help-27

[past wyvern]

So B whould be 1 then?

[dark lava]

Not quite either, when p is 2, it's a quadratic function

[past wyvern]

It would be 2 then. Right?

B=2?

[dark lava]

Yep

[past wyvern]

Would c=4 then?

[dark lava]

no

[past wyvern]

C would equal one then. Right?

[dark lava]

no again

[past wyvern]

Okay so that means c=3

Then that should mean D=1 and A=4

Hopefully

[dark lava]

Yes

[devout snow]

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[marble hound]

I just wanna understand how it all works

[cosmic trail]

how many times bigger is the bug in the photo than in the real life

[marble hound]

yeah

I got several different answers

[cosmic trail]

what did you get

[marble hound]

37.5

@cosmic trail

[cosmic trail]

what's 37.5

[marble hound]

37.5 cm

[cosmic trail]

what is

[marble hound]

the actual length

I know it doesn't make sense

[cosmic trail]

answer this

I didn't ask for the length

[marble hound]

the question is "What is the actual length of the bug"

the scale length is 2.5 cm

what is the real length

[marble hound]

I'd need to know how big it is to answer that

[cosmic trail]

no

it's in the information given

and then you find out how big it is form that

[marble hound]

what do I need to do then

[cosmic trail]

what does the ratio 15:1 mean

[marble hound]

it is scale ratio

[cosmic trail]

ok so what does that mean

[marble hound]

its like a comparison

like length on drawing to actual length

[cosmic trail]

yeah

but say it mathematically

what does it mean

[marble hound]

idk man mathematically

I just need to confirm this answer

is it 0.1667 cm

[cosmic trail]

yes

the picture is 15 times bigger

so you div ide by 15

[marble hound]

thank you

Initially I did 15 over 1

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[restive river]

Did I do this right

[devout snow]

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[restive river]

hey! so im new to this and i was curious if i could fine soem math problems honestly and im am just confused im in an 7th grade level and im also needing help on explaining my classmates how i do math im in scientific notifications per ex:. 0.07 x 10^3 = 70 and im simply confused waht forum i can go to tlak about this

[restive river]

<@&286206848099549185>

ok im certain now that im having an actual bad day

<@&286206848099549185>

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[restive river]

When you see 10^3, it means you have to move the decimal place 3 times.

0.07 x 10^3
0.7 x 10^2
7x 10^1 = 7x10
70

You can think of it like multiplying by 10 3 times

[restive river]

I hope the rest of your day gets better :)

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[little fjord]

wjat does this m,ean

[fallen quiver]

They are proportional

[little fjord]

yes

[fallen quiver]

30/6 = 65/New volume

[covert pelican]

just set up a poprotion equation

[little fjord]

how do i

nvm

m=kv or something?.

[covert pelican]

no

30/6

then 65/v

and it must be equal to each other

[little fjord]

ok

[covert pelican]

so 30/6=65/v

Notice how both the kgs are on thee numerator and the volume on the denominator

[little fjord]

the constant is 5?

[covert pelican]

what constant?

i mean yea it increases by 5

[little fjord]

ok thanks

[covert pelican]

but we don;t need to know that

[little fjord]

i see

[covert pelican]

just solving the proportion equation will directly give us the answer and is much faster

[little fjord]

ohhhhh ok

[covert pelican]

also btw u can flip the euqation to 6/30=v/65 and still get the same answer

just makee sure its all consistent

[little fjord]

okay thx

wait so then qwhats the new value

volume

[covert pelican]

v will give u the volume

did u solve the equation?

[little fjord]

30 divided by 5 is 6

[covert pelican]

why are u divding by 5?

[little fjord]

i mean

30 divided by 6 is 5

[covert pelican]

ok so 5 = 65/v

[little fjord]

so 65 / 5?

[covert pelican]

yes

[little fjord]

13

so it's 13 right

[covert pelican]

yea thats ur answer

[little fjord]

thanks

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[frail spade]

hello can someone help me solve this problem

[devout snow]

@frail spade Has your question been resolved?

[frail spade]

<@&286206848099549185>

this one too

[late niche]

hey. have you tried something ?

[frail spade]

hey

[frail spade]

i solved the second one

not the first one

i keep on messing up when multiplying the denominator with the numerator

i multiply -3sqrt8 by 36sqrt160 right?

[late niche]

you want to reduce the fraction, right ?

[frail spade]

i dont know

[late niche]

what's the question asking ?

[frail spade]

i dont know

im so sorry

[late niche]

dhjsqfhjsqdf well

[frail spade]

all i know is that

[late niche]

i think it's about reducing

[frail spade]

i need to multiply the top and bottom by

-3sqrt8

right

[late niche]

have you tried to simplify the square roots first ?

[frail spade]

wdym

like 36sqrt160?

dividing the 160?

[late niche]

sqrt of 160 can be reduced

or like yea multiplying by -3 * sqrt 8

[frail spade]

hmmm

im sorry i had to go use the restroom

one sec

lemme do the 160

ok

i got 144sqrt10

do i multiply that by -3sqrt8

nvm

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[robust linden]

Ik this isn’t math it’s geography

[robust linden]

Can someone help@me

[uncut crow]

lmaooo

[robust linden]

Please

I know it’s not math

Pls

[robust linden]

Can you help

[uncut crow]

noooo sorry i don't know any geography 😭

[robust linden]

Bruhhhh I’m fucking screws

I have a big test tmrw and

[covert pelican]

can u not read a map?

[robust linden]

No I’m sped

[covert pelican]

💀

[robust linden]

break it down to me pls

[covert pelican]

1st one is 50 degrees F

2nd one is Albuquerque

last one is 60 degrees F

[robust linden]

U Hindu?

[covert pelican]

🤨

[robust linden]

Cause I’m Hindhu/punjabi

Cause my mom is punjabi and my dad hindhu

I can tell by that pfp

[covert pelican]

guess where

[robust linden]

Idk

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[alpine grail]

are the derivatives of two integrals of a function the same if the integrals are just across different lengths

[alpine grail]

like is the derivative of the integral of sin^2x from 0 to x

the same as the derivative of the integral of sin^2x from 2 to x

i feel like they should be different but i have no idea how

[ripe flint]

What's sin^2(0)

And sin^2(2)

This is FTC

[alpine grail]

sin^2(0) is 0

and sin^2(2) is not 0

so would the derivative of the integral of sin^2x from 0 to x be sin^2(x) - 0 or sin^2(x)

and the derivative of the integral of sin^2x from 2 to x be sin^2(x) - sin^2(2)?

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[thorn wren]

https://media.discordapp.net/attachments/486844829209198613/1039095762870603777/unknown.png

[thorn wren]

anyone understand how to do this question??

[devout snow]

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@thorn wren Has your question been resolved?

[ocean garden]

It's from differential equations. The correct answer is (x+4)²=y+3

[bright burrow]

You are in someone else's channel

However i think your mistake is definetly what youve written in the lhs

That would be the avg rate of change over an interval, not the slope of the tangent at (x,y)

[ocean garden]

Oh I didn't know I thought these are channels to ask questions 🥹

Swory

[thorn wren]

wtf

[rotund heron]

They are

#❓how-to-get-help

But you have to get your own channel

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[tropic grove]

Hello

[tropic grove]

(x) is always independent = input

time is an example

if we made a chart including hours and minutes

minutes should be the input

but in reality its output

why does minute depend on hours

weeks should depend on days

Example

<@&286206848099549185>

[devout snow]

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[undone garnet]

Trying to find x1 and x2. x1 + x2 = 1 , this is a unit circle, that is the center, I know the two theta angles

[fallen quiver]

umm... intersecting chords theorem?

[scarlet sequoia]

• fact that x1 + x2 = 1

[undone garnet]

Ok so I guess I gotta find the other distances

wait they aren't chords that go across the whole diamter

Isn't intersecting chords theorem for 2 lines that touch both sides

[fallen quiver]

just extend x2 x1 to the other side

[undone garnet]

huh, I'll try that

[devout snow]

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[slim lintel]

😐

[devout snow]

Please don't occupy multiple help channels.

[slim lintel]

😀

Pls help me need answers

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[restive river]

Simplify $(y+2x^2)(y^4+2x)$.

[woven radish]

miky

[restive river]

i got uhh

$y^5+2xy+2x^2y^4+4x^3$

[woven radish]

miky

[restive river]

but when i put it into a calculator

it gives me $y^5+2yx+2x^2y^4+4x^3$

[woven radish]

miky

[restive river]

is it the same or not

[pseudo basin]

multiplication is commutative so yes it is the same

[restive river]

actually wouldnt it be correct

yeah

i was just about to say that

sorry for the dumb question

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[hardy jungle]

Hello

[lime vector]

hello there, may i help you with anything today ?

[hardy jungle]

can I show my exercice in french ?

[lime vector]

sure go ahead :DD

[hardy jungle]

ty man

if u need i can translate

[restive river]

french is my 3rd language 😎

[lime vector]

yeaa.... i think i need some translate :Đ

[hardy jungle]

A parchment attributed to Rackham the pirate has just been found. On this parchment appears the plan of an island and the following message:
"30 paces separate the flagpole and the coconut tree. On the line that joins them, I have hidden a treasure. Twice the distance from the treasure to the flagpole, plus three times the distance from the treasure to the coconut tree equals 65 steps."

I use translater sooo im not sure if its very english lol

[lime vector]

okayy, so you need to call the distance from the flag pole to the treasure is x (x is a positive number:)

(uhhh, 30 paces = ? steps ?)

[hardy jungle]

wdym ?

oh yes

paces = steps

[lime vector]

ohhh, okay

so you have

oh wait wait

[hardy jungle]

yes take ur time 🙂

[lime vector]

since the distance from the treasure to the flag pole is x

then the distance from the treasure to the coconut tree is 30-x

so now you have

2x + 3*(30-x) = 65

can you solve it from now ?

:))

=> x = 25

=> the distance from the treasure to the flag pole is 25 steps :DD

are there any question ?

[hardy jungle]

ohhh thanks 🙂

yes

uh wait

We assimilate the line to a graduated line of origin M (the mast) of unit 1 step.
The coconut tree is at point C with abscissa 30.
x is the abscissa of the point T representing the treasure.

how can i represent the line ?

[lime vector]

if you dont know now to represent something, just draw it out

like

on your homework notebook (or whatever), draw a line with 2 ends name C (for the coconut tree) and F(for the flag pole)

[hardy jungle]

C ------------- F like this ?

[lime vector]

between the line, add a T (for the treasure) and start counting

[lime vector]

yes

C---------------------T-------------F

[hardy jungle]

ok ok and I just have to represent that?

[lime vector]

yea yea

copy the whole thing i wrote :))

okayyyy, if there are no further question, type ".close"

[hardy jungle]

man

i love u

ty 🙂

.close

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[spare trail]

this question if for avg rate of change

[spare trail]

there is a table

f(a) is 77 and a=10

and f(b) is 88 and b=17

would the answer be 11/7

[sand dove]

yes

[spare trail]

ight thanks

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[burnt zenith]

hello , please someone can tell me how i can solve this

[scarlet sequoia]

Is l'Hospital rule allowed?

[burnt zenith]

nope

[honest aurora]

$$\frac{\text{exponential}}{\text{not exponential}}=\text{divergence}$$when both functions are growing functions

[scarlet sequoia]

then maybe series expansion

of the numerator

[woven radish]

Duh Hello

[burnt zenith]

<@&286206848099549185>

[scarlet sequoia]

series expansion can help I guess

use

in fact the above thing is true, if it's sufficient for you u can just follow it

[burnt zenith]

okeey thanks !!

[devout snow]

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[tulip summit]

Karl builds his houses of cards on a table. There is a correlation between the number of cards
the table and the number of floors in the house of cards. For example, there are 6 cards touching the table in the house of cards with 3
floors.

2.2 How many cards touch the table in a house of cards with n floors?

[sand dove]

Try to draw the house of cards for small values of n

Start with n = 1, then n=2, etc...

[tulip summit]

but what is n

[sand dove]

n is any positive integer we want

[tulip summit]

so its kinda like X

[sand dove]

Yes

[tulip summit]

but we decided

[sand dove]

But just for positive integers

[tulip summit]

ok so it cant be -5

[sand dove]

Does it make sense for a house of cards to have -5 floors ?

[tulip summit]

nah

[sand dove]

Yep

[tulip summit]

i just asked hahhaha

[sand dove]

Ik dw :)

[tulip summit]

never heard of n before thank you

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[wary fractal]

why cant you do 9C3 here

[wary fractal]

or actually 9P3

im having a hard time understanding when to use which rule

[prime egret]

Repeated are allowed

And order matters

[wary fractal]

oh true

[prime egret]

Just think about it you have 9 choices for the first digit 9 choices for the second digit and 9 choices for the third

So 9 * 9 * 9

[wary fractal]

yea i ended up getting that after 3 tries but was just unsure

thanks!

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[boreal reef]

i dont understand exponents

[boreal reef]

can someone help e

me

i dont know the basic laws

[boreal reef]

ty mate'

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[full notch]

this stuff always trips me up, why cant I multiply both sides?

[deep cove]

The sign of x is unknown, so you won’t know whether or not you need to flip the inequality once you multiply x.

BUT, you do can multiply x^2 on both sides, since this is guaranteed to be positive, and it change the question into a quadratic inequality.

[full notch]

hmm ok

the set notation is 0 < x < 4 tho

im confused why it is

[torn vessel]

you have to argue why x is positive before multiplying it over to solve.

[full notch]

ty

.close

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[chrome ridge]

You have a drum of water, a 5-quart pail, a 3-quart pail, and an empty drum. You need to measure 1 quart of water.Describe how to measure exactly 1 quart of water using these TWO pails. Assume you have a large container that will hold as much water as you need. how should i draw this problem?

[devout snow]

Please don't occupy multiple help channels.

@chrome ridge Has your question been resolved?

[devout snow]

@chrome ridge Has your question been resolved?

[midnight dirge]

um

idk how u wld draw

but

u can fill the 3 p

put 3 in the 5p

fill 3p again

pour water in 3p to 5p till it is full

ull b left w 1 in 3p

@chrome ridge

[devout snow]

@chrome ridge Has your question been resolved?

[chrome ridge]

can you please expound this one?

@midnight dirge

im not sure whats next tho

[midnight dirge]

lkike

like

the 5p is like

it alr has 3

so when we put in another 2 its full

[chrome ridge]

someone sent this but then could not really understand the 2,4,2 part

[chrome ridge]

am i doing it right tho? or not?

[midnight dirge]

er

did u understand the first q

idk y u ask me elab on the first n u go on to ask another 2 Qs

[chrome ridge]

not really

[midnight dirge]

then

dont ask other Qs..

[chrome ridge]

sorry, that is why i asked if the illustration i am doing is fine to check if im doing it right or wrong

[midnight dirge]

yea idk

why u have diff bucket sizes

its originally 3 and 5 right

like

[chrome ridge]

yeah but there is an empty drum

[midnight dirge]

anyway

idk reread it

its

oh i guess i can do this

amount of water / total

p3 0/3
p5 0/5

p3 3/3
p5 0/5

fill p3

p3 0/3
p5 3/5

p3 to p5

p3 3/3
p5 3/5

fill p3

p3 1/3
p5 5/5

p3 to p5 till p5 full

then u hv 1 in p3

p5 is irrelavent now

n u don

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[hot basin]

can someone help with part b? How do i find the range of g?

[hot basin]

im assuming the domain is {t1, t2, ... , tn}

[torn vessel]

no, domain is power set of T_n

[hot basin]

so {t1, t2, ..., tn} is the range? I thought I am restricting g of f to the domain {t1, t2, ... , tn}

[torn vessel]

nope, the range is in the non-negative integers.

you're taking S, a subset of T_n, and mapping it to the cardinality S, cubed

So take n = 2
what is the power set of T_2?

[hot basin]

{empty set, {1}, {2}, {1, 2}}

[torn vessel]

ok, so now f maps each of those things to their cardinality cubed

[hot basin]

ohh wait

im sorry

i mean part b

[torn vessel]

oh poop lol I missed that, my bad

[hot basin]

no worries

[torn vessel]

ah, ok, so you should show g is 1-1 with that restriction, since T_1, T_2, T_3,...., T_n are each a subset of P(T_n)

[hot basin]

so with that restriction we are restricting the domain right?

and i guess the range as well based on what the domain is mapped to?

so g of f is mapped to {1, 8, 27, ... n^3}

and we know that is invertible (all domains and ranges are mapped)

[devout snow]

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[little kayak]

The height of a cylinder is decreasing at a constant rate of 3 feet per second. The volume remains a constant 462 cubic feet. At the instant when the radius of the cylinder is 44 feet, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V=\pi r^2 h.V=πr
2
h. Round your answer to three decimal places.

[olive fjord]

48/226 I believe

[little kayak]

cap

[olive fjord]

u can .close it now

[little kayak]

.close

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[vernal spindle]

What is the radius of a circle in which an angle of 3 radians cuts off an arc of 45 cm?

[vernal spindle]

Would anyone know how to go at this? I am confused at where to begin

[torn vessel]

1 radian is the angle such that the arc is equal to the radius

so the arc for 3 radians would be 3 times the radius

[vernal spindle]

So you mean that the radius would be 15cm since 45 is 3x 15

[torn vessel]

yep

[vernal spindle]

And the same logic would be applied to:

What is the angle determined by an arc of length 5pi meters on a circle of radius 15 meters?

so it would be 5pi * 5 meters?

[torn vessel]

no, you're going the other direction

arc length would be (radius)(angle in radians) which is how you got the first one, by factoring out the angle from the arc length

Now you have 5pi = 15(angle)

[vernal spindle]

What is the formula to solve these equation types?

[vernal spindle]

Aren't I trying to find the radius?

[torn vessel]

it says the radius is 15

and you want the angle determined by.....

[vernal spindle]

Oh

Didnt read that part

So what do I do with 5pi = 15m?

.close

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[graceful lava]

easiest way to memorize trig funcs? (30, 45, 60, 90)

[dense jay]

draw the triangles

[proud perch]

really you only have to memorize the first quadrant

or the first half quadrant actually

everything else is symmetry and reflection.

so you only have to remember that:

sin(30) = 1/2
sin(45) = sqrt(2)/2
sin(60) = sqrt(3)/2

[charred bolt]

Think of your unit circle and remember it intuitively. On your circle the cos value is the x and your sin value is your y. From there the value goes in arithmetically increasing steps either up or down. Your value will go from 0 to sqrt(1)/2, sqrt(2)/2, sqrt(3)/2, sqrt(4)/2 respectively

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[restive river]

3C2 / 25C3

[slim thorn]

divide them?

[torn vessel]

Yes

But the bottom should be 25C2

[hidden moth]

condition / total possibilities

[restive river]

its 1am idk if my brain is still functioning but shouldnt it be the total number of deprived objects so 3 not 2

defective *

[hidden moth]

but it's two possibilities? I just got past this part so I could be wrong but you're still picking 2 parts

[torn vessel]

Yes, but you’re still choosing 2 things.

[slim thorn]

Ya it says 2 parts are selected w/o replacement

[restive river]

right i need to sleep

[slim thorn]

lolll

Ok so 3C2/ 25C2

and we are trying to find the probability that both would be defective

[torn vessel]

That is the probability that both are defective

[restive river]

💀

[hidden moth]

another way to think of it 3C2 22C0 / 25C2 as you want 2 defective parts and no non-defective parts

[slim thorn]

How do we solve that? 🤣 cause i have like 2 other questions just like it just finding probability for other stuff

Im used to having it like

P(B)

P(A or B)

[hidden moth]

Do you know the combination formula? n!/(n-r)!r!

[restive river]

P(2defective) = 3C2/25C2

[slim thorn]

Oh ya combinations and permutations

Ik that

r factorial

[restive river]

in this case its a combination

[slim thorn]

Ohhh ok

[restive river]

[slim thorn]

so 3 combinations 2 divided by 25 combinations 2

[restive river]

ja

[slim thorn]

I got 3C2=3

25C2 is 300

0.01

is the answer?

[devout snow]

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[maiden marten]

Im not sure how to do no. 14

[wooden wraith]

Looks like you started okay.

I see $\frac{\frac{1}{\cos^2\theta}}{\tan^2\theta}$

[woven radish]

tatpoj

[wooden wraith]

which is a good start

Not really sure what I'm looking at beyond that though

[wooden wraith]

The hint I'd give you from here is to express tan in terms of sin and cos

@maiden marten

[maiden marten]

I tried that

And then it became 1/cos(sin)

Can't do anything with tagt

@wooden wraith

[wooden wraith]

That doesn't seem right

You have tan^2

I think you accidentally just took it as tan

[maiden marten]

Oh yea

I think it right

Let me check again

Yeah it worked

Csc2x was the answer

Thx

[wooden wraith]

Yep

No problem 👍

[maiden marten]

. close

.close

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[restive river]

.close

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[dusky adder]

$\int_0 \pi e^{2x}sinxdx$

[woven radish]

Dr. Leonard McCoy

[lone elbow]

<@&286206848099549185>

[dusky adder]

uhm

I already claimed this channel

[magic thicket]

Have you tried integration by parts ?

[dusky adder]

yeah, I know I'm supposed to IBP

I'm just not sure what you do when you have like a circular situation

$\int_{0}^{\pi} e^{2x}sin(x) dx$

[woven radish]

Dr. Leonard McCoy

[magic thicket]

Let's call this integral I.
Then suppose that after 2 IBPs, you get something like I = f(x) - I/4 (not sure, didn't do it).
Then 5I/4 = f(x) so I = 4f(x)/5

You end up getting an equation in I and need to recognize it as such

[dusky adder]

uhh

ok

.close

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[graceful lava]

why is this true

[restive river]

because $e^\ln{\text{something}} = \text{something}$

[woven radish]

Maxim
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[midnight dirge]

hey this looks like complex exponential

[restive river]

e and ln are inverse functions

[midnight dirge]

no they

arent quite inverse functions

ln is multivalued

in C

but i guess they can b inverse in the domain they exist in

in R

[proud sleet]

https://youtu.be/xq6yAOqS-mE watch math

It’s math

Trust me

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[devout snow]

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[hardy marsh]

Someone pls walk me through how to solve 4(ax+3)-3ax = 25+3a

(Find x)

[hardy marsh]

You distribute first so it

4ax - 3ax + 12 = 25 + 3a

now right?

Wait I think I got it

Nvm I don’t got

It

Nvm I do got it

.close

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[bright gulch]

How do you test with Divergence Test?

[bright gulch]

This was on my exam.

I've memorized it in my head during the test to ask here.

How do you test the above infinite series using the Divergence Test?

[uncut crow]

rewrite 2^(3n) as 8^n

then do you see why all the terms will be >1 or <1?

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[lofty crater]

why does the |1^x| get rid of the x

[covert pelican]

forget about the absolute value, if it was just 1^x then x would go away because 1 to any power is 1

the x is redundant

[lofty crater]

https://tenor.com/view/lord-pleas-help-oh-no-gif-25461814

im loosing my mind

im sorry

thank you very much

[covert pelican]

np

[lofty crater]

.close

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[bright gulch]

Obviously it's >1... do i also have to absolute value so that (-1)^n gets cancelled out.

[bright gulch]

?

[uncut crow]

i’d just say all the terms are greater than 1 in absolute value so they can’t converge to 0

[bright gulch]

Yup so it diverges right?

[uncut crow]

yep

[bright gulch]

Ok thanks..

[uncut crow]

np ^-^

[bright gulch]

It's off topic but i'm just really stressed because my professor is a hard grader and thinking that i didn't do well on the test today it gets me stressed

[devout snow]

@bright gulch Has your question been resolved?

[uncut crow]

it'll be ok!

there's still time, even if you didn't do well

[devout snow]

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[mossy condor]

@covert pelican thats why i wanted to call lol

[covert pelican]

yea i can’t call

sorry

[restive river]

You can also use the alternating series test and notice how the limit of a_n does not converge to 0 indicating that it is divergent

[devout snow]

@mossy condor Has your question been resolved?

[uncut crow]

that's not how alternating series test works

[restive river]

Why not

[uncut crow]

it's not an iff theorem

it just says if something holds then the series converges

it doesn't say if it doesn't hold then it diverges

[restive river]

It does though, because you are basically using the divergence test when you are testing for convergence

If the limit of that sequence is not going to be 0,thats just the definition of the divergence test, no?

[uncut crow]

what you said doesn't have anything to do with alternating series test

like yes, limit of a_n does not converge to 0 indicates that it is divergent

but that's just divergence test

[restive river]

But it indicates that the alternating series does not work here which is the thing I was trying to say

[restive river]

Thats something you can also assume with the alternating series test because you are doing the same procedure but you want it to go to 0, else it will be divergent with the divergence test naturally

[uncut crow]

what i'm trying to say is alternating series test hypotheses not holding doesn't indicate the series is divergent or convergent

[uncut crow]

You can also use the alternating series test
was confusing to me then

[devout snow]

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[rotund dawn]

I'm supposed to give this in 𝑦 = 𝑘 • x ^ p form
I've got y = 25 • pi x ^ -2
Is that correct?

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[grim mountain]

I have this number 0,13125, can I make this into fraction

[grim mountain]

0.13125/1

0.131251 00 00)/ 1 100 00 = 13125/100 00

[stone stump]

\* for *

but yes

[grim mountain]

What should I think next Uhm

[stone stump]

although you need one more zero

well now it is a fraction

[grim mountain]

No its a 5 zeros

[stone stump]

and you put 4 zeros

[grim mountain]

Oh my bad

Yes now its a fraction

[stone stump]

and that's what you wanted

[grim mountain]

I want to shorten it too

[stone stump]

well then reduce the fraction

[grim mountain]

How can we know How much

[stone stump]

do it step by step

can you see any common divisor of 13125 and 100 000 ?

[grim mountain]

From 10000/ 100 000 =0.1

You mean that way or

[stone stump]

you want to reduce the fraction 13125/100000

when can you reduce a fraction

[grim mountain]

When we have similiar factors

[stone stump]

ok

can you see one similar factor

[grim mountain]

No tbh

[stone stump]

can you tell me a factor of 13125

[grim mountain]

Yes by 5?

[stone stump]

good

and what is 13125/5 ?

[grim mountain]

13125/5 = 2000+600 + 20 + 4 + 1

26241

[stone stump]

no

[grim mountain]

?

[stone stump]

2625

[grim mountain]

Oh Ops

[stone stump]

ok

[grim mountain]

Haha

[stone stump]

is 5 also a factor of 100000 ?

[grim mountain]

Yes

20000

[stone stump]

one zero less

ok, what do we get now if we cancel the 5 from our fraction

[grim mountain]

Yes we lose the zero from our factor

2625/20000

[stone stump]

good

and now we repeat this

can you tell me a common factor of 2625 and 20000

[grim mountain]

5

[stone stump]

yes

[grim mountain]

Or is there a quicker way

[stone stump]

do you know the euclidean algorithm?

[grim mountain]

No

[stone stump]

then I don't really know a faster way

except "seeing" bigger factors

[grim mountain]

Is this something you can explain quick

I have a quick mind

[stone stump]

the euclidean algorithm is an algorithm to calculate the gcd of two numbers

essentially we repeatedly use division with remainder

[grim mountain]

Gcd is global cooldown?

[stone stump]

greatest common divisor

[grim mountain]

Ah ok

[stone stump]

can you see how knowing the gcd is relevant here?

[grim mountain]

Yes it’s the closest common numerator of the two factoris

For instance 42/100 = 21/50

[stone stump]

cause gcd(42, 100)=2, yes

so, in our case we would want to calculate the gcd of 13125 and 100000

we do this by repeated division with remainder

what do you get if you divide 100000 by 13125 with remainder

[grim mountain]

Remainder is?

I know that we would get 0.13125

[stone stump]

well that would be the other way around. and also not with remainder

I mean dividing 100000 by 13125 by hand

[grim mountain]

For every 0. 13125 number would jump in decimal

[stone stump]

and then stopping when you would need to introduce the decimal point

[grim mountain]

Yes by eliminating our divider of zeros.

Our decimal point is when value of our numerator has No more ten numbers to divide

[stone stump]

do you know how to divide by hand

[grim mountain]

Uhm. Im assuming its a method? But i dont know it

[stone stump]

isnt that usually taught in like 3rd grade or something?

long division?

[grim mountain]

I am not good with names

Oh by remainder you mean the what cant be divided is the remain?

[stone stump]

yes

[grim mountain]

Ok so for instance : 5/4 is 1 remain 1

[stone stump]

yes

[grim mountain]

So.

Why we need that

what do you get if you divide 100000 by 13125 with remainder.

[stone stump]

well its part of the euclidean algorithm

[grim mountain]

How do we know gcd

[stone stump]

this would go faster if you just did what I said and then we can do the questions later

[grim mountain]

Ok

Im not sure tbh

I dont think we can utilise the fraction with a remainder

13125/100 000 =

[stone stump]

can you just divide 100000 by 13125 with remainder. completely ignore the fraction and anything, just to this calculation

[grim mountain]

13125/100 000 = 1,3125/10

[stone stump]

no, other order

[grim mountain]

Oh

[stone stump]

and that's also not a division with remainder

[grim mountain]

1000 00/13125 this way?

Ok this got rough I have no idea

But in a sense if I assume an example of a lower fraction numbers 2/10 it’s 0 and remainder 2

Oh the remainder is 13125?

[stone stump]

no

100000 divided by 13125 is 7 with remainder 8125

cause 100000 = 7*13125 + 8125

[grim mountain]

Why did we change the fractions in order

[stone stump]

cause otherwise as part of the euclidean algorithm we would immediately switch the order

during the EA you always divide the bigger number by the smaller number

[grim mountain]

Doesent that make the numerator fraction a^-x

Oh intresting

[stone stump]

again, can you forget the fraction and everything

we are doing EA

EA calculates the gcd of two numbers

[grim mountain]

Oh ok

What are the rules of EA

[stone stump]

do you know what I did here. not why I did it, just what I did

[grim mountain]

Yes how many times does our numerator able to divide with a primal number and the rest is remainder.

[stone stump]

ok

there is a theorem which now says that gcd(13125, 100000) = gcd(13125, 100000-7*13125) = gcd(13125, 8125)

now as the next step of the EA, we divide 13125 by 8125 with remainder

what do we get

[grim mountain]

1 and remainder x

Remainder doesent matter since we can’t do that next step

[stone stump]

what who says we cant do the next step

remainder definitely matters

[grim mountain]

Okay so I got this in calculator

1,615384615384615

So what we do here is 13125-8125

So it’s 1 and 5000 remainder

[stone stump]

ok. again by the previously mentioned theorem, now gcd(13125, 8125) = gcd(8125, 5000)

so as the next step, we divide 8125 by 5000 with remainder

[grim mountain]

Correct

Gives is 1 and r= 3125

[stone stump]

ok and next we divide 5000 by 3125

[grim mountain]

5000-3125= 1975

This got quite odd

[stone stump]

1875

and next divide 3125 by 1875

[grim mountain]

1300

[stone stump]

1250

and next 1875 by 1250

[grim mountain]

625

[stone stump]

and 1250 by 625

[grim mountain]

2

[stone stump]

and remainder?

[grim mountain]

0

[stone stump]

ok and because the remainder is 0 we now stop

and the previous remainder is the gcd we have been looking for

https://i.imgur.com/GEdytZ3.png

[grim mountain]

What the

That’s our gcd?

[stone stump]

yes

[grim mountain]

Intresting

So by default we divide our fractions with 625

[stone stump]

at every step we reduced the numbers
gcd(13125, 100000) = gcd(13125, 8125) = gcd(5000, 8125) = gcd(5000, 3125) = gcd(1875, 3125) = gcd(1875, 1250) = gcd(625, 1250) = gcd(625, 0) = 625

where we always replace either the first or the second number by the next remainder

[grim mountain]

13125/625)/100000/625)?

[stone stump]

yes

[grim mountain]

What do we get?

[stone stump]

well what is 13125/625

[grim mountain]

😑

Im gonna use calculator?

[stone stump]

well you could do it by hand

[grim mountain]

With EA?

[stone stump]

but so far you didn't want to so it would surprise me if you want to do it now

long division

[grim mountain]

Imma do it 😂

Ok so 21

[stone stump]

good and what is 100000/625 ?

[grim mountain]

Ugh I’m Gonna calculate

160

21/160

[stone stump]

yes

I want to mention that you usually don't have that many 1s during the EA https://i.imgur.com/JdbSOmU.png

[grim mountain]

Ah why’s that

[stone stump]

just coincidence here

[grim mountain]

Ah I see

[stone stump]

anyway, I would argue that the method we used before is faster

at least as long as the factors we find are small

[grim mountain]

Yeah this was too long

[stone stump]

if the smallest factor is like 47 or something, you would never find that otherwise

without EA

so a good idea is to combine both algorithms. first do the first one with the small factors like 2,3,5 etc

and then maybe after that use EA

[grim mountain]

Ah I see. Is this in university too?

Never seen it before

[stone stump]

well you use EA in university, yes. but that's related to number theory and not reducing fractions

[grim mountain]

Ah I see

[stone stump]

in university it is assumed that you can do all that stuff

[grim mountain]

Yeah. I just began uni so all math is new to me

[stone stump]

have you never had math at school?

we learned fractions and all that stuff in grade 6

[grim mountain]

Oh fractions I know. It’s the language barrier that confuses me

I think

[stone stump]

oh did you move to another country?

[grim mountain]

No no. I’m from Sweden

We don’t use English math words here

[stone stump]

oh you mean it like that

[grim mountain]

Also I’m multitasking with a project for a circuit haha

[stone stump]

hmm I don't know about swedish. but I would assume that for the common stuff you can just google the english word, open wikipedia and then change the language to swedish

or vice versa for that matter

[grim mountain]

Yeah That works great

Are you good with circuit?

[stone stump]

what exactly do you mean?

like electronics and stuff?

[grim mountain]

Yeah

[stone stump]

I only know the absolute basics. I doubt I could help

[grim mountain]

Oh okay

[stone stump]

haven't done that stuff in like a decade

[grim mountain]

Ahh haha

Maybe it’s not practical in work

[stone stump]

probably is. just not relevant to anything I'm doing

[grim mountain]

Ah I see. Well I should do another help here, thank you for help.

.close

[devout snow]

Channel closed

Closed by @grim mountain

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[red helm]

Hello, i have a question regarding algebra

[red helm]

I managed to find 2 eigenvalues for a transformation in R^3, how can i transform the matrix of this transformation to a diagonal matrix when i don’t have 3 eigenvalues to make an eigenbasis ?

[stone stump]

well you can still sometimes find 2 linearly independent eigenvectors for the same eigenvalue

think of the identity matrix. only has one eigenvalue (1) but still an eigenbasis

[red helm]

Oh wow i see

How can i find 2 linearly independent vectors ? Just through trial and error ?

Or is there a general method ?

@stone stump

[stone stump]

well how do you find one

find the kernel ker(A-lambda I)

or rather, find a basis for it

[red helm]

By setting the independent variables to any value and deducing the others

[red helm]

That’s to find the eigenvalues right ?

[stone stump]

no

det(A-lambda I)=0 is to find the eigenvalues

ker(A-lambda I) is to find the eigenvectors after you found the eigenvalues

[red helm]

Oh yes that’s what i meant

So you just end up with a system

[stone stump]

yes

[red helm]

So yes i can then deduce infinity vectors

But how can i efficiently find 2 linearly independent vectors like you said ?

Just by setting the independent variables to different values and checking if the vectors are independent ?

Because i’m only finding linearly dependant vectors @stone stump

[stone stump]

are you sure that your matrix is diagonalizable?

not all matrices are

[red helm]

Yeah the question is to find it :/

[stone stump]

can you show your work

[red helm]

I can send you my work so far

Sure

Ok so this is the matrix of the transformation, it’s in french but you just need the matrix

Engenvalues :

And eigenbasis for the eigenvalues ( no idea how to say E2 and E4 in english )

Tell me if anything needs translating @stone stump

[stone stump]

E_2 and E_4 are called eigenspace

for E_2 y can be anything

y doesn't have to be 0

[red helm]

Oh really ?

[stone stump]

yes

[red helm]

Why ?

[stone stump]

0y is always 0

[red helm]

Oh

Daaamn

So i can just chose ( (1,0,1), (1,1,1), (-1,3,1) ) as an eigenbasis of the M matrix ?

@stone stump

[stone stump]

yes

[red helm]

Love you bro

[stone stump]

I would choose (0,1,0) but whatever, still works