help-0

[gilded cliff]

cuz input of -1, you get output of 0

[real gazelle]

yup

so the range has to include 0

so it can't be (1, infinity)

[gilded cliff]

hmm

[real gazelle]

okay I have to go now

[gilded cliff]

ty for ur help

[real gazelle]

but try drawing a graph

no problem!

[gilded cliff]

🫡

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[lone heart]

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[misty cedar]

help me with some algebra

[misty cedar]

Let $g(x)=2x-4$, and $(f\circ g)(x)=\frac{7x+3}{5x-9}$, find $f(2)$

[ocean seal]

Glitchy

[vale wigeon]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[misty cedar]

1

[vale wigeon]

do you know how to find inverse functions?

[misty cedar]

the f-1(x) thing?

[vale wigeon]

yes but not for f

$f = (f \circ g) \circ g^{-1}$ is the idea you'll want to use here

[ocean seal]

Ann

[vale wigeon]

so you will in fact need the value of $g^{-1}(2)$ to find the thing they ask for

[ocean seal]

Ann

[vale wigeon]

do you understand why this is the case

[misty cedar]

hm

does it makes the g cancel out each other?

[vale wigeon]

yes, g and g^-1 cancel each other out.

they're inverses.

[misty cedar]

oo tysm

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[winged haven]

can i please get a detailed solution, i am stuck on this problem, unable to solve after factoring

[winged haven]

express in reduced form

i might be doing something wrong

what do i do after this

im sorry if thats a dumb question

this is the answer

[vale wigeon]

why does this say (a) while your problem says (b)

[winged haven]

OHHHHHH

MB

this is the answer mb

[vale wigeon]

anyway (x^2 - 1) is factorable

[winged haven]

it is ?

does it become (a^2-b^2)

yes it does

[vale wigeon]

bad wording

(x^2 - 1) is a difference of squares yes but you do not have any variables named a or b in your problem

[winged haven]

yes sorry mb

what after this

oh its solved

thank you

[vale wigeon]

why cross out the whole (x-1)^2 tho

[winged haven]

ah mb lol, silly mistake

i got how to solve this

👍

[lone heart]

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[half blaze]

So I have two matrices: C and F. C is a symmetric square matrix of real values, and F is a complex matrix with more rows than columns, but all its columns are linearly independent.

I follow along this guy's work, right? And he gets for some equation the result Hermitian(F)*C*F. I, on the other hand, avoided solving the equation in the traditional way (i.e., knowing what you are doing) by instead reading Wikipedia articles on matrix properties until I got PseudoInv(F)*C*Transpose(PseudoInv(F)).

Are these identities?

[half blaze]

Wait I made my question too long:
tl;dr PseudoInv(F)*C*Transpose(PseudoInv(F)) == Hermitian(F)*C*F?

[lone heart]

@half blaze Has your question been resolved?

[half blaze]

I shall ping <@&286206848099549185> but once.

[lime bobcat]

You can reping helpers

[half blaze]

Yeah part of me thinks I should like, get a latex representation of this problem to make it more attractive to look at.

$F^{#}C(F^{#})^T = F^{H}CF$?

[ocean seal]

chazm

[half blaze]

Where H is the conjugate transpose, and # is the Moore-Penrose PseudoInverse?

And T is just a transpose

[lone heart]

@half blaze Has your question been resolved?

[half blaze]

Ok because that one guy implied I could I shall ping <@&286206848099549185> one more time, but I kind of understand that this question is a bit niche.

[half blaze]

Ok let the record show that I've somehow made negative progress with this.

I found a property saying that the pseudo inverse of a matrix with orthonormal columns

!help

[lone heart]

Please read #❓how-to-get-help

[half blaze]

I found a property saying that the pweudo inverse of a matrix with orthonormal columns is its complex conjugate

But that would imply...

$F^{#}C(F^{#})^T = F^{H}CF^{*}$?

[ocean seal]

chazm

[half blaze]

...Which is in fact not what I was supposed to get

Ah well

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[vast burrow]

hello i am back this time i would like help with this question

[vast burrow]

i have diffrentiated x correctly but the answer say that i have diffrentiated y incorrectly

[west cipher]

what did you get

for y

[vast burrow]

i got the same asnwer

te^t

[vale wigeon]

incorrect

[west cipher]

use product rule

[vast burrow]

so t+1e^t?

[west cipher]

no

how did yoy get t

in t+e^t

[vast burrow]

oh wait t diffrentiates to 1, and te^t diffrentiates to te^t so will it be 1+te^t

[west cipher]

you do not need to differentiate te^t

a'b+b'a=(ab)'

let a = t and b = e^t

[vale wigeon]

• not =

[vast burrow]

so 1+e^t?

[west cipher]

how did you get one

[vast burrow]

a' = 1

[vale wigeon]

how about you write it down on paper

properly

[west cipher]

and b=?

[vast burrow]

e^t

ok let me write this

[west cipher]

,rotate

[west cipher]

yes

[vast burrow]

It's a long way of doing it lol

[west cipher]

no need to use u and dv though

oh wait

yeah

you did it right

[vast burrow]

Oh good finally learning this topic slowly thanks to this server and you

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[topaz tartan]

Is this the right approach towards a ODE equation?

I believe something is quite off

[lone heart]

@topaz tartan Has your question been resolved?

[topaz tartan]

<@&286206848099549185>

[lone heart]

@topaz tartan Has your question been resolved?

[lone heart]

@topaz tartan Has your question been resolved?

[gusty crater]

lim sin 3x=0
X—>0
Proof using epsilon delta definition

[topaz tartan]

OK

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[alpine sable]

I don't understand the question, can anyone help

[vale wigeon]

it is phrased in somewhat of a stilted manner

[alpine sable]

It's from the chapter simultaneous linear equation in my book

[vale wigeon]

would you like to have it rephrased in a more understandable way?

[alpine sable]

Yeh :3

[abstract hinge]

@vale wigeon it's similar to question that some had for 10x + y

[vale wigeon]

There are two numbers.
Doubling the larger number, then subtracting 16 gives half of the smaller number.
Dividing the larger number by 2, then subtracting 1 also gives half of the smaller number. 
Find the two numbers.

[alpine sable]

Alright

[vale wigeon]

does this make the problem make sense to you?

[alpine sable]

Yeh i understood , thanks :3

I got the answer , thanks

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[cloud jetty]

Hi can someone explain how - 298K (75jk/mol) became 22400?

[cloud jetty]

Can someone explain this part here on how they got 22400?

<@&286206848099549185>

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cloud jetty]

<@&286206848099549185>

[tardy tapir]

dont ping the helpers before 15 mins!

[cloud jetty]

Oh sorry i thought 15 mins has passed

[earnest pawn]

Bro

Ill help u

Send me the assignment in dm

[cloud jetty]

Ok

[earnest pawn]

Send the dm then

[cloud jetty]

Cant

[earnest pawn]

Why

Add me

[cloud jetty]

Not accepting dms

[earnest pawn]

Thats why

[cloud jetty]

@earnest pawn Thanks man

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[gusty crater]

Find inflection points for
fx=|x-2|+|x-4|

[lone heart]

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[edgy moss]

what does the sentence circled in red mean?

[twin nimbus]

If μ is the mean and σ is the standard deviation, it's asking you for the percentage of your data between μ-2σ and μ+2σ

[edgy moss]

thanks :)

[twin nimbus]

You'll find that this should be essentially all of it except for a few outliers.

[edgy moss]

ok

95% right?

[twin nimbus]

Yeah

[edgy moss]

alright

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[deep grotto]

when i expand the bracket as the first step, i get positive 5/2, but when i divide both sides first by 5, i get -5/2

is it not possible to expand the brackets?

30x + 35 = 20x + 10

[twin nimbus]

You should get the same answer either way

[deep grotto]

35 = -10x + 10

-25 = -10x

[twin nimbus]

There's the error

35 - 10

Is 25 not -25

[deep grotto]

why did i make that error over and over

i even did it twice

lol thank u

[twin nimbus]

Yw

[deep grotto]

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[proper garnet]

can someone help me on this please

[proper garnet]

its physics but if you know how to help please help

[abstract hinge]

U can refer physics server for help #old-network

[rustic flax]

I know this is a math server but where are you stuck

[proper garnet]

i think a) is correct but im not really sure how to do b)

[rustic flax]

wait one sec

I don't think a is correct

I think you have to find the value of all the resistances

[vague coral]

tbh

find the equivalent resistance in all the circuit and apply ohm law

[proper garnet]

how do i do that

[vague coral]

you dont have a course on that ?

[proper garnet]

no im just forgetful

[rustic flax]

you add the resistances (the way to do that changes depending on wether the resistances are in line or parallel)

[proper garnet]

isnt it v=ir on all the resistors

[vague coral]

welp, on the right there are parallel resistances there, you apply this :

1/Req = 1/30 + 1/60

[rustic flax]

you know what a parallel resistance is?

[proper garnet]

so series and parallel

[proper garnet]

yup

[rustic flax]

yeah series mb

[proper garnet]

u do 1/resistance

right

then add together

[rustic flax]

yeah, but only for parallel resistances

[proper garnet]

yeah

for series u just add them together normally dont u

[rustic flax]

yeah

[proper garnet]

would i have to redraw the diagram or can i just do it as it is

[vague coral]

redraw if you want to add the equivalent resistance

[rustic flax]

no need though

[proper garnet]

do i need the equivalent resistance in this scenario?

oh okay

[rustic flax]

I mean it could help you picture it better

[proper garnet]

oh okay

[rustic flax]

but if the question doesnt ask it then I don't see why you can't just do the calculations

[proper garnet]

how would i do it

[rustic flax]

the equivalent resistance will help you find the current

[proper garnet]

and is a) right

[proper garnet]

how though

[rustic flax]

no, you used only the 20Ohm resistance

[vague coral]

we said no

[proper garnet]

how do u do it then

[vague coral]

do you read what we say :/
find the equivalent resistance of all the circuit and apply ohm law then

[rustic flax]

so to find the current in the whole circuit, you need to find the equivilent resistance and apply Ohm's law

[proper garnet]

so we need to find the equivalent resistance

[vague coral]

yes

[rustic flax]

yeah :/

[proper garnet]

tuby just said we wouldnt in this case

algtho

ill do taht

[rustic flax]

I said you don't have to redraw the diagram

[proper garnet]

ohh okay

but it would make it simpler right

Is this correct

as the simplified drawing

[vague coral]

yes it is

[rustic flax]

yeah

[vague coral]

but you just redraw the diagram you did nothing yet

[rustic flax]

although try to end the voltometer lines where the 60 Ohm resistor starts and ends

you don't really have to though

[vague coral]

its still correct

[rustic flax]

yeah

[proper garnet]

is the first step finding the thing for 20 ohms

[vague coral]

what thing

[proper garnet]

the current

sry

my brain is kinda fucked

[rustic flax]

Listen, the question asks to find the current on A1 right?

nah dw

I was confused when I learned that too

ok the meter at A1 measures the whole current in the circuit

to find the whole current we told you what to do

[vague coral]

^

[proper garnet]

ohh okay

[rustic flax]

@vague coral I gtg, stay to help please

sry

[vague coral]

np

[proper garnet]

ty for helpong @rustic flax

to find out the equivalent resistance yk how i have to add resistance for each point

oh wait

im so dumb

the resistance is given

sorry

[vague coral]

you have 2 ways to find equivalent resistance :
when the resistances are in parallel, you do 1/Req = 1/R1 + 1/R2 where Req is the equivalent resistance

when the resistance are in serie, you just add the resistance

here on the right, you have 2 resistances in parallel

use the formula I just gave you

[proper garnet]

is this correct

sorry for bad handwriting

[vague coral]

1/Req1 = 1/30 + 1/60
1/Req1 = 3/60
Req1 = 20 Ω

Req = 20 + 10 + 20
Req = 50 Ω

[vague coral]

it is

[proper garnet]

what do i do after this step

just v=ir?

[vague coral]

yes, I said after all that you can use ohm law

[proper garnet]

wait what does the equivalent resistance do?

like whats the point of finding it?

[vague coral]

to find the current of the whole circuit of course

[proper garnet]

ohh okay

i got 0.24A

is taht right

[vague coral]

I didnt calculate idk

[proper garnet]

i just did 12V/50ohms

[vague coral]

V = R I
I = V/R
I = 12/50

[proper garnet]

i thnk its right

what do i do with that

the 0.24A

[vague coral]

well you found the answer for A1

[proper garnet]

wait how is a1 the entire circuit's current

is it because it hasnt been split up by any resistors

@vague coral

[vague coral]

in series, the current is the same in all the wires

but on the right, we have two resistance in parallel so the current is split on 2 two wires

[proper garnet]

so how would you do question b)?

@vague coral

[vague coral]

kirchhoff law again

[proper garnet]

wtf

isnt that for reflections

[vague coral]

what... ?

[proper garnet]

oh okay

[proper garnet]

could u explain that in my scenario pls

im a bit confused on how to do that

[vague coral]

you calculated the current measured by A1, and you can find the current measured by A2, so you can deduce the current that goes through the resistance of 60 ohms

In short, the sum of the currents that go in a node is equal to the sum of the currents that go out of the node

[proper garnet]

which ones go in and out in my case

sorry im really bad at understanding things

[vague coral]

so you dont know the direction of the current...

[proper garnet]

isnt it all just going to output

[proper garnet]

so how do i find the charge of 60ohms

the current*

[lone heart]

@proper garnet Has your question been resolved?

[lone heart]

@proper garnet Has your question been resolved?

[vague coral]

kirchhoff current law

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[haughty fiber]

Dumb question but, how do I go about calculating probability?

I tried googling but no one explained it well enough for me to understand.

My hypothetical is... Let's say I have to answer a question that has 3 answers but it has 2 right answers. Not only that but you get to guess 2 times. What's the probability I get the answer right?

[pallid scarab]

Well here for example, when each answer has the same probability to be correct (here it would be 2/3), the probability that you pick the 2 correct answers out of 3 is the same as the probability of not picking the wrong answer, which is 1/3

Many formulas can be used to compute probabilities of an event.

[vale wigeon]

Dumb question but, how do I go about calculating probability?
well this question is too broad tbh lol

[dull dove]

You have to calculate the probability of both failing / getting it correct if I recall correctly

[vale wigeon]

My hypothetical is... Let's say I have to answer a question that has 3 answers but it has 2 right answers. Not only that but you get to guess 2 times. What's the probability I get the answer right?

gonna need some clarification here -- there could be at least three different scenarios here:

1. this is a "select all that apply" question with 3 checkboxes, the correct answer is to select exactly 2 particular checkboxes, and we know this. and we get two guesses.
2. same as the previous scenario, but we don't know that the correct answer has 2 checkboxes ticked (thus more options for us to be wrong)
3. this is a multiple-choice (select only one) question, in which 2 of the answers are correct. we need to hit at least one of the right answers and are given two guesses to do so

@haughty fiber which of these do you mean

[lone heart]

@haughty fiber Has your question been resolved?

[lone heart]

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[alpine sable]

Hcf for q5 is 18

But 72 divided by 18 is 4

And 90 divided by 18 is 5

THEY AINT EFEN EQUAL

THEY SHUD BE EQUAL AAA

[pallid scarab]

We never asked to get the same amount of pieces from each rope

We only asked for all the pieces to be of the same length

[alpine sable]

The. Whats the point of hcf

I couldve just use any fsctor

For both of em

[alpine sable]

.

[pallid scarab]

Because we want the greatest length

True, you could cut them all in lengths of 1

But that's not "the longest pieces of equal length possible"

[alpine sable]

Well i could just find the highest factor for both of thrm

Instead of finding the common one

[prime badge]

the highest factor is the whole rope

so you don;t make cuts, and you don;t end up with equal sized ropes

so has to be common

[alpine sable]

Huh

[prime badge]

common is what makes them equal

[alpine sable]

They are ewual?

Both are?

[pallid scarab]

We want the resulting cuts to ALL be of equal length

And we also want to have the greatest length for each of them that verifies that

[alpine sable]

I thought the q said both of the ropes to be equal when cut in pieces like piece of rope A should be equal to piece of rope B

[prime badge]

"factor" ensures that there's no leftover rope
"highest" ensures the pieces are longest
"common" ensures you don't get 2 different piles but one pile

[alpine sable]

Maybe its 5 for rope b coz its 90 like bigger scale

[alpine sable]

Yea

[pallid scarab]

I understand your confusion, but the criterion is not about the amount of cuts, it's about their lengths

[prime badge]

maybe you;re missing that pieces of rope 1 have to be equal to pieces of rope 2, not just between the same rope

[alpine sable]

So this true?

[prime badge]

that's actually not explicitly said

[alpine sable]

Like

If they wanted long pieces cut evenly for each rope, they couldve just picked the highest factor

For both numbers

Like for 90, 45 like 45 m in two parts of the rope

And for 72,36

36 m into two parts of the rope

[prime badge]

yes, that's not the goal

[alpine sable]

Then?

What the point of common

If piece of rope 1 (4m for each part) ain't equal to piece of rope 2 (5m for each part)

[prime badge]

you will get pieces of length 36 and pieces of length 45

and they want pieces to be of one length

and they don't really say that

but they mean it

[alpine sable]

Unless

[prime badge]

unless you use the same factor

[alpine sable]

Unless, They actually meant both of em to be equal and for rope 2 it was 5, coz it was 90m so the scale was bigger

)-:

[prime badge]

the amount of ropes you get doesn't have to be equal

[alpine sable]

Then why use common

Thing

[prime badge]

like

72 divided by 18 is 4
90 divided by 18 is 5

all pieces are 18

18 is the length and the length is what we want

oh right, you said it's not the length

it should be the length

now you understand everything

[alpine sable]

Oh yea the end part of the question said about length so 18 is the length so for rope A, (72m) the rope will have 4 pieces each of 18m length and the rope b (90m) will have 5 pieces of 18m length each

[prime badge]

yep

[alpine sable]

“Common” makes sense now D:

Thank u

?close

?close

.close

[lone heart]

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[alpine sable]

Smh

[lone heart]

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[idle maple]

ok i already sent it here before but i still cant solve it

[idle maple]

331

i need to solve it, but without using derivatives

i need to factorize it and also use functions equal to infinitesimals

oh never fucking mind

i got it

.close

[lone heart]

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[tepid drum]

ig it is done by multiplying by conjugates of num and denom

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[gilded cliff]

f is an even function
g is an odd functoin

a) fg
is this even or odd?

my work:
f (x) = f(-x)
g(x) = -g(-x)

fg
f(-x) (-g(-x)) = - fg(x)

[gilded cliff]

what do i do from here?

[sour dove]

what's the defintion of even and odd functions?

[gilded cliff]

even: f (x) = f(-x)
odd: g(x) = -g(-x)

or u can write it as:
even: f(-x) = f(x)
odd: f(-x) = -f(x)

but i prefer the first one, helps me see it better

but not that i have -fg(x)

what do i do from there

how can i deduce if its even or odd

[worn fox]

you have a new function fg, defined by fg(x) = f(x)g(x), just check the even, odd properties on this new function

[gilded cliff]

its an odd function?

no wait

is it neither

🧍

[sour dove]

So:

1. if f(x) is even, then f(-x) = f(x).
2. if g(x) is odd, then g(-x) = -g(x).

So then you you get f(-x)g(-x) = f(x)(-g(x)) = -f(x)g(x)

so waht does that tell you that we went from f(x)g(x) to -f(x)g(x)?

[gilded cliff]

can you use this instead

it helps me make sense of it more

[gilded cliff]

im not sure

from fg(x) to -fg(x) just means that all the y values are negative

so instead of q1 ur in q3?

thats not a reflection of the y-axis nor symmetrical in respect to the origin

it would be neither right? @sour dove

[sour dove]

that's an incorrect definition of odd.

What f(-x) = -f(x) means is that whenever you have a negative x value, the output is the negation of of the positive x value

there's not translations to the function happening there

[gilded cliff]

🧍

u still get -(fg)x

how can u tell that from -(fg)x it is an odd function? @sour dove

[sour dove]

ok I haven't seen that definition. I guess it makes sense but I've always seen odd defined my way. Same difference I guess.

regardless, it's an odd function

because it fits your definition just fine

[gilded cliff]

i got -(fg)x

[winter light]

You're wrong

Stop it please, you're spamming also in other channels...

[gilded cliff]

bruh yall are confusing me 🧍

[winter light]

Yes, he's a spammer, ignore him

So, if fg (-x) = -fg(x) it means that fg is odd, right? @gilded cliff

[gilded cliff]

i got:

f(x) g(x) = f(-x) (-g(-x)) =

[winter light]

Yes

But you know that f is even, therefore f(-x) is f(x)

[gilded cliff]

im using these defintions of even and odd

[winter light]

Yes

Which are the ones you stated at the beginning

[gilded cliff]

where do i go from here

[sour dove]

bro

[winter light]

Again, you know that f is even, therefore f(-x) is f(x)

[sour dove]

no

<@&268886789983436800>

[gilded cliff]

so the negative goes on the outside:

• (f(-x) * g(-x)) = - (fg) (-x) ?

[gilded cliff]

then by this definition its odd

[winter light]

Almost, it should be:

(f(-x) * g(-x)) = - (fg) (x)

[winter light]

And this means that fg is odd, yeah

[gilded cliff]

-g(-x)

what about the negative in front of the g

[winter light]

Leave it there

[gilded cliff]

u took it out for the left side of the equation here

[winter light]

Remember that $-g(-x) = (-1) \cdot g(-x)$

[ocean seal]

Alberto Z.

[winter light]

@gilded cliff

<@&268886789983436800>

[gilded cliff]

ig my question is that how do u go from:

f(-x) * g(-x) = fg(x)

[winter light]

<@&268886789983436800>

[winter light]

You don't reach fg(x), but **-**fg(x)

[gilded cliff]

nah i just mean generally:

so lets say you have: h(-x) * k(-x)

[sour dove]

bro x^5 is not even

[gilded cliff]

wouldnt that give you: hk(-x)? @winter light

[sour dove]

but they said that it's odd right here. Que?

[gilded cliff]

is this wrong?

[winter light]

It depends on what types of functionjs h(x) and k(x) are

[gilded cliff]

both are even

[winter light]

If both are even, then h(-x)·k(-x) = h(x)·k(x)

[gilded cliff]

so the two negatives become positive HM

i wasnt sure if that applied here

thx

[winter light]

Yes, because you said that h and k were even, meaning that h(**-x) = h(x) and also k(-**x) = k(x)

[gilded cliff]

@winter light what would f o g be then

[winter light]

How are f and g? f is even and g is odd?

[gilded cliff]

f(g(x)) = -f(g(-x)) =

[winter light]

No, let's do things one step at a time

First, let's call f(g(x)) with another name, such as h(x), ok?

[gilded cliff]

hmm alright

[winter light]

Now, if we show that h(-x) = **-**h(x), then our f(g(x)) (which was h) will be odd

If, instead, we show that h(-x) = h(x), then our f(g(x)) (which was h) will be even

[gilded cliff]

yes

so it f o g would be odd

[winter light]

No, $f \circ g$ will be even

[ocean seal]

Alberto Z.

[winter light]

h(-x) = f(g(-x)) = f(-g(x)) = f(g(x)) = h(x)

This means that h(-x) = h(x), therefore h is even

But h was f o g, hence f o g is even

[gilded cliff]

like that right

@winter light

[winter light]

Yes, that's another possible way, correct👍

[gilded cliff]

@winter light

im good right?

[lone heart]

@gilded cliff Has your question been resolved?

[agile grove]

The simplest way to remember even and odd functions is to firstly recognize that even sounds like "smooth," "nice flow," etc. Its even about the y axis (symmetrical). Now how can we prove this scenario? Well lets say we had I x I a symmetric function and applied a horizontal reflection. So I -x I it would still be symmetric.

For odd function picturize a linear function x where it would not be symmetric about the y axis.

[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[blissful garden]

Could someone explain how to raise a regular number to the power of a matrix? Like, say I had to evaluate this:
1 2
2 ^ 2 1

or this:
1 2 3
2 ^ 3 2 1

how would I go about doing that?

[tacit arch]

https://brilliant.org/wiki/matrix-exponentiation/

[blissful garden]

So you just raise the number to the power of each element, and replace each element with that, unless the element is zero, in which case you just leave it?

[tacit arch]

No. did you read the article?

[blissful garden]

I did, and that's what I thought it said. Could you explain it for me?

[tacit arch]

For non diagonal square matrices you have to diagonalize then follow the procedure

Work through the example at the bottom

[gilded cliff]

@winter light

[lone heart]

@blissful garden Has your question been resolved?

[winter light]

Yes, correct

Sorry I didn't see it earlier

[blissful garden]

Ok, so I'm not familiar with eigenvalues, eigenvectors, or the taylor series. Is there some simple way to do this, or is knowing like advanced calculus the only way to do it

I'm asking because I had this question on an SAT prep thing. No shot all the questions are like "John is buying apples for $5 each and bananas for $3 each, but he can't spend more than $20 - make an equation to model this" and "How many radians are in 180 degrees" and then the only way to do this one problem is with eigenvectors and shit

[lone heart]

Channel closed

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[blissful garden]

.reopen

[lone heart]

✅

[blissful garden]

<@&286206848099549185> any simple way to diagonalize a matrix, or solve the above problem? Or do you have to know advanced calculus to do it?

[wary stream]

diagonalize a matrix
That's a linear algebra topic, not calculus

[blissful garden]

Okay. That makes sense - I was just struggling to follow the explanation on the website riemann linked me. For example, stuff like "If we write AA in its eigenvector form, then A=SΛS −1 ⟹e A
=Se ΛS −1 , where SS is the eigenvector matrix and \LambdaΛ is the diagonal eigenvalue matrix", and stuff about the Taylor series.

So, is there a way to diagonalize a 2 x 1 matrix, so that you can then raise a regular number to the power of it?

[wary stream]

You can diagonalize square matrices

[blissful garden]

Gotcha. So, is it possible to raise a regular number to the power of a 2 x 1 matrix by some method other than diagonalization?

[lone heart]

@blissful garden Has your question been resolved?

[blissful garden]

Anyone have an answer?

Eh. Just gonna try and figure it out myself. I appreciate the attempted answers though 👍

.close

[lone heart]

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[lone heart]

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fleet owl]

Positive negative integer help

[fleet owl]

I am having a test for positive and negative integer this Thursday’s we are covering , absoulte vaule, positive and negative integer on the number line postive and negative integer word probelms and more

<@&286206848099549185>

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[fleet owl]

Mb

I’m sorry

I forgot

I forgot

[lime bobcat]

You didn't ask anything specific

[fleet owl]

Oh mb

Like if you can give me probelms

And I can see if I’m knowledgeable enough

@lime bobcat

[chilly idol]

Is this similar enough

[fleet owl]

Nope

EX greater - 34,914 or - 78,828

Or absoulte vaule

EX what’s the absolute vaule of -20

[chilly idol]

oh

[fleet owl]

EX sort these on the number line - 83 -67 -60 12 13 24

And one last EX

Pick the integer 1/2 3/4 -1 1 1.2

[chilly idol]

Im asumming this too isnt what your looking for

[fleet owl]

Yeah no

I’m not using C

X

[chilly idol]

ok

well ive got nothing for you

[fleet owl]

Do yk anyone who does

Or can find somome

[chilly idol]

its better to send in a specific question rather than asking for a review on a various amount of topics

[fleet owl]

Wym

[chilly idol]

like if you found a question that is relevant to your topics you need help on

thats the best way you can get the best out of this server

[chilly idol]

No i dont know anyone

[fleet owl]

I can pull up my computer and show you my completed assignments

Of this

[chilly idol]

yeah thats better send in those questions you've completed

[fleet owl]

?

Ok

I’ll be back

[chilly idol]

yeah btw i have a class in 5 minutes

so i got to go

[fleet owl]

Oh

Wait

Then can who help me?

Can you ping somome

[chilly idol]

use the helper ping

but not now

[fleet owl]

After I get ready?

For school

Tomorrow

@chilly idol ?

Which is like 10 minutes

[chilly idol]

wait im confused

your school is in 10 mins?

[fleet owl]

I have to get ready for school which is tomorrow

I need to be extra prepared

And ready

Should I ping them when I’m done

[chilly idol]

@fleet owl cant stress enough but if you want to get as much help from here. You NEED TO SEND A QUESTION YOU NEED HELP ON or a question if you are confused on. You need to send specific questions not broad topics.

Sorry for caps

[fleet owl]

I will

Send it

[chilly idol]

Anyways im going, if you find a question you need help on, use the helper ping

[fleet owl]

Let me pull up my computer

<@&286206848099549185> can I send you a picture of some class work I completed and you can send me a mini test of it I’m pulling up the screenshots now

He said to ping if I needed help

So sorry

[oak chasm]

We can't really give you a mini test ourselves, but we can show you where to take one on https://www.khanacademy.org/ for the same kind of thing as your classwork.

[fleet owl]

Can I send you some pictures of the answer key I completed the homework so it doesn’t matter and you can find the best possible place for me to go

[oak chasm]

Sure.

[fleet owl]

I’m gonna send you the paper for each there 7

[oak chasm]

OK.

[fleet owl]

And that’s everything covered

That’s every page

I’m sorry

@oak chasm

I’m sorry

That’s to much

But that’s Al the pages

@oak chasm

@oak chasm ?

[oak chasm]

For the number line stuff, it looks like this has some quizzes: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic.

And ordering numbers.

[fleet owl]

What about for the rest

@oak chasm ?

[oak chasm]

It looks like that handles opposite numbers, too.

That does absolute values too.

[fleet owl]

I didn’t understand this

[oak chasm]

OK, so what's the absolute value of -2/3?

@fleet owl

[fleet owl]

I don’t know?

[oak chasm]

OK, so what absolute value does is it takes away a negative sign if there's one there.

Like |1| is 1.

[fleet owl]

Yes

[oak chasm]

There was no negative sign to take away, so it stays the same.

|-5| is 5

It had a negative sign and that was taken away.

[fleet owl]

But it’s a fraction

Right?

[oak chasm]

Right, it works the same for fractions.

Does -2/3 have a negative sign?

[fleet owl]

Yes

[oak chasm]

So, |-2/3| is what?

Remembering how it worked above.

What's your guess for that?

[fleet owl]

I don’t understand still

[oak chasm]

OK, so let's say we have a number.

We look and see if it has a negative sign.

If it does, we remove it.

If not, we don't do anything to the number.

[fleet owl]

Why would we remove it

[oak chasm]

Because that's what absolute value is supposed to do.

It gets rid of negative signs.

[fleet owl]

But wouldn’t the absoulte vaule of -10 be 10

[oak chasm]

Yes, it got rid of the negative sign.

[fleet owl]

Ohhhhh

That’s what you mean

But a fraction

Wouldn’t it be 2/3

[oak chasm]

Yes.

[fleet owl]

If we remove the negative

[oak chasm]

Yes, so |-2/3| is 2/3.

That's the easy explanation of absolute value.

[fleet owl]

But it says for the number line

[oak chasm]

Right, so they want you to pick one of the points they made on the number line.

They want it to represent |-2/3|.

That means they want it to represent 2/3.

Does that make sense so far?

[fleet owl]

Yes

I also need help with one more

[oak chasm]

OK.

[fleet owl]

This one really got me

[oak chasm]

Question 3?

[alpine sable]

Which one

[fleet owl]

Question 5

[oak chasm]

OK, so you look at the number line.

See the little | marks on the number line?

[fleet owl]

Yes

[oak chasm]

They're all spaced a certain amount away from each other.

So, look at two of them that are marked with numbers, like the -8 and -4.

Those numbers are 4 apart from each other, right?

[fleet owl]

A, b , c , d ?

The ones

[oak chasm]

No, the numbers below the number line.

[fleet owl]

Those ones

[oak chasm]

Like -8 and -4 and 0 and 4 and 8.

[fleet owl]

Oh wait it is

Cause -8 -4 0 4. 8

[oak chasm]

Right, so each one is 4 more than the previous one.

[fleet owl]

You mean 4 less

8- then comes -4?

[oak chasm]

Yes, so it goes up by 4.

[fleet owl]

Oh wait

Are you saying the smaller it is the bigger for the negative?

And the bigger the smaller

[oak chasm]

-8 + 4 = -4
-4 + 4 = 0
0 + 4 = 4
4 + 4 = 8

No, I mean start with the number on the left.

-8.

[fleet owl]

Yes

It goes down

[oak chasm]

How much does it have to go up by to get the next number?

Like -8 goes up by what to get -4?

[fleet owl]

Minus 4

Cause that’s subtracting - 8 from -4

[oak chasm]

That's OK, you'll learn that in that section I linked to.

But how many | lines do you go right by to get from -8 to -4?

Like you start at the -8 of the | lines, right?

[fleet owl]

Yes

[oak chasm]

Then, you go over one | line to the right.

Then, you go over another | line to the right.

Then, you're at the -4 line.

Does that make sense?

[fleet owl]

Your going down to negative -4 right

[oak chasm]

No, I mean if you're trying to get from -8 to -4.

You start at the -8 line that's |.

You go to the right one more | line.

You go to the right one more | line.

Then, you're at the -4 line, right?

[fleet owl]

Ohhh

Everytime you go to the right your trying to get to -4

[oak chasm]

Right.

And you have to move right by two | marks to get from -8 to -4.

[fleet owl]

Yes butt there Point B in the middle of that

What would that mean

[oak chasm]

Yes, but we're ignoring that for now.

[fleet owl]

Ok

[oak chasm]

We just want to figure out the | marks for now.

[fleet owl]

Ok

[oak chasm]

Do you see how if you start at -8 and go two | marks right, you end up at -4?

[fleet owl]

Yes

But how can it be 2 if that’s 4 away

[oak chasm]

Well, the | marks count for more than just 1.

They count for 2.

So, like, if you start at -8 and go one | mark to the right, you get to -6.

[fleet owl]

Yup that’s what I was thinking

[oak chasm]

Then, if you start at -6 and go one | mark to the right, you get to -4.

So, we need to know how far apart the | marks are, which is 2.

[fleet owl]

Everytime you move to the right that’s 2?

I get that

[oak chasm]

OK, so now we look at B.

[fleet owl]

Yes

[oak chasm]

It's halfway between two | marks, right?

[fleet owl]

Correct

[oak chasm]

So, it's like the | marks are 2 apart, but if we only go halfway, that's 1.

So, B is 1 to the left of the -4 mark, right?

[fleet owl]

Yes

[oak chasm]

So, what number is B?

[fleet owl]

5 and 1/2

[oak chasm]

Not exactly.

You have to remember two kinds of things.

One is the | lines.

One is the actual numbers.

Each | line is 2 away from the next one.

[fleet owl]

Yes

[oak chasm]

So, if you're halfway between two | marks, you're half of that, or 1 away from those nearby | marks.

So, what number is one away from -4?

[fleet owl]

Oh

4 and 1/2

?

[oak chasm]

No, take the number -4.

Now change it by 1.

[fleet owl]

Add 1 to it?

[oak chasm]

Or subtract.

What do you get when you add 1 and when you subtract 1?

[fleet owl]

You add 1 thay would be -5 then subtract that is -4 in this case.

[oak chasm]

Oh, no, I mean adding 1 to -4 and subtracting 1 from -4.

You should get -3 and -5.

[fleet owl]

Ohh

Ok

[oak chasm]

Because those are the numbers that are 1 away from -4, right?

Now, B is to the left of -4, right?

[fleet owl]

Correct

[oak chasm]

So, B is more negative than -4.

[fleet owl]

Correct

[oak chasm]

-3 is a bit less negative.

But -5 is one more negative than -4, right?

So, B must be -5.

Does that make sense?

[fleet owl]

But oh wait

Let me check the question

[oak chasm]

OK.

[fleet owl]

OH.

I see

That

Ohhh

Ok

[oak chasm]

The confusing thing about it is that the | marks are worth more than 1.

[fleet owl]

I see it now

[oak chasm]

Like, you'd think that going a 1/2 of a | mark from -4 would be like -4 1/2.

But since the | marks are worth 2 instead of 1, you get a half of that, which is 1.

It's kind of like money.

[fleet owl]

No

[oak chasm]

Try one of the MATH HELP (AVAILABLE) channels.

Just above the MATH HELP (OCCUPIED) section of the channels.

Like let's say each | mark is worth $5.

If you go halfway between them, that's like $2.50.

[fleet owl]

What

I don’t understand that

[oak chasm]

Let's say the number line is for money.

[fleet owl]

Are we using the same number line

Thay I have

[oak chasm]

No, a different one.

[fleet owl]

Ok

[oak chasm]

Like let's say each | mark is $5 away from the next one.

[fleet owl]

And what’s the first number?

[oak chasm]

Let's say you're at the $50 mark.

You go halfway to the next | mark.

Since each | mark is worth $5, you went up by $2.50 to get $52.50.

[fleet owl]

That be $45 right?

[oak chasm]

Oh, if you want to go to the left, not exactly.

If you go halfway between the $45 mark and the $50 mark (because those are $5 apart like the | marks are), you get $47.50.

That's because you go down by half a mark, and each mark is worth $5.

So, you go down by half a mark, which is $2.50.

[fleet owl]

Yes

[fleet owl]

It be $45 if we went to the left

[oak chasm]

Yes, if you go left by a whole mark, it's $45.

[fleet owl]

Now this caught me off

[oak chasm]

Oh, how so?

[fleet owl]

How we get from $50 to $2.50

[oak chasm]

OK, so each mark is $5 away from the next one, right?

[fleet owl]

Yes

[oak chasm]

So, if you start at $50, and you go down half a mark, you don't go down by $5.

That would be if you went one whole mark to the left.

Because the marks are $5 apart.

[fleet owl]

You would be at $47 if you did a half

[oak chasm]

Yes, $47.50.

That's kind of how your problem works.

Each mark is $2 away from the next.

If you start at the -$4 mark and go half a mark to the left, that's -$5.

Because half a mark is worth $1.

Does that make sense?

[fleet owl]

Wouldn’t half a mark Be 2

[oak chasm]

No, a whole mark is worth $2.

Because each mark is $2 apart.

[fleet owl]

Oh a half a mark is 1

[oak chasm]

Right.

[fleet owl]

Yes

Ok carry on.

[oak chasm]

So, that's how you figure that out.

First, you figure out how far apart the numbers written under the number line are.

Here, they were $4 apart, right?

[fleet owl]

Yes

[oak chasm]

They were 2 | marks apart, right?

[fleet owl]

So the answer 4?

Yes

[oak chasm]

So, each mark is $2.

Do you see how I got that?

[fleet owl]

Yes

[oak chasm]

Then, you look at where B is.

[fleet owl]

That went down by 3 tho

[oak chasm]

What went down by 3?

[fleet owl]

8-3 = 5

[oak chasm]

Oh, OK.

So, B is 1.5 marks away from -8, right?

[fleet owl]

1.5

Why 1.5

[oak chasm]

Well, look at the number line in your problem.

Start at the -8 mark.

[fleet owl]

If b is -5 it be -3?

[oak chasm]

I'm not sure what you mean.

[fleet owl]

B is 5 rigjt

[oak chasm]

It's -5.

[fleet owl]

Still

And the staring point is -8.

Right

[oak chasm]

OK.

[fleet owl]

And if we go down by 1 is 7

-7

[oak chasm]

If you go half a mark to the right, you get -7.

Because each mark is worth 2.

And half a mark is worth 1.

So, if you start at -8 and go half a mark right, you get -7.

[fleet owl]

Wait

I get it now

If we go down by -2 that’s -6

[oak chasm]

Right, and that's 1 mark to the right.

[fleet owl]

We are just looking at the middle part

Which is -5

[oak chasm]

Right, you go one mark to the right to get to -6.

Then, you go a half of a mark to the right from -6 to get to -5.

[fleet owl]

Yup

I got it now

[oak chasm]

It's important to realize that the | marks don't have to stand for 1. Here, they stand for 2.

If you got that, you'll understand the problems better.

[fleet owl]

Yes

I got that

[oak chasm]

OK.

[fleet owl]

Now what

[oak chasm]

Oh, I'd check out https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic.

[fleet owl]

Wait

What’s the final answer

[oak chasm]

Oh, B is at -5.

[fleet owl]

Yes

[oak chasm]

They give the answer in red.

[fleet owl]

So it’s -5? Or -4?

[oak chasm]

No, the | mark is for -4. Then, half a mark to the left is B, so since a mark is worth 2, half a mark is worth 1, so B must be -5.

[fleet owl]

Oh so the whole thing we had to figure out what was the number in between -8 and -4?

Or still more

[oak chasm]

Yes, you have to figure out what a mark is worth, then figure out the B point's value.

[fleet owl]

Ohhh

[oak chasm]

And we're done because we know it's -5.

[fleet owl]

Awesome thank

You so much

[oak chasm]

No problem.

[fleet owl]

Goodbye God bless.

[oak chasm]

That Khan Academy link seems to be exactly what these problems are dealing with.

[fleet owl]

Alr

[oak chasm]

It has video lessons and practice quizzes if you're interested.

[fleet owl]

I’ll send it to my school email

[oak chasm]

OK.

[fleet owl]

Is that just everything that covers it

Btw

[oak chasm]

There are probably other sites, but Khan Academy is pretty good and it's free.

I don't know if it covers everything you showed in those problems when we began, but it seems to either cover everything or very close to everything.

[lone heart]

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[molten pivot]

hey guys

[molten pivot]

3.2 seconds

only 9 digits

n = 10,000,000

wtf!

granted this is a very naive approach. but it seems like integration itself is a very slow process

[lone heart]

@molten pivot Has your question been resolved?

[lone heart]

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[real pasture]

hello, i need some help with this limit

[real pasture]

i tried dividing the terms in the numerator by x

which gets me -3

but the teacher's work looks like this

not sure where the absolute value x came from

are we just considering the important variables or something? -3x/sqrtx^2?

oh i guess that's it

i always manage to figure out the solution after posting in this server

[vocal hawk]

posting a question makes you structure the problem logically, which makes you sometimes find the missing hole in your understanding

basically you can ignore the +3 and the 5

and they have no effect

[real pasture]

good point, ty

.close

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[solid fog]

im confused and dont know how to graph well.

[lone heart]

@solid fog Has your question been resolved?

[solid fog]

<@&286206848099549185>

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@solid fog Has your question been resolved?

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<@&286206848099549185>

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@solid fog Has your question been resolved?

[topaz tartan]

Think of it as transformations

First, list all the transformations you know