u get 3.8?

Or can we work through it together step by step cause im rlly confused

@desert juniper

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[rough matrix]

<@&286206848099549185>

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[static dawn]

I’m dealing with a compound interest question, I get an abnormally large number when I try to plug it in, so I can’t really seem to find out what i’m doing wrong.

[static dawn]

question 16

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[static dawn]

<@&286206848099549185>

[obtuse plover]

@static dawn

Still need help?

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@static dawn Has your question been resolved?

[static dawn]

yes, sorry for late response

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[lean otter]

should I study riemann steiltjes integral in depth before starting lebesegue theory or can i skip it

[devout shale]

#real-complex-analysis is probably better to ask this in

[lean otter]

.close

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[solar hazel]

you can skip it

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[random copper]

how can i do this

[tepid walrus]

multiply the numerator and denominator by s and you'll get a form like $\frac{1}{a^2+s^2}$

[flat frigate]

ℑμΤ𝛄𝛗θ

[tepid walrus]

oh wait nvm no

I misread

[lean otter]

uhh

[gusty trench]

multiply the top and bottom by S

and you'

you'll get something like a constant on top and a quadratic in S on the bottom

which you can mess around with to get into a form like either formula I or formula K here

correction, it will specifically look like formula I

[random copper]

soo, i get $\left[ \frac{1}{100s + 20000 + s^2} \right]$

[flat frigate]

Melo

[random copper]

what i do then

[gusty trench]

can you factor the denominator

sorry, to clarify you might not necessarily be able to factor it, but can you get it into the form (s - a)^2 + b^2

perhaps by completing the square?

[random copper]

$ \left(s+50\right)^2 + 17500 $ ?

o my

$(s+50)^2 + 17500$

[flat frigate]

Melo

[random copper]

does it have to be a subtraction?

[gusty trench]

it doesn't have to

if it was subtrarction, that would look like formula K

but here you get something that looks like formula i

a would be -50, and b would be sqrt(17500)

this is almost in the correct form, except you have 1 / ((s+50)^2 + (sqrt(17500))^2)

and you want it to look like sqrt(17500) / ((s+50)^2 + (sqrt(17500))^2)

as per the formula from the table

[random copper]

then I take 50 as negative..

[gusty trench]

so if you multiply and divide by sqrt(17500) you can get something of the right fomr

[random copper]

i didn't know that I could change the sign

[gusty trench]

you're not changing the sign

the formula has their example looking like (s-a)^2

but here you have (s + 50)^2

comparing things in the formula, this means -a = 50 so a = -50

anyway you have it in the right form so you can identify what a and b are, plug them into the inverse laplace transform formula on the right, and then there's your answer

[random copper]

oh right, so i have $e^{-50t} \mathscr{L^{-1}} \frac{1}{s^2 + 17500}$

[flat frigate]

Melo

[random copper]

$e^{-50t}\cdot\frac{1}{\sqrt{17500}}sin(\sqrt{17500})$

[flat frigate]

Melo

[random copper]

¿?

.close

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[lean otter]

can someone explain me derivates in limits (the basic fundamentals and some ideas to calculate them)

[slender nacelle]

you mean first principle definiton

right?

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@lean otter Has your question been resolved?

[lean otter]

yes

ping me when u respond

so i can see faster

[slender nacelle]

imagine this curve and suppose we have joined the two points A(x,f(x)) and B(x+h,f(x+h))

[slender nacelle]

so what we do is we basically find the slope of this line AB and put the limit of h to tends towards zero

which means we find the slope as the point B comes really close to the point A but never coincides it

[lean otter]

oh

[slender nacelle]

we can make the point B come closer to A by reducing the distance between them to 0

[slender nacelle]

which we do by putting the limit of h tends to 0

[lean otter]

so lim of h tends to 0 of what i need to calculate to find the slop of the AB

[slender nacelle]

yeah

[lean otter]

oh

[slender nacelle]

that is the derivative of this curve

what you are supposed to do is first find the slope of the line AB

i.e. f(x+h)-f(x)/h

and then put the limit of h tends to 0

[lean otter]

but why mathematics genius needed this problem solved

like how it beggined?

[slender nacelle]

I mean like you know Newton invented calculus to build his laws of motion and all

[lean otter]

yes

[slender nacelle]

To understand the motion of an object we need to find its accln and velocity right?

and all of those things is basically the rate of change of position

[lean otter]

yes

[slender nacelle]

that is where all of this generated

that is why we find the derivative of a function which literally means the rate of change of the function

[lean otter]

oh so with this formula we can know the rate of the new pos?

[slender nacelle]

its like imagine this curve to be the graph of position of an object vs time

then the rate of change of this curve gives us the velocity of the object

[lean otter]

oh wow

interesting

[slender nacelle]

like in this case we find the derivative at A right so we can find the velocity at that instant

[lean otter]

so the curve can give the rate of velocity?

[slender nacelle]

similarly if we find the derivative at all the points we can graph the velocity vs time graph of the object

[lean otter]

ye and make a statistic based on that

[slender nacelle]

yeah the tangent of the curve is the graph of the velocity at the instant

[lean otter]

tysm

[slender nacelle]

you can see the light blue line is the tangent here

[slender nacelle]

nvm

[lean otter]

.close

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[ruby delta]

Which expression can be represented as the square of the sum or the square of the difference?

[ruby delta]

<@&286206848099549185>

<@&286206848099549185>

[young nexus]

!status

[safe radish]

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

[ruby delta]

1. I don't know where to begin.

[young nexus]

do you understand what youre asked to do? if yes, explain it in your own words.

[ruby delta]

sec

[ruby delta]

no

.close

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[chrome rampart]

so I have 2sin^2(theta) + tan(theta) and I have to differentiate it wrt theta

[chrome rampart]

I applied power rule and got 4sin(theta) + sec^2 theta. Isnt it correct?

[remote verge]

Chain rule

[chrome rampart]

Why tho

I watched online videos about this question and they said the same too, but I dont get the logic

as we're differentiating theta wrt theta, so why use chain rule?

[remote verge]

The power rule you use here is only applicable on simple powers of x

Like x²

[tidal imp]

Because when you use power rule, you end up differentiating with respect to sin x

[remote verge]

Chain rule allows you to have anything as that base

[chrome rampart]

isnt theta wrt theta same as x wrt x?

[tidal imp]

Yes but again using the power rule on sin^2(x) is with respect to sin(x)

[chrome rampart]

like cant we consider

   d(x)

[tidal imp]

Well yes but that’s why chain rule exists

[chrome rampart]

Uh I dont understand...

I was taught we use chain rule when differentiating wrt something else...

[tidal imp]

Try this

Differentiate wrt x: $(2x+1)^2$

[flat frigate]

CST (please ping when replying)

[tidal imp]

Use chain rule first, then expand and do power rule

They should be identical

[chrome rampart]

2(2x+1) * (2)

8x +4?

[tidal imp]

Yep

Notice: why did you multiply by 2 again?

[chrome rampart]

because We need to multiply by the derivative of the inner function

[tidal imp]

Yes!

Same thing with sin^2(x)

Except instead of 2x+1, it’s sin(x) in the inner function

[chrome rampart]

isnt derivative of sin^2(x) wrt x = 2sin(x)?

[remote verge]

No

You have the apply the same thing you just did for (2x+1)²

[chrome rampart]

OH WAIT

[flat frigate]

CST (please ping when replying)

[chrome rampart]

yeah

makes more sense now

so it will be 2sinxcosx

right?

[tidal imp]

Ye

[chrome rampart]

ohh

fk

i was analysing my test lol, now its a -1 mark 🥹

if I didnt make that dumb mistake it wouldve been +4 instead

Anyways, thanks for the help!

btw

I have another question

integral(3sin(2x) dx) limits: 0 --> pie/2

we get (3/2) * integral(sin(2x) d2x)

equals -3cos(2x)/2

wait...

im so bad

.close

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brazen parrot]

How would i do bii

[split fulcrum]

BUM CHICKEN

[brazen parrot]

HI WATERBEAM

i did my englishe xam today

it was so bad

[brazen parrot]

HOW WOULD I KNOW ITS NEGATIVE

[split fulcrum]

The cosine of an obtuse angle is negative

[split fulcrum]

F

[brazen parrot]

how do u know its an obtuse angle

[split fulcrum]

Doesn’t the question tell u that

[brazen parrot]

WAIT

is there any orher way to know

thats too hard to tmb

rmb

cuz i dont understand it

[desert pasture]

if the angle is more than 90 but less than 270 its cosine is negative

[brazen parrot]

oh makes sense

LOL

its in the second quadrant

[slender nacelle]

you can rmb by the unit circle rule

ASTC

[brazen parrot]

all students talk crap

f(3x)

waii do u hav any idea how i can do bii

[desert pasture]

nice keyboard :D

[brazen parrot]

thx :P

[desert pasture]

let me think

[brazen parrot]

this my whole setup dont mind its a little bit messy

yk exam week

[desert pasture]

one minute

[desert pasture]

woah

[slender nacelle]

my friend has the dream setup

[desert pasture]

well, f(3x) means that each input is tripled

[brazen parrot]

how come it gets smaller?

[desert pasture]

so at one it's mapped for f(3)

[split fulcrum]

Basically it’s going to horizontally dilate by a factor of 1/3

[brazen parrot]

why

[slender nacelle]

yeah

[split fulcrum]

Every x coordinate will now be 1/3 the original

[desert pasture]

you're tripling each input

so you're squishing the graph

[brazen parrot]

so da input is

it starts at -6,-3

uh

-6x3 ?

[desert pasture]

pretty much, but you only know the output for f(-6)

so take x=-2

[brazen parrot]

im confused how did it get smoller

so how would i use f(3x) to graph it

[desert pasture]

you only know f(-6)