help-13

[dire geode]

a v' = b - cv => dv/(b-cv) = dt/a. integrate both sides

[potent echo]

im trying

ill let you know

[cedar kiln]

@potent echo Has your question been resolved?

[potent echo]

@dire geode fixed thanks!

[cedar kiln]

@potent echo Has your question been resolved?

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[cedar kiln]

@verbal pebble Has your question been resolved?

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[cedar kiln]

Please don't occupy multiple help channels.

[lunar plank]

im really unsure about this answer

would love any help or if someone could do it out and lmk if they get the same

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[sleek tiger]

is the answer A?

?

YOOOOOOOOO help me

[crimson sedge]

i got option b

[sleek tiger]

oh but thats shells method

and to use shells method you need to convert in terms of y

but b is in terms of x

[crimson sedge]

u are right

my bad

[sleek tiger]

its fine

<@&286206848099549185>

[cedar kiln]

@sleek tiger Has your question been resolved?

[bold vine]

i think so

[sleek tiger]

alr thx

.close

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[hot storm]

In triangle ABC, angle A is 122.5, angle B is 45, angle C is 22.5

[hot storm]

Prove that the angle bisector from B, the altitude from A, and the median from C are concurrent

I was thinking about using ceva or angle bisector theorem

<@&286206848099549185>

[cedar kiln]

@hot storm Has your question been resolved?

[hot storm]

<@&286206848099549185>

<@&286206848099549185>

[scenic heron]

can you send a picture

of the problem

or is text all u got

[hot storm]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

Anyone out there?

[cedar kiln]

@hot storm Has your question been resolved?

[hot storm]

<@&286206848099549185>

[cedar kiln]

@hot storm Has your question been resolved?

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[verbal tundra]

hi

[verbal tundra]

im new

[unique nest]

hi. the "math help" channels are for asking questions and help with exercises. Do you need such help?

[verbal tundra]

not now

why are u laughing @unique nest ?

[manic kelp]

Then please close the channel by typing
.close

[verbal tundra]

.close

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[final drum]

!help

[cedar kiln]

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

[final drum]

if a car can only accelerate or decelerate by a units (instantaneously) each step, and has to stop x units from its current position, and has an initial velocity of v units, how can it be determined what series of changes make it stop perfectly at x units
for example if it has an inital velocity of 0, and needs to stop after traveling 35 units, and its acceleration is 10 units, it would be 0 + 10 + 15 + 10 + 0, but how would i write an equation, or a series of simple steps, to solve this regardless of a, v and x

[wraith dagger]

Pro_Hecker

[final drum]

what does that do

[cedar kiln]

@final drum Has your question been resolved?

[crimson sedge]

i dont get the question

u must find a ?

[final drum]

nah

uhh

[crimson sedge]

i should be able to help if i understand well, do you have the initial problem ?

[final drum]

does this help?

nah thats probably more confusing

[crimson sedge]

both

is this the full problem ?

[final drum]

this is like

rules for what the solution has to be

the car starts with a velocity of v, each next velocity can only go up or down by a, and it has to somehow stop at x

as another example, if v is 30, x is 10, and a is 10, then a solution that works is 30 + 20 + 10 + 0 - 10 - 20 - 20 - 10 + 0 or
[30, 20, 10, 0, -10, -20, -20, -20, 0]

[crimson sedge]

every second ig ?

[final drum]

sure

[sacred bolt]

Hi

[final drum]

hi

[sacred bolt]

Lemme see

[crimson sedge]

and you can go back too ?

[final drum]

yes

[sacred bolt]

Not home

[final drum]

well itd probably be better to think of it as turn based

each turn the car moves by its velocity, and then can change its velocity by up to 10

and it has to end up at x in the least amount of turns

[crimson sedge]

so you have to find a sequence of accelerations with the minimum size ?

[final drum]

if you mean the least amount possible, ye

its fine if it always moves by 10 or -10, just that there wasnt a faster way to stop at x

like a way that used less turns

[crimson sedge]

so if u have to travel a distance x, you could take only a=2*x/t^2 and it will be only 1 change of acceleration ? or i still dont understand

because distance = a*t^2/2

[final drum]

its turn based so accerlation kinda happens instantly

so like
velocity = 30
turn 1: x = 30
velocity = 30 - 10
turn 2: x = 30 + 20

[crimson sedge]

by "turn", you mean change of acceleration right ?

yea anyway i dont understand sry

[final drum]

yes

.close

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[oak beacon]

two 2x2 matrix A and B are multiplied AB. the new matrix has entries which are double of matrix A. find such A and B matrix which will satisfy those conditions

[idle tusk]

so you have that $AB = 2A$

[wraith dagger]

artemetra

[oak beacon]

yes

but they must be non-scalar

[idle tusk]

are we given whether A is invertible

[idle tusk]

if A is invertible, left-multiply both sides by A^{-1}

[oak beacon]

ok

[cedar kiln]

@oak beacon Has your question been resolved?

[oak beacon]

actually this is not possible

only scalar matrices can satisfy the condition

[wraith dagger]

Wild123

[unique nest]

case 1: A is invertible; That means B-2I=0, so can find B easily.

case2: A is not invertible; You take
A= (a, b)
= (xa, xb)

from what I see, you just have to find some examples; you take, for example, a=1, b=2, x=-1, an arbitrary B, and solve AB=2A...

[unique nest]

I guess I should have tagged you at some point

[cedar kiln]

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[karmic timber]

[\int_{0}^{2\pi} \frac{xsinx}{3+sin^2x} , dx]

[wraith dagger]

Amadeus

[karmic timber]

i know how to evaluate this when its pi, but not sure how to start on 2pi?

[twilit escarp]

int^a _b f(x) = int f(a+b-x)

king proprety or smth

[karmic timber]

yeah i did it but

[twilit escarp]

#help-48 message

[karmic timber]

u end up with

[twilit escarp]

actually

[karmic timber]

0 = 2pi ...

[twilit escarp]

we did it earlier

[karmic timber]

i did 0 to pi

im having trouble with 0 to 2pi

[twilit escarp]

why so ?

[karmic timber]

because

let I = that integral

then by kings property

u will get

I = 2pi - x f(sin(2pi-x)) dx

since since(2pi-x) = -sin(x)

if you expand it out, you end up with

I = -2pi integral (sinx)...dx + I

so 0 = -2pi integral ...

idk

[twilit escarp]

look through the channel

and see where it went wrong

[karmic timber]

i know how to do 0 to pi

i did exactly that

its just that 2pi

is a bit different

because of the negative

my final answer is half of the correct answer for some reason when i do 0 to 2pi

What the hell

[cedar kiln]

@karmic timber Has your question been resolved?

[karmic timber]

.close

[cedar kiln]

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[terse ember]

Hi can someone teach me how to solve the Riemann hypothesis 😂

[dire geode]

<@&268886789983436800>

[slate lintel]

sure can't

also don't troll in help channels thanks

.close

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[crimson sedge]

hi

[versed jasper]

bruh

[summer otter]

close this channel if you don't have any question @dusty yacht

[cedar kiln]

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[vocal fern]

Which factorization should i choose for the following questions ?

[cedar kiln]

@vocal fern Has your question been resolved?

[vocal fern]

<@&286206848099549185>

[vestal bluff]

for part 2, you can use the most factored form to find the critical points and signs in each interval

part 3 you have to do it in the most expanded form, set it equal to 0 and refactor it all

[vocal fern]

Can you give me an example

Since im going to be based on the second factorization . How do i solve the following questions?

[cedar kiln]

@vocal fern Has your question been resolved?

[vocal fern]

<@&286206848099549185>

[half apex]

this is Polynomial ?

[vocal fern]

Wdym

Idk

[stark crypt]

They are the same
In the left one, take x common and you get the right factorised form

[vocal fern]

How to solve the inequation (solve for x)
x³ - 3x² + 2x = 12?

[karmic timber]

subtract 12

on both sides

what the hell is an equation

inequation*

inequality?

[vocal fern]

Yes

[karmic timber]

subtract 12

so its gonna be

... <= 0

wait nvm u want >= 0

let me just write it down for you

[stark crypt]

Sir.. he already factorised it

[karmic timber]

u cant factorise thiis

[stark crypt]

U can

[karmic timber]

there are no integer roots

[stark crypt]

Oh wait, i thought V is factorised nvm

[stark crypt]

He factrosied V here

[vocal fern]

The factorised form is x(x-1)(x-2)

Now i need to solve x(x-1)(x-2) - 12 = 0

[karmic timber]

wait

[stark crypt]

X is not pretty

[karmic timber]

only integers or not? because if intger then its impossigle

[vocal fern]

I dont know

[karmic timber]

what course is this

[vocal fern]

What?

Wdym

[karmic timber]

like what class is this

[vocal fern]

9th grade

[karmic timber]

well

i guess ur allowed a calculator

just use desmos

[vocal fern]

Calcs arent allowed

[karmic timber]

how the fuck

are u meant to sovle it

let me try

[vocal fern]

Yes

[stark crypt]

Error in the question ig

[stark crypt]

Don’t

[karmic timber]

yea its not possble

oh

you dont need the roots

use vieta's formulas

[karmic timber]

@vocal fern u dont need roots

loook

[vocal fern]

First time seeing this monstrosity

We havent reached vieta yet

[stark crypt]

U dont’ need vieta’s

[stark crypt]

Q3. Is the weird one

[karmic timber]

what does the problem say

i dont speak french

or spanish

its spanish right

[vocal fern]

French

[karmic timber]

whoops

yeah frnech

[vocal fern]

3. If V = 12 , find every value of x

[karmic timber]

???

it wants the domain?

[vocal fern]

I.think its an equation to solve

Like uh

[karmic timber]

x(x-1)(x-2)=12

[vocal fern]

Yes

[karmic timber]

solve for x

well

u cant without a calculator

[stark crypt]

These are the values of x

[vocal fern]

And how to show that V >=0 ?

[stark crypt]

U factored it, use that

[karmic timber]

?

no say

when x is between 0 and 1

its posibitive because

positive * negative * negative = positive

bruh this isnt even right

when x is between 1 and 2, its negative

[vocal fern]

Oh

[karmic timber]

so like

the problem is wrong

idk

[stark crypt]

They probably assumed something like x only belongs to Z+ or something

[vocal fern]

Could i magically replace x¹ and x² with 4
And x with 2

[karmic timber]

how

arent they the same x?

[vocal fern]

Idk tbh

Could i maybe replace = with =< and get multiple xs?

[cedar kiln]

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[dark kite]

If anyone knows German and understands how to solve this, your help would be greatly appreciated.

[dire geode]

probably would get help faster if you translated to english

[cedar kiln]

@dark kite Has your question been resolved?

[dark kite]

(a) For a function g:R→R, it is known:
𝑔(5)=2 and g′(5)=−3.
i. Draw the tangent defined by these conditions!

ii. Sketch a possible curve for 𝑔
g in the vicinity of the tangent point in the coordinate system on the right!

How do i find function with two points one with differentiated?

[crimson delta]

you dont need to find g

you just need to find a possible sketch

[hard thistle]

it can even be a line lol

[dark kite]

how can i find slope?

[crimson glen]

Is this a general question, or is there a specific question you are looking at with a given values?

[hard thistle]

the slope is given when you plug in 5 the slope is -3

[dark kite]

𝑔(5)=2 and g′(5)=−3.

[cedar kiln]

@dark kite Has your question been resolved?

[cedar kiln]

@dark kite Has your question been resolved?

[dark kite]

.close

[cedar kiln]

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[dark kite]

.close

[cedar kiln]

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[crystal canopy]

How to calculate BMI?

[cedar kiln]

Please don't occupy multiple help channels.

[digital cliff]

generally?

google it

In a maths problem?

depends on what you have

[crystal canopy]

The BMI is calculated by dividing an adult's weight in kilograms by their height in metres squared

@digital cliff what’s your weight?

[digital cliff]

70000 skittles, but you shouldnt ask such questions

[crystal canopy]

Ok I have 50 kgs

And I’m 1,6 m

1,6 * 1,6

2,56 m

50:2,56

19,5 BMI

OMG IM NORMAL

OMGFGGGGGG

😁😁😃😃😄😃😃😃😄😁😁😃

YESSSSSS

IM NORMALLLLLL

[dull oxide]

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[spark nexus]

Slay!!

[cedar kiln]

@crystal canopy Has your question been resolved?

[cedar kiln]

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[dire radish]

,rotate

[merry magnet]

<@&286206848099549185> im a modular i dont know where do i learn this

i need some help here kinda confuse

[digital cliff]

uh

context?

[cedar kiln]

@merry magnet Has your question been resolved?

[cedar kiln]

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[small barn]

in this solution how do I determine the concave up and concave down on the table

before and after the x values

[cedar kiln]

@small barn Has your question been resolved?

[neat pulsar]

Do you want to know how to assess concavity?

[small barn]

I already know

when y’’ = 0 and we find the value of x

wait

I forgot

[neat pulsar]

Could you state your question more precisely?

[small barn]

how do I determine these

is this good ?

[neat pulsar]

OK

@small barn Pick a value for each interval

(-inf, 0)

(0, 1)

(1, infty)

Evaluate the second derivative for each value

Give me the values you chose and their y'' value

[small barn]

0

[small barn]

y’’ is 0 for 0

[neat pulsar]

No

Read again what I asked from you

Notice I asked for values in open intervals

[small barn]

yes

[neat pulsar]

?

[small barn]

wait

I don’t get it

what’s the rule of concavitu again?

[neat pulsar]

Rules of concavity are

Given an interval $I$, if $f''(x) > 0$ for all $x \in I$, then $f$ is concave up

[wraith dagger]

Max Hetfield

[neat pulsar]

But if $f''(x)<0$ for all $x \in I$, then $f$ is concave down

[wraith dagger]

Max Hetfield

[small barn]

what is that symbol?

x something I

[neat pulsar]

$\in$ means "belongs/belonging to"

[wraith dagger]

Max Hetfield

[small barn]

oh

alr

man im still not sure

can you help with explanation

how do I get second derivative of an interval?

I know functions but haven’t learnt that

[neat pulsar]

Mate, with all due respect

You aren't doing any effort at all

[small barn]

im trying but

im 14 in gr9

[neat pulsar]

No, you aren't

[small barn]

ok im sorry

[neat pulsar]

Second derivative

Get your function y and get its derivative

Then get the derivative of that derivative (that's the second derivative)

So if you got a function $2x^3$, what's the first derivative?

[wraith dagger]

Max Hetfield

[small barn]

6x^2

and then second derivative

12x

[neat pulsar]

And the second derivative?

Exactly

[small barn]

but im not sure what you mean by this

[neat pulsar]

OK

Fact: Concavity can only change at inflection points.

[small barn]

Yep

[neat pulsar]

Inflection points can be located by finding where the second derivative is equal to 0

or where the second derivative is undefined

[small barn]

Yes also aware of that

[neat pulsar]

Note: This does not mean that if a second derivative is equal to 0 or undefined, it automatically becomes an inflection point

[pastel vault]

between any two points where a function is 0, that function can only be either positive or negative

that function can be the y-value
it could also be the first derivative
it could also be the second derivative

[small barn]

ohhh

okey

[neat pulsar]

That's what they're doing in the exercise

They solve for f'' = 0

And find that f'' = 0 when x = 0 or 1

[small barn]

but how do we determine

[neat pulsar]

Is that clear?

[small barn]

whether the concavity is up or down

after the point

[neat pulsar]

Good, that's what I'm going to now

[small barn]

yes

that part is clear

[neat pulsar]

Now, for now we only know that when x = 0 or 1, f'' = 0

So we suspect

@pastel vault I got this one

Please let me finish

[pastel vault]

from this, this part is super important:

you can just test the sign of the second derivative at one point

and every other point in the interval (between the zeroes of the function) will have the same second derivative sign

also concave up means 2nd derivative is positive
concave down means 2nd derivative is negative

[pastel vault]

(assuming there are no asymptotes or discontinuities)

[small barn]

ahh

[neat pulsar]

OK, so know we suspect that x = 0 or 1

[small barn]

alr

[small barn]

yes

[pastel vault]

ok I'll let you continue Max

[neat pulsar]

Nah

You interrupted me alreadsy

[small barn]

😭

[neat pulsar]

What he said zodv1k

[small barn]

yep

About concavity

[neat pulsar]

I I don't know why people gotta be like that

In the middle of an explanation and they just come and interrupt

That's reude

[pastel vault]

yeah actually hopefully you can sketch 12x(x - 1)

leading coefficient of quadratic = 12 > 0

so the graph of the 2nd derivative is concave up

so you do get plus, minus, plus

[neat pulsar]

But the important thing it's that you finally understood it

[small barn]

wait

so

[small barn]

in this

[small barn]

how would we use this concept

[small barn]

yea we got that

[pastel vault]

this is how you use the concept

plus, minus, plus

but plus = concave up and minus = concave down

[small barn]

then why is there concave down between x values 0 and 1?

[pastel vault]

did you sketch 12x(x - 1)?

[small barn]

yes

[pastel vault]

yeah then you just need plus = concave up and minus = concave down

[cedar kiln]

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[dire radish]

,rotate

[dire radish]

Am i currently on the right path

im unsure

in order to find the shadow at a instant

i need to find dy/dt right

i think this is related riates

since its time

wait uhh it gives me dy/dt

☠️

uhh what am i finding can someone help me

[dire radish]

and can someone tell me if im on the right path

is it

[dire radish]

the hyp of the big triangle

but dt

actually what do i do

i thin im confused

[wraith nacelle]

I'm sorry hold on, I am looking at your picture right now

so your y calculation is correct.

[dire radish]

Ok cool

Can I ask

What am I finding?

[wraith nacelle]

so basically, what's going on is, you're trying to find how fast the tip of the shadow is moving. Once you have this y, you notice that the top left angle increases as the ball moves downward, and hence the bottom left angle (theta) decreases as the ball moves dowward.

the rate of change of the top left angle is the same in magnitude as the bottom right one.

give me one second I am drawing a diagram

I think there is a simpler explaination.

[cedar kiln]

@dire radish Has your question been resolved?

[wraith nacelle]

@dire radish I think this was the intended solution. it's simpler and does not use trig, but directly uses the similarity of the two traingles.

plug in the value for $g$ as 32 freedom units per second.

[wraith dagger]

PinkPurpleBlue

[dire radish]

Looking

i believe i understand

i will try

[wraith nacelle]

if you want me to explain more I can.

[dire radish]

i succummbed to the answer key because i was mad or something

it seems so much easier once i see it like this

☠️

i guess i just gotta think

more optimal

[wraith nacelle]

I mean honestly speaking, the picture I sent and this one is equivalent. I just used symbols before I substituted stuff. and maybe worse notation lol. In the last part you have to take the derivative.

[dire radish]

yeah

i guess i couldnt visualize it properly

[wraith nacelle]

don't worry about being optimal. Trying to get to the solution on your own will usually be messy, and that's good. That means that you're not afraid of thinking. Trying to always write the cleanest most simple and short solution is a lot easier once you know the moving parts.

[dire radish]

thank youf or your help[

i do papreicate iut

a lot

[wraith nacelle]

no worries.

have a good one

[dire radish]

have ablessed

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[dire radish]

night

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[modest sparrow]

I wanted to ask, what help does the fact "the graph crosses the x-axis at integer values of x" do, I found out that a=7, but im stuck now

[crimson sedge]

You can equate teh function here to 0

Substitute the value of a

Use the quadratic formula to find the subsequent value of b

by taking integer values of x

[modest sparrow]

So I have to try a hit and miss?

[crimson sedge]

That's what I can think of

I am sure there may be a more elegant solution

[modest sparrow]

Thats what I was thinking

[crimson sedge]

But I would have to work this out to see if there is one

[modest sparrow]

I thought of the hit and miss

[modest sparrow]

Thank you for your help

[crimson sedge]

No problem good luck

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[cedar kiln]

@exotic jay Has your question been resolved?

[somber canyon]

what exactly did you want help with?

[cedar kiln]

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[exotic jay]

how to find the solution interval

without using programs

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[somber canyon]

you can probably just manipulate it algebraically

[somber canyon]

what

[somber canyon]

question at hand ^

[exotic jay]

can you help? I'm stuck on a decision

[somber canyon]

oh actually looking at it now, you have a trig function mixed with an algebraic function, im not sure if you can easily solve it without a calculator

im going to close it rn cuz its not my thread, try reposting it to see if anyone else has an idea

.close

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[mint python]

Does anyone know why I'm not getting the answers in the mark scheme even though the rest is correct ??

[small plaza]

$\tan \frac{7\pi}{4} = \tan -\frac{\pi}{4} = -1$

[wraith dagger]

emlis

[mint python]

So it's the same thing??

[small plaza]

yeah

here a graph :

[mint python]

So it doesn't matter what way I write it?

[small plaza]

maybe matter, it depends on the range of theta

[mint python]

Ahh ok i get it now

[small plaza]

tan x = tan x + 2 pi

[mint python]

U use a cast diagram??

[small plaza]

what? i get the diagram from wolfram alpha

[mint python]

No I mean you can use a cast diagram

[small plaza]

oh ok i getted

[mint python]

Yh

Thank u

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[narrow leaf]

hi

[cedar kiln]

@narrow leaf Has your question been resolved?

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[wicked grotto]

Hi guys, I'm trying to show that the Expectation of the Commutator of L_3 with any operator, A, in an eigenstate of L_3 is 0

[wicked grotto]

I think using L_3 P=\lambda P will be useful but can't get much further

"Prove that { [ ˆL3, ˆ A] { = 0 when the expectation value is taken in any eigenstate of ˆL3, for any operator A"

[cedar kiln]

@wicked grotto Has your question been resolved?

[wicked grotto]

<@&286206848099549185>

[worldly chasm]

We have v^T [L_3, A]v = v^T (L_3 A - A L_3)v = v^T L_3 A v - v^T A L_3 v

@wicked grotto

[wicked grotto]

yees

[worldly chasm]

Is that a "yes, it's clear to me now?" Or a "yes, I've gotten to this point but am still confused?"

[wicked grotto]

yes i'm still confused lmao

mb mb

[worldly chasm]

Now use your eigenvalue identity

[wicked grotto]

I've gotten to the point where i need the expectation of "L_3 A" to equal the expectation of A multiplied by the eigenvalue i've called lambda

[worldly chasm]

One sec

[wicked grotto]

Trying to use Hermitian nature of L3 now..

[worldly chasm]

No need

[wicked grotto]

Ok i've managed to get it using Hermitian nature but I'm interested in your method too 👀

[worldly chasm]

\begin{align*}
p &= \bra{\psi} [\hat{L}_3, \hat{A}] \ket{\psi} \
&= \bra{\psi} (\hat{L}_3 \hat{A} - \hat{A} \hat{L}_3) \ket{\psi} \
&= \bra{\psi} \hat{L}_3 \hat{A} \ket{\psi} - \bra{\psi} \hat{A} \hat{L}_3 \ket{\psi} \
&= \bra{\psi} \lambda \hat{A} \ket{\psi} - \bra{\psi} \hat{A} \lambda \ket{\psi} \
&= \bra{\psi} \lambda \hat{A} \ket{\psi} - \bra{\psi} \lambda \hat{A} \ket{\psi} \
&= 0
\end{align*}

[wraith dagger]

OmnipotentEntity

[worldly chasm]

I guess I do implicitly use the hermitian nature of L_3 here

[wicked grotto]

Yh I think from line 3 to line 4 maybe?

[worldly chasm]

Yup

[wicked grotto]

Alright perfect thank you that was the little piece of information needed 🙏🙏

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[cedar kiln]

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[crimson sedge]

i need help with maths

[crimson sedge]

its factorization

[craggy tiger]

Use the quadratic formula

[crimson sedge]

yes

[crimson sedge]

how?

[unique nest]

look at formula for roots y1 and y2. look at polynomial. use formula. get y1 and y2.

[icy zenith]

if you are going to use formula, you never will understand factorizastion and how polynomials work

[crimson sedge]

never seen a thing like this before

iam in class 9

[craggy tiger]

9th grade?

[crimson sedge]

yes

[unique nest]

then maybe you're taught to look for 2 numbers, a and b, such that a+b=13 and ab=-4.

[craggy tiger]

Basically using the quadratic formula it'll give you the two "roots" or "solutions" to the polynomial. You just have to plug in the numbers

[crimson sedge]

this is the question

[unique nest]

oh, it's slightly different due to that -3 ahead. It might be harder with sum and product, since those give fractions...

[icy zenith]

damn, guys?

[cyan eagle]

better way to think about it is factoring the polynomial into two terms because it's of degree 2. $(ax+b)(x+c)$. Since we know the $y^2$ term has a coefficient of -3, have $(-3y+b)(y+d)$. Then you want to find out which values of b and d give 13y and -4

[wraith dagger]

fish

[icy zenith]

why do not you write: $-3x^2 + 12x + x -4$

[wraith dagger]

mathell

[cyan eagle]

that's another way to do it

[icy zenith]

$-3x(x-4) + 1(x-4)$

[wraith dagger]

mathell

[icy zenith]

$(-3x+1)(x-4)$

[wraith dagger]

mathell

[unique nest]

Because now you'll likely have to explain how you knew to divide in 12x + x 😛

[icy zenith]

you mean that it is impossible for university student to see things like that? even 9th grade student who will always try to factorize by divind will gain enough experience to see things like that

[cedar kiln]

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[spice basin]

Hello! I wass wondering how you start solving this

[dire geode]

What does the 2 mean in the top left

Base?

[spice basin]

Yes I think that's how we note it

[dire geode]

Also what is there to solve? There's no instructions

[spice basin]

Oh ye mb

[copper meteor]

use log (a/b) = loga -logb

[spice basin]

I gotta get the derivitive off it

My bad for not mentioning it

[sage epoch]

Apply this and differentiate via the chain rule

[spice basin]

Alright let me try

[spice basin]

Wait so that would be (^2log-1) - (^2log1)

[sage epoch]

no

where did the x's go?

[spice basin]

Well I assumed the derivitive took it away

@sage epoch (Sorry for the ping)

[unique nest]

know the chain rule?

[spice basin]

I should

[unique nest]

for example, there is a formula to differentiate ln x. but there isn't one for ln (1-x)

(f(g(x)))'=g'(x)f'(g(x))

[spice basin]

Ah yes I have it on my paper

[unique nest]

here your "g(x)" is 1-x, for one of the logs.

[spice basin]

Yes

[unique nest]

so, what's (log (1-x))'?

I assume that's log base 2, in original ex.

[spice basin]

ah so I should do 1/1-x *ln2

[spice basin]

yep

[unique nest]

hmm

what's (1-x)'?

[spice basin]

-1

[unique nest]

what's (log x)'? with the log you have there

[spice basin]

1/x*lna with a = base

Ah but I still have to do D1-x

[unique nest]

so log(1-x)' = - 1/(1-x)*ln2

[spice basin]

wait that's what I said no?

ohh -1

yes

I see ccuz you still have to do D(1-x)

Soo, following that, - 1/(1-x)*ln2 - 1/(1+x) ln2

[unique nest]

one of them had 1+x though?

[spice basin]

Well yes, but but the rule is a - b

so a - +b = a-b no?

oh wait

[unique nest]

well, yes, but why would that change the denominator too?

[spice basin]

I copy pasted too fast

• 1/(1-x)*ln2 - 1/(1+x) ln2 And I don't think you can simpl8ify that further can you? without actually calculating the ln2

right?

[unique nest]

Looks fine, I think. not sure if amplifying both fractions to make it into 1 fraction is necessary, although it might look slightly better/ more compact.

[spice basin]

Oh but that's just putting it on thhe same denominator and adding them up right

[unique nest]

also first fraction probably had a -

[spice basin]

I should be fine with that

[unique nest]

so it's - fraction - fraction.

[spice basin]

Oh ye I forgot to type that

but had it on paper

So thank you for your help here! you really helped

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[unique nest]

You're welcome 🙂

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[plucky edge]

hello, i am curently working on a presentation about ellipses in mathematics, the pic shows a slide wich describes the ratio of ellipses to a circle. my question is if i maybe forgot to add smth

[plucky edge]

<@&286206848099549185>

[cold timber]

What language is that

[twilit escarp]

German

[plucky edge]

german haha

sorry bout that

is there maybe like a formula i should add?

[twilit escarp]

Idts

[plucky edge]

?

[twilit escarp]

I don't think so

[plucky edge]

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[median orbit]

-m + 2 (a)^-0.5n = 5
a > 0 m is a real number
if n is larger or equal to 0 what conditions apply to a and m if the equation must be true

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[kind saffron]

The solution set of the equation X power 2/3 = 25 in R is ?
I thought it was {125} only but I checked the answer and it was positive and negative 125. I thought the negative is excluded in log questions. Why is it included here

[opaque root]

I dont see any log

In your exercise

In any case

Cubic root of 125=5

5^2=25

Same with -125

Cubic root of -125=-5

(-5)^2=25

2 solutions

@kind saffron

[kind saffron]

Idk what exactly I'm talking tbh I watched a quick revision yesterday and I probably confused things together

Prob sth like this

Idk

Ty tho

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[civic tangle]

How could I show that lambda is also the minimum of that set?

[civic tangle]

I know where it says for all p in P you could replace that with for any p in P and get the same set and thus the same lambda
the set in question is of the form (lambda , infinity) or [lambda , infinity) hopefully the later

the inf does exist for all P in all P^n(S)

[cedar kiln]

@civic tangle Has your question been resolved?

[twilit bison]

i'm confused with the definition of Q

[civic tangle]

yeah Im not entirely sure the best way to write that

its supposed to be the set of all sets containing n non-overlaping "tiles"

[twilit bison]

i think i get it

[civic tangle]

then lambda is basically the smallest number you can scale a tile with to completely cover a packing or arangement of tiles

[twilit bison]

the tile and the packing are both open

that seems important

[cedar kiln]

@civic tangle Has your question been resolved?

[twilit bison]

let $S_1=\left{s\in\mathbb{R}^{+}|\left[0,2\right]\subseteq \left{sx|x\in\left[0,1\right)\right}\right}$\
$\inf (S_1)=2$ but $2 \not\in S_1$\
let $S_2=\left{s\in\mathbb{R}^{+}|\left[0,2\right)\subseteq \left{sx|x\in\left[0,1\right)\right}\right}$\
$\inf (S_2)=2$ and $2 \in S_2$

[wraith dagger]

Axe

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[cursive bison]

hey can you explain to me how to do long devision with decimals?

[vestal bluff]

its like normal long division, just find the new spot for the decimal point

[cursive bison]

huh

im confused

[vestal bluff]

do you have a soecific example

[cursive bison]

Im in middle school 😭

[pallid atlas]

Ok let me come up with something for ya

Is there a decimal in the problem?

Or are you struggling with remainders

[cursive bison]

There’s a decimal but i’m not sure what the numbers after it is

[pallid atlas]

Ok

$246.8/2$

[cursive bison]

.

[pallid atlas]

Oh come on

[wraith dagger]

Milo Thatch

[pallid atlas]

Can you do that?

[cursive bison]

the problem’s like that but i just dont understand it

[pallid atlas]

What do you think you’re supposed to do when there’s a decimal?

Give me a guess

[winter moss]

ok

can u do

[cursive bison]

take it out and put it back in?

[winter moss]

1/2

[cursive bison]

Yea

[winter moss]

it is?

[cursive bison]

0.50

[winter moss]

ok

now do

0.1/2

[cursive bison]

uhm is it 0.05.

[winter moss]

yup

so 0.4/2

[cursive bison]

0.2?

[winter moss]

yup

so decimal are the same thing with regular division

[cursive bison]

ohhh

[winter moss]

just gotta know where the decimal place was

lemme give u a harder one

0.210/3

[cursive bison]

im not sure

[winter moss]

ok

21/3?

[cursive bison]

7

[winter moss]

great

210/3

?

[cursive bison]

70…?

[winter moss]

yes

now

notice how it went from three digits

210

to two

70

that means the hundreds place

is 0

also seen as

070

so in decimal

the 0 before numbers matter

[cursive bison]

oh

[winter moss]

meaning 0.210/3

[cursive bison]

Is 0.070

[winter moss]

yessir

[cursive bison]

YAYYY

[winter moss]

alr

one last

0.575/25

[cursive bison]

i dont know my 25 time tables 😭

0.255?

Or 0.0255…?

[winter moss]

oh

nah dont worry about it then

as long as u understand basic decimals you should be fine

[cursive bison]

i tried thi

kk

[winter moss]

its 0.023

[cursive bison]

oh

[winter moss]

cause 25*23 = 575

so

0.575=25*0.023

[cursive bison]

ohh

thank you!

[winter moss]

type .close if u got helped :D

or if ur question is answered

.close

damn

[winter moss]

u mind if u close this

[dusk goblet]

.close

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[pallid atlas]

You should know those especially because currency is based in 25’s

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[fallow arrow]

How can I understand what this means?

[dire geode]

What math knowledge do you know up to

[dire geode]

Also should give more context what every variable means in the picture

[fallow arrow]

I understand what derivatives are and have programmer experience

[dire geode]

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum

[fallow arrow]

so this is for gaussian splatting which I am trying to implement

C is the color along a ray

[twilit bison]

for i in [1...N]:
    C += T_i * c_i```

[fallow arrow]

oh that is helpful to see it

I am also not sure about exp(-𝜎i𝛿i)

not sure what exp is doing

[twilit bison]

exp(x) means e^x

[fallow arrow]

so it is something like:
C += T_i ^ (1-( -𝜎[i]*𝛿[i] )) * c_i?

[twilit bison]

not quite

[fallow arrow]

ok so I messed up on the multiplication
C += T_i * (1- e^( -𝜎[i]*𝛿[i] )) * c_i
is this better?

[twilit bison]

that looks right

[fallow arrow]

Oh thank you!

[cedar kiln]

@fallow arrow Has your question been resolved?

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[swift coyote]

hello

[swift coyote]

how do you do all parts of this question

[humble karma]

Implicit differentiation.

https://tutorial.math.lamar.edu/classes/calci/implicitdiff.aspx

[swift coyote]

ok I got that, what about part C and D

[blazing zephyr]

whats the slope of the line thats tangent at x=1?

[swift coyote]

.close

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[crimson sedge]

Hello I had a question. Based on this chart, what is the f^-1(x) = 7?

[vestal bluff]

you can rewrite f^-1(x) = 7
into x = f(7)

[modern copper]

f(7)

yeah

[vestal bluff]

by applying the function on both sides

[modern copper]

u can apply the f function to both sides

f and f⁻¹ cancel

and on the left u get f(7)

be careful of not making the mistake of multiplying thru by the f
and getting smth like f(x) • 7
thats wrong

a lot of students do that tho

[crimson sedge]

Does x = 4 or 1

I thought the inverse just swaps the values

[modern copper]

whats f(7)

[crimson sedge]

X & Y

[modern copper]

from ur table

whats the output when x = 7

[crimson sedge]

When x is 7

1

[modern copper]

yes exactly

[crimson sedge]

Okay I thought so

Shit was driving me nuts people kept saying it was 4

[modern copper]

so u js need to know

$$f^{-1}(x) = y$$
$$f(f^{-1}(x)) = f(y)$$
$$\cancel{f(f^{-1}}(x) = f(y)$$
$$x = f(y)$$

[wraith dagger]

MILO

[crimson sedge]

Right, you apply the function to both sides and the inverse will cancel out

[modern copper]

yesss

[crimson sedge]

Awesome, thanks.

[modern copper]

by definition

[modern copper]

nws!!

[crimson sedge]

Wait so the answer is f^-1(1) = 7?

You just put the one for x right

Or since it says solve you put x=1

[modern copper]

$$f^{-1}(x) = 7$$
$$f(f^{-1}(x)) = f(7)$$
$$\cancel{f(f^{-1}}(x)) = f(7)$$
$$x = f(7)$$
$$\text{whats the output of the f function when x = 7}$$

[wraith dagger]

MILO

[modern copper]

x will be 1 yes

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[sage sapphire]

hi yall. im trying to fit a function to this data plot and this is as far as i can seem to find how to do it. anyone have any ideas on things i could do or test to try to get it to repeat every 5?

[worldly chasm]

Is it actually periodic?

[sage sapphire]

somewhat periodic, the y goes down by 3 each time

but wraps around the 0

up to 6

[worldly chasm]

So the pattern is -3 then +4 and everything is mod 7?

[sage sapphire]

roughly. the pattern is actually just always -3 mod 7, but it ends up looking like -3 +4

[worldly chasm]

And f(0) = 4

[sage sapphire]

yeps

[worldly chasm]

Oh ok hmmm

So you're looking for a function that will fit this data by drawing a line between it that doesn't wrap around the mod and does go greater than 6?

What are the rules you want to follow for allowable functions?

You seem to be trying with arccos cos currently

[sage sapphire]

anything that's graphable via desmos

yeah

[worldly chasm]

Ok that's great

@sage sapphire https://www.desmos.com/calculator/iq4mcls467

Here is a starting point

5 cases remain 🙂

[sage sapphire]

oo piecewise is smart omg

tytytytytytytyyty

[worldly chasm]

Though actually you can do it in 4 thinking about it

[sage sapphire]

o yea

alrighty i think i know what i must do,, ty so very much

i'll close thiis then

[worldly chasm]

You're very welcome

[sage sapphire]

.close

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[hasty pendant]

I'm learning about Derivaties of implicit realtions

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[nimble lintel]

Can someone explain how did he get the F5 base 16 when converting from the 110101 base 2?

[nimble lintel]

This is the original question
Perform the following arithmetic operations using 6-bit two’s complement represen-
tation for the given base-10 numbers. Present your results in hexadecimal. If an error
would occur, indicate why

[clear umbra]

i think using 8 bit would make it clear

instead of 6

[nimble lintel]

I agree, but the prof made the question fixed 6-bit unfortunately

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[crimson sedge]

Yes

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[winter mantle]

Could someone help me fix this:

[brazen wind]

Smaller amplitude if that green line is what you're going after

[winter mantle]

slightly a bit off

better look of the green line mb

[cedar kiln]

@winter mantle Has your question been resolved?

[pastel vault]

the amplitude should be around (2 - 0.5)/2 = 0.75

yeah and (2 + 0.5)/2 = 1.25

so try 1.25 cos(x) + 0.75

[cedar kiln]

@winter mantle Has your question been resolved?

[winter mantle]

<@&286206848099549185>