help-26

[jade thunder]

you can tell if you're calculating above or under

it probably is much faster to do when h = 0

look at this

obviously x starts at 0

so here if u took the 2 roots u find and find its difference it would be the time under

[gritty compass]

Yh that makes sense

Ok kl thank you

[jade thunder]

but there's one i want to show you as well

[gritty compass]

Yh which one

[jade thunder]

look at this

if u took the first 2 x intercepts and found its difference

you'd be finding the time it spends above water

it matters if it starts above or below water aka is h positive when t = 0

[gritty compass]

In this case is h positive when t=0 ?

[jade thunder]

in your case yes

[gritty compass]

So if I find the diffenrce it would be the time under

[jade thunder]

yes

but know that if P started under the water

you'd actually be taking 1 revolution - difference of the intercept

[gritty compass]

Ok cool

So basically I should always check if where p started

[jade thunder]

yes

[gritty compass]

Thank you for your help

[jade thunder]

use .close to finish when you're done :p

[topaz sinew]

@gritty compass Has your question been resolved?

[gritty compass]

Part(b)

@jade thunder

[jade thunder]

,rotate

[gritty compass]

I can’t see the connection between part a and b

That is part (a)

[jade thunder]

sec is 1/cos

[gritty compass]

Yh

[jade thunder]

probably you can turn everything into cos

[gritty compass]

But how does part a help

It says hence so I need to use part a

[jade thunder]

oh wait

yeah i see it

you see that 2nd baracket

(1-cos2x)

that's just what u proved

then you can divide both sides by tanxsin2x

then u have only cos and tan left

[gritty compass]

And then with cos and tan how can I solve it with two trig functions ?

[jade thunder]

tan = sin/cos

wait

[gritty compass]

But then I would have sin and cos

[jade thunder]

is that that

[gritty compass]

What?

[jade thunder]

yeah it's sin/cos ok

so you have 1/cos^2 on 1 side

and sin/cos on the other side

[gritty compass]

Is this what your talking about

@jade thunder

[jade thunder]

hmm im going down a sub route but it seems really hard

im not sure if this is how you do it

[gritty compass]

Yh same. I tried doing this but it became really difficult

[jade thunder]

there's probably an easier way maybe

[vital blade]

you can seperate 1 in terms of cosx and sinx

in the 1/cos^2x

[gritty compass]

As in sin^2 + cos^2

[vital blade]

yea

[jade thunder]

yeah that's where sub leads

[cold night]

What is the question? I may be able to help :3

[vital blade]

and then it would turn into a quadratic eq

[jade thunder]

part b

[jade thunder]

no it doens't

u need a sub before and even then it's not a quadratic

u have sinxcosx on 1 side

and sin^2x on the other

[vital blade]

sin^2x/cos^2x

[jade thunder]

what?

[vital blade]

isnt 1/cos^2x is 1+ tan^2x

[jade thunder]

oh maybe that's the identity you should use

[vital blade]

on the right you have 3tanx so its quadratic

[jade thunder]

yeah

[gritty compass]

Wait, what happens after this step?

[jade thunder]

ok you're right

i forgot about that one

[jade thunder]

use this identity

[gritty compass]

Where is the 1/cos2x

[cold night]

I did it

[gritty compass]

Send working

[cold night]

Wait

[jade thunder]

i went down a bit of u = tan(x/2) kind of route

that is a very long route dont do it

[gritty compass]

Where did the 1/cos2x come from when you used the identity

[jade thunder]

.

sec^2x

sec is 1/cos

[gritty compass]

Oh

Yh ok that makes Sense

[jade thunder]

sry i haven't done this kind of question in a bit but u pinged me :/

[gritty compass]

It’s alright thank you

[cold night]

,rotate

[cold night]

Look at this one first

I messed up the order

[gritty compass]

Perfect thank you all

[cold night]

:3

[gritty compass]

Ok last one. Q4 second part

[wet bough]

,rotate

[cold night]

This is simple ;(

Try :3

I mean atleast the first part of the question is quite simple

The second part is understandable still

If you're stuck in the second part lemmino

The first part should be simple

[gritty compass]

Yh I said only second part

@cold night

I did first part already

Don’t worry I’ve finished both parts

[cold night]

Ohz well done

[topaz sinew]

@gritty compass Has your question been resolved?

[topaz sinew]

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[safe chasm]

Can some tell me if this triangle counts as a vertical angle( at T), cause i don't think i can prove both tringles are congruent unless it counts

[blissful lagoon]

wdym by vertical angle

90°?

[safe chasm]

Like when to angles cross the oppsoite angles created are equal, do the angles ATW and ETR count?

[storm monolith]

There’s no reason to assume that

Are angle TAW and RET equal?

[blissful lagoon]

I'm not that familiar with trigonometric proofs, but I presume the only information the picture provides is that the two triangles have a common point T, that WR is divided by WT in half

and that AT and TE are equal in length

[safe chasm]

yes

[blissful lagoon]

if they're equal then ATW and ETR are equal as well

[storm monolith]

I’m guessing that’s what the angle symbol there means, if so you can prove they’re congruent assuming both triangles are right-angled

[blissful lagoon]

due to angle sum

[safe chasm]

Can i assume that?

[blissful lagoon]

what specifically do the angle symbols and line symbols suggest in your picture

and what does the task say

[safe chasm]

That AT and ET are equal and angle A and E are the same

[blissful lagoon]

ok

and WT and TR don't have to be parallel?

[safe chasm]

I don't understand what you mean?

[blissful lagoon]

W to T and T to R

are segments of the same line

[safe chasm]

Yeah

[restive inlet]

no, they aren't considered vertical angles

[safe chasm]

why

[restive inlet]

by definition

[safe chasm]

oh

[storm monolith]

Yikes bad wifi

[safe chasm]

so the triangles arent congruent?

[storm monolith]

They almost certainly are

If we can assume the ‘obvious’ stuff, like them both being right-angled, line segments lying on same line etc

[restive inlet]

depends if you assume AW perp WR and ER perp WR
if that info wasn't already given to you

[safe chasm]

it didnt say anything about that

[storm monolith]

They probably are, so consider how you would show the triangles are similar

[safe chasm]

by AAS

[storm monolith]

And then make use of the sides being equal

[safe chasm]

ok thank you

.close

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[mild tiger]

1/100x^2+g(x)+1/4=0

[mild tiger]

any help?

I didn't know what to do with the g(x) and x^2 in the same equation, so I just guessed

iirc the answers were like 1/2, 1/5, 1/10, or 1/20

I think

[knotty ledge]

You need to tell us what the question is

[mild tiger]

uhh

I don't really know lol

I've just never seen anything like it before

[knotty ledge]

How is anyone going to help you if you don't know what the question is?

[mild tiger]

I think the most likely question would be solve for g(x)

[cold night]

Hello old teammate

[mild tiger]

no way

[knotty ledge]

Do you not have the question in front of you? What's the point in guessing

[cold night]

$\frac{x^2}{100}+g(x)+\frac{1}{4}=0$

[mild tiger]

no but I'd like to figure it out

[cold night]

Is this what ur working with?

[mild tiger]

x^2 wasn't in the denominator

[knotty ledge]

The question could be literally anything?? I don't understand what you want anyone to do, you have not supplied a question

[mild tiger]

it was like (1/100)x^2

[cold night]

Oh, see that's why i wrote it in LaTex

[thorny flame]

Lelouch

[cold night]

✅ ?

[mild tiger]

was written like that

[cold night]

Yeah but now it's correct right?

[mild tiger]

yea

[cold night]

And what's the question?

[mild tiger]

I just got really confused at there being g(x) and x^2 in the same equation

[mild tiger]

I can't remember it now, don't have the test anymore

iirc it was solve for g(x)

[cold night]

Yeah so solve for g(x)

._.

[mild tiger]

idk how to do that lol

oh wait fuck

would it literally just be moving shit to the other side?

so g(x)=-(x^2/100)-(1/4)?

[cold night]

Lmao yeah

Seb is getting old :3

[mild tiger]

could probably put that into calc and find zeros from there

bc answers were like 1/2 1/5 1/10 or 1/20

damn

[cold night]

Yeah so do that

He is retiring isn't he

[mild tiger]

yea, hope he goes to indycar ngl

[cold night]

He said against F1 int terms of , climate change and shit , what a snitch

On the Bbc

Now he says that he is a hypocrite and what not

Now that he retiring he is saying it lmao

[mild tiger]

I don't believe him it's due to climate change entirely, I think he just wants a reason to get out lol

[cold night]

Max and Charles >>>> Seb and Hammy

[cold night]

If that's the case i love him, but as of now he a mad snitch

[mild tiger]

being a 4x world champion, can't be fun running around with lance stroll

[cold night]

LMAOO

Fr

[mild tiger]

well he's right, F1 is probably the least environmentally friendly sport on earth

[cold night]

I mean he is basically back to red bull ifykwim

[mild tiger]

think about all the garages and parts etc. that have to be moved around in order to stage a race

[cold night]

But how much impact does it have ? It's for the sake of sport , do u not urself drive a car ?

[mild tiger]

even just setting up the track takes so much time and energy

[mild tiger]

I do drive a car, but his point is that he feels hypocritical racing in F1 while pledging that we need to save the earth

not like it's gonna make a difference largescale, but for him it would

[cold night]

Allthe F1 drivers say this shit just for brand deals , they don't really give a f

The whole F1 racing #WeRaceAsOne is just a load of bullshit for brand deals they don't really care about the communities

It sos that they can get good sponsors

[mild tiger]

I think really only seb and lewis care about the we race as one thing tbh

[cold night]

And the drivers have to put upwith it

[mild tiger]

all the rest just wear the shirt to not stir shit

[cold night]

I disagree

[mild tiger]

with what part of it

[cold night]

I don't think seb and Lewis care

See in camera they will give speeches and what not u have no idea about the reality

Like if u were a homophobe , and someone gave you 30million$

[mild tiger]

lmfao

[cold night]

And they dared u to appreciate gay people , then the homophobe would def do it

Even if he hates gays

[mild tiger]

I really do think seb and lewis care, the rest of the grid that could go for

[cold night]

Agree to disagree

[mild tiger]

but seb and lewis do a lot of stuff outside of just the we race as one standard shit

[cold night]

Cuz they have to make it look legit

How else would people believ em?

It's easier to promote brands that way ,it's a marketing strategy

[mild tiger]

who wouldn't believe them, not being homophobic is kinda baseline nowadays lol

[cold night]

Cuz LGBTQ+ are really good customers of alot of the brands

[cold night]

It is but they wouldn't be arsed with it if their salary wasn't 40 mil

[mild tiger]

oh yea of course

when you have that much money, you can realistically do whatever you want

[cold night]

Like rarely anyone is a homophobe , but no one like talks so openly about it it's normal , when these guys do it it's kinda cringey hence why i think they make em do it

[mild tiger]

I think it's done a lot bc of how many anti gay oil countries they race in

[cold night]

Bruh the hypocrisy

They are hypocrites

Fia is all in it for the money

Literally they couldn't care less

[mild tiger]

kinda trying to offset the fact they race in countries like the UAE, Saudi, qatar etc.

[cold night]

As i said they are bag chasers

[mild tiger]

ok I gotta go mow the lawn now, see ya

[cold night]

See ya , goodnight

Nice talk

[topaz sinew]

@mild tiger Has your question been resolved?

[topaz sinew]

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[spare marsh]

how do i do this

i have no idea whewre to start

[jade thunder]

what points of information do you know?

[spare marsh]

initial volume = 300

2 minutes to drain 220

rate of flow is proportional to amt of liquid

[jade thunder]

"At time t minutes after the outlet is opened, the amount of liquid in the tank is V cm^3"

can you write this part out using math?

[spare marsh]

i can't

V = t

[jade thunder]

V(t)

this means Volume is a function of time

[spare marsh]

yea

[jade thunder]

now using V(t), write what you said in math

[spare marsh]

V(0) = 300

[jade thunder]

same here

[spare marsh]

V(2) = 80

[jade thunder]

you sure?

oh wait

[spare marsh]

V is the liquid left

[jade thunder]

yes you're right

ok now

[jade thunder]

can you write this in math

[spare marsh]

rate of flow = k x V(t)

[jade thunder]

ok have u learned calculus yet

[spare marsh]

yes

[jade thunder]

what does the rate of flow mean

[spare marsh]

dV/dt

is it

no i dont thinkso

rate of flow means how much is flowing

out of the tank

[jade thunder]

this means change in volume over change in time

[spare marsh]

yea

[jade thunder]

if it's changing 1L per second

is that not the rate of flow outwards

[spare marsh]

yes

[jade thunder]

so dV/dt is rate of flow

[spare marsh]

oh okay

[jade thunder]

so with dV/dt = k V(t) can you solve for V(t)

[spare marsh]

how

all are variables

[jade thunder]

remember you have
V(0) = 300
and
V(2) = 80
to help you

[spare marsh]

yes

but

theres a K

what is dV/dt gonna be equal to

v(2) = 80

dV/dt = k x 80

nothing else i can do

or would it be 220/2 = k x 80

[jade thunder]

wait let me do the question first

ok

so from dV/dt = kV(t)

you move the V's to 1 side and t's to the other

dV/V(t) = kdt

Spoilers for my working out, I’m really tired so at least you can look through that if I don’t reply and fall asleep

[topaz sinew]

@spare marsh Has your question been resolved?

[spare marsh]

wat

u integrated

then took ln

wat

[jade thunder]

i didn't take ln

the evaluation of the integral gives ln

[spare marsh]

idk how that works tbh

[spare marsh]

didnt know that

we havent done a lotta calc

[jade thunder]

oh

[spare marsh]

this is what the answer sheet says

[jade thunder]

im not sure how to do this without integrating 1/x

...

okay well if you go "oh it must be exponential"

then sure

[spare marsh]

yeah

[jade thunder]

but this proves that it's an exponential

[spare marsh]

yes

[jade thunder]

e^x is the only type of function where its derivative is the "same" as itself

and you get that via f(x) = f'(x)

anyway the point is that you only know that Ae^(kt) is the form because when you integrate that's what u get

[spare marsh]

yes

[spare marsh]

oh okay

anyways

thanks for ur time

helping me

.close

[jade thunder]

👍

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[long fern]

https://cdn.discordapp.com/attachments/297337558159851522/983079704254885908/unknown.png
https://cdn.discordapp.com/attachments/536995777981972491/983081165651066930/unknown.png

[long fern]

can someone help me make sense of c (question and answer)?

https://cdn.discordapp.com/attachments/297337558159851522/983080131998396486/unknown.png

this is my drawing

from which alpha comes out to -3pi/4

which is not the same as 5.82

[topaz sinew]

@long fern Has your question been resolved?

[topaz sinew]

@long fern Has your question been resolved?

[long fern]

anyone?

[long fern]

.close

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[sweet gale]

hello, im trying to understand how to get the answer for 2.

ive already derived for y from the first equation and found the slope of the second equation but dont know where to go now

[vale jacinth]

Solve y’(x)=6

[neon iron]

i think she is having problem in 2nd one

[sweet gale]

so 6e^3x = 6?

[sweet gale]

The first one in the two questions shown, im quite confused

[vale jacinth]

Yeah

[neon iron]

ohh fine

[sweet gale]

This would go on to be e^3x - 1 though

Then how would I find x?

ln e = 1

so then divide it by 3????????

[vale jacinth]

x=0

[sweet gale]

oh

OH

omg thank you

jeez

[vale jacinth]

Np

[sweet gale]

wait, but does that answer the question though because its asking for me to find an equation

so if x=0 then the equation would be null

[vale jacinth]

(y-2)=6(x-0)

[sweet gale]

ahhh i see

just paste it into the second equation

almost

eh

[vale jacinth]

y-f(0)=f’(0)(x-0)

[sweet gale]

ohhhh okayyy

thank a you sir

[vale jacinth]

Np

[sweet gale]

.close

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[neon iron]

I was wondering if there was a faster way to solve this instead of just FOIL

[odd pagoda]

let y=x+1 and rewrite everything in terms of y

then it looks slightly nicer

use difference of squares

although in the end you have to sub x back in. so I'm honestly not sure if that is even worth it

[neon iron]

hmm

the numbers are consecutive so I thought there was an easier way

could I use the binomial theorem on this?

[odd pagoda]

no

[topaz sinew]

@neon iron Has your question been resolved?

[sweet shard]

No

[sweet shard]

Also, they're not consecutive

• is not the same as +

[neon iron]

ah okay thanks

.close

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[pine forge]

idk how to do it

[odd pagoda]

we have $5=a\cdot 1^3+b\cdot 1 + 4$ and $8=a\cdot 2^3+b\cdot 2 + 4$

[thorny flame]

Denascite

[odd pagoda]

solve for a and b

[pine forge]

simultaneous?

[jade thunder]

the function f(x) = ax^3 + bx + 4 tell us what f(x) is when x is some number

and you know that (1,5) and (2,8) are on the cubic function

[odd pagoda]

yes. two equations, two unknowns

[jade thunder]

you know that f(1) = 5 = a(1)^3 + b(1) + 4

and then same with (2, 8)

[pine forge]

oh so you just

[jade thunder]

which is how denascite got his simultaneous equations

[pine forge]

plug the x value

of both of them?

[jade thunder]

well they are both on the line

so they both must be true

if they weren't true they wouldn't be on the line

[pine forge]

what do you do here

like

[jade thunder]

well when x = 1

[pine forge]

do you do the samae

thing with teh other one

[jade thunder]

y = 5

[pine forge]

and just

[jade thunder]

yes

when x = 1, y = 5

that's what the point (1, 5) means

and the question tells you this point is on f(x)

you also know when x = 2, y = 8

that's also a given

[pine forge]

so I have

f(1) = a+ b + 4

rn

now what

I do

f(2)

yea

[jade thunder]

what's f(1)

[pine forge]

5

[jade thunder]

there's a value for it

right

so 5 = a + b + 4

[pine forge]

yeyae

[jade thunder]

then do the same for the other point

[pine forge]

oh ok

[jade thunder]

notice how in the function ax^3 + bx^2 + cx + d

there's 4 unknowns

aka u need 4 points to define a cubic

in this case c = 0, d = 4

so you need 2 more points

aka (1, 5) and (2, 8)

so there's only 1 cubic that fits all these descriptions

for parabolas you need 3 points

[pine forge]

right?

[jade thunder]

yep

now u have 2 equations and 2 unknown

i forgot what it's called, 2 non-trivial equations?

[pine forge]

so

I'm going to

make one of them

equal like a

and sub that in the other one

and then solve for b

and then sub that b value into one of them

to get a

yah?

[jade thunder]

you can but there are other methods

[pine forge]

like what

[jade thunder]

like 2nd equation minus 2 times the first

that eliminates the b

so

[pine forge]

wait did you mena

mean

times the first equatin

by 2

[jade thunder]

  - 10 = 2a + 2b + 8

then u get

-2 = 6a - 4

a = 1/3

sometimes this method can be faster than making 1 variable the subject then subbing

then subbing again for the other

[pine forge]

I got

a=1/3 and b= 26/3

but this is the answer to the question

[jade thunder]

,w solve for b, 8 = 8a + 2b + 4, a = 1/3

[thorny flame]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[jade thunder]

you did the arithmetic wrong

also look at the question

it's asking for the rule of f(x)

[jade thunder]

you want it in this form

not "a = 1/3, b = 2/3"

this is not the right answer

[pine forge]

yea

[jade thunder]

the right answer should say f(x) = 1/3 x^3 + 2/3 x + 4

[pine forge]

what did I do wrong

I probably made a really stupid mistake

wait

ik

[jade thunder]

what did you do at the end

[pine forge]

whatI d

nah nah

Ik ik

I'm actually tripping

[jade thunder]

XD

[pine forge]

bro

I did

negative

4

https://tenor.com/view/trip-homer-autsch-nein-gif-22036301

alright thanks for the help @jade thunder I'm going to go now

bye

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[neon iron]

I got a bit comfused with part b

can someone help me pls?

[loud ingot]

what changes can you see from fx to b=

[neon iron]

fx has move down one and then flip over
@loud ingot

[loud ingot]

good

for moving down what do we do?

[neon iron]

I think f(x)-1

[loud ingot]

good

now what do we do for flip

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[trim quartz]

is this the correct way to show that if f is invertible, then f ° f is too? given f : A -> A

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[odd pagoda]

kind of? but honestly it's just symbol salad. hard to read, hard to understand, easy to make mistakes, ...

you shouldn't get into the habit of writing proofs like that

[trim quartz]

yeah i understand

how should i write better proofs?

[odd pagoda]

we want to prove that $f\circ f$ is surjective and injective.

surjective:

let $z\in A$. then we know as $f$ is surjective there exists an $y\in A$ such that $f(y)=z$. Further we know there exists an $x\in A$ such that $f(x)=y$. Putting these together we have $f\circ f(x)=f(f(x))=f(y)=z$ and $f\circ f$ is surjective.

injective:

let $f(f(x))=f(f(y))$ for $x,y\in A$. As $f$ is injective, this means $f(x)=f(y)$ and then $x=y$. So $f\circ f$ is injective

[thorny flame]

Denascite

[odd pagoda]

more words, less symbols. sure, it makes the proof longer, but it's way easier to understand

[trim quartz]

thank u

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[strong lark]

how does the first line go to the second line?

[strong lark]

i assumed cross multiplication, that works for the numerator but i'm not sure where the denominator came from

[hazy pumice]

did you try getting a common denominator?

[hazy pumice]

"cross multiplication" is a thing with equations, not expressions

[strong lark]

ah

how would i get a comon denominator with an expression?

[hazy pumice]

multiply left term by sinx/sinx

multiply right term by (1-cosx)/(1-cosx)

the point is that each of these operations is equivalent to multiplying by 1

which is always allowed

even if we don't attempt to "balance" the operation on other terms
...and we get the missing factor in each denominator this way

[strong lark]

ah okay

let me try quickly

ah so because they come out with the same denominator

you can smush them togehter

[hazy pumice]

yes.

[strong lark]

and add the numerators

[hazy pumice]

that is how we choose the thing we make into the fraction

we choose the factor/s that is missing

[strong lark]

riiight

thank you <3

[hazy pumice]

np

[strong lark]

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[viscid pier]

.

I got 5pi/8

[viscid pier]

here is how i solved it

could someone tell me what I did wrong ?

[coarse sierra]

sin(3π/4)=-1/√2

ah

hmmm or 1/√2

either one

[coarse sierra]

this

sin(3π/4)=1/√2

[viscid pier]

yeah i thought it was 3pi/2

[viscid pier]

thx

[coarse sierra]

lol i see

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[sweet drift]

would i just write 16c - 7 = 13.32

[runic ether]

yes thats correct

[sweet drift]

oh ty

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[sweet drift]

.reopen

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✅

[sturdy oracle]

Treat it as an equation

Isolate the x term first

[sweet drift]

/12 - 5 > - 2

i got it :D

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[flint orchid]

Hello friends, double integrals in polar coordinates. I’m stuck on d) there is a photo of my best atempt. The expected answer is pi(1-cos((pi/2)^2)

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@flint orchid Has your question been resolved?

[ashen eagle]

Don't use polar coordinates from (0,0) use from (1,0)

x=1+rcos(θ)
y=rsin(θ)

that way you have (x-1)²+y²=r²

So the integral is simpler

¿Entiendes lo que digo, @flint orchid?

[flint orchid]

Yesss I understand thank you very much that was exactly what I missed, the center is not (0,0), now everything got much simpler, really thank you brother

I will close now

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Channel closed

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[tardy basin]

.close

can someone help explain this

sorry i accdientaly used 2 channels

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[cinder rover]

are you having trouble understanding the concept

[cinder rover]

or the method

@tardy basin

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[neon iron]

]

[neon iron]

Is there a formula to get from the bottom left to 2tan^-1 u + C?

[past kayak]

You can either remember that the integral of 1/(u² + 1) is arctan(u) or you can use trig sub

[bitter socket]

mmmh trig sub

[neon iron]

dam trig sub is a pain

so that formula only works strictly when it is in that format right?

1 / (u^2 + 1)

[past kayak]

I can never remember the inverse trig integrals, so I always just derive it via trig subs. You mag want to remember it though

[neon iron]

otherwise i would need trig sub

[past kayak]

Gimme a sec

[bitter socket]

yea Im pretty sure

[neon iron]

ahh snap, gotta memorize it i suppose

[past kayak]

That image isn't very comprehensive

[neon iron]

well i get it, a^2 = 1 anyways in this case

so 1/1 arctan u / 1 + C

[past kayak]

I never memorize it. I always just trig sub, but I dunno if that's good practice or not

[neon iron]

i'd rather just memorize, as trig subs tend to get long and complex

more room for error

[bitter socket]

yea memorize it but learn the proof

[neon iron]

okay thanks guys

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[sturdy oracle]

It's an identity

[sturdy oracle]

Oops

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[sweet drift]

do u just do 200 x 6?

[sweet drift]

seems easy

[opaque mason]

Why you not helping me

[sweet drift]

um bc

i dont know the answer

[empty sail]

Create a proportion

[sweet drift]

200 x 6

i believe

1,200

[empty sail]

That should work

[sweet drift]

yes

ty

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[dusty spindle]

Hi, can someone help?

[fading glacier]

can you elaborate not really sure

[dusty spindle]

that's the whole question

[fading glacier]

no like hwat is 5 perm

[dusty spindle]

permutation

and 5? idk

[fading glacier]

so the question is asking how many 5 permutations of 5 are there?

[dusty spindle]

ig

[fading glacier]

hint: order of elements do not matter

[dusty spindle]

ok, how do I solve this questioN?

[fading glacier]

Im here to try and help you, not solve if for you

[dusty spindle]

help me understand the question first

[fading glacier]

its vague, but from what I understand I think its asking you for 5 spots which the 3 elements can cover

and how many of them have 5 in them ig

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[gloomy dune]

Guys

[gloomy dune]

How would I get the IC?

The instantaneous center?

It’s really confusing

Ain’t it should be no IC?

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[formal dew]

I've already solved this problem, but I have a question about one of the last things I have to do in this problem.

Here's what I did so far, and... Do I need to add the different rate percentages I got? Is that what the problem is implying by "Calculate the total rate of return received by the owner" ?

[topaz sinew]

@formal dew Has your question been resolved?

[solid wing]

Wouldn't total rate of return be total profit / total cost

With profit from sale being 351500-300000

Savings being 20700*5

So total profit is sum of these

And total cost is 300k

But anyway

It should be equivalent to adding the percentages

Of APR and multiplying by 5

But I don't know if you computed the one on the right correctly

As that is the compounded rate of return

And to me it makes sense to use raw return here

Not totally positive though

@formal dew

[formal dew]

I only learned the compound way In my class I think

So I added 6.9% and 3.2% = 10.1%

[solid wing]

The raw return of the sale would just be 51500/5

If you're supposed to use compound then use compound return

But the premise of adding the APR is valid

You have to multiply it by the years tho

For total rate of return

Which is 5

[formal dew]

I used 5 in the formula

[solid wing]

I'm saying this

Is *5

[solid wing]

It's > 50% total return

10% something is just the annual rate

of return

[formal dew]

Ohh. So I have to multiply that by 5? Sorry this stuff is just confusing me, especially this problem. A lot going on

Somebody else told me to just add the two percentages. But now I’m multiplying by 5?

[solid wing]

Adding the percentages gives you the annual rate of return

But the investment is over 5 years

So the total rate of return should reflect this

Perhaps they could be total annual rate of return, but it is unlikely

[formal dew]

What did this exponent of 5 do then? In my formula: f = p * (1 + y)^n ?

[solid wing]

Compounds the return

[formal dew]

Okay so I’m taking 10.1% * 5?

[solid wing]

if u want to use compounding return

I think it is raw return

,ask 155000/300000

[thorny flame]

Results provided by WolframAlpha

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Requested by Skid#0001

[formal dew]

Okay. Would you mind if I shared an example from my course and maybe you can tell me from there if I need to do the multiplication by 5 or not?

[solid wing]

Ok

[formal dew]

@solid wing Alright. Can I pm you?

[solid wing]

Ok

[formal dew]

Alright

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[vivid spire]

Hi i don’t understand how to solve this i made the little graph thing but im really confused

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[vivid spire]

<@&286206848099549185> 🙏

😭😭 bro plesse someone

[vivid spire]

Okay this is just sad now

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[vivid spire]

I think i mightve figured it out if someone can just like check me

[gray ridge]

Hello there @vivid spire
Mean should be correct, however s.d. is not

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[ripe mason]

.close

[ripe mason]

hi i dont know how to get the standard deviation

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[vivid spire]

Hi sorry this is late but can u explain why its incorrect and how to find it

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[stable talon]

A committee is to be formed of 3 people where it has atmost 2 males, out of a group of 5 males and 2 females. How many ways can a committee be formed such that, Travis, a male from that group, will always be in the committee? Also, what is the probability of forming the committee in such a way that Travis, the male person of the group, will always be in the committee?

[fading glacier]

okay so in actuality how many people can be selected for the group

[stable talon]

3 people committee.

Given we have 5 males and 2 females.
Restriction: Committee can have at the maximum 2 males.

Oh, i missed another part.
Also, what's the probability that Travis, the male, will be in the committee?

[ashen tusk]

So you know travis is always in the committee

So there's two slots left

Since there are a maximum of two males, those two slots will either be one male and one female or two females

[fading glacier]

^this

[stable talon]

2C2 + 4C1 x 2C1, right?
i think, i messed up at the probability.

[fading glacier]

you should have it such that

you take cases

1 where its 2 males and 1 female and the other being 2 females and 1 male

also you odnt need to include Travis

because travis is a given

just talk about the 2 spots left

[stable talon]

Okay, i think i understand.
But if we are to find out the probability, what will be the sample space? Like I thought 7C3, but it says atmost 2 males..

[fading glacier]

sample space with the given travis

or without

because one of them is conditional probability

while the other isnt

[ashen tusk]

Can you give the exact wording of the probability question

[stable talon]

I think isn't. I mean, that was in the tutorial question set, so I'm not sure

Okay, a minute please.

What is the probability of forming the committee in such a way that Travis, the male person of the group, will always be in the committee?

[fading glacier]

uhh i think this is conditional?

usually the word 'given'

is there

try it with conditional probability

if it doesnt work try it without

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[limpid plinth]

How would you do this

[drifting swift]

recall what the word "perimeter" means

[fading glacier]

what have you tried?

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[coral sapphire]

I need help with the walkway part of the garden

[restive inlet]

did you do part a)?

[coral sapphire]

Yeah

[restive inlet]

are you able to calculate the area of the large square?

[coral sapphire]

Yeah but isn’t that part a?

[restive inlet]

no

that was the area of the green part only

[coral sapphire]

Yeah that’s part a right

[restive inlet]

part a) is the area of the square shaded in green

not what i'm currently asking you

[coral sapphire]

Ok what are you asking me right now

[restive inlet]

the area of the large square

the one that includes the garden and the walkway

i.e.

[coral sapphire]

No I didint do that,

[restive inlet]

the area of the whole thing

not asking whether you did

asking whether you can

[coral sapphire]

No

[restive inlet]

would you be able to determine the length of the red line?

i.e. the length of the side of the large square

[coral sapphire]

X+2x+3?

[restive inlet]

no

[coral sapphire]

ok

[restive inlet]

that only gets you the value of the orange line

actually there's a simpler way to do this that i overlooked

[coral sapphire]

Ok

[restive inlet]

actually, nvm it makes some questionable assumptions

continue with what we started with

[coral sapphire]

I don’t know how to get the length

[restive inlet]

doing x + 2x+3 only gets you the length of the orange line

it ignores the purple part

[coral sapphire]

Alright x+x+2x+3?

[restive inlet]

yes

[coral sapphire]

Ok

[restive inlet]

now you have the length of a side of the big square

would you now be able to find its area?

[coral sapphire]

no, I’m still confused on how to find the area of part b

[restive inlet]

not what I'm asking you to do atm

we're getting there

take this one step at a time

i'm not just getting you do to random unrealated stuff

you were able to calculate the area of the green because you knew the side lengths of the square right?

[coral sapphire]

Yes

[restive inlet]

now you have the side length of the the big blue square

x+x+2x+3 (which can be simplified)
and you can apply the same idea to calculate the area of that

[coral sapphire]

Ok

I got 16x^2+24x+9

[restive inlet]

now consider that
area of garden + area of walkway = total area of big (blue) square

[coral sapphire]

I got 20x^2+36x+18

Is that the final answer or is there more

[restive inlet]

is incorrect

[coral sapphire]

What was I supposed to do

[restive inlet]

now consider that
area of garden + area of walkway = total area of big (blue) square

it feels like you added
area of garden with total area

which isn't what you're supposed to do

G + W = T
W = ?

[coral sapphire]

Area of walkway is which one

[coral sapphire]

This one or 4x+3

[restive inlet]

neither

[coral sapphire]

oh

[restive inlet]

area of walkway is what you're trying to figure out

[coral sapphire]

But you told me to add them

[restive inlet]

you know the total area which was the area of the big blue square

no i didn't

where did i tell you to add the area of the garden with the total area

[coral sapphire]

Which ones the total area then

[restive inlet]

the area of the big blue square

[coral sapphire]

But I don’t have that yet right

[restive inlet]

you just calculated the area of the big blue square moments ago

i got you to find its side length

and you squared it to find the area of that square

now you have the side length of the the big blue square
x+x+2x+3 (which can be simplified)
and you can apply the same idea to calculate the area of that

Ok
I got 16x^2+24x+9

that was the area of the blue square (total/combined area of the garden and walkway)

[coral sapphire]

Yeah

And then I added that with the one in the middle square

[restive inlet]

you also know the area of the garden from part a)

no

why are you adding the total area with the area of the garden

[coral sapphire]

Oh

[restive inlet]

area of garden + area of walkway = total area of big (blue) square
g + w = t
w = ?

[coral sapphire]

How do I get the walkway then

[restive inlet]

area of garden + area of walkway = total area of big (blue) square
do you agree with this relation between the 3 areas?

[coral sapphire]

Yeah

[restive inlet]

now for simplicity lets use the bolded letters to get the equation
g + w = t

would you be able to solve that equation for w?

(for this don't worry about anything else, just focus on this equation and nothing else)

[coral sapphire]

Yes

[restive inlet]

Yes
what would the equation/result be?

g + w = t → w = ?

[coral sapphire]

What do you mean

[restive inlet]

you said you would be able to solve
g + w = t
for w

i.e. get an equation into the form
w = stuff

what will that equation be?

just like how solving
x + 3 = 5 for x leads to the result
x = 2

i'm asking you to do the same for w in g + w = t

do not overthink this

[coral sapphire]

Oh

Ok

I get it know

I think

I got to subtract g to t and leave w by itself right?

[restive inlet]

subtract g from t

"to" wasn't the appropriate word there

[coral sapphire]

Yeah from

But am I right?

[restive inlet]

write that mathematically to be unambiguous

[coral sapphire]

(4x^2+12x+9)+w=16x^2+24x+9

I only got 7 minutes left

Hello

Nevermind I got until tonight

<@&286206848099549185>

[loud ingot]

Area of the garden is (2x+3)^2

Kinda fitting because I just finished my first day job as a gardener lol

[coral sapphire]

Lol

Yeah I know that part but it’s everything else that is confusing

[loud ingot]

What's confusing?

[coral sapphire]

The walkway part

[loud ingot]

What's the area of that one box labelled?

[coral sapphire]

I don’t know

[loud ingot]

Huh? The box with the x and x sides

[coral sapphire]

X^2?

[loud ingot]

Yes

Now many of those boxes are there on the walkway

[coral sapphire]

16

[loud ingot]

Yes so the area of the walkway?

[coral sapphire]

16x^2?

[loud ingot]

Yes

[coral sapphire]

What do I do next

[eternal spoke]

the garden is a square

whats the area of a square

[coral sapphire]

You do side*side right

[eternal spoke]

yeah

,w 3x=2x+3

[thorny flame]

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Requested by Master Oogway#0599

[eternal spoke]

x is 3

right?

so whats the area of the graden/

?

[coral sapphire]

Wait what where’d the 3 come from

[eternal spoke]

look closely

\

all these guys are x

[coral sapphire]

Yeah

[eternal spoke]

cuz every tile is a square

and the sideof the garden is made out of 3 tile lenghts