help-13

[dense wing]

Cause systems of DEs require much more stuff than just 1st order DE

[sturdy grove]

and I assume that that's the more accurate model?

[sturdy grove]

oh I seeeee

[dense wing]

• they come after nth order DEs, around when you introduce Laplace transforms

[sturdy grove]

interesting

[dense wing]

1st order, 2nd order, nth order, Systems/Integral transforms

$\dot{T}=-k(T-T_s) \ \dot{T_s}=m(T_s-T)$ I believe would work, not sure tho

[wraith dagger]

Mosh

[sturdy grove]

oh that's smart actually

it probably does work

[dense wing]

then you go through with all the eigentheory that you've now introduced

[sturdy grove]

in our course, we're only scratching the surface of DE's

[dense wing]

yes, hence why I said it comes later.

[sturdy grove]

so I won't be solving these probably

[cedar kiln]

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[dense wing]

so pick $N\in\mathscr{P}(X)$?

[wraith dagger]

Mosh

Yeetus

[sick ruin]

N is a collection of subsets, but not necessarily all subsets

It can contain all subsets, some subsets, or in their case, no subsets

If it contains no subsets, it is empty, so $\cup N$ and $\cap N$ are empty as well. Does that make sense?

[wraith dagger]

abs_0

[sick ruin]

Idk what they’re saying with the “is equal to Ø respectively X”

Like idk what that’s supposed to mean

Yeah lol

Just do it yourself

If N = Ø, then union and intersection are both empty.
If N = P(X), then union = X and intersection = Ø.

Yeah lol that’s weird idk either

Oh oh ok

Just try proving this yourself

Let X be a set. No matter what topology T you choose, both Ø and X are in T, so they are both open. Since their complements are X and Ø respectively, which are both open, then Ø and X are both closed as well. @steep meadow

Idk if this is what they’re trying to prove

What’s their definition of open/closed in a metric space

How would you say the empty set is open then?

There’s no point in the empty set, so there’s no open ball, right?

Hahaha

Oh you’re saying:

Let X be a set. A subset U is open if for every x in U, there exists epsilon>0 such that an open ball centered at x blah blah blah.

Since there is no x in Ø, this is satisfied right

Side question: is “for all x in A, P(x)” defined as

x in A => P(x) is true

?

Because then since “x in Ø” is never satisfied, ie it is always false, the entire conditional statement is always true

[cedar kiln]

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[gusty orchid]

im trying to solve this but everytime i get somewhere it just ends up being useless

[bright surge]

pythagorean theorem?

a^2 + b^2 = c^2

therefore b^2 = c^2 - a^2

[gusty orchid]

i need to find the altitude tho

i mean im been using the theorem but idk how to reach a point where i can express the altitude in terms of the hypotenuse

[bright surge]

ohh

so

divide it into 2 triangles

[gusty orchid]

i did, but then what? my main problem is trying to find what B (the other leg) is, is that something i should find or not?

[golden sundial]

you could find the other leg with the pythagorean theorem

[bright surge]

express that other leg as a function of the hypotenuse as well?

b^2 = c^2 - a^2

[golden sundial]

let the hypothenuse be H

the known leg A = 4cm

B = the other leg

now we find B using the pythagorean theorem

so B = sqrt(H^2 - 16)

is it clear?

[gusty orchid]

yep

[golden sundial]

perfect, now the area of that triangle can be expressed as B * A * 1/2

2*sqrt(H^2 - 16) in the end

because it would be

[gusty orchid]

OHHHH

ok i see

[golden sundial]

$\frac{1}{2} \cdot 4 \cdot \sqrt{H^2 - 16}$

[wraith dagger]

Thunder7

[gusty orchid]

i see now ok u would then equate that to the sum of the two similar triangles and u would get it... but why do you find the area, and do you need to find the area to solve it or?

[golden sundial]

yes

you can also express the triangle's area as 1/2 *H * K (altitude perpendicular to the hypothenuse)

so

$2 \cdot \sqrt{H^2 - 16} = \frac{1}{2} \cdot H \cdot K$

[wraith dagger]

Thunder7

[golden sundial]

two different ways to express the area of the triangle

but they are equal ofc

[gusty orchid]

ok yea i didnt know about the altitude * hypotenuse thing that would have been good to know beforehand

i was trying to get it solely through side lengths but to no avail

[golden sundial]

so now you just isolate K

[golden sundial]

it's just the triangle's area formula

base * height * 1/2

[gusty orchid]

well i should say i didnt think of it as the altitude * hypotenuse

[golden sundial]

oh yeahh

$K = 4 \cdot \frac{\sqrt{H^2 - 16}}{H}$

[wraith dagger]

Thunder7

[golden sundial]

so this will be your answer

[gusty orchid]

yep i got that thanks for the help

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[golden sundial]

yw

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[grand drum]

i need help

um woops

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[proven wren]

Looking back at my previous calculus test, and don’t know how to do this. Correct answer is circled in purple. Any help would be appreciated

[upper abyss]

Which?

15?

I also have no idea how to do that?

What's the bounds on the integral?

[floral thistle]

none of those are the answer

the stuff with t is constant for the derivative

so f’(x) is purely in terms of t

so basically a constant

this is assuming that t is it’s own thing and not a function of x, which i think is a safe bet

[upper abyss]

Something seems pretty broken about the question, yeah. Bring it up to teach.

[proven wren]

Yeah number 15

And oh Fr? Hmm

[floral thistle]

weird that there’s a mistake this big on a test

happens though unfortunately

[proven wren]

Hmm I was thinking they gave the derivative of f, which is f’, so we would have to do the opposite of it which would be the Antiderivative(integral)

[floral thistle]

they didn’t give the derivative

they gave the original function

[upper abyss]

They gave you f(x), and are asking you to find f'(pi).

[floral thistle]

sqrt(pi) actually

but whatever

answers are wrong anyways

[proven wren]

Ah i see okay Thankyou

[floral thistle]

remember to .close

[upper abyss]

I'd ask the teacher for the solution to the problem. Feel free to upload it here if you can't find the problem with it

[proven wren]

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[golden sundial]

ok

[warm vector]

I’m confused with the gradient part

[golden sundial]

gradient?

[vernal palm]

british word for slope

[warm vector]

Yes

Slope

[golden sundial]

the slope is just defined as the difference of the y coordinates divided by the difference of the x coordinates

[warm vector]

Yes but I don’t understand how to create an equation
Y=mx+c

[golden sundial]

for a) you have two points

[warm vector]

Yep

[golden sundial]

(2,4) and (0,2)

[warm vector]

Oh

[golden sundial]

the gradient would be the difference of the y's divided by the difference of the x's

[warm vector]

Yep

[golden sundial]

so how much is it?

[warm vector]

I got it thanks

I just wasn’t taking the o,..

Thanks,

[golden sundial]

np

ig

[warm vector]

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[warm vector]

Question f.

[keen elbow]

have you done the other the same step? you can divide everything by 2 then it will be the same as the other ones

[warm vector]

Oh ok got it thanks.

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[limber crane]

$\int[\frac{sin(x-a)}{sin(x+a)}]^\frac{1}{2}$

[wraith dagger]

Kd

[floral thistle]

this is pain

[cedar kiln]

@limber crane Has your question been resolved?

[cedar kiln]

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[limber crane]

.reopen

.reopen

[cedar kiln]

✅

[limber crane]

<@&286206848099549185>

[keen elbow]

$\int[\frac{\sin(x-a)}{\sin(x+a)}]^\frac{1}{2} \ dx$

[limber crane]

ye pls help

[keen elbow]

what did you do thus far?

[limber crane]

tried trigo manipulation

and some basic integrals

but cant find it

[keen elbow]

what are you integrating by dx or da?

[limber crane]

dx

[keen elbow]

okay

[limber crane]

yea

[wraith dagger]

KillerWhale2498

[limber crane]

ig trying and expanding sin then rationalising and then trying to solve further

but i cant carry with it ahead

idk

help pls

[keen elbow]

is this a question from book?

[limber crane]

nahh

sir jusss gave me

[keen elbow]

juss?

[limber crane]

just*

as a homework q

like there were 30 qs

and the nly one i didnt get is this

[keen elbow]

It seems this has to do with trig identites. let me see if I can find it

[limber crane]

yeeee ty

[keen elbow]

So I found this

[limber crane]

yea i used em

we use this

then rationalise

by multiplying the expanded form from cosasinb+sinacosb/cosasinb+sinacosb

then what to do i cant really figure out

[cedar kiln]

@limber crane Has your question been resolved?

[cunning quail]

are you sure there's a square root in the question?

sin(x - a) / sin(x + a) can be integrated with u = x + a, but with the square root there doesn't seem to be a real antiderivative (i'm not 100% here)

[worldly iron]

The graph really seems very tangent like

ngl

Anyways

@limber crane

I guess you only have one option left then

go the hard way

Use IBP

[limber crane]

Yup there is

[limber crane]

Lol idts can work

Ill ask my sir tom , how he did it

[worldly iron]

nah no need

https://youtu.be/LcSdDXkO9_M

see this

[limber crane]

Hahaha

Tyy

[worldly iron]

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[kind bronze]

Hello, I need help with this feedback I got from my professor on a question i only got half a point on

Question: A number of soldiers who are under 165cm tall are needed for a special mission, average height is 178cm and the standard deviation 7cm. Calculate with standardization to the default score Z how big the percentage % of the population who can be assumed to be shorter than 165cm.

So I calculated corrently which is Z = x - m / s
Z = 165 - 178 / 7 = -1,86

The feedback I got was "-1,86 should be read in the table"

I also don't get how to calculate the percentage

[kind bronze]

What do i do with the table

[elder parrot]

What are you supposed to do?

[kind bronze]

Huh

I wrote it

How do i read -1,86 in the table to get the percentage of ppl under 165cm

[elfin hemlock]

take mean of the percentages you read on -1.8 and -1.9 and its good enough approximately

[kind bronze]

I dont get how i get a percentage out of this

She just said in my paper "-1,86 you look in the table"

[elfin hemlock]

says % sign in the title of the table

so idk what you mean

it is in %

just read for the z value at -1.8 and at -1.9

[kind bronze]

All these numbers are a blur for me rn i dont understand

Idk which one to use

Its 54%??

Like

I dont

[elfin hemlock]

read which one says to the left

since we want 165 cm or less

read the value

[kind bronze]

What value

[elfin hemlock]

read which title says to the left

read the value in that column

(in the row for z=-1.8 and z=-1.9)

like I have said a few times

[kind bronze]

2,9 and 3,6????

[elfin hemlock]

yes

[kind bronze]

Ok and what do i do with that

[elfin hemlock]

.

[kind bronze]

No it doesnt matter how many times you repeat

My brain doesnt understand

Im too fucking stupid

[elfin hemlock]

you don't know what a mean is?

[kind bronze]

Average value and middle value

Idk in english

[elfin hemlock]

so take the mean

of the two values

like I said?

[kind bronze]

Like i said

Please

Fuck this

.close

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[elfin hemlock]

(2.9%+3.6%)/2?

like what?

how hard can it be

[cedar kiln]

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[warm vector]

Question 1 b.iv

[livid hound]

have you done b) ii?

[long arrow]

Can you find an equation of a line which passes through given two points?

aa

iv only

[warm vector]

Yes

Just b iv

[livid hound]

can you show what you got from b)ii)?

[warm vector]

Yes

X+2y+6

[livid hound]

is not an equation

[warm vector]

X+2y+6=0

[livid hound]

rearrange that equation into slope-intercept form
and/or apply the definition of y-intercept

[warm vector]

Ok

Y=-x/2-3

[livid hound]

if you were able to do all of part a) and/or b)iii)
b)iv) shouldn't be an issue

[warm vector]

But what do I have to do to get the value

Oh ok nvm

[kind bronze]

.reopen

[warm vector]

Thanks

.close

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[long arrow]

$$\int \frac{x}{\sqrt{e^{x}+(x+2)^{2}}} \ dx$$

[wraith dagger]

Modus

[cedar kiln]

@long arrow Has your question been resolved?

[river talon]

what have u tried

[cedar kiln]

@long arrow Has your question been resolved?

[cedar kiln]

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[meager bear]

hi i dont really understand this question i searched up tutorials on yt but they all give the same solution which involves differentiation and i dont really understand why or how the differentiation works

[meager bear]

ik how to differentiate in graphs and stuff but i just dont see how it can be applied in the area of a rectangle

[dense wing]

Area is a function

Google "Optimization calculus"

[meager bear]

okay ty

.close

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[tawny shale]

if a ∈ R-Q, can i find an order n∈N of a radical so n√a ∈ Q?

[cedar kiln]

@tawny shale Has your question been resolved?

[upper abyss]

"n ∈ N of a radical" doesn't parse

If a is irrational, then √a is too.
Because if a is rational, then a² is too.

Then no, nq, for some irrational q, can never be rational. If it were, then q would be rational in the first place

Oh wait, that's nth root, isn't it?

[tawny shale]

there is no n so a^n∈Q for a irrational?

yeah

[upper abyss]

If a is irrational, then ⁿ√a is too
Because if a is rational, then aⁿ is too.

[tawny shale]

thank you

.close

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[crimson sedge]

There are 100 bags with coins. One bag contains 100 fake coins weighing 9 grams each, the remaining 100 bags contain 100 genuine coins weighing 10 grams each (the coins are otherwise indistinguishable). What is the minimum number of weighing to find the bag with fake coins using a scale which will show the weight (in grams) of the coins placed on it. Prove your answer!

[crimson sedge]

did they make a mistake

there are 100 bags

one of the bags is fake

so why did they say "remaining 100 bags"

[livid hound]

probably a typo

unless you copied the down the exact wording incorrectly

[crimson sedge]

i copied and pasted

[livid hound]

should be remaining 99 bags

[crimson sedge]

yeah

[livid hound]

hint: the number needed is probably lower than you think

[crimson sedge]

they just sent an email yesterday

[crimson sedge]

i think i have a strategy

i was thinking of starting by doing 50 by 50

[livid hound]

is not the ideal strategy

[crimson sedge]

ok

let me think of another way

[livid hound]

hint: bags can be opened

note that this is very different to having 100 coins where 1 is fake

[crimson sedge]

i dont think that that is possible

[livid hound]

why not?

[crimson sedge]

using a scale which will show the weight (in grams) of the coins placed on it

they never say anything about opening bags

[livid hound]

are you implying that bags are indestructable?

and that you can't access the $$$ you have in said bags

[crimson sedge]

no, but they never say we can open

[crimson sedge]

we are just trying to find the fake ones

[livid hound]

well its implied that you can open them

otherwise there would be literally no point to saying that they have 100 coins inside

[crimson sedge]

right

[livid hound]

note that this is very different to having 100 coins where 1 is fake

[crimson sedge]

they are 10000 coins in total

oof

[livid hound]

if they didn't want bags to be opened, then they would've just set the problem up as

100 coins where 1 is fake

the fact they they have 100 coins in each bag and and the exact properties of the real coins and counterfeits
allows a clever solution

[crimson sedge]

oh man

does any of this have to do with division

like multiples

[livid hound]

too vague

[crimson sedge]

we have something like that, except 10000 coins where 100 are fake

[livid hound]

hint: consider numbering your bags from 1→100

[crimson sedge]

im bad at these solutions

[crimson sedge]

hmm ok

[livid hound]

and that's as much as I'm gonna hint at this point

[crimson sedge]

fair enough

im trying to udnerstand where labeling the bags comes in when we are working with weights

i honestly wouldnt see a need for opening bags either

it jsut makes things more messier

[livid hound]

that's why numbering the bags helps

perhaps do something based on the numbers on the bags

allows a clever solution
the number needed is probably lower than you think
like a lot lower

[tropic oxide]

isn't crabbo the one who objected to things like labeling coins in weighing problems

[livid hound]

nope

[crimson sedge]

when did i do that?

[tropic oxide]

might not have been you

[livid hound]

that was someone with a green helper tag

[tropic oxide]

ah, then i am misremembering

[crimson sedge]

is it 1

[livid hound]

yes. you can find the fakes with 1 weighing

you just need to properly justify that

[crimson sedge]

i guessed

[crimson sedge]

i dont even know how that is possible

you just dump all the coins on the floor and find the fake

[livid hound]

consider my hints/comments

[crimson sedge]

do we number each coin in the bag with the number as well?

maybe we can turn this into a 100 coin and 1 coin fake problem

[livid hound]

specifically

consider numbering your bags from 1→100
perhaps do something based on the numbers on the bags

do we number each coin in the bag with the number as well?
theoretically this is a simple task

irl you could just organise them nicely

[crimson sedge]

so this problem is about organizing the bags?

[livid hound]

too vague

the problem is about taking advantage of the fact that each bag has 100 coins
and that all 100 fake coins are in a single bag

and that you know the exact properties of a the real and fake coins

[crimson sedge]

do what

is what i dont see

[crimson sedge]

can we try and make this a different problem?

[livid hound]

have a think about it for more than 30 minutes

instead of expecting a solution

[crimson sedge]

your hints are vague

[livid hound]

i suppose you could reduce it down to 4 bags with 4 coins in each bag (where there are 4 fake coins in one of the bags)

[crimson sedge]

im not expecting more hints

[crimson sedge]

i dont even know hwo i would do that

[livid hound]

the idea/solution is pretty much exactly the same

hints are deliberately slightly vague to encourage more critical thinking from you

[crimson sedge]

thank you

(not being sarcastic)

[livid hound]

there isn't that much you can do based on the number on the bag that would make sense in the context of the problem

[crimson sedge]

so if i figure out how i can do that, I can figure out the solution?

the only thing is, I dont know how you can do that since you dont know which bag contains the fake coing

[livid hound]

this bag has the number 50 on it,
so lets add 50 spiders to it

[crimson sedge]

with the coins?

ew

[livid hound]

as i've mentioned multiple times,
you are told the exact properties of the real and fake coins

ok i'll give another stronger hint

[crimson sedge]

right

ah

let me think

but that would add extra weighings

[livid hound]

consider how much the scale would show if all the coins you chose to put on the scale were real

[crimson sedge]

wouldnt it be just 10?

[livid hound]

are you saying that if i were able to randomly pick a bag of real coins, and put it on the scale,
that the scale would show 10g?

10g is the weight of one real coin

but hopefully you don't plan to put just one coin on the scale

you'd be putting on a pile of coins

or to simplify the problem, what would be the weight of n real coins

and then think about what the scale gives you when you place n coins on the scale (where of those n coins, there are reals and fakes)

[crimson sedge]

it would show 1000

[crimson sedge]

10n

[livid hound]

are you saying that no matter how many (real) coins you put on the scale,

it will always be 1000g

[crimson sedge]

fake coins would be 9n

[crimson sedge]

no no

only for 100 coins

[livid hound]

i didn't really ask you about the weight of n fake coins

[crimson sedge]

ok. for n real coins its 10n

[livid hound]

and then think about what the scale gives you when you place n coins on the scale (where of those n coins, there are reals and fakes)

[crimson sedge]

If they are all real, I get 10n, but if they are fake, I get 10n+9f where f is the number of fake coins

[livid hound]

no

either you're implying that replacing real coins with fake coins increases the weight
or you're using n to represent different things

or doing something else i'm having trouble describing

[crimson sedge]

Hmm

Yeah, it doesn’t add weight

[livid hound]

n is intended to represent the number of coins being put on the scale

lets use some numbers.

if i put 11 coins on the scale, what would you expect it to show if they were all real?

is not a trick question

i am also expecting a quick response

[crimson sedge]

Oh I see

[crimson sedge]

110

[livid hound]

now if the scale shows
107
would you be able to determine how many coins are fake?

[crimson sedge]

Yeah

I guess so

[livid hound]

how many coins are fake and how did you determine it

[crimson sedge]

Is the answer 3 fake coins

[livid hound]

yes

and how did you determine it

[crimson sedge]

I subtracted a multiple of 9 that gets to a multiple of 10

Which was 27, which is 9*3

I still don’t see where numbering the bags comes in

[livid hound]

you over complicated the calculation needed

[crimson sedge]

It wasn’t complicated for me to do in my head

[livid hound]

imagine if it could be even simpler than that

[crimson sedge]

Hmm

[livid hound]

note that replacing a real coin with a fake reduces the weight by 1g

[crimson sedge]

Ah

It takes replacing 3 fake coins with real coins to get the weight to a multiple of ten

I see

[livid hound]

no

[crimson sedge]

No?

[livid hound]

flawed reasoning

are you implying that lets say instead there were 15 coins,
and the weight came out as 138g

then there would be 2 fakes as replacing 2 fakes with reals gets you 140g, ( a multiple of 10)?

[crimson sedge]

I see

[livid hound]

note that replacing a real coin with a fake reduces the weight by 1g

and all you really needed was 110 - 107 = 3

[crimson sedge]

Why 110?

[livid hound]

from the initial example

[crimson sedge]

Oh

I didn’t know we were using gm that

Well then

Now we know how to find the fake coins

[livid hound]

you know how to find the number of fake coins on your scale

[crimson sedge]

No we can do this

[livid hound]

now find a way to link that to the number on the bags

and that's really as much as i'm gonna give you

[crimson sedge]

The number of fake coins goes to the bag of that number

[livid hound]

someone else will be able to confirm your final wording and solution

[crimson sedge]

Ah ok

I don’t even know if what I just said is correct

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

o man

im stuck

i really dont know how to use the labels

[crimson sedge]

<@&286206848099549185>

[crimson sedge]

anyone pls

i ask you

[crimson sedge]

Since we can take out coins from a bag, know the number of coins in a pile and the weight, we can figure out the amount of fake coins. Since every real coin weighs 10 grams, than the total weight of n real coins is 10n. So, if we have n coins, we can find the number of fake coins by doing 10n-(the weight of the coins) since replacing a real coin with a fake coin decreases the weight by 1 gram.

i was able to write out what we did so far

thats all

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[agile quarry]

Hi - I have a question about how to discern a function from tables of input and output values. Hard to summarise - details here: https://stackoverflow.com/questions/70598736/how-to-draw-overlapping-images-with-varying-offsets-with-gdi

[violet flume]

wait what

its not really clear

why is that of course

"i know why, of course"

[dusky gate]

Maybe more programming oriented servers can help you better

[violet flume]

i mean i might be able to

if i understand the problem

right now it seems like you want to pass a number to some control thats equal in magnitude to the input from offset

if offset is negative, it should go to rig, if its positive, it should go to game control

thats pretty trivial to code

@agile quarry

but its not really clear to me what the problem is exactly

[agile quarry]

I need to discern a function to calculate the Rig and Game x and y values from the top left of the container (think 0,0 cardinal at the top left)

something like Rig = 2xOffset + 1 (which of course is very wrong)

so in the table at the bottom of that post, if Offset = y and Rig = x

[violet flume]

and these numbers are percent?

[agile quarry]

well those numbers are just an abstraction of the problem - if I can find the function to solve the table, I can manage the percentage issue myself

or functions possibly - one for RigControl + one for GameControl

[violet flume]

no offense but i dont think youve done a very good job of describing this problem

[agile quarry]

how can I help you understand?

[violet flume]

why are you using negative numbers at all

[agile quarry]

the offset is user set. negative numbers allow you to move the offset to different angles around the base image

tbh, I think we just have a breakdown in communicaiton. I think it's pretty clear. I'll let you move on to help someone else. Have a good day.

.close

[cedar kiln]

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[violet flume]

good luck

[cedar kiln]

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[glad blade]

Hi

[glad blade]

I have a spreadsheet I use for budgeting, but was resetting it every 4 weeks when I was paid specific income, now I need to convert it to monthly as paid on the 20th of every month and I'm getting really confused to be honest

[violet flume]

so it was every 28 days but now its on the 1st or something?

[glad blade]

yeah so basically I get PIP which is 350 a month but was resetting my spreadsheet every 4 weeks
but realised I should not be doing this till I get paid from my job because that is 1500 and covers all the bills

if that makes sense

but as it's the 20th of every month not sure how I'd go about changing everything to account for a month because it changes all the time

Bills
Gas & Elec (4th) £160.00
Welsh Water (23rd) £20.00
Virgin Mobile (24th) £21.22
Virgin TV (5th) £33.00
Accountant - Put in Barclays Savers Act £30.00

Subscriptions
Netflix £3.18
YouTube Premium (4th)?? £1.50
Gym (8th) - Jake £14.99
Gym (8th) £18.99
Dog £30.00
Cats £15.00
Barclays Blue Rewards. (Thu - Start of month) £4.00

Shopping
Food - Week 1 (Thu) £42.00
Food - Week 2 (Thu) £42.00
Food - Week 3 (Thu) £42.00
Food - Week 4 (Thu) £42.00
Toiletries £15.00

Petrol
Petrol - Week 1 £30.00
Petrol - Week 2 £30.00
Petrol - Week 3 £30.00
Petrol - Week 4 £30.00

Debt, Credit & Loans
SCS (1st) £34.65
Carpetright £34.23
BPO £5.00
Student Loan - 20th £5.00
DWP - 10th £10.00
Hotel Pot £50.00
Save towards tax owed 21-22 Jan 23 £41.00
Carpetright £34.23

Housing
Rent - Week 1 (Friday) £90.06
Rent - Week 2 (Friday) £90.06
Rent - Week 3 (Friday) £90.06
Rent - Week 4 (Friday) £90.06

[violet flume]

hmm

i guess id have to see how its coded tbh, when you say 'reset' what do you mean?

sorry if im not being as helpful as youd hoped \

[glad blade]

No, don't be silly, gonna send a few screenshots and explain further

So this is the main sheet

You see there is a bit for bills due this month

which is this...

every time a bill is taken out I update the balance of my bank on the main sheet and delete it from the 'Current Outgoing Bills' sheet

and when I press "reset" it copies all the monthly bills that are left and still not taken and pasted them to the right bit of the sheet (as they are still due)
Then it copies all the monthly bills again and puts them back on the left

hope that makes sense

[violet flume]

oh wow

so you take it out automatically right?

i guess that portion wont change

[glad blade]

well I update the bank balance on the main sheet myself, and gets copied all automatically and moved when I press reset yeah

but I update bank balance myself and delete this bills myself when they are taken out, wish I could automate that haha

[violet flume]

im sure you could

so i understand the sheet you have

[glad blade]

I'm so glad, it's hard to explain 😂

[violet flume]

but what is automatic that needs to be changed?

thats the part im confused about

you reset manually and move the bills manually?

[glad blade]

so forget about that part, I reset it by pressing reset button maually then it is done automatically

but only after my input

basically my issue is I budgeted for payment every 4 weeks when I should have been budgeting for payment on 20th of every month

so not sure how to convert all this to account for every month as obviously don't want a seperate sheet for seperate months

[violet flume]

maybe im having a slow morning. I don't really understand because it seems like the bills will still be due regardless of when you get paid, couldn't you just reset on the 20th instead of every 4 weeks? or does that change the amount of the bills since you had planned on slightly overpaying?

i might not understand budgeting enough to be able to help haha

[glad blade]

I could but it's not really accurate then

[cedar kiln]

@glad blade Has your question been resolved?

[cedar kiln]

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[ember phoenix]

how does (n+1)! = (n+1)n!

[floral thistle]

write out the first few terms of each

then you’ll see

[ember phoenix]

umm thats what im kinda confused on

like ik 3! is 3x2x1

but how do i write the first couple terms of (n+1)!

oh wait

is it (n+1)(n)(n-1)(n-2)

?

[ember geode]

yes

[ember phoenix]

so how does the (n-1)(n-2)...

cancel

?

[floral thistle]

(n+1)! = (n+1)(n)(n-1)(n-2)(n-3)…

notice that (n)(n-1)(n-2)(n-3)… = n!

[ember phoenix]

ohhhh

i see

[floral thistle]

so (n+1)! = (n+1)n!

[ember phoenix]

that makes sense

tysm

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[modest sequoia]

im not sure what this question is asking

[ember geode]

It wants you to say what happened to the boats velocity in terms of scalar multiplication

[bright surge]

well, the velocities can be represented as vectors, you can find a scalar so that, when multiplied by the original velocity vector (25km/h north) gives the second one (5km/h south)

[modest sequoia]

so i would just find that scalar?

[ember geode]

Yes. And then answer in a sentence of course like "the boats velocity vector was multiplied by 7"

7 obviously not being the correct answer

[modest sequoia]

oh okay i see

thank yous

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[torn hare]

can I get help on a statistics/probability question?

[bright surge]

maybe drawing a venn diagram will help

[torn hare]

i tried that, but i was unsuccessful

[bright surge]

what did you get in your venn diagram?

[torn hare]

.5 + .5 -.8 = p(A u B)

so p(a u b) is .2

and then i got stuck

[bright surge]

wait a sec-
how can P(A n B) be larger than both P(A) and P(B)

🤔

[torn hare]

ummm

i feel like i wondered the same

[bright surge]

it can't be larger than the probability of either event

[torn hare]

true

could you help me get on the right path?

[bright surge]

well.... with this huge roadblock i don't think i can continue the solution, like, at all

but if the values were correct, you could:

1. find P(A n B)

2. find P(A n B'), since P(A n B') + P(A n B) = P(A)

[torn hare]

is P(A n N) .8?

[bright surge]

uhhhh. in this problem, yes

[torn hare]

i got it

ty

also, do you know how to do independent events?

IK this is an easy question, but I forgot how to do it and need some guidance

[sick ruin]

Well if $A$ and $B$ are independent, $P(A \cap B) = P(A) \cdot P(B)$

[wraith dagger]

abs_0

[sick ruin]

@torn hare

(Hint: substitute in the corresponding values, and then solve for what you need.)

[torn hare]

im sorry, i did know that. and i i tried to but it originally didn't work (probably a calc error). but i got the right answer now ty

[sick ruin]

Oh haha don’t be sorry

That’s just a rule, now you know!

[torn hare]

i have another question, i have so many math problems to do, and im so behind

[sick ruin]

Go ahead

[torn hare]

are the percentages relate the number of people who are high/low ranked? or is it just Daniel's skill? I wasn't sure based on the wording of the question

[gusty orchid]

its just his skill

[torn hare]

that was my original thought, and thus i wasn't sure what to do.

[sick ruin]

Let’s start with the first problem. It says there are 12 players and Daniel is in 3rd place. That means there are 2 people ahead of him and 9 people behind him, for a total of 11 other players.

An opponent is chosen randomly from the 11 other players. Let’s split this into two cases. There is a 2/11 chance the opponent is ranked higher; if this is the case, Daniel has a 30% chance of winning. Thus his chance of picking a higher opponent AND winning is 2/11*.30 = 6/110. There is a 9/11 chance the opponent is ranked lower; if this is the case, he has a 70% chance of winning, so the probability is 9/11*.70 = 63/110.

So the chances of him (choosing higher and winning) OR (choosing lower and winning) is

6/110 + 63/110 = 69/110.

@torn hare not totally sure if this is right though

[torn hare]

that makes total sense. I think my problem was I didn't understand the question and the wording, but the math makes sense.

[sick ruin]

Yeah. Again I’m not sure if the “(higher and win) or (lower and win)” logic is sound. I’m gonna ping <@&286206848099549185> : can you check out the last image and try to solve it? Lmk if you get 69/110

[keen elbow]

what image?

[sick ruin]

This image, #6

[torn hare]

I don't see another way of looking at it that would be capable of solving

[keen elbow]

oh sorry, never had a course in probability

[sick ruin]

Np

Hm

[torn hare]

@sick ruin ty for helping me solve the the baseball one. i checked your math and the answer and it all checks out

i started with a tree diagram for 7

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[deep heath]

You know cos($\theta - \phi$) = cos($\theta$)cos($\phi$)+sin($\theta$)sin($\phi$) and sin($\theta + \phi$) = sin($\theta$)cos($\phi$)+cos($\theta$)sin($\phi$). Apply that to this question.

[wraith dagger]

Plegasus

[valid rampart]

Thank you

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[fickle thicket]

hi guys, need help with understanding this question
An open cylindrical jar should have a volume of 125 cm 3 . What dimensions should the can have in order for the material consumption to be as small as possible?

[cedar kiln]

@fickle thicket Has your question been resolved?

[cedar kiln]

@fickle thicket Has your question been resolved?

[dense kayak]

you want to minimize the surface area of a cylinder with its top removed
i'd start with differentiating an equation for the SA (to find the minimimum)
you'll have to incorporate an equation involving the given volume

[cedar kiln]

@fickle thicket Has your question been resolved?

[gentle lintel]

let r = radius h = height
it’s given that r²h = 125/π, and we want to minimise 2πr (r + h)
we know h = 125π/r², so we want to minimise 2πr (r + 125π/r²)

the rest is calculus

[cedar kiln]

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[coarse coral]

What is the area of a square with side length 5 2/3 cm?

[coarse coral]

Do i just Multiply 4 times

I know its 25

just dont know the other part of the fraction

[gentle lintel]

area of square is defined to be side length squared

A = (side length)²

[coarse coral]

I know what area is

I know the its gonna have ^2 at the end these are the options that i have as answers

or

<@&286206848099549185>

[stray tendon]

this (assuming the 2 is supposed to be a squared)

unless 5 2/3 means 5 + 2/3

then its something else

[coarse coral]

Thats what i picked and they said it was wrong

[stray tendon]

ok then im guessing 5 2/3 means 5 + 2/3, in which case the answer is whatever (5 + 2/3)^2 is

[coarse coral]

Oh ok

[stray tendon]

ye, mixed fractions are dum -_-

[coarse coral]

XD

Thats still wasnt correct

@stray tendon

<@&286206848099549185>

[stray tendon]

what did you get?

[coarse coral]

wdym

[stray tendon]

what answer did you put that was incorrect?

[coarse coral]

This

[coarse coral]

I put this the first time and it was incorrect

[stray tendon]

are there other options?

im getting 32 + 1/9 cm^2 assuming the side length is 5 + 2/3

[coarse coral]

These 2 but they dont make sense

[coarse coral]

Oh ok

[stray tendon]

this basically seems like a trick question about what 5 2/3 means

[coarse coral]

Ohhhh

[stray tendon]

5 2/3 means 5 + 2/3 and (5 + 2/3)^2 = 32 + 1/9

and the units are cm^2 for area

[coarse coral]

Thats makes much more sense thxs

[stray tendon]

np 👍

[coarse coral]

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[tired hinge]

I’m currently stuck on problem 6 of this review here, and I’m unsure of what error I’m making. I thought I could use Pythagorean theorem to solve here, but my problem is that after splitting the polygon to find the side length of the drawn right triangle in the top right corner, I can’t solve for the hypotenuse

[tired hinge]

YES

[iron saffron]

Could you show the polygon without your pencil marks? It’s hard to tell lol

[tired hinge]

aight

[graceful karma]

It doesn't look like you'll need pythag

But yeah it's a bit hard to tell

[tired hinge]

is this better?

[graceful karma]

Yes

[iron saffron]

You could just split it into a rectangle and a parallelogram

[tired hinge]

okay, would i split it from the top to down, or from left to right?

[iron saffron]

Left to right

[tired hinge]

okay

[iron saffron]

I mean either works tbh

[tired hinge]

i'm working rn

[dense kayak]

I'd just like to interject for a moment. What you're referring to as a parallelogram,
is in fact, a trapezoid, or as I've recently taken to calling it, parallelogram with one less parallel side.

[graceful karma]

[iron saffron]

https://tenor.com/view/bruh-moment-gif-23616422

[tired hinge]

I was going to make a stupid pun but im not going to cuz i'd probably get banned for terrible humor

What’s still tripping me up is this 6 on the right side. If I split the shape in half, shouldn’t the right length also be split to some degree?

I’m not sure if I’m just stupid

[iron saffron]

Bro split it where the edge is above the 6

[calm sierra]

@dense kayak pls dont shitpost

[graceful karma]

I don't think he was

[dense kayak]

sorry 😦 i did mean to correct the shape as well

[iron saffron]

That length there will be 6

So then you have all the sides you need just a matter of plugging in the numbers

I think your mistake is that you seem to assume the shape is drawn to scale when it isn’t

[calm sierra]

its right but said in a dumb confusing meme format

[graceful karma]

Why not split it into 2 rectangles and a triangle

[tired hinge]

I have no idea, I'm the guy that's asking for help

[dense kayak]

i think it's easier to take the whole rectangle minus the top-right triangle

[iron saffron]

That works aswell

[graceful karma]

Based on your previous work it looks like you recognized that splittage but did a few extra steps

Here's what you had before without the other stuff

[tired hinge]

I split it directly in the center

[dense kayak]

it's not drawn to scale

[tired hinge]

yeah, I think that's my problem here

[graceful karma]

Mine is directly in the center too

[iron saffron]

Not really

[graceful karma]

It's 4 on both sides

[iron saffron]

Nah I didn’t mean it like that lol

[dense kayak]

papabread's not drawn to scale either 😜

[graceful karma]

Oh you meant like

If you took out a ruler

[iron saffron]

Yeah

Lol

That’s the guys problem

[graceful karma]

Yeah the diagram isn't the best in the first place

[tired hinge]

That's what i did and drew it

[graceful karma]

And neither is ios markup

[iron saffron]

Yeah don’t ever do that

[tired hinge]

aight

[iron saffron]

I’ve never seen a question where it’s drawn to scale

[graceful karma]

I wish

[tired hinge]

[rain vessel]

You could draw something to scale with desmos.

But I'm sure just about everyone would be faster with just plain algebra

[tired hinge]

So I did this

[graceful karma]

Whenever I try to draw something to scale in geogebra or desmos it just confuses me

There's no point cause you have to solve it to draw it

[iron saffron]

Where did you get the 4 from on the left hand side above the 12

[graceful karma]

I think it was just because it looks smaller

[tired hinge]

o im dum

you're right, that should be 6

[iron saffron]

You could just use the formula for a parallelogram area lol

[graceful karma]

Or just rectangle and triangle

[tired hinge]

get trolled

[iron saffron]

Or should I say trapezoid

[graceful karma]

I don't think anyone memorized the trapezoid formula until calculus

[rain vessel]

Takes me 2min to draw to scale, except I have made no progress on the problem

[graceful karma]

For horrible manually calculated reimann sums

[tired hinge]

I still can't remember it

[graceful karma]

Fair

[tired hinge]

Hopefully this is the correct revised version

[graceful karma]

Looks right

That should be enough to find the area

[tired hinge]

cool

[rain vessel]

Took a lot of brain fart but this would be the answer given the power of a very strong calculator like desmos

So theoretically, you could do it in ~1min with a strong calculator

And if you understand line equations really well, and know how integrals tie into area

[tired hinge]

looks like you're the guy for that

[rain vessel]

Simpler to take the rectangle and deduct the triangle obviously

[tired hinge]

That's what everyone says

[graceful karma]

Now find the area of that shape rotated about a kiloparallelepilogram in 6D space

[tired hinge]

[graceful karma]

Do you recognize the way you can split it to get the area alone though?

You just wanna get that triangle alone

[tired hinge]

well, I've already found the area for the rectangle at the bottom, so It's only a matter of finding the area of the trapezoid at the top

[graceful karma]

Yes

[tired hinge]

A= a+b/2 * h, right? I know it looks stupid but discord can't write math

[graceful karma]

I mean yeah that's the formula for the area of a trapezoid

[tired hinge]

cool

[graceful karma]

But there's an arguably easier way

Just splitting it along that 4 line

[tired hinge]

Which is the method you're talking about

[graceful karma]

Into a rectangle and triangle

But yeah if you can memorize the trapezoid area formula that works perfectly fine

I personally am bad at memorizing random fun facts

[tired hinge]

just like me!

It’s jumbled, but the area should be 84, correct?

wait no

hang on

did i just do that pythag for nothing or did i miss a step somewhere?

okay I did but I got the answer to the problem, thanks for the help, guys!

.close

[cedar kiln]

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[cedar kiln]

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[grave rain]

I have 2 different sets of data, one with mean 60.8 and Standard deviati15.233 and another with mean 60.68 and standard deviation 15.275. I wanna figure out the probability of data set 1 happening according to data set 2. Is it possible to do this? I tried making a distribution chart but I didn’t know where to go from there?

[grave rain]

I also tried using the x-u / sd formula (-0.12 / 1515.275) = -0.007856 but that’s about where I stand

<@&286206848099549185>

[cedar kiln]

@grave rain Has your question been resolved?

[cedar kiln]

@grave rain Has your question been resolved?

[elfin hemlock]

“According to data set 2”? What is that supposed to mean

[elfin hemlock]

But sounds like something you need to know the actual distribution of (and the parameters) to calculate

[grave rain]

The data sets are of races. Data set 2 contains the fastest times ever possible and data set 1 is another race, but is an actual human attempt

I want to find the possibility that race 2 will occur using information from race one

[elfin hemlock]

You can’t with that information

[grave rain]

What other information would I need?

[grave rain]

I'm not really good at statistics so I'm not really sure what that is

[elfin hemlock]

1st of all you need a time frame/# of attempts otherwise the only answers are prob 0 or prob 1

2nd of all you need a distribution of the racers time

[elfin hemlock]

There is likely no good distribution to fit this, so stuck

[elfin hemlock]

If impossible to reach computer level then prob 0 otherwise prob 1

[grave rain]

Not sure if this helps but these are the values for data set 2
73.6
34.6
68.7
50.7
75.5
75.0
46.63
And these for data set 1
73.6
34.6
68.9
50.8
75.7
75.0
47.1

[elfin hemlock]

It doesn’t

[grave rain]

Alright

[faint dirge]

in many physics problems where there are NO*** specified forces (like X newtons), gravity and such scale with mass
*** edited because I made a grievous error and you can't edit messages in temporarily archived channels.

[elfin hemlock]

Say if you knew to pull off computer time a racer would need to do 1/1000 jump and then do a good run in general (like 1/10) or whatever

Now you can actually compute probabilities

What you have said doesn’t help at all in calculating probabilities

[grave rain]

Thanks for the help

I think I have a solution

.close

[cedar kiln]

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[shell agate]

Heep on letter C please

[shell agate]

I've been told i did somethign wrong

but i cannot find what that wrong thing is

wtf tho>

the distance between the particles is changing

[ember geode]

yeah sorry i deleted that

that was brainrot on my part

your arithmetic at the end is wrong

somewhere in these steps

let me check exactly where

[shell agate]

ok thanks

[keen elbow]

I got 76sqrt(5)/45

[ember geode]

here you did it wrong somehow

[shell agate]

54 instead of 52 damn

[ember geode]

the correct answer is what killerwhale said for reference.

[shell agate]

thank you

.close

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[wary tendon]

Okay so I might have been taught this a different way but I need help on how to check this problem like in order of operations

[wary tendon]

4th one

[glad kestrel]

what exactly are you having trouble on

cause i'm not sure your work makes sense

[wary tendon]

No it’s not about the work

It wants me to check my answer using order of ops

Just mainly do you know how I could check the question -16=-293.4 using order of ops?

[glad kestrel]

you're asking about the 5th one?

or the 4th one

[wary tendon]

Oh wait 4th one I meant lol

Read the wrong one

[glad kestrel]

well your answer is incorrect

what's the first step you should do when isolating P?

[wary tendon]

Ik my answer is correct but it wants me to self check the equation and I don’t really know how

[glad kestrel]

your answer is not correct

seems you misread a number

to be fair it's an awful font

but that's -116, not -716

[wary tendon]

Ik

[glad kestrel]

and to check your work, you'd simply plug in your answer for P

and see if the equation holds true

[wary tendon]

Yeah but how would I rewrite it as order of operations

If yk what that is

[glad kestrel]

i'm not sure what you mean by rewrite "as order of operations"

order of operations is just the order in which you add, subtract, multiply, or divide

[wary tendon]

Well yeah but that’s how i’m supposedly supposed to say it like that

But would yk how

[glad kestrel]

i have no idea what that means

it doesn't make sense

[wary tendon]

!?

What did I click on

[glad kestrel]

a server emoji lmao

[wary tendon]

Oh lol

[wary tendon]

Yeah do you know how to write the equation out like that?

[glad kestrel]

you don't

[wary tendon]

That’s how I’m supposed to do it for some reason

[glad kestrel]

you can't "write it out as order of operations"

[glad kestrel]

this is my best guess

[glad kestrel]

order of operations would come in to use here

but that's when you're calculating

[wary tendon]

Oh ok

Well idk if I’m wrong or not or if it is just the way I’m being taught but thanks

And I’m sure I needed to simplify it or whatever but I think I was just saying it wrong

[cedar kiln]

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[leaden crater]

is my answer correct? 1. no limit 2. 3

[ember geode]

Looks correct.

[cedar kiln]

@leaden crater Has your question been resolved?

[cedar kiln]

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[oblique needle]

I've figured part a but I need help with (b)

[cedar kiln]

@oblique needle Has your question been resolved?

[deft cipher]

isn't it just a single problem with two simultaneous conditions?

[cedar kiln]

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[stuck snow]

Can anyone help with 12)e pls

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[solemn torrent]

Mid point formula?

[cedar kiln]

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[crimson sedge]

jus tryna find the equation first

y=c(a)^x

im jus trying to get that equation

for the table

jus general question on getting equation frm a table

not rlly atm practicin other stuff atm so tryna figure out getting equations atm

here is an example

for a diff question

w a table

i jus dont get where they r getting the exponent frm

oh

ok

.close

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[rough mango]

I saw in a video this problem. sin(2x)=1/2

The vid said 2x represents the sine wave's periodicity not steepness. How does it correspond to its period and not steepness?

[rough mango]

I am also aware x is an angle, so how does multiplying 2 with an angle give two points in a graph

[graceful karma]

I guess you could argue it increases its max steepness

[violet flume]

[graceful karma]

Its typically given as the frequency though

[rough mango]

wdym by this? it changes its range?

[graceful karma]

Ye

[rough mango]

so it's 2 to -2 now?

[graceful karma]

The rate is

As in the derivative

[rough mango]

im confused

[graceful karma]

Are you familiar with derivatives

[rough mango]

ye i guess

[graceful karma]

It doubles the derivative as well as making the wave twice as frequent