help-0

[nova anvil]

double jump 🙂

[shrewd sable]

Have you tried taking the derivative of your u with respect to t?

Not sure why you have the cos term

[nova anvil]

ok so, what happens is that i think the general form is just $u(t) = e^{\lambda t}$

[ocean seal]

Anticipation

[shrewd sable]

Yeah

[nova anvil]

but since lambda is a complex number and it asks for solution on a real interval

im not sure anymore

so i used euler formula and got rid of the complex part

[shrewd sable]

t is on a real interval, lambda can still be complex

[nova anvil]

i see, thanks

out of curiosity, for 2nd order linear homogenous ODE why is there no complex numbers?

wait i think i see

[sick palm]

how would i make this a algebraic expression?

[nova anvil]

m+5 = m/4-3

[sick palm]

thank you

[tepid cargo]

Anyone have a answer for this?

The question is Lauren is 3 years older than Megan and Alyssa is 3 years younger than Megan. The sum of their ages is 42. How old is each girl?

[sick palm]

there's 3 girls correct?
Lauren - Positive
Megan - Neutral
Alyassa - Negative.
create a function. then you got your answer (im p sure atleast. im not great at math myself)

[tepid cargo]

U r correct. Wdym by creating a function?

[shrewd sable]

What do you mean by positive, neutral and negative? All their ages will be positive numbers

[sick palm]

like i said im not sure lmao

[shrewd sable]

Let their ages be L, M and A

From the first piece of info, how are L and M related?

[tepid cargo]

L is 3 years older than M

[shrewd sable]

yes

So $L = ...$

[ocean seal]

0003c9fe

[tepid cargo]

M+3

[shrewd sable]

Yep

And then now you can do a similar thing with M and A

[tepid cargo]

A=M-3

[shrewd sable]

Yep

And for the last piece of info?

[tepid cargo]

42=L+M+A

?

[shrewd sable]

Yup

So that gives you 3 equations, which you solve simultaneously to get the ages

[tepid cargo]

Still a bit stuck on that

[shrewd sable]

Do you know how to solve systems of equations which have 2 variables?

[tepid cargo]

Yes I just need to figure out what I'm solving for in the equation. For example, am i solving for m in "L=M+3"?

[shrewd sable]

Well if you subsitute L = M+3 into the L in the other 2 equations, then you just get a system of equations with 2 variables M and A

Then you can solve those for M and A, and then L is just M+3

[nova anvil]

so heres my solution for this problem, idk if its correct to say U(T)-> infty if re(lambda) > 0 when theres a residue complex part, since i havnt done complex analysis before lol

complete noob at complex number

oh and my alpha is just re(lambda), its a typo

[sick palm]

do math use all greek leters? i.e alpha, beta, gamma, delta, episolon, etc.?

[shrewd sable]

Those are greek numbers, but yes

[sick palm]

lmao my b

[shrewd sable]

And yeah I'm not really sure on the complex analysis part so can't help there

[rich basin]

<@&286206848099549185> please help

[shrewd sable]

1. You have to wait before pinging helpers
2. You already have the function x, so just calculate the first and second derivatives and subsitute them in?

[rich basin]

what do you mean by the second derivative?

[alpine sable]

the thing you get when you differentiate a function twice

[rich basin]

how does this want me to find the second derivative

[alpine sable]

d^2x/dt^2 is the second derivative

in leibnitz notation

its the same as x''(t)

in newton's notation

[rich basin]

i mean if i do that, this willb e an extremely messy equation

[alpine sable]

its not that bad

just use the product rule

then just plug in the 1st and 2nd derivatives into the equation

[muted raft]

This is going to have a very clean derivatives compared to many other functions.

[tired wharf]

ahem how do i do this

[shrewd sable]

Dont multipost, your question was already answered in the other channel

[tired wharf]

I didnt get what they meant though

[shrewd sable]

I explained it as well

And if you didn't understand an explanation just ask for clarification in that channel rather than posting it again elsewhere

[tired wharf]

oh i didnt see let me go look

[rich basin]

so for a derivation of 25te^5t

i mean 5te^5t. do you use use the product rule?

what would the derivaive of that would be

[muted raft]

,w derivative (1+t)*e^(5t)

[ocean seal]

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[shrewd sable]

Yes you use the product rule

[rich basin]

,w derivative 5te^(5t)

[ocean seal]

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[edgy zealot]

Yes right ?

[shrewd sable]

Yes

[edgy zealot]

@shrewd sable I kind of get it but I sort of don’t because I got one wrong earlier I’d there a way to figure out how

[shrewd sable]

do you notice anything in particular about the side lengths of the triangle?

[edgy zealot]

I might sound dumb but no

[shrewd sable]

3^2 + 4^2 = 5^2

[edgy zealot]

25=25

So basically if they equal the same they’re tangent right ?

[shrewd sable]

What type of triangle does Pythagoras theorem apply to?

[edgy zealot]

Right triangle

[shrewd sable]

Yes, so that top angle is a right angle

So the line KM is at a right angle to the circle

So it's tangent

[edgy zealot]

For this one I got no

73^2+29^2=79^2

5329+841=6241

6170=6241

[shrewd sable]

Yep, so it doesn't follow Pythagoras theorem, meaning it's not a right angle triangle

[edgy zealot]

Bet I get it now thank you

Now I’m stuck on this one

[shrewd sable]

In a right angle triangle the hypotenuse is the longest side

[edgy zealot]

N is the right triangle and q is the hypotenuse

[shrewd sable]

You could also think of the line NM as being x long, and then noting there's no solution to x^2 + 24^2 = 18^2

[edgy zealot]

I don’t get what u mean

[shrewd sable]

well if it was a right angled triangle, then it follows Pythagoras theorem, right?

[edgy zealot]

Yes

[shrewd sable]

So then (NM)^2 + 24^2 = 18^2

But no matter what length NM is, that's not true

[edgy zealot]

So what would I do

[shrewd sable]

Well it's the same as the previous ones, it doesn't follow Pythagoras theorem, so it's not a right angled triangle

Oh wait I misread the question

[edgy zealot]

But for this one I have to put a number

[shrewd sable]

Thought it was another tangent one whoops

[edgy zealot]

Oh lol

So would I do the same

[edgy zealot]

.

[shrewd sable]

Not quite, let me write it out again

So since they're both a radius, NM = QM, right?

[edgy zealot]

Yes

[shrewd sable]

So then how long is PM?

[subtle bay]

a radius that meets a tangent has to be right angled

so MNP is the right angle right?

[edgy zealot]

Yes

[subtle bay]

then from there you can pythag things or even use vectors and dot products if thats whats required

ah wait

i didnt see the Q

[edgy zealot]

Im so confused is there a formula that I should know

[subtle bay]

okay okay, no its that they both ahve to be radius's coming from the centre of the circle

[edgy zealot]

Yea

Nm and mq are the same

[subtle bay]

so we will treat the radius as x right

[edgy zealot]

But I’m confused on how to find that number

Yes

[subtle bay]

(18+x)^2=x^2+24^2

[edgy zealot]

How did u find that formula

Wait nvm I get it

[subtle bay]

thats jsut pythagorus, oh okay cool

yea its wierd cause technically you have two missing values but its kinda the same value so you can just algebra it in with pythagorus

might be wrong though

[edgy zealot]

Would the first part be 324x

Or 324 + x

[subtle bay]

324+x^2+36x=x^2+5776

[edgy zealot]

I don’t think that’s right because I end with decimals

[subtle bay]

yea, i got no clue then

[shrewd sable]

That's the correct method

[subtle bay]

thought so

[shrewd sable]

You should get an integer, since it's 7

,ask solve 324+x^2+36x=x^2+5776

[ocean seal]

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[shrewd sable]

hmm maybe you expanded wrong

,ask solve 24^2 + x^2 = (18+x)^2

[ocean seal]

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[shrewd sable]

Yeah, the method is correct

[strong furnace]

8 km is the diameter not the radius

Bruh

You're not supposed to get help for your test

The rules

<@&268886789983436800>

[muted raft]

I can easily tell whether a question is from a test or practice.

At least most of the time.

Which is why I only decide to help by checking the questions out first...

[echo pawn]

What do R and L represent in this?

[shrewd sable]

It probably says it earlier in the document, or its defined in your notes, but if I had to guess it would be the right or left hand Riemann sum with n rectangles

[echo pawn]

nah, not mentioned earlier, that's the top of the doc, but I think Reimann makes sense!

[latent thistle]

<@&286206848099549185>

[alpine sable]

ok

please help in the 3rd one

<@&286206848099549185>

[acoustic shadow]

x(x+1)=2862 solve this expression @alpine sable

[alpine sable]

bruh what

i havent even learned that

where did algebra came in

this is square roots

[edgy zealot]

A^2+5^2=12^2?

Is my equation right

Wait nvm I got the right angle wrong

[acoustic shadow]

How old are you

[alpine sable]

13+

why do you care?

[edgy zealot]

Damn chill lol

[acoustic shadow]

Because if you can’t solve quad equations you’re not 13

[alpine sable]

i know people who are below 13 cant be on discord

i know linear equations lmao

i learnt it when i was 11

[acoustic shadow]

Not a good progress from 11 then

[alpine sable]

2x+1-2862?

then 2x= 2862-1

am i right or wrong

[acoustic shadow]

Wrong

[alpine sable]

then correct me

and tell me the right equation

[acoustic shadow]

It’s straight forward ig you must figure it out yourself

[oak lodge]

if you write it out and do the line arrow from x going to the x and to the 1 it makes it easier

[alpine sable]

@acoustic shadowplus did you read my question? it says long division method

[acoustic shadow]

Yes I’ve read your question

Just telling you a very quicker approach so you can always recheck your answers within seconds

[alpine sable]

we gotta do this

[alpine sable]

yea but the question asks something else

[acoustic shadow]

Nvm

[oak lodge]

god damn long division is aids. never learned that even when i was that age haha. calculators saved me

this looks like a good practice for long division https://www.onlinemath4all.com/square-root-by-long-division-method.html

[alpine sable]

yeah long division is a pain in the ass

[rich basin]

,derivative 5/(2+3e^(-t))

,w ,derivative 5/(2+3e^(-t))

,w derivative 5/(2+3e^(-t))

[ocean seal]

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[rich basin]

i'm rather confused on how did they get this derivative

[acoustic shadow]

Quotient rule

[rich basin]

couldn't i just use chain rule and bringing it to the top

wait i can't

[solar cradle]

The chain rule does work here too

[rich basin]

how do we find the range of the left hand side

[solar cradle]

The range of the derivative?

It's the same as the range of the right hand side, it's an equality

[rich basin]

i mea nthe range of the lefthand side

[solar cradle]

oh the range of the original function, the range is the set of all possible values the function can take

[rich basin]

so what method do i use to find the range of this

[solar cradle]

Assuming the function is defined on for all real t, you can think about the maximum and minimum values the function can take. If the function is continuous, then the range is all values in between

[rich basin]

yes

[solar cradle]

The only function you'll need to consider here is the f(x) = e^(-x), then given that range you can determine the range of the function you're interested in

[rich basin]

So i jsut basically plug key numbers in the calculator

such as t = 0 and t negative infinity and positive

[solar cradle]

not exactly, you'll be working with infinity. Have you covered limits?

[rich basin]

yes

so i just make it limit of t as it approaches infinity into the calculator

as well as limits of t approaching negative infinity

[solar cradle]

Yes, but you won't need to use a calculator and it'll probably be better practice to not use one

[rich basin]

i mean multiplying numbers of t with the e is extremely large quanity number when approaching infinity

[alpine sable]

@solar cradle hi how old r u u seem like 20 or above just askin

[solar cradle]

Why do you ask lol

[alpine sable]

just askin XD

if u dont wanna tell its ifne

fine

[rich basin]

so 2.5

because the e disappears as it reaches an infinite number

[solar cradle]

Yes, but be a bit more careful, e^(-t) goes to zero as t goes to infinity

[rich basin]

yeah, that was what i had an idea of

[solar cradle]

@alpine sable I'm a student in university if that's sufficient lol

[alpine sable]

Well cool

[solar cradle]

Great, now just consider what happens as t goes to negative infinity

[rich basin]

doesn't the value become a smaller number

because 5/ any infinity quantity would make it extremely small

[solar cradle]

Exactly, more specifically it goes to zero

[rich basin]

wait why

wouldn't any number divide by 0 become undefined

and with an expoenntial it can't go down to 0

[solar cradle]

As t goes to negative infinity, 2 + 3e^(-t) goes to infinity. So 5/(2+3e^(-t)) approaches 5/ (infinity) = 0

[rich basin]

oh yes it does, i remember that the limit for the infinity is not exactly the 2.5 but i just rounded it up to 2.5

[solar cradle]

The limit as t approaches infinity is exactly 2.5

[rich basin]

One question so for the limits right, what number do i round up to?

like i could say that t approaches infinity as well can be 2.49

Anyways, thanks alot

[alpine sable]

Hello

[solar cradle]

No, the limit is never rounded. I would suggest reading up on the explicit definition of the limit @rich basin

[rich basin]

okay thnaks

[simple hamlet]

hi guys im new here

[split slate]

Good to see you! Welcome! Just as a sidenote, please try to keep these channels for help only. Feel free to to either #discussion or #chill (#chill is better)...

[sullen steeple]

I need quick help. I consulted my friend and he said that x=7 because the bases of the logs are the same so we could divide to get 7 and i agreed. But I used a math calculator just incase because the property "log(a•b) = log a + log b" was confusing me a bit, but it got x=24.

[rigid smelt]

divide what by what

[sullen steeple]

4 to 28

[rigid smelt]

you meant divding both sides by log_6(28)?

here you can have two options, either, apply the product identity which you said above, or use the inverse identity

and btw, the answer is not x=24

you might have done something wrong

[sullen steeple]

phew alright, it was driving me crazy for a while now

[rigid smelt]

i dont really understand what your friend did, but applying the product identity is the correct path

[sullen steeple]

ill try to use those tips, thank you. ill come back in a bit if i need more help

[alpine sable]

What the line called?

like that line

8/6 like that

[rigid smelt]

division line?

or fraction

i guess

or division bar

[alpine sable]

@waler#0265 So

How do I solve it

[rigid smelt]

its not really an equation to solve

[alpine sable]

@rigid smelt can I have help tho?

[rigid smelt]

i suppose you meant calculating

and you dont have to ping me

[alpine sable]

Ok

[rigid smelt]

so, first could you tell me what is a/a is?

where a is some number not equal to 0

[alpine sable]

It's a new lesson for me 👀

My module doesn't even give a single clue

It's like answer this thing!

[rigid smelt]

then thats kind of weird how you have to do these exercises

you should probably read your resources first

or else its gonna be a hassle

[alpine sable]

It doesn't even give me resources.

My module didn't give me a single clue

[rigid smelt]

have you asked your teacher about it

or have your teacher taught you anything?

If not, i think it would be better if you do this after they have taught you, else doing these exercises wouldnt mean anything

[alpine sable]

@rigid smelt how do I solve it tho?

[rigid smelt]

like i said, if you havent been taught about this, you shouldnt be doing this just yet

[latent thistle]

Hi can someone help me with pt 2 i got 1 and know how to get 3 <@&286206848099549185>

[radiant skiff]

,iam Advanced

[ocean seal]

Gave you the Advanced selfrole.

[lucid shuttle]

Well hello there

I have this question

if Y = 4x^2 times log(x)

then what is Y' =

[shell widget]

use product rule

[pastel jasper]

Anyone with good maple knowledge who can help me real quick?

Is there a way to make a custom shortcut like this?

[vast blaze]

I think you can make custom shortcuts with Maplets

https://www.maplesoft.com/applications/view.aspx?SID=4264&view=html

[pastel jasper]

@vast blazeIs this something that is already installed?

or do i have to install it first

[vast blaze]

I believe so

[vast blaze]

It's been months since my last time using Maple, so I can only help you redirecting to the link for further instructions on using the Maplets lol

The last time I used Maplets, I believe we can already use it the time we install Maple

[pastel jasper]

No problem i have no knowledge what so ever but I'll figure it out dw

lol

thanks a lot though

[vast blaze]

No problem, good luck!!!

[pastel jasper]

ty

@vast blazeI usually use Document but would i need worksheet for this?

[vast blaze]

I've never used document lol, the last time I used Maplets was on Worksheet

[woeful pulsar]

??

oh maple

[pastel jasper]

hmm

[sweet mural]

can i ask someone to review my way of doing one question and tell me if i am allowed to do it that way ?

,rotate

[sweet mural]

so question is the number of solutions of the inequality belonging to the segment [0, pi]

Am i allowed to do it this way ?

[full walrus]

hello can someone help with the following

How to prove this without a calculator

[woeful pulsar]

rationalise the denominator

[full walrus]

next?

[sweet mural]

it's true i can tell you

[woeful pulsar]

keep squaring both sides until you get integers

[full walrus]

thanks i think thatll work

[woeful pulsar]

another way is probably geometrically

[sweet mural]

@woeful pulsar have you saw my question here ?

[woeful pulsar]

??

[full walrus]

hahhaahahah ja imena u covjeka

[sweet mural]

XD hvala ljubi brat

so question is the number of solutions of the inequality belonging to the segment [0, pi]

[woeful pulsar]

what's that question?

oh

the solution set?

[sweet mural]

yes

i showed my way of finding the answer

am i allowed to do it that way ?

[woeful pulsar]

is it "solution set" or "number of solutions"?

it doesn't look complete yet

[sweet mural]

answer is that there is 3 solutions which i got with this method

[woeful pulsar]

are you supposed to find

1. number of solutions among a predetermined set of answers?
   or
2. solution set?

just checking

[sweet mural]

1

[woeful pulsar]

then that's okay

though I can't be sure if you read the question wrongly

[sweet mural]

i maybe dk how to translate it to eng corectly

it's only asking how many answers there are in segment from 0 to pi

[woeful pulsar]

maybe show the original question?

that doesn't sound right

[sweet mural]

for the inequation that i wrote up

sound better now 😄

[woeful pulsar]

erm

can you just give the wording of the original question so hopefully we can google translate it?

[sweet mural]

question number 9

it's on Serbian 😄

[woeful pulsar]

yeah

your method is incorrect

there's enough information there to guess

because what if there was a solution at a point you didn't consider?

does E) say "more than 3"?

[sweet mural]

yes

[woeful pulsar]

yeah your method is inconclusive

[sweet mural]

ok ty

[thick sigil]

Does anyone know how to solve this?

Unknown value is pi = 205.1 which leads correctly to = 1

but how do you solve this lmao am i not seeing it or just dumb

[shell widget]

@woeful pulsar @sweet mural Maybe first consider 0<=x<=pi/2, that way |sinx| + |cosx| <= 1 gives us sinx + cosx <= 1, which is just sin(x+(pi/4)) <= 1/sqrt(2), which gives us x <= 0. Since we have 0<=x<=pi/2, this gives us x=0.

Similarly for pi/2<=x<=pi

and that gets us x=pi/2

i pinged you element cause i cant seem to find x=pi, the third solution using this way

[woeful pulsar]

hmm

yeah you need to split it into two cases yeah

[woeful pulsar]

wait a minute, shouldn't this give you x=pi/2 too?

pi/2<=x<=pi
then you have sin x - cos x <= 1

[shell widget]

Yeah

and that gets us x=pi/2

[woeful pulsar]

erm

can you show your steps here?

[shell widget]

sinx-cosx <= 1

[woeful pulsar]

yeah

then you R-formula

[shell widget]

sinx-cosx = sin(x-(pi/4))

yeah

and so x-(pi/4) <= pi/4

x <= pi/2

[woeful pulsar]

looks wrong

[shell widget]

why?

[woeful pulsar]

solve sin(x-(pi/4)) <= 1/sqrt(2), for x in [pi/2, pi] right?

[shell widget]

Yeah

[woeful pulsar]

then x-pi/4 ranges from [pi/4, 3pi/4]

[shell widget]

okay, and?

i guess im not seeing it

hm yeah maybe then break x-pi/4 first into [pi/4, pi/2] and then [pi/2,3pi/4]?

so that the function is increasing and then decreasing?

so inequality is preserved?

still gets us x=pi/2 when x-pi/4 is in [pi/4,pi/2]

Okay yeah and then considering x-pi/4 in [pi/2, 3pi/4], we have that sin(x-(pi/4)) <= 1/sqrt(2) when x-pi/4 >= 3pi/4 which gets us x >= pi

since we had x<=pi as well, that gets us x=pi our third solution

kinda hard if u dont have desmos with you 😛 for the graphs

[alpine sable]

How do I answer algebra verbal expressions?

[shell widget]

wdym

[cinder lily]

depends post your question

[sweet mural]

u2 explained a lot XD

[alpine sable]

25+h

[shell widget]

its all element

[alpine sable]

@cinder lily 25+h

[shell widget]

"Twenty five + h"

h being the sound of h, "ECH"

xd

[cinder lily]

what does it equal

i dont understand, are you trying to solve for h?

[alpine sable]

verbal expression

[cinder lily]

what do you need help on? XD

[alpine sable]

Algebra

[shell widget]

Twenty five + h

thats it

[cinder lily]

^

[gray isle]

look at the examples above

[alpine sable]

fuck

it's that easy

[gray isle]

something more than something else
something less than something else etc

or however you want to word it

[thick sigil]

Can anyone help me in this?

[cinder lily]

solve for pi?

or x?

[thick sigil]

pi

basically pi(x) = 205.1

which correctly leads to = 1

but if you shift the LHS 1 to RHS 1, becomes 0 then you can't ln(0)

i think its just simple algebra but i can't see where im gng wrong lol

[cinder lily]

yeah no real solution if thats the case

[thick sigil]

so only way is through trial and error?

[plucky crow]

Hey I have a question about graphs

[cinder lily]

no wdym

[plucky crow]

After bob finishes

[cinder lily]

can you post your question? @thick sigil

[thick sigil]

part b)

formula for minimum price for a financial asset is :

[thick sigil]

and my solution above:

[cinder lily]

ok

the probability that she sells at 600 is 0.4?

[thick sigil]

yes and 0.6 for 200

[cinder lily]

oke

-e^(-0.1(600)) isnt exactly -1

[thick sigil]

yeah it's -8.75x10^(-27) but when you take 1 - that = 1 bc its too small no?

[cinder lily]

i dont know if thats what you do in economics

$e^{-0.1 \pi^s (x)} = 0.4 e ^{-0.1(600)} + 0.6e^{-0.1(200)}$

[ocean seal]

Yes ツ

[thick sigil]

Ahh yes I see it now

[cinder lily]

do you have the answer?

[thick sigil]

yes it's correct, 205.1

what's the difference with your method and evaluating the inside brackets first then multiplying by 0.4?

I don't quite understand sorry what do you mean?

[cinder lily]

oops i mean

[cinder lily]

here

on the Right hand side

you said the exponentials are too small so you let them be zero?

[thick sigil]

yes, you can't do that?

in this case doesnt BODMAS come into play? where you evaluate the brackets first

[cinder lily]

um yeah

but

the exponential isnt actually 0

and that messed with it

the equality

[thick sigil]

hmm yeah this makes sense

thanks I kinda get it now 🙂

[cinder lily]

:)

[alpine sable]

hi guys, i kinda need help here with a formula, i'm trying to make one to keep track of pricing, but it's getting a bit confusing

(3x-100)/4 is what i'm trying to come up with, but the answer doesn't seem to make sense

how do i plug in the x for different numbers and see if it works in excel or something

[cinder lily]

if x = 2

3 times 2, minus 100 then divide by 4

is what will happen

[alpine sable]

right, is there a way to do that on excel so i can see updated values depending on what i change x to?

[cinder lily]

ill see if i can find out

[cinder lily]

cant you just make a formula and let x be a cell?

[gray isle]

set a list of values you want to test in one column

in the adjacent column type
=(3(reference the respective cell)-100)/4

and drag down to apply the formula to what you want

[alpine sable]

I'm getting a parse error for some reason

[gray isle]

hmm

[alpine sable]

oh I guessi have to do *

[cinder lily]

not getting an error on mine

[gray isle]

you shouldn't need it

[alpine sable]

i thoguht 3x is automatically 3*x

but i guess not

[gray isle]

multiplication is already implied for stuff adjacent to parentheses

[cinder lily]

why did you delete lol

looked fun

[celest wagon]

can anyone guide me to which channel to go to for help with inductively defined sets?

[cinder lily]

discrete math maybe or just here

[celest wagon]

Well i can try here

cant seem to find the pattern here

im supposed define this set inductively

[cinder lily]

i see

ok

[quasi scarab]

do we know anything else?

[celest wagon]

No, just that its supposed to be defined inductively

[pearl wedge]

how do you do this type of question?

[celest wagon]

and the basis step has maximum 2 elements

[cinder lily]

wdym

[celest wagon]

hold on, let me try to rephrase

1 and 2 are in the set from the beginning, before the inductive step, if that makes sense

[cinder lily]

oh

why?

[celest wagon]

just how it was presented

[cinder lily]

ok

[celest wagon]

base case is maybe the correct term

[cinder lily]

just an idea

maybe try looking at in binary

[celest wagon]

never thought of that, will do 😉

thanks

[pearl wedge]

i just dont understand the working out to the probability trees questions

[celest wagon]

try #probability-statistics

didnt find a pattern in binary :/

[quasi scarab]

did u do sth similar?

[celest wagon]

what do you mean?

[quasi scarab]

another one where u have to find the pattern

in class or idk

[celest wagon]

oh yes but those were trivial

like 0,2,4,6,8 pattern

this one is irregular when it comes to the increment, because its not based on if the number is even/odd or the index of the number

[quasi scarab]

i dont think its a correct task

[celest wagon]

maybe I phrased it the wrong way, because several students have solved it

[quasi scarab]

we can say then the pattern is +1 +3+2+3+2+13+2 and repeats

[celest wagon]

thats a possible way to think of it

but i think thats too easy. I dont know, its not mandatory but I wanna solve it

also thats not inductive

but thanks anyways

[quasi scarab]

btw u mean recursive?

[celest wagon]

this is an example

[alpine sable]

wait sorry WRONG QUESTIOn

SORRY

@alpine sablethis one

7

So, the least no. Of 6 digits is 100000

Again just square root it by long division method

can we not do ldm

And if u get the remainder just add it to the no.

long division method

[alpine sable]

Well we can't solve this q without ldm

bruh

ok

square root of 100000?

U can guess but it won't be appropriate

but their are many ways of square rooting it

ok ok

[cinder lily]

If we have odd and even or even and odd we add 2

If two odd we add 2

If two evens we add 13

Does this work?

[celest wagon]

ill try, thanks

[cinder lily]

So I’d expect the next to be 30

[celest wagon]

but how do you address that in an induction step, by indexes?

[cinder lily]

I’ll show you

[celest wagon]

ok

[cinder lily]

One sec

[celest wagon]

np

[cinder lily]

$a_1 = 1, a_2 = 2 \ a_{i} = \begin{cases} a_{i-1} + 3& a_{i-1}\text{ and } a_{i-2} \text{are both odd }\ a_{i-1} + 2 & a_{i-1}, a_{i-2}\text{ are even and odd respectivly, or the otherway around} \ a_{i-1} + 13 & a_{i-1}, a_{i-2} \text{ are both even}\end{cases}$

i think this works?

[celest wagon]

Thanks!

[ocean seal]

Yes ツ

[hot osprey]

sorry for interrupting but if anyone could help me out at #help-3 I'd be really thankful...

[cinder lily]

sure

[quasi scarab]

but then it would be 1 2 4

[cinder lily]

yeah so lets define a_3 = 3 a_4 =7

and i>= 5

[celest wagon]

cant define more than 2 elements

[cinder lily]

oh :(

[celest wagon]

but thanks anyways, i think youre onto something

with the even/odd combinations

[alpine sable]

sure

[bronze dust]

46...

[solar pebble]

$\sin^2 \beta = \sin \alpha \cos \alpha$

[ocean seal]

Xetrov

[bronze dust]

but sin^b = - sinacosa also

is there a reason to reject the negative value?

[thorn kindle]

Principal square root

[bronze dust]

what is thay

that

[thorn kindle]

the square root of 25 is 5

It is a confusing convention but it makes sense if you think about it

The square root function must return one value

So we choose to only define the curve y=sqrt(x) on the range 0<=y<inf

And the positive square root therefore becomes the principal root

As in the square root

[bronze dust]

so the square root is a geometric mean is always a principal square root?

[thorn kindle]

Yeah you only use positive numbers in a geometric mean anyways

[bronze dust]

okk

thxx

[hot osprey]

When a polynomial f(x) is divided by a
polynomial g(x), there are quotient g(x)-3x^2
and the remainder g(x)-3x^2
Assume the leading coefficient of f(x)=1 and
f(-3)=-196, then what is f(3)?

<@&286206848099549185> this was something i asked about an hour ago and someone kindly tried to help me but could not solve it. i would really appreciate it if someone could explain it so i can turn it in and get some rest...

[velvet dune]

how can I find out m?
f is derivable

[glass lichen]

not enough info from just the function itself

since cbrt can take pos or neg values

[hot osprey]

god please help me, i haven't been able to sleep for 2 hours because of this question

please...

[quasi scarab]

the remainder still has g(x)?

ur question is wrong

[hot osprey]

i've been trying to figure it our

here's the question

[ocean seal]

dackid (jump king +)

[velvet dune]

well... this is the exercise...

[glass lichen]

No, you posted just the function

[hot osprey]

i'll be in question 3, that's where i was originally at

[ocean seal]

dackid (jump king +)

[velvet dune]

yeah, this is the whole exercise

[glass lichen]

Post the actual question, in an unused channel

[velvet dune]

it's in romanian

[coral pagoda]

I answered your question. Hope it helps

[velvet dune]

it gives me the function and says that f is derivable on R

[hot osprey]

@coral pagoda i got to that. i don't know anything afterwards

[glass lichen]

"what values of m make f differentiable on R"

[hot osprey]

$f(-3) = -196 = g^2(-3) -26g(-3) - 27 \newline f(3) = v = g^2(3) -26g(3) -27$
TeXit
BOT

[ocean seal]

lllllOmOlllll

[hot osprey]

this is what another guy got me to

and now i am lost

[coral pagoda]

I'm not entirely sure how knowing g(-3) is useful for knowing g(3)

[hot osprey]

i am not either

this was something another user offered

i am dumber than a brick, so I tried to google similar problems, tried applying weird crap that seemed to resemble that of an answer

but nothing. nada

[coral pagoda]

Hmm, sorry. I am not too sure where to continue. This one is tricky

[hot osprey]

i've slammed my desk so many times out of frustration, pretty sure it's pregnant now

this is the last fucking question i need to finish to get me some sleep

[coral pagoda]

Seems like a doozy of a question

[muted raft]

which question?

[coral pagoda]

This one

[hot osprey]

i am starting to lose my mind

[coral pagoda]

If it's not due tonight, I recommend you get some sleep and come back at it tomorrow.

[hot osprey]

the professor gave this assignment on saturday midnight

[analog swift]

Given 5 letters and 5 addressed envelopes, in how many ways can the letters be placed in the envelopes so that no letter is in the correct envelope?
plzz help

[hot osprey]

it's now monday midnight for me

and it's due in less than 7 hours

[coral pagoda]

Email the professor for some guidance then

They should know how to solve it

[hot osprey]

same replies. read the textbook and apply the formula

it's like a fucking macro dude

[drowsy shadow]

@hot osprey i think i can help with the problem

do you want?

[hot osprey]

then you are a godsend mate

pray tell me...

[drowsy shadow]

can you go to call

[hot osprey]

uh yeah one moment

[drowsy shadow]

ok

[analog swift]

Given 5 letters and 5 addressed envelopes, in how many ways can the letters be placed in the envelopes so that no letter is in the correct envelope?
plzz help @charred flint

[drowsy shadow]

im at the maths voice chat

[charred flint]

do you know principle of inclusion-exclusion?

[hot osprey]

be there in a sec, thanks bro...

[charred flint]

!5 is the notation for what the answer is but obviously that doesn't teach you why

[analog swift]

!5 is 120

[charred flint]

,w !5

[ocean seal]

Results provided by WolframAlpha

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

Requested by Plurmorant#1811

[glass lichen]

5! = 120

[drowsy shadow]

54321=120

[quasi scarab]

after that, can u tell us the solution? im curious, and prob the other ones who tried to help too

[charred flint]

.

[drowsy shadow]

i will try

i have an idea i don t know if it works but we will try if you want join us to help or to listen

that voice call can be 5min or 10min dependes if you think my idea is good or not

this is worldwide or just europe

[analog swift]

bruh what

[analog swift]

i dont this this is right

[charred flint]

44 is the answer tho

do you know inclusion-exclusion

[analog swift]

nope

[quasi scarab]

https://www.vedantu.com/question-answer/there-are-5-letters-and-5-addressed-envelopes-class-12-maths-cbse-5f58e7698f2fe24918043449

and for the others: it was !5 not 5!

[hot osprey]

@muted raft sorry for the tag bro, but you've helped me out with great explanation many atimes and I couldn't resist asking you....

[clear portal]

Can someone help me set up the integral to find the area of the region using dx and dy integrals?

[glass lichen]

well do you have a function?

[clear portal]

Yup my bad its y=1, log base 3 of x, and x=9

[glass lichen]

so you have to find the area wrt y and x, or just one?

[clear portal]

both, but its 2 different question

s

[glass lichen]

Ok so what are the x bounds

[clear portal]

1 to 9 right

[glass lichen]

x bounds means x values

[clear portal]

oh so its 3 to 9

[glass lichen]

yes, and it's area b/w 2 curves, so you need the top function - bottom function

[clear portal]

oh so it would just be integral from 3 to 9 of log base 3 of x - 1?

[glass lichen]

$\int_3^9\log_3(x)-1\dd{x}$

[ocean seal]

Mosh

[clear portal]

do i just do the same for y, but convert the functions in terms of y and change the bounds to 1,2

but what about x=9

[glass lichen]

so for y it's bounded by x=9 and the log graph

cause you look at everything from the y axis

[clear portal]

yeah my bad so its 9-log_3 x

from 1 to 2

[glass lichen]

functions of y

so what's y=log_3(x) as x=f(y)?

[clear portal]

9-3^x

[glass lichen]

yes

$\int_1^2 9-3^y\dd{y}$

[ocean seal]

Mosh

[clear portal]

thanks!

wait so if i wanted to revolve it around the x axis with washers and shells

[hot osprey]

@glass lichen do u think you can help me with my question T.T.... i am about to give up and sleep

i've been on this question for 3 hours now

[clear portal]

would i just make the outer radius log_3 x and the inner raduius for washers from 3,9

[solar cradle]

Yes that should work @clear portal

[clear portal]

ok thank you! but idk for shells?

[solar cradle]

Oh I misread your msg earlier, for shells you would use log_3(x) for the upper radius, and for washers you'd integrate log_3(x) - 1 from 3 to 9

[clear portal]

oh right thanks! and it would be log_3x^2 for washers right?

[solar cradle]

Oh yes

for sure for sure

[clear portal]

for shells what would the integral be?

would it be y*3^y dy?

[solar cradle]

Close, I believe it should be (9-3^y)y dy

[clear portal]

ok thank you! sorry to keep bothering you but how do i solve this around x=-1 with shell and washer?

[versed osprey]

Could someone help me simplify the expression in example 6 on the 2nd last line?

[solar cradle]

@clear portal It would just change your radius, so for washers your inner and outer raidi would both increase by 1. For shells, you would multiply by y + 1 instead of just y

[alpine sable]

This is the Taylor formula , does anyone know where I can find a proof

for the Remainder R_{n} that is this is the formula ?

[clear portal]

ok thank you! so would it be like this for washers?

[alpine sable]

is this open? ill just leave this here

[tawny lion]

@alpine sable

what are you given in this question

[frosty heart]

Is anyone able to help/guide me with this question? We haven't really done this before in class and I've done everything I could think of. (for a I've tried to do the female total + the female who study french & more)

[frosty heart]

<@&286206848099549185>

[chilly hatch]

the question says or, so either condition works

[carmine stump]

help?

<@&286206848099549185>

[steep briar]

1. You'll need to wait 15 minutes before pinging helpers. Reframe from doing that again. 2. Physics questions are best asked in the physics servers. 3. What is your attempt at the question? What are the forces acting on the particle?

[carmine stump]

this is my further maths mechanics

sorry about the ping

i equated the tension force to the max friction force and got 9a/10 = r

i can't seem to find a simutaneous equation to get rid of a

[steep briar]

Is there a tension force? The question only mentions friction.

oh

[carmine stump]

sorry centripetal force

[steep briar]

Yeah that's my initial guess

Remember the equation of force for that?

[carmine stump]

F = mv^2/r

or F = mw^2 x r

[steep briar]

Indeed,

Uh

Yeah there we go for that second line

Now the other force is still friction,

[carmine stump]

yh

[steep briar]

So since that's the only force acting horizontally they should be equal (Centripetal = Friction)

[carmine stump]

mw^2r = mgu

[steep briar]

Yep

[carmine stump]

r = ug/w^2

r=9a/10 D:

[steep briar]

Um

Is what I got

[carmine stump]

yh and i subbed in u = 0.6

wa

hmm

yh ur right

r = 3a/4

[steep briar]

Yeah

[carmine stump]

when i was rearranging accidentally read my 5 as a 6

so anyways how do we kill off this a

[steep briar]

I don't think you can

[carmine stump]

o

i guess i'll just leave it as that

[steep briar]

Yeah, probably the only thing you can do with the given info

[carmine stump]

thanks for correcting my fraction anyways

[steep briar]

unless they mean a is the bohr radius haha (units wouldn't match :( )

np

[steep briar]

What would be the first step?

(remember, what you do to one side, you'd do to the other)

[alpine sable]

Isn't this it

X = 3g +2 ; 3g= 2 - x ; g= 2-x/3

[steep briar]

Not sure why you negated x and not 2 heh

[alpine sable]

Show me how you do it please

[steep briar]

x=3g+2 -> x-2=3g

Since you're subtracting 2 from both sides

Agreed?

[alpine sable]

Yes

[steep briar]

Then you divide both sides by 3

x-2=3g -> ⅓x-⅔=g

Agreed?

[steep briar]

?

[alpine sable]

Idek

It says its wrong

[steep briar]

what'd you put

looks blank

[alpine sable]

Tha?

[steep briar]

interesting, should be correct

It says it's wrong? It's green

[alpine sable]

Ohhh

I think what u said is right ty

[meager crescent]

HI

would events not 'being employed' and 'not supporting shorter opening hours' be statistically indepedent

this is assuming i asked them both questions]

<@&286206848099549185>

[meager crescent]

<@&286206848099549185>

[alpine sable]

is this open? ima leave it here

[heady sequoia]

Does it matter if it's open for the volume?

[steep briar]

He meant the channel itself.

[steep briar]

Have you tried breaking up the volume into basic shapes? I'd suggest you break it into a rectangular prism and a triangular prism.

[vast blaze]

I believe it doesn't

[heady sequoia]

Ye I was saying as maybe to guide the answer

Mb tho

[vast blaze]

Wait, just to clarify.. by open, you mean the shape is 'open' right?

Ah okay

[heady sequoia]

I think they would be correlated thus dependent

[steep briar]

??? volume of an open shape? lol

[languid ore]

C? Its to find parallelogram

[heady sequoia]

Set up the area of a parallelogram symbolically and then plug in

[languid ore]

Thanks, could u help with D?

wait it would be the same thing

[heady sequoia]

Yeah all of them are fairly similar

I thought you asked for help on h lol

[languid ore]

Oh lol, could you help me check an answer for D is it 21/5?

[viscid yacht]

Can someone help me on question 2?

[heady sequoia]

Plug it back in and make sure it fits the description

[heady sequoia]

What have you tried

[viscid yacht]

Its a regents review and i forgot if this is explicit or recirsove formulas or idk

[steep briar]

Just need to plug in values, no worries.

[viscid yacht]

Ohhh okay

[languid ore]

Is 4x+x=21 the correct way to plug it in? @heady sequoia

for d

[viscid yacht]

That makes so luch sence

Ty

[heady sequoia]

Not quite. This is Saying the base is 4 times the altitude

First part needs to be x+4

[steep briar]

Lemme ask, what's your equation for the area of a parallelogram given its altitude and its base?

[languid ore]

Base times height

But idrk how to plug it in

@steep briar

[steep briar]

Yea height = altitude

So B‧α=A

And if B = α+4

What'd the formula look like using only A and α?

(or a instead of α whoops)

[languid ore]

Is it 4x*x=21?

[steep briar]

Close-ish

So what I was refering to was (α+4)α=A

If you factor distribute* the α (or x) you'd get?

[languid ore]

x=3 or x=−7

?

@steep briar

[alpine sable]

Is there a method to work out the equation of an exponential line when you have coordinates on it

[steep briar]

yeah it seems lol

But the height cannot be negative

[languid ore]

Oh word so its 3

thanks

[steep briar]

Yep

[languid ore]

E?

Of a parallelogram

[steep briar]

Same formula for the area, correct?

[indigo stream]

is undergrad econ allowed here?

[steep briar]

I likely wouldn't be able to answer it personally, and this channel is occupied 0.o

[indigo stream]

O, sorry ;-;

[languid ore]

(x+2.5)x=90?

[steep briar]

Oh so I don't think I agree with the B=(x+2.5)

So it says the ratio of B:α = 5:2, so I think that means B=(5/2) α

[languid ore]

Oh its the base my bad

(5/2)a=90 would be the way to plug it in? @steep briar

[steep briar]

That's saying B=A, we also need the other α

so (5/2)α²=90

since Bα=A

[languid ore]

So the base would be 6?

thats what I got when I plugged it in

[steep briar]

Yep

[steep briar]

Also next time be sure to ask the actual question so no one's put on the spot. Otherwise no one'd reply to avoid utter dishonor towards their families and can help when they can.

[languid ore]

Im back, I just want to clarify how is it 6 if the base is 5:2 to the altitude and the area is 90

[indigo stream]

noted. thank you !

[steep briar]

Well Ba = A, and if B/a=5/2 then B=(5/2)a therefore [(5/2)a]a=A which simplifies to a²=(2/5)A, which is a²=36 for A = 90, and finally to a=6

[marsh summit]

https://cdn.discordapp.com/attachments/843640244921565184/843641165647577108/8f0ecc2914152955f3d7e3cb7fa13daa.png

can someone assist me

please

[stone isle]

what's the total number of students?

[marsh summit]

idk it doesn’t tell me

that’s all the info it gives me

[stone isle]

you can count them from the table

[marsh summit]

oh okay i just assumed u would know lol

the total is 29

LOL

27

[stone isle]

and how many students have the property needed

[marsh summit]

16?

[stone isle]

and so the probability is?

[marsh summit]

16/27

[alpine sable]

Kinda confused on how to do this

[marsh summit]

it says it’s wrong

[stone isle]

oh I read the question wrong

it's conditional probability

[alpine sable]

Wouldn't that be 8/9?

[marsh summit]

how do we get to that

[alpine sable]

There are 18 students who passed the test

16 did the homework

16/18 = 8/9

[marsh summit]

ohhh

so i would use the 2 because they still passed the test

bro they confused tf outta me

[alpine sable]

Yes

No

[marsh summit]

does anyone know how to do this one?

[alpine sable]

13/15

[marsh summit]

15

[alpine sable]

I take that back

[marsh summit]

oh

[alpine sable]

Its 2/5

[marsh summit]

bro the wording fucks me up

[alpine sable]

No way to know

[viscid yacht]

Question 5?

[marsh summit]

vouch

[alpine sable]

Looks like D

I mean 4

[marsh summit]

LMAO do u guys mind helping me some more with these

im trying myself but its too much for my brain to comprehend

[alpine sable]

^^^^

[alpine sable]

1/7

[marsh summit]

i tried 1/7

didnt work

[alpine sable]

It uses geo theorems

I dont think it uses any trig

Oh yeah its 6/7 my bad

[marsh summit]

14

[alpine sable]

I read it wrong

[marsh summit]

12

12/14

gotcha

simplified 6/7

guys

i tried this one

6 times

i have 4 more attempts

[alpine sable]

8/13

[marsh summit]

BRO

HOW ARE U SO GOOD AT READING

[alpine sable]

Line up the two things given

So there are 8

That will be your numerator

[marsh summit]

13 play instruemnt

8

[wary stream]

It's asking how many play an instrument that doesn't play a sport. So out of the total that plays an instrument, how many doesn't play a sport

[marsh summit]

guys

dont

tell

me the answer

just run me through it

[alpine sable]

I only need number 6 now

[marsh summit]

5

or in total

5

[wary stream]

So how many people total don't have a bother but have a sister?

[alpine sable]

Puppas read that again

[marsh summit]

7?

wait

19

?

[alpine sable]

Here I have another idea

Line up the two conditions

[marsh summit]

wait

https://cdn.discordapp.com/attachments/490557019623915520/843656394829332540/2cb30dc7002ce3b166bbbb996186a0b4.png

ima repost it real qhuick

5