help-10

[fierce lagoon]

And use negative exponent laws

[scenic hedge]

aight

thank you

[fierce lagoon]

Np

[obtuse pebble]

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[red lynx]

https://media.discordapp.net/attachments/938192269553598537/963899697045594112/IMG_20220413_223246.jpg?width=494&height=464 , any idea what i did wrong here? when i tried to calculate it with fromulas An , Sn , S5 equals 65 , but when i tried just summing a1+a2+a3+a4+a5 , i got different result althought i think i should get exactly same thing

[obtuse pebble]

@red lynx Has your question been resolved?

[red lynx]

<@&286206848099549185>

[novel knoll]

What formula is that?

[red lynx]

its artihmetic progression

[novel knoll]

Standard formula is k(k+1)(2k+2)/6

[red lynx]

huh , we use Sn = n/2(a1 + an)

nevermind i just skip that one

[novel knoll]

Is your series on that form?

[red lynx]

yea

[novel knoll]

No it is not

[red lynx]

it is

[novel knoll]

No it is not

[red lynx]

yes it is

[novel knoll]

Which you clearly also see

Because you get a wrong answer

NO IT IS NOT

[red lynx]

hmm

i hate maths

.close

[obtuse pebble]

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[novel knoll]

When I ask is in on this form maybe recheck what arithemetic progression even is before saying “yes” multiple times

[obtuse pebble]

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[mellow fog]

I am able to do (a) and the first part of (b). However I am unsure on how to approach the second bit of (b) and the entire of (c).

[fierce lagoon]

Ah I see

Okay so

Use your limit chain rules

C(1 - exp( [lim] -at))

Im too lazy to use latex

[mellow fog]

I may have not learnt that yet

[tardy epoch]

you haven't learned limits but you're doing differential equations?

[mellow fog]

Nope, this was just given

[fierce lagoon]

They usually don't teach limit chain rules

Which is dumb, they should

Or whatever it's called

[mellow fog]

Oh, i’ll look that up right now

[tardy epoch]

https://www.youtube.com/watch?v=_MbyTm9H48c

[mellow fog]

Thank you

[fierce lagoon]

Basically you wanna take the limit of the actual t

And then take that value

And use it as part of the function

[mellow fog]

Ohh

Ok 👍

[swift marsh]

Idk if he's from here, but in the UK standard curriculum is that significantly more is taught about differential equations before anything more than a basic understanding of the concept of a limit is taught

[mellow fog]

Yep from UK, the concept of limit wasn’t really taught much

Probably with differentiation but it was more of just memorising than explaining

The limit video still confused me but i’ll just try to solve it

[swift marsh]

Yeah there's much more to limits and solving them than differentiation from first principles

There's some limit stuff in FP1

[mellow fog]

I think i’m okay doing the rest of the question so thank you

.close

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[golden bone]

I need help with some combinatorial optimization.
The problem I am trying to solve is this: Say I have an item that I want to craft, which requires a certain amount of 6 elements in order to craft, those elements being Wind, Water, Life, Fire, Void, and Death. In order to craft this, I must combine parts which each have their own elemental values. What is the minimum amount of parts needed to craft an item such that the sum of the parts is at least the requisite value?

My understanding is that this is some sort of knapsack problem, however what I fail to understand is because there is no weight limit, only a minimum threshold that must be met, the programming is a bit different. I have tried to adapt code for a knapsack problem with one constraint, to no avail. Additionally, most code tells you the maximum value you can have with the given weight limit, but I need to return a list of the number of each item it will take to satisfy the recipe (e.g. "You need 3 Discombobulators, 2 Recombobulators, 1 Dislocator, and 3 Relocators."). I have looked into this wikipedia article (https://en.wikipedia.org/wiki/List_of_knapsack_problems#Multiple_constraints), but the contents fly over my head. I have even tried reduced row echelon form matrices, which works fine when there is only one solution, but spits out gibberish when there are multiple solutions. Can anyone please help me?

[golden bone]

<@&286206848099549185>

[tardy epoch]

Say I have an item that I want to craft, which requires a certain amount of 6 elements in order to craft, those elements being Wind, Water, Life, Fire, Void, and Death. In order to craft this, I must combine parts which each have their own elemental values. What is the minimum amount of parts needed to craft an item such that the sum of the parts is at least the requisite value?
depends on the rules for combination

[golden bone]

There aren’t any rules, you can have as many of the same item as needed, and there are no forbidden combinations

[tardy epoch]

if you have 1 wind, can that turn into 6 elements? 1 of each element

[golden bone]

Every item you would be combining is guaranteed to have some integer amount of the 6 elements. So one might have 5 wind, 3 water, 0 life, -6 fire, 3 void, and 2 death

And say, for example, you have an item that you want to craft that requires 50 wind, 25 water, 0 life, 15 fire, 70 void, and 30 death

In my real data set, I have 69 possible items to be combined, each with their own elemental values

[tardy epoch]

just pick an order for your 6 elements, say alphabetical, and phrase your problem in terms of vectors of length 6

you have [d,f,l,v,wa,wi] of stuff. what is your question regarding crafting

$[d,f,l,v,wa,wi] \in \N^6$

[warm shale]

riemann

[golden bone]

So, I want to figure out the combination using the least number of items

[tardy epoch]

so you want to minimize $d + f + l + v + wa + wi$ subject to some constraint. define that constraint

[warm shale]

riemann

[golden bone]

Hmmm

Well I would want the number of items used to be as close to 0 as possible, is that a valid constraint?

[tardy epoch]

Say I have an item that I want to craft, which requires a certain amount of 6 elements in order to craft, those elements being Wind, Water, Life, Fire, Void, and Death. In order to craft this, I must combine parts which each have their own elemental values. What is the minimum amount of parts needed to craft an item such that the sum of the parts is at least the requisite value?
rephrase this explicitly. define "combine", "own elemental values" etc.

[drifting wraith]

you have 69 types, with unlimited amount of each right?

yeah, you said as many as needed ok

[golden bone]

I must add the values of an item's respective elemental values to a running total based on that element. If I combine a dinglehopper with wind = 6, water = -2, life = 3, fire = 7, void = 0, and death = 5, with a tinglestopper, with a wind = 2, water = -4, life = 0, fire = 2, void = 1, and death = 7, the total is wind = 8, water = -6, life = 3, fire = 9, void = 1, and death = 12.

They have their own elemental values, meaning that each item has 6 immutable properties that contribute to the running total. The goal is to have said running total be at least the amount required to craft the item

[tardy epoch]

Yea this is a dynamic programming problem

I'd look on leet code for something like this

[drifting wraith]

it's linear programming

from wiki on simplex method

it's exaclty like this, you minimize a+b+c+d...

and you have conditions like -7a + 4b ... >= something

[obtuse pebble]

@golden bone Has your question been resolved?

[drifting wraith]

(unless it can't handle negatives)

[golden bone]

So how would I state that the number of items should be as close to zero as possible?

[drifting wraith]

"minimize a+b+c+d+e"

i found a problem, it's about reals

[golden bone]

Could this be related? https://en.wikipedia.org/wiki/Integer_programming

Also, what does Z represent?

[drifting wraith]

it's just the target

it's either maximized or minimiazed

it basically worked

give a real example

i'll translate to whatever this is

[golden bone]

A real example?

[drifting wraith]

i meant like full 69 variable data

to test

[golden bone]

[[0,-2,3,5,0,1],[2,-2,0,3,0,5],[0,2,3,0,-2,5],[3,-2,0,5,0,2],[2,0,3,-2,0,5],[0,5,2,-2,3,0],[5,-2,2,0,3,0],[3,0,5,0,2,-2],[5,2,3,-2,0,0],[5,-2,2,0,3,0],[-2,0,3,0,5,2],[5,0,-2,2,3,0],[2,0,-2,0,5,3],[1,0,0,-2,5,3],[5,0,2,0,3,-2],[5,0,-2,0,3,0],[2,5,3,0,-2,0],[5,0,3,0,2,-2],[2,3,5,-2,0,0],[3,-2,0,5,0,2],[0,-2,2,5,0,3],[0,0,3,2,-2,5],[2,-2,0,5,0,3],[2,0,0,-2,3,5],[2,5,0,-2,3,0],[3,0,2,0,5,-2],[0,5,3,-2,2,0],[0,-2,3,5,0,2],[2,0,3,-2,0,5],[2,0,3,0,-2,5],[0,2,3,0,5,-2],[0,0,3,-2,5,2],[3,-2,0,5,2,0],[0,0,3,-2,5,2],[5,3,0,-2,0,2],[0,-2,3,5,0,2],[2,2,5,-2,3,0],[0,5,3,-2,0,2],[5,-2,0,0,3,2],[2,0,3,0,5,-2],[0,0,5,3,2,-2],[0,0,3,2,-2,5],[3,-2,0,5,2,0],[0,3,5,0,2,-2],[0,0,3,2,-2,5],[5,0,-2,0,2,3],[0,3,2,-2,0,5],[0,-2,5,2,3,0],[0,5,3,-2,2,0],[5,2,-2,3,0,0],[0,2,3,0,-2,5],[0,3,5,-2,2,0],[2,0,0,-2,3,5],[0,-2,2,5,0,3],[-2,3,0,2,0,5],[5,2,-2,0,3,0],[5,3,-2,0,2,0],[5,0,3,-2,2,0],[3,0,-2,0,2,5],[2,-2,5,0,3,0],[0,3,2,0,-2,5],[2,0,3,0,-2,5],[2,0,-2,5,0,3],[2,0,-2,5,3,0],[0,2,3,-2,0,5],[3,-2,3,5,2,0],[0,1,5,-2,0,3],[3,0,0,-2,2,5],[3,0,-2,0,5,2]]

I don't know if that helps

[drifting wraith]

yeah perfect

[golden bone]

Each list is an item, and each number is an elemental value

Index one is wind, index 2 is water, etc.

And a recipe I'd like to figure out is [45, 80, 150, 5, 45, 10]

[drifting wraith]

yep almost done

solved instantly with 38 items

the solution can;t uh

be read

it's in this scrolling thing, i'll need to find a way to format it

[golden bone]

Ah okay, being able to interpret the output is kinda the whole thing lol

Ideally I’d like the final output to be “You need x of this item, x of this item, and x of this item”

[drifting wraith]

the point was that it doesn;t like choke because of 69 variables

[golden bone]

I have a list of the names as strings, if the program accepts those

They’re index-matched

[obtuse pebble]

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[timid silo]

how is this the wrong parameterization? i tried negative as well

[timid silo]

.close

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[bronze bronze]

can you solve for zeros in terms of one variable when there are two vairables in the equation?

[bronze bronze]

For example:

x^2-x(0.4+y)+y-0.6=0

[short spruce]

you can rearrange that as a function of y in terms of x

[bronze bronze]

what would that accomplish?

[short spruce]

do you know how to find zeroes of an equation?

such as y=5x+3?

[bronze bronze]

u set y=0 then solve from there yeah?

[short spruce]

right

[short spruce]

so rewrite this as y= something

set equal to zero and solve

[bronze bronze]

ok thanks, Im trying to find the eigenvalue of a matrix when the matrix has an unknown variable in it so I'll try to apply this to that then

ty

.close

[obtuse pebble]

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[bronze bronze]

.reopen

[obtuse pebble]

✅

[bronze bronze]

one more thing quick sorry, if I'm trying to get y = I get y-y on the left side, does that mean I should do something differently or do I just solve for zeros normally since it's always equal to 0 then

[short spruce]

i think you might be messing up somewhere

[bronze bronze]

never mind actually I did it wrong lmao, it was yx-y which wouldnt get to y-y bc u cant pull out x from both

yeah I always make small mistakes like that smh

lmao ty again

.close

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[knotty lodge]

3. c)

not sure what im supposed to do here

use factor table?

[obtuse pebble]

@knotty lodge Has your question been resolved?

[knotty lodge]

<@&286206848099549185>

thank you!

<@&286206848099549185>

?

??

[knotty lodge]

.close

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[jagged dagger]

let $x,y,z$ be positive real numbers such that $x+y+z=1$. Find the maximum value of $x^3y^2z$

[warm shale]

suck2015

[jagged dagger]

How would you solve this w/ AM-GM?

[obtuse pebble]

@jagged dagger Has your question been resolved?

[jagged dagger]

.close

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[rugged flower]

I worked out the equation (8w^2 +3w^3 +4w =170) for the container but what confuses me is the problem asking me to use the iterative method to determine the solution

[obtuse pebble]

@rugged flower Has your question been resolved?

[obtuse pebble]

@rugged flower Has your question been resolved?

[rugged flower]

why does it keep saying that?

[obtuse pebble]

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[shell hull]

Total area?

[weary spruce]

Can somebody explain to me these two things

1. Why did they convert -5 to positive +5? Would an answer be possible with -5 in the first quadrant?

2. Since the x1-x2 (x - y = 0) line is 45 degree, how do we know which side to shade

oh its taken

[gentle notch]

Is the 1/4 circle a length or a percentage of the circle

[shell hull]

A percentage of the circle

[gentle notch]

Is it the same circle as the semicircle on the bottom

[scarlet locust]

clearly its not

I don't think that diagram has sufficient information

[gentle notch]

I think it does

[shell hull]

It's not in the question, idk

[gentle notch]

What is the overall shape defined as?

@shell hull

[shell hull]

Nothing

[shell hull]

I have written all the assumptions.

[gentle notch]

I am guessing left and right sections on the egg, are sections of a circle with an angle of 45 degrees?

[shell hull]

I have calculated the area of the triangle and the 1/2 circle and I need to find the area of the parts of circles and the 1/4 circle.

[shell hull]

It is not mentioned in the question, I do not know

[gentle notch]

Because it says the curve is apart of a circle the curve will have a constant change in angle,
And Given the angle doesn't change between sections.
Therefore If you can figure out what change in angle is of the arc. You can figure out what percentage of a circle it is

right?

[shell hull]

Wdym?

[gentle notch]

Trying to figure out what percentage of a circle arc for the left and right sections

To use find an expression for the radius of the top circle

[shell hull]

Did you get the answer to the question?

[gentle notch]

no I am bit stuck I can see that it is possible though making a model in desmos lol

[gentle notch]

Do you get What I mean with the change in angle?

[shell hull]

No

My problem is in calculating the area of the circle parts
What can we do for that?

[gentle notch]

well we need the angle and the radius from the centre of each circle section

[shell hull]

How can I find it?

[gentle notch]

The change in the arc angle from horizontal is the same as the angle from the centre for the Sections on the left and right

[shell hull]

Please show your solution

[gentle notch]

i am not there yet

sorry

<@&286206848099549185>

The left and right sections are 1/16th of a circle

[shell hull]

Ah I got what you mean

I can do the rest

[gentle notch]

You can create 2 simulatanous equations with the Point of at the end of the left arc interms of the top circles radius and then again with the left sections radius

[shell hull]

the radius of the 1/4 circle is 4-2√2

[gentle notch]

I don't think so

[shell hull]

Why?

The side of the triangle is 2√2 right?

[gentle notch]

yeah but the top circle radius is not that i only because it doesn't line up on the desmos model though

[shell hull]

AB=AO+OB
4=AO+2√2
AO=4-2√2=OD
AB=BC=CD=CB=4

[gentle notch]

top radius$ = 2\sqrt{2}+2\sqrt{2+\sqrt{2}}-2-2\sqrt{2}\sqrt{2-\sqrt{2}}$

[shell hull]

$2\sqrt{2}+2\sqrt{2+\sqrt{2}}-2-2\sqrt{2}\sqrt{2-\sqrt{2}}$

[warm shale]

Tanjiha

[gentle notch]

Does the 2nd line come with question

[shell hull]

Which one?

[gentle notch]

4=AO+2√2

because that is just giving you the radius

[shell hull]

The area is:
$6-4\sqrt{2}$

[warm shale]

Tanjiha

[gentle notch]

Is this the whole question or just the assumptions you made

[shell hull]

The assumptions I made

[gentle notch]

idk https://www.desmos.com/calculator/nnatrjtp83

I made a mistake

https://www.desmos.com/calculator/9jtakp0gq5

@shell hull the side circle radius is 4

[shell hull]

I know

[gentle notch]

i am dumb

[shell hull]

I got $12\pi-4\pi \sqrt{2}$

[warm shale]

Tanjiha

[shell hull]

The options:
$$(10+4\sqrt{2})\pi-4$$
$$(12-4\sqrt{2})\pi-4$$
$$(10+4\sqrt{2})\pi-4$$
$$(12+4\sqrt{2})\pi-4$$

[warm shale]

Tanjiha

[shell hull]

It should be $$(12-4\sqrt{2})\pi-4$$ lol

[warm shale]

Tanjiha

[shell hull]

I will close this channel.
Please dm me if you could find anything.

.close

[obtuse pebble]

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[hexed imp]

any idea how do i do q4ii? my working for 4i is there

[royal basin]

@hexed imp do you know how to find equations of tangent lines?

[hexed imp]

y=mx+c

[royal basin]

...i didn't ask you to rattle off a formula

[hexed imp]

?

[royal basin]

i asked you a yes/no question

but let me be more explicit

if you were given the graph of a function y = f(x) and asked to find the equation of its tangent line at x=c, would you be able to do it? yes or no

[hexed imp]

yea... sorry I didn't read ur question properly lol

[royal basin]

:|

but ok

so...find the equations of both tangent lines, then find their point of intersection

[hexed imp]

welp I guess I kinda understand... thanks hahaha

. close

.close

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[compact remnant]

I need help

[winter aurora]

ok

so lets say

A+B+C=429

[compact remnant]

Yeah

No but it’s says ‘the sum of this number and the three individual digits add to 429

[winter aurora]

yeah

[compact remnant]

So won’t it be the number + a + b + c

[winter aurora]

so lets assume that the house number is abc then

[compact remnant]

Yeah

[winter aurora]

uh gimme a moment

ik the answer but im trying to find a way to explain it

[compact remnant]

Ik the answer

But I don’t know how to do it

I am practicing for the junior ukmt

In fact it gave a brief paragraph of how to solve but I don’t get it

Here it the answer but I don’t get the explanation

[winter aurora]

ok

so lets try

trial and error

[compact remnant]

Here were the five choices

[winter aurora]

its 28

[compact remnant]

Ik but how?

[winter aurora]

oh wait

ik now

the sum of a+b+c is at most 27

because 9+9+9 is 27

right

and u cant go any further

now moving on

and the numbers must be in the 410s or the 420

so lets say

the last digit is d right

lets say its in the 410s

do 410+2d+5=429

2d=14

d=7

that means 417

[obtuse pebble]

@compact remnant Has your question been resolved?

[obtuse pebble]

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[odd stag]

I'm trying to prove that the Sorgenfry line is totally disconnected

[odd stag]

,tex
Let $I$ be an interval in the Sorgenfry line for $a,b \in \mathbb{R}$ where $a \le b$
If $a = b$, then $I$ is a singleton set and that it is connected.
if $a \neq b$, then $\exists c \in \mathbb{R}$ s.t.\ $a \le c \le b$. Then $[a,c),[c,b) \in I$, we see that $[a,c) \cap [c,b) = \emptyset$ and $[a,c) \cup [c,b) = I$, so $[a,c)$ and $[c,b)$ are disconnected

[warm shale]

ArtyLeAardvark

[odd stag]

This is what I have so far so I have 2 disconnected intervals what can I do from there?

[royal basin]

well you have shown that any interval of the form [a,b) decomposes into the union of two disjoint open sets

and hence is disconnected

any two points can be disconnected in this way

[odd stag]

So my proof is complete?

[odd stag]

I'm also not sure if this needs more explanation, but it is obvious right?

[royal basin]

yes

[odd stag]

Ahh brilliant thank you

.close

[obtuse pebble]

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[stark igloo]

hey guys i want to ask a silly question

[stark igloo]

if the

the hanging mass should be 55g? or 50g?

[dark cloak]

Hii can someone help me with those questions

[royal basin]

@dark cloak this channel is occupied, please read #❓how-to-get-help

@stark igloo yes, this reads as though it should be about 55g (depending on how much "about 50g" refers to)

[stark igloo]

ok thank you

[obtuse pebble]

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[violet widget]

1. x=60

[tall nebula]

How

?

[violet widget]

<adc = <dcb

[tall nebula]

?

How

[violet widget]

cuz circle

ab = diameter

wait f no

ok here

since its a circle

unless there are 2 parallel chords, you will not get perfect multiples of 10

[tall nebula]

Ok

[violet widget]

heres why

[tall nebula]

But how do I get x

[violet widget]

so

draw another diagonal from the other side

db

ok?

[tall nebula]

How does that help

I need to find x

[violet widget]

listen ._.

i know bro chill

[tall nebula]

Ok

[violet widget]

so the triangles

dcb and adc are congruent

[tall nebula]

Ok

[violet widget]

so

bcd = 120

angle

bcd

then

angle bad = angle abc right?

cuz trapezium

in a circle

u there?

[tall nebula]

Ye

S

[violet widget]

so did u get what im saying?

[tall nebula]

Not really

How do these steps help to find x

[violet widget]

im using triangle congruency to find all angles of the triangle

[tall nebula]

Ok then how is x 60

[violet widget]

ye i messed up my maths a bit

its 30 but ill explain

nvm ig

[tall nebula]

<@&286206848099549185> can you help

<@&286206848099549185> pls

Hello

Pls

@helpers

[verbal pendant]

alright what part are you having difficulty with

@tall nebula

[obtuse pebble]

@tall nebula Has your question been resolved?

[obtuse pebble]

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[dense bridge]

how would i find the dimensions of a square based prism if its height is twice the side length of the square?

[junior fog]

like this?

oh dimensions

[dense bridge]

yep

[junior fog]

does it need to be in terms of anything

[dense bridge]

mm

[junior fog]

you know what dimensions are?

[dense bridge]

if thats what youre asking

yeah like the length and stuff

but im stupid

lol

[junior fog]

yea, just say the dimensions

in units I’m assuming

[dense bridge]

we can use units then i can change it

[junior fog]

in millimeters*

[dense bridge]

so in this instance the volume is 1228.25 mm cubed

i know what the answer is but i want to know how to get it

[junior fog]

then do l•w•h=1228.25

plug it in as the solution

kinda giving you the answer

whoops

[dense bridge]

yeah but im not supposed to know the answer

[junior fog]

basically

you know the formula for volume?

[dense bridge]

area of base x height

[junior fog]

yea

set that equal to the end result

which is volume

[dense bridge]

what is 'that'

[junior fog]

bh

so bh=1228.25

[dense bridge]

essentially

[junior fog]

then plug the values of the dimensions in terms of x for base and height

and then solve for x

[dense bridge]

wdym plug

[junior fog]

basically make b the area of the square and h for the height of the prism

[dense bridge]

2x + 2x = 4x

so

[junior fog]

the squares side length is x

[dense bridge]

yeah

[junior fog]

do you know the formula of a square?

[dense bridge]

.

[junior fog]

it’s x^2

not 2x

[dense bridge]

x times x woops i thought that was 2x

always make that mistake

[junior fog]

dw I make that mistake too

[dense bridge]

x^2 + 2x = 1228.25

[junior fog]

it’s annoying

[junior fog]

it’s base times height

you’re adding the height to the base

[dense bridge]

x^2 x 2x\

[junior fog]

you can actually simplify that

[dense bridge]

so dont simplify

or do

[junior fog]

it does

have you learned exponent rules?

[dense bridge]

2 x x^3

[junior fog]

get rid of the extra x

and you’re fine

[dense bridge]

one of them is time

i should do * instead

[junior fog]

nah discord doesn’t allow it

[dense bridge]

2*x^3

[junior fog]

yea

[dense bridge]

so then what

just put into my calculator?

[junior fog]

2x^3=1228.25

and simplify until you get x=answer

If Im not stupid then the answer should be ||8.5||

[dense bridge]

so theres an issue

[junior fog]

what is the issue

[dense bridge]

i cant find the indices button on my calculator

[junior fog]

exponent?

button?

[dense bridge]

there is no exponent

[junior fog]

there is no need to use exponents

do you have cube root on your calculator?

[dense bridge]

yes

[junior fog]

you simplify by reversing pemdas

and doing the opposite operation

ok fine

basically

2x^3

in order to simplify it we need to find the operation closest to addition

which in this case is multiplication

[dense bridge]

this is my calculator where is the exponent button

[junior fog]

too blurry

and you don’t need exponents for this problem

[dense bridge]

indices

[junior fog]

fine indices

[dense bridge]

yes

[junior fog]

but you can just do x^3 as (x^2)(x)

[dense bridge]

i have an idea

[junior fog]

how do you get rid of the two?

[dense bridge]

divide both sides by 2

[junior fog]

yea

[dense bridge]

x^3=1228.25/2

[junior fog]

and do inverse operations for x^3

[dense bridge]

yes

cube root

that gets me to 8.5

[junior fog]

yea

that’s the answer

actually no

you have to find the dimensions

[dense bridge]

8.5x8.5x17

[junior fog]

mhm

[dense bridge]

lemme write all this down now

ok done

thanks!

that helped

.close

[obtuse pebble]

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[thorn kite]

How do I change y=mx+B formula for a Fc vs. v^2 graph

[obtuse pebble]

@thorn kite Has your question been resolved?

[obtuse pebble]

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[timid silo]

Yo

[timid silo]

Someone help me intergrate this motherfucker

[novel knoll]

Its just splitting the integral up

[timid silo]

Sn

[novel knoll]

?

[timid silo]

So

3x^4/2x

-4/2x

[novel knoll]

Split it up correctly

[timid silo]

3x/2

-2/x^3

??

[novel knoll]

Yes

Can you integrate those?

[timid silo]

Yh

Give me 5

Got distracted

Is this right intergral

Bruh sending taking ages

Ok I’ll write it

Took out a factor of 3/2 for the intergral of x

Then took out a factor of -2 for the integral of 1/x3

[obtuse pebble]

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[native anvil]

if you need to make up a basis for a subspace that you have the equation of, I thought you needed to have the same number of vectors in the set as the dimension of the subspace. In one of our Gram-Schmidt process examples, the subspace is x-y+z = 0 but the basis the prof came up with only had two vectors (1,0,-1) and (1,1,0). Wouldn't you need 3? Maybe I'm just really confused but could someone explain?

[brittle girder]

If your system is x-y+z=0, you have 2 free variables and 1 dependent variable, so you have a 2-dimensional subspace of R^2

[native anvil]

oh ok. How do you know that? I saw the x, y, z and assumed it was R^3

[haughty coyote]

The number of variables involved isn't the dimension of the subspace. The number of equations (that are not redundant) determines the number of dimensions you lose. Here since you have 1 equation in 3D you have a 2D vector space. The number of variables used in the equation(s) is irrelevant: x+y+z=0 and x=0 both determine a plane

[native anvil]

Oh ok that makes a bit more sense. Could you provide an example of when it would be in R^3?

[brittle girder]

Vectors in your space look like $\begin{pmatrix}y-z\y\z\end{pmatrix}$

[warm shale]

Zorn's Lemon

[brittle girder]

What you have is the equation defining a specific plane in 3-dimensional space, basically. Try plotting your equation in geogebra 3d to see what you get: https://www.geogebra.org/3d

[native anvil]

which one is the dependent variable?

[brittle girder]

The way that I wrote it is with y and z free and x dependent, but you can take your choice of the three

Which is to say, if you know two of your three coordinates, you can use the equation you have to find the third.

[native anvil]

could you give me an example of when it would be in R^3? Would it need to be two equations?

[native anvil]

oh ok

that kinda makes sense lol

[brittle girder]

Well your plane is already in R^3, it's just only part of R^3

Imagine you have a plane with a line on it

The plane is 2d, the line is a 1d subspace of the plane

Defined by 1 equation

This is just the same situation 1 dimension up

[native anvil]

I'm still confused on how to tell what the dimension is. If it's in R^3 why doesn't the basis have 3 vectors?

[brittle girder]

Because it's not all of R^3. The basis has 2 vectors because it's a 2-dimensional part of R^3

Do you have a piece of paper?

[native anvil]

yeah I do

[brittle girder]

The piece of paper is 2d, right?

[native anvil]

yes

[brittle girder]

It's in 3d space, right?

[native anvil]

yes

[brittle girder]

You can define any point on the piece of paper in 2 vectors

If you have a third vector, it's either not linearly independent so useless, or it points to somewhere not on the piece of paper

[native anvil]

oooh that makes sense now.

[brittle girder]

The subspace you have, a subspace of R^3 defined by your 1 equation, is a 2-dimensional space in R^3. Just like how your piece of paper is a 2-dimensional space in our 3-dimensional world

[native anvil]

that does make sense now! Ok One more question would be, what would the equation need to look like if it wasn't a plane but a 3D object?

[brittle girder]

Well, we'd be working somewhere other than R^3

If you wanted a 3d subspace of $\mathbb{R}^4$, you could try a single equation again, and you'd get vectors like $\begin{pmatrix}y-z\y\z\w\end{pmatrix}$.

[warm shale]

Zorn's Lemon

[brittle girder]

If you wanted a 3d subspace of $\mathbb{R}^{5}$, it would be defined by two equations. Etc.

[warm shale]

Zorn's Lemon

[brittle girder]

The only 3d subspace of R^3 is R^3 itself. There are shapes in 3d that are proper subsets of R^3 (say, a filled-in sphere), but they aren't vector spaces.

[native anvil]

oh ok I think that's where I was confused maybe. Because the plane isn't in R^3 but it's just a subspace of R^3

right?

[brittle girder]

Well it's "in" R^3 in the same way as your piece of paper is in our 3-dimensional world

Subspaces are indeed proper subsets

[native anvil]

right but the basis for it is in R^2?

[brittle girder]

The basis for it is vectors in R^3. It happens to be that it is isomorphic to R^2 as a vector space, but it is not itself R^2

[native anvil]

Oh ok

I think I understand it a lot better now

[brittle girder]

Put in some practice and I'm sure you'll get it.

[native anvil]

thank you so much!

[brittle girder]

If you're done remember to .close

[native anvil]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

aa

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[stable plume]

hello ive came across problem that im a bit confused with: basically u need to express point B with a, ive tried to play around with coefficients because both lines are tangents of parabola, however then idk what to do

[stable plume]

heres my thought process

[obtuse pebble]

@stable plume Has your question been resolved?

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[obtuse pebble]

@sterile basin Has your question been resolved?

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[stray summit]

i have a word pronlem about algebra

[stray summit]

Mr. Avramenko would like to be more dashing, so he purchases a horse, a carriage, and a top hat for $11 557. The horse cost $350 less than the carriage but was more expensive than the top hat by a factor of eight hundred. How much did each item cost?

[obtuse pebble]

@stray summit Has your question been resolved?

[stray summit]

<@&286206848099549185>

[obtuse pebble]

@stray summit Has your question been resolved?

[stray summit]

Where is helpers

[stray summit]

Ig I'll just close this one

.close

[obtuse pebble]

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[stiff minnow]

A purely notational question here, I suppose. Ignoring the difference between a distance and a norm, pretending all norms can be distances in this scenario, I understand that the l^2 norm is the Euclidean distance, i.e., the square root of the sum of the squares, and the l_1 is the Taxicab distance. But, notationally, why is it written l^2 and l_1, a superscript and a subscript?

[civic zealot]

notation like that can sometimes vary from book to book. Your text might write it with a superscript to evoke the idea of the squares. But other texts won't.

[stiff minnow]

it's weird, i've seen it in pretty much everywhere as l^2 and l_1

[civic zealot]

you can see ok wikipedia they mark them both as |x|_1 and |x|_2

[stiff minnow]

like it makes sense, just wondering if there was a more concrete reason than 'idk just is' floating around

[civic zealot]

https://en.wikipedia.org/wiki/Norm_(mathematics)

[stiff minnow]

yea that's for denoting the actual norm, but they'd say 'this is the l_1 norm and the l^2 norm, |x|_1 and |x|_2'

well not wikipedia specifically, but most texts and books

[civic zealot]

not that I know of. maybe someone more familiar in analysis/topo might know though

[stiff minnow]

perhaps, just a random 1:30 am thought haha

thanks anyway

.close

[obtuse pebble]

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[ivory spoke]

Hello. I tried to compute x, and I got 20:

15/30 = 10/x
15x = 300
x = 20

I tried to compute y as well, and I got 24 :
15/30 = 12/y
15y = 360
y = 24

BUT when I try to compute the scale factor/similarity ratio, it results to 1/3:
15/45, lowest term: 1/3

The problem is, the things that I've computed are all scaled to 1/2, not 1/3:

15/30 = 10/20 = 12/24
1/2 = 1/2 = 1/2

[ivory spoke]

did i miss something?

[long sinew]

15/30 = 10/x doesn't work

[ivory spoke]

oh

[long sinew]

The 30 isnt part of a triangle

[ivory spoke]

so it should be... 15/45?

[long sinew]

Yes

15/45 and 10/(x+10)

[ivory spoke]

oh

the same goes with y right

[long sinew]

Yes

[ivory spoke]

12/y+12

alr, i'll try that

[long sinew]

Wait

y+12??

[ivory spoke]

oh

is it not

[long sinew]

Compare the big triangle to the smaller

y/12 and 45/15

or reverse it

12/y and 15/45

[ivory spoke]

oh okay

i'll try that wait

oh yeah they all resulted to 1/3

but

[long sinew]

I solved both, and checked it

What did you get?

[ivory spoke]

why is y/12 not 12+y, isn't 12 the smaller figure, and so i'm just adding the smaller figure to the partial measure of the bigger figure to get the overall measure of the bigger figure

idk if that make sense

[long sinew]

No

y is the entire part of the larger triangle

[ivory spoke]

OH

yeah

that make sense

[long sinew]

Yes

[ivory spoke]

alr, thank you so much

[long sinew]

If they gave you a 12 and a y then y = 24

[ivory spoke]

yep

[long sinew]

Since the overall length has to be 3 * 12

You seem to get the idea though

Do you have any more questions?

[ivory spoke]

yeah

none, thank you

.close

[obtuse pebble]

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[sleek sinew]

Need help with volume of frustum

I dont know how to find the second base area

Or is it based off a)? We find volume of full pyramid and subtract smaller pyramid

[long sinew]

Total area - area of cut shape

Yes

[sleek sinew]

Part a is here

[long sinew]

That

That is exactly how you should do it

[sleek sinew]

Alright ty

.close

[obtuse pebble]

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[stray summit]

Rayan makes $5 for every $3 that Stefan makes. When comparing their yearly salaries, if Rayan bought a $36000 car, they would have the same amount of money in the year. How much money did each person make?

[long sinew]

Set up an equation to model the problem

[stray summit]

I would do 360000 = 5-3x?

[sleek sinew]

Think you need system of equations

First one is R - 36000 = S

2nd one is more tricky

[stray summit]

how would i find the second one?

[sleek sinew]

R = (constant)*S

How much Ryan makes is a constant tines the amount Stefan makes

Say you know Stefan makes $100

Or $500

To find Ryan, you multiply by the same number

[stray summit]

so if he made $500 it would be $2500?

[sleek sinew]

That ratio would be 5:1

The current ratio is 5:3

Stefan makes 3, Ryan makes 5

Stefan makes 21, Ryan makes 35

[stray summit]

Oh

so if s made 2500 r would make 1500?

[sleek sinew]

But we need a general formula

R = 3/5 x S or R = 5/3 x S?

[stray summit]

R = 3/5x S

[sleek sinew]

Should be other way around

[stray summit]

oh

[sleek sinew]

Ryan makes more

[stray summit]

Right

[sleek sinew]

If S = 1000, your formula says Ryan makes less

[stray summit]

so R = 5/3 x S would be correct?

[sleek sinew]

Yeah

[stray summit]

would i replace r with 36000?

[sleek sinew]

You have R = 5/3 x S

R - 36000 = S

You have one variable isolated in system of eqns

So substitution is appropriate

[stray summit]

so
R = 5/3 x S
R - 36000 = S

and thend i would use subsitution method?

[sleek sinew]

Yes

[stray summit]

How would I do it with this equation?

[sleek sinew]

R = 5/3 X S

Imagine deleting R in the second equation

Replace with 5/3 X S

So you have a 3rd equation, with only S

[stray summit]

So I would do
5/3xS=R
(5/3xS)-36000=S

[sleek sinew]

Yeah

Now just need to do some algebra

[stray summit]

K

[stray summit]

I try to do system of equations with these 2 equations but it doesnt work

[sleek sinew]

Get S by itself on left side

Move constants (36000) to right side

Do the opposite operation

On the RHS, we have positive 1S

Do the opposite to get S all on left side

Did you get (5/3)S - 1S?

[stray summit]

I got something different but is this what I'm supposed to get?

[sleek sinew]

Well you got (5/3)S - 36000 = S

We want S on left side, constants on opposite side

Subtract S both sides

(5/3)S - 1S = 2/3S

Add 36000 both sides

Then we get (2/3)S = 36000

Did you get that?

You can do other methods but should be sameish process

[stray summit]

Yes

Now I just do algebra?

[sleek sinew]

Yeah just isolate S

Just get rid of 2/3 and make S by itself

[stray summit]

I got s = 54000

[sleek sinew]

Yep

Just needa find R now

[stray summit]

Equation for that is
54000/(5/3)?

[sleek sinew]

R = 5/3 X S

[sleek sinew]

If you did this, R would be less

This would be 54000 X 3/5

[stray summit]

Oh I c

So x = 90000

?

[sleek sinew]

Yes R = 90000

If you want to dbl check, your answers should work for both eqns

[stray summit]

K

[stray summit]

So r made 90000 and s made 54000?

[sleek sinew]

Yeh

[stray summit]

K ty

[obtuse pebble]

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[hidden bluff]

HEWLLO

[hidden bluff]

I HAVE a realllly quick question that i really needs

Say you have f(x)=50+a lnx, and you have a point, (2, 15). How would you use this point to solve for a?

[nocturne minnow]

f(x) also means y, correct?

[hidden bluff]

yeh

[nocturne minnow]

The point (2, 15) is an x, y coordinate pair

Plug in that coordinate and solve for a

[hidden bluff]

But its logarithmic

Idkd if it works like that

[nocturne minnow]

alnx is a * lnx

Which is multiplication

You don't need the decimal equivalent of lnx

[hidden bluff]

I seE

One last question

For exponentiala decay how do you know when y = 0, like isnt there an asymptote there

This equation for example

if I want to find how long it takes for this to reach 0 is there anythin i can do

[nocturne minnow]

You can still do 0 = 100(0.5)^x and solve for x

[hidden bluff]

what are the tsteps

[nocturne minnow]

Actually wait

[high lily]

it won't reach 0

but it can get really close

[hidden bluff]

ah

Hm

so when youre asked "find when this equals 0" is it impossible to do with exponential decay?

[obtuse pebble]

@hidden bluff Has your question been resolved?

[obtuse pebble]

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[harsh badge]

i hav eno idea

[tardy epoch]

pick one and spend some time working on it

[harsh badge]

i do not know how to do it

and when i look it up its all behind chegg or study.com

[tardy epoch]

google the formula for length of a curve and understand it

[harsh badge]

so f'(x) is e^2x+2e^x+1 and i just find anti derivative

isnt dy/dx = dy/dt / dx/dt

.close

[obtuse pebble]

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[weary spruce]

Pls help

[weary spruce]

I am getting answer
2x = 2y + z

:c

[nocturne minnow]

Post work

[weary spruce]

@nocturne minnow sorry for the handwriting, I didnt expect to get a wrong answer and post here

There is a podsibility the question is wrong

[nocturne minnow]

Your method for taking the determinant looks very confusing

[weary spruce]

wdym

thats how they teach us in india

[nocturne minnow]

You should simplify that matrix first

[weary spruce]

so theres a possibility

[weary spruce]

oh

you mean i shoulda first evaluated

[nocturne minnow]

Element (3, 1 )is that 4 - 2?

[weary spruce]

yeah 4-2

i think the question is wrong

this book is trash

[nocturne minnow]

No you did math wrong, from what it looks like

[weary spruce]

impossible

💀

let me try doing it again

by simplifying

[nocturne minnow]

Determinant of 2 x 2 is ad - bc, correct?

[weary spruce]

wait

check element

check when i found z's minor

it should be +4

alright dude

it was calculation error

although i checkced it twice before posting

💀

ty

[nocturne minnow]

And you said it was impossible that you did math wrong

[weary spruce]

:skkull

i checked it twice

From next time i wont skip steps

[nocturne minnow]

Or make your life easier by evaluating and make the matrix simpler to handle

You can make more mistakes doing mental math

[weary spruce]

💀

now i 100% understand why i score so less in maths even when i solve 90% of the paper

💀

this one was completely unexpected, i did it twice

:Skkull

[nocturne minnow]

Doing it twice doesn't necessarily mean that you did math correct the second time

[obtuse pebble]

@weary spruce Has your question been resolved?

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[jade sail]

Hello

[jade sail]

Could someone please help me understand the highlighted lines of working out in my study notes? Thank you

[tardy epoch]

do you know the geometric series expansion?

[jade sail]

Yes I do

I have trouble using it to obtain the next lines of working out

[tardy epoch]

can you write out the geometric series for that?

[jade sail]

Do I throw a negative sign in there to make the denominator 1 - D/2?

Okay

I actually don't know

[tardy epoch]

no. you don't invent negative signs out of thin air

$\frac{1}{1 + x} = \frac{1}{1-(-x)}$

[warm shale]

riemann

[tardy epoch]

Now do you know how to compute the geometric series?

[jade sail]

Yes

That's what I meant sorry

Okay I know how to compute the geometric series but I still don't understand how I get from here to here

I feel like it's really obvious

[tardy epoch]

Use the definition of D

those all look like different questions. putting them next to each other back-to-back-to-back is confusing

pick one and understand it first before moving on to new problems

[tardy epoch]

stick to this one

[obtuse pebble]

@jade sail Has your question been resolved?

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[old saddle]

Hey guys I need help finding hcf of this it is very hard <@&286206848099549185>

[old saddle]

Are these correct

Hello anybody here <@&286206848099549185>

[idle ferry]

Seems okay to me

Pretty much alright

[old saddle]

Thanks 🙏 god bless u

[upbeat ruin]

.close

[obtuse pebble]

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[timid silo]

i would like someone to walk me through set theory and subsets i think

[timid silo]

i have a practice problem and id just like to be taught maybe

"Let A and B be subsets of the universal set U. Is the following statement true or false?"

B⊆(A∪B)

going in blind but i imagine it isnt that much

[obsidian isle]

what does U mean

Think!

Best practice is to translate set theory into english

I'll just do this one for you.
"B is a subset of the union of A and B."

[timid silo]

A union B
U is the universal set that contains all?

Alright, let me process this real quick haha

"B is a subset of the union of A and B."

is the union of A and B the universal set, as they are the subsets of U

i think that's what we figured out?

which would mean it's true

[obsidian isle]

Let's say the universe is integers. And A is (1,2,3) and B is (4,5,6). Then what is A U B?

A+B doesn't have to be the Universe

[timid silo]

ok
A u B would be
1,2,3,4,5,6?
because those are just the sets that are contained
but even though those are all integers they're not all of them in the universe
im sorry if im getting confused
which would make that one false if it's asking if A u B is the universe is integers?

[obsidian isle]

Right, but it's not asking whether A u B is the universe. It's just asking whether B is a subset of A u B

[timid silo]

4,5,6 would be a part of (1,2,3) (4,5,6) so yes?
or is it false

[obsidian isle]

Yes its true

[timid silo]

oh alright, so my explaining of the union and A and B was right?

is there like a way im supposed to write this out in work form, or is it kinda of just figured through logical thinking

[obsidian isle]

Yeah you can just use words

[timid silo]

alright
ill just ask one more of these problems

is there a difference between these?

[royal basin]

of course there is

$\overline{A \cup B}$ consists of points that are not in the union of $A$ and $B$

[warm shale]

Ann

[royal basin]

$\overline{A} \cup \overline{B}$ consists of points that are not in $A$ or not in $B$

[warm shale]

Ann

[timid silo]

Oh, so that's simple. It's just false.
Thank you.

i guess that's all, thanks!

[steep cedar]

I think you should just keep in mind how contrapositives work

i.e $\overline{A\cup B} = \overline{A}\cap\overline{B}$

[warm shale]

tw4040

[timid silo]

im listening
wondering if maybe i picked up on it being false wrongfully

i think im just doubting myself there. think it is false
but what do you mean with this example?

[steep cedar]

You are correct in that it's false

$\overline{A\cup B} = \overline{A}\cap\overline{B} \neq \overline{A}\cup\overline{B}$

[warm shale]

tw4040

[steep cedar]

I'm saying this question is easily solved by keeping in mind how to do contrapositives

[timid silo]

ohh i see

[royal basin]

wrong name

it's de morgan's laws

nothing to do with contrapositive

[steep cedar]

yeah mb

but ye

[timid silo]

alright de morgans laws. i know a bit about those
okay i think i got it.
im actually going to bed now
thank you all

[obtuse pebble]

@timid silo Has your question been resolved?

[royal basin]

.close

[obtuse pebble]

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[royal basin]

(seeing as they went to bed...)

[obtuse pebble]

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[steady zenith]

J’aurai besoin d’aide sur cette exercice svp

[obtuse pebble]

@steady zenith Has your question been resolved?

[obtuse pebble]

@steady zenith Has your question been resolved?

[obtuse pebble]

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[alpine flare]

Hey
I'm learning "new stuff", I have a 2d (vec2 and later 3d-vec3) question,.
Say I have 2 points, what do I call the thing that I'm trying to do that determing point between these 2 points using t, or % or distance, say what coordiante would a point have lying between the 2 vec2 points, what at 10% etc etc

[finite vector]

not sure what u mean but ur prolly looking for 'parametrization'?

[alpine flare]

I think its this https://math.stackexchange.com/questions/393168/how-do-i-find-the-point-between-two-point-at-a-specific-distance-in-x-y-coordin

[nocturne sun]

pythagoras theorem?

[finite vector]

ok for these u could prolly use section formulae

[alpine flare]

hmmmm

[finite vector]

with a combination of parametrization if it's 3D

[alpine flare]

lets start with 2d...