help-13

[quaint cove]

oh so thats what you meant we distribute the udu

wait

[cosmic steppe]

Distribute sqrt(u)

[quaint cove]

done

rght?

in udu?

[cosmic steppe]

$\frac{1}{2}\int(u^{\frac{3}{2}} - 8\sqrt{u})du$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

You'll get this

You understand how I got here?

[quaint cove]

uhm why not distribute udu?

[cosmic steppe]

You can't distribute udu

Where did you get udu

[quaint cove]

the x^2+8 then du=1/2x I guess

[cosmic steppe]

Well don't do that

You want to it be in terms of u to simplify

[quaint cove]

I really can't think rn, idk whats happening to me

[cosmic steppe]

legit just evaluate this

Since it's "du", you have to use "u" is a variable

[quaint cove]

uhm are u available tomorrow?

I think I really need to sleep so that my senses will come back

[cosmic steppe]

Yeah I should be lol

Take a rest

We've all have these "bruh moments"

But it's morning for me rn so

[quaint cove]

I really appreciate ur patience in me

[cosmic steppe]

If it's nighttime for you rn, then there's gonna be time conflictions

Lmao no problem

[quaint cove]

lol so dumg rn

[cosmic steppe]

Take a rest

Let's see if you can do it again tomorrow

[quaint cove]

okay2 thank you so muchh!!

[cosmic steppe]

No problem

[cedar kiln]

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[tepid pier]

Discrete mathematics

I’m just completely confused on like how to even think about this

[elfin hemlock]

Hint: ||its false, f needs to be surjective||

[tepid pier]

How would I express that in a counter example is my question I guess

[elfin hemlock]

There are very minimal counterexamples

Here is the most minimal one: ||X={1}, Y={1,2}, B={2} and f(1)=1||

[tepid pier]

What makes that a counter

[elfin hemlock]

Compute the things

[tepid pier]

Sorry if I’m asking stupid stuff I’m just trying to understand

[elfin hemlock]

What is f^-1({2})

What is f taken on that?

Is it equal to {2}?

[tepid pier]

No it’s -2

[elfin hemlock]

What?

[tepid pier]

Wait

I’m dumb

No it’s not equal to 2

Never mind I’m just confused again. I’m gonna look at this for a minute

[elfin hemlock]

Does f map any element to {2}?

[elfin hemlock]

(Any not surjective function works as a counterexample as long as you pick B not a subset of f(X))

[tepid pier]

So if we were to stick 2 in there or B in our case what would come out

[tepid pier]

Like what is the answer to this. Just making sure I fully wrapped my head around this

[cedar kiln]

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[fiery frigate]

guys i need help

[glass oasis]

with what?

[glass oasis]

ahh

hmmm

[fiery frigate]

how to solve this? i am a calc 3 student

sir gave this

as a "joke"

said noone will solve it

im stuck

[glass oasis]

oh

are we testing convergence?

[fiery frigate]

yes

[glass oasis]

have you tried just plugging in the infinity?

[fiery frigate]

yep

if i dont mind you asking are you a teacher or a student

[glass oasis]

show it's non zero

[glass oasis]

student

[fiery frigate]

ah tcool!

[glass oasis]

Just studied the tests for convergence

I'm first year university

[fiery frigate]

thats nice!

im doing BSC math

[glass oasis]

same

[fiery frigate]

which uni btw? im doin from MIT

[glass oasis]

MIT 💀

please, i'm at a uni around 200th on qs

but that shouldn't matter

[fiery frigate]

yep!

well i got into Harvard's waitlist but they didnt select me but my friend whos SAT was only 1570 ..

i got a 1590

[glass oasis]

1/k will get smaller

[fiery frigate]

isee

[glass oasis]

because k is increasing from 1 to N

I conclude it to be divergent

the limit of the summand is undefined

k will inevitably get to N, which is infinity

[glass oasis]

sound so salty

jheez

[glass oasis]

@fiery frigate

[still barn]

That is not divergent and you are likely talking to a troll

[glass oasis]

explain how not divergent?

[still barn]

That limit is the euler mascheroni constant: see https://en.wikipedia.org/wiki/Euler's_constant

[glass oasis]

k

[cedar kiln]

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[onyx wing]

Is $\frac{\partial}{\partial x}(\frac{\partial}{\partial y}(f(x,y))) \equiv \frac{\partial}{\partial y}(\frac{\partial}{\partial x}(f(x,y)))$?

[wraith dagger]

EpicnessLord12

[lament sonnet]

See here, for the theorem of Schwarz. https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives

[cedar kiln]

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[onyx wing]

Thank you!

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[tough crow]

Bill Smart wants to withdraw $6,000 at the beginning of every three months for 20 years, starting on the day of his retirement. If he retires in 18 years and interest is 4.68% compounded quarterly, how much must he deposit into an account every quarter for the next 18 years, starting now?

[potent bough]

I hate problems like this, it can be ambiguous, is it multiple choice?

I would approach the problem like this

[tough crow]

Nope

Not multiple choice

Its show ur work

Same i hate problesm lioke this

[potent bough]

Ok

[tough crow]

which is hwy im stuck

why

So A would be 6000 right

[potent bough]

Well

Let’s pretend you don’t get interest

After you retire

You do but let’s pretend for a second

You would need to earn 6000*4*20

Which is $480,000

And here’s the formula for future value

You need 480,000$ so set that as your FV

Then you solve for p

Actually to solve for the FV you should do the same equation , with -6000 as your payment, interest as the rate per period

And 80 as your number of periods

[potent bough]

Then set this FV to that calculated value

Ignore the first pic I sent it’s more complicated than that

Or something

Due to the time crunch I didn’t spend much time thinking

[tough crow]

Sorry i was trying to figure it out im back

@potent bough im so sorry I have 2 mins left

Ill just have to

try to find on internet

Its gona take atleat a min for me to submit the documnet

[potent bough]

Ok then start with 480,000 as your value

And get partial credit

[tough crow]

K

[potent bough]

480000=P((1+0.0468)^80-1)/80)

Solve for P

[tough crow]

Got it

[tough crow]

iS IT DIvided by 80?

I just submitted it

I used divide by 80

on the "/"

u did

but there was as bracket

[potent bough]

Yea

[tough crow]

I did 1035375 as the answer

was that right

i did it in a hurry

lol

[potent bough]

I didn’t solve it myself but no that shouldn’t be right

[tough crow]

Shit

I had no time to solei t so i just typed in solve for p on calculator

solve

[potent bough]

Well, should have given yourself more time lol

Trust me I’m the same way

It only gets worse as the math gets more complicated

[tough crow]

lmao fr

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[full trail]

Let X be normally distributed with mean of 75 and standard deviation 5. Given that P(X<65) = P(X>a), find the value of a?

[cedar kiln]

@full trail Has your question been resolved?

[cedar kiln]

@full trail Has your question been resolved?

[full trail]

can someone please help me with this question if you can?

[dire geode]

Use $P(X < a) = 1 - P(X > a)$

[wraith dagger]

riemann

[full trail]

so do i first find P(X<65)?

[full trail]

then use this?

[dire geode]

you don't need hand holding. just try different things until you get an answer or get stuck

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[balmy lark]

Could anyone help me out with question 3

[balmy lark]

I don’t understand

I tried doing this way but my teacher said it’s wrong

<@&286206848099549185>

[crimson sedge]

u might wanna take the derivative of the function

she said succesively smaller changes

which typically means the limit of the fermat difference quotient

[balmy lark]

I still don’t quite understand

[crimson sedge]

u know what a derivative is right?

instantaneous rate of change

so differentiate that function

and plug in 7 to get the rate of change

which is what she wants

[balmy lark]

Do u mean like this?

This is the feedback my teacher gave me but I still don’t know what he means

<@&286206848099549185>

[cedar kiln]

@balmy lark Has your question been resolved?

[balmy lark]

❌

[cedar kiln]

@balmy lark Has your question been resolved?

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[crimson sedge]

Where is the sin coming from?

I tried this problem and just did substitution

Where u = 2-x^2

And du = -2x(dx)

[dire geode]

where does that get you?

[crimson sedge]

i roughly solved it

[dire geode]

did you get the same answer?

[crimson sedge]

-(2-x^2)^(3/2) / 3x^3

no

im wondering where sin even came from

do you need sin in this problem?

it looks like it has nothing to do with trig

so i was wondering what im missing

[dire geode]

your solution probably has a mistake

[crimson sedge]

i mean i assume wolfram is right

but looking at its step

i cant even know where sin was pulled from

[dire geode]

have you never learned trig sub?

[crimson sedge]

oh is that a thing..?

so u cant solve this with just substitution?

[dire geode]

you should do these problems
https://tutorial.math.lamar.edu/problems/calcii/trigsubstitutions.aspx

and if you've never seen it before:
https://tutorial.math.lamar.edu/classes/calcii/TrigSubstitutions.aspx

[crimson sedge]

okay thanks, i'll take a look

and weird, im in calc1 but we are doing this

and im tryna study up for my midterm

this is the last section of what will be on the midterm

.close

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[frigid canyon]

what's the problem bro?

[charred skiff]

i dont know what to do

[crimson sedge]

ㅣㅐㅣ

[charred skiff]

dy=e^x y dx

this right?

[frigid canyon]

yes

wouldn't it be nice if all y are on the other side as well

[charred skiff]

how

[frigid canyon]

dy/y=e^x dx

wait what is that?

[frigid canyon]

nope nope

take y to the other side and then integrate

[charred skiff]

both sides?

[frigid canyon]

yes ofc we always integrate both sides

[charred skiff]

lny=e^x

[frigid canyon]

+c

now you got it

right

[charred skiff]

y=e^e^x + C

[frigid canyon]

no no no

lny= e^x +c

y=3 when x=0

[frigid canyon]

c=ln 3-1

now do it

[charred skiff]

it is C

acutlaly im not sure which one it is

[cedar kiln]

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[crimson sedge]

no answer in the back of the book for this practice problem

does it look correct?

[dire geode]

,w integral sqrt(2-x^2) / x^2 dx

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[dire geode]

looks the same

[crimson sedge]

thank you

.close

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[viscid narwhal]

Hi. I just have a quick question about leading ones in a matrix. My prof was doing an example that involved creating the REF form of a 3x5 matrix. And he just kinda said that the most amount of leading 1s you can have is 3. He didn't explain why though. I'm just confused about why it couldn't be 4 or even 5 leading 1s. And also what if it were a different matrix, such as 3x6 or 4x6. What's the max amount of leading 1s you could have there?

[random shale]

Number of rows = Maximum number of leading 1s

3 rows $\Rightarrow$ Maximum 3 leading 1s

[wraith dagger]

Max..

[viscid narwhal]

oh I must have missed that in an earlier lesson or it wasn't fully explained. But that makes a lot more sense. Thank you!

.close

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[glossy citrus]

I can tell that the numerator and denominator are related but I don't know how to actually get the answer

Like I would think "oh just square root both the x and the -25" but I'm 90% sure I can't do that

[livid hound]

consider using conjugates and/or difference of two squares

[glossy citrus]

to be honest that just sounds like jargon to me Idk how to do that

I'm thinking of complex conjugates but I don't know how to apply that concept

[livid hound]

there's radical conjugates as wll

the idea is very similar

[glossy citrus]

It's been a year since I've done complex conjugates anyway

All I remember is it's like reversed imaginary numbers or something

[livid hound]

since you've mentioned complex conjugates, you would done stuff like multiply numerator and denominator by the conjugate of the denominator to real-ise the denominator

similarly here, you can multiply the numerator and denominator by the conjugate of the numerator to rationalise the numerator

alternatively you could view $x-25$ as $(\sqrt{x})^2-5^2$ and factorise that as a difference of two squarees

[wraith dagger]

ℝamonov

[glossy citrus]

hjow would one obtain the conjugate of the numerator

I don't know how radical conjugates work

and I don't remember how complex ones worked

[livid hound]

the conjugate of
a+b is a-b

[sand ether]

$x-25 = (\sqrt{x}-5)(\sqrt{x}+5)$

[wraith dagger]

azeem321

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[crimson sedge]

hey

[crimson sedge]

would read be the correct ans for this?

I think so

what about this one

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[upper garnet]

y''-2y+y=e^x

[wide light]

at the end

for some reason, everything cancelled out.

that should not have happened......... where have i went wrong

[upper garnet]

e^x is Axe^x

[wide light]

i think i got a feeling why.... basically i wasn't actually meant to do this question. it tells you what the particular integral is and its got an x^2 in it.

is this for some reason a special special case though? i dont understand why my usual method didnt work.

[wide light]

im not sure what this means.

[upper garnet]

not (A+Bx)e^x

but Axe^x

[wide light]

are you saying that i should not have put (a + bx)e^x as the complimentary function

but the complimentary function is just axe^x ???

[upper garnet]

it's axe^x

[wide light]

this is mark scheme i was given

why do they put (a + bx) on the complimentary function?

sorry

i should post full questoin

full question

(i know i wasn't meant to work out particular integral myself for this question, but i wanted to try)

[upper garnet]

idk

if axe^x ain't a solution just go one rank above

ax^2e^x

[wide light]

@upper garnet its a repeated root

which is why you do (a + bx)

i had forgotten that you do that for repeated roots

then its a special case

so i think you multiply it all by x once again

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[dapper crown]

Would this inscribed polygon be a triangle or square I'm confused

[cedar kiln]

@dapper crown Has your question been resolved?

[dapper crown]

<@&286206848099549185>

[cedar kiln]

@dapper crown Has your question been resolved?

[gray condor]

unclear

@dapper crown

this feels like a very specific part of geometry you’d done in your school / uni

all I know is that those points are equidistant because it looks like a compass mark

[dapper crown]

This is for a program I do out of school for extra curricular just because. But yes those are compass marks I was just having a hard time dictating whether it was a square or triangle but after further research I went with square.

[gray condor]

oh, where are you planning on applying for uni?

if it’s anywhere in england I could help ya

[dapper crown]

I’m applying for Cambridge University in London. I’m currently doing a curriculum in the states known as the Cambridge and AICE program that provides me with credits for the university and I believe a grant.

[gray condor]

bro, cambs is in cambridgeshire

I live in england

[gray condor]

and what subject if I may ask ?

[cedar kiln]

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[mint sorrel]

Partial fractions decomposition question

[mint sorrel]

Why can we seemingly ignore the B, C, and D variables

and just solve for A?

.close

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[wraith dagger]

MasterBenny

[hoary patrol]

I've never seen that notation

[twin scroll]

Would you like to see an example problem

Using 2d Cartesian vectors?

[hoary patrol]

What do you call that down arrow operator?

[twin scroll]

Projection

[hoary patrol]

Oh I see

Well the solution is wrong because it's not a scalar multiple of w, right?

[twin scroll]

Im not sure if it needs to be a scalar, maybe because it’s a Cartesian vector. Initially I did get a scalar multiple but after seeing an example problem I found that it just produces another vector

[hoary patrol]

Multiplying w by 5/29 gives (20/29,-15/29,-10/29)

Projection is a scalar multiple of the vector projected on.

[twin scroll]

A true, well that is a problem jaja

I don’t know if I understand what you mean by scalar multiple, isn’t that just a single variable rather than a vector ?

[hoary patrol]

Yeah so a scalar multiple of a vector, v, is a vector that can be written in the form av where a is a scalar.

Projection yields a scalar multiple of the vector projected on by definition.

[twin scroll]

Ok thank you : )

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[cedar kiln]

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[twin scroll]

I actually had another question, for a question like c, would the answer simply be, it depends on the scalar projection of w on v?

And vice versa for d

[crimson sedge]

magnitude should be scalar projection

so i think so

[hoary patrol]

The magnitude is equal to the dot product of w with the unit vector in the direction of v.

By the definition of projection.

[twin scroll]

Ok, yeah I’m doing an online course and they only used 1 sentence to explain this so I still find it a bit unclear.

[hoary patrol]

All good. =]

[twin scroll]

Sorry to be so wordy but would my answer sufficient, or would this be the correct answer

[hoary patrol]

Oh, yeah that's probably good enough. Haha

Forgot what scalar projection was tbh

[twin scroll]

Np, I can hardly remember and I’m doing the course rn

Anyways thanks both of you guys for all the help

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[wicked brook]

Let $H<G$ be a subgroup containing $S_{q_i}$ for some primes $q_i$ and let
$q$ be an other prime dividing $n$. Is it true that $H\cdot S_q$ only
contains $S_{q_i}$ and $S_q$ but no other minimal normal subgroup?

[wicked brook]

How do I answer this?

[wraith dagger]

ohNoiAmHere

[wicked brook]

I'm pretty sure the answer should be yes, but how do I show this?

[cedar kiln]

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[crimson sedge]

How can U not be a subspace of R^2?

[mighty drift]

scalar multiplication turns a point into a line. Sums keep lines to lines. Could having several lines work ?

[crimson sedge]

So several lines can be a vector space?

And the reason it isn't a subspace is because adding them will make something outside the lines?

[random shale]

Subspace contains 0 right?

[mighty drift]

two lines, generated by 2 numbers, will generate (unless you took them aligned) all of R². But each line is stable by multiplication

[mighty drift]

yes

[random shale]

Just find an affine subspace such as a line that doesn't go through 0

[crimson sedge]

But why isn't it a subspace

[mighty drift]

not stable. take a point in R² and multiplication stability will give you the entire line passing by 0 and that point

[random shale]

True and surely that scalar a can be 0

[mighty drift]

take 2 points on different lines. Their sum is not on either line, so not stable by sum. You can show that 2 non-aligned points are enough to generate R² using vector space operations (i.e. linear combinations)

[crimson sedge]

Do these lines have to be linearly independant?

If you can even apply that term to a line

[mighty drift]

points are linearly independant, not lines. For lines that's more like being parallel. But since they go through zero that becomes equality

[crimson sedge]

How come they must go through 0

[mighty drift]

0*a = 0 so you always get 0 from multiplication

[crimson sedge]

I see

I am starting to picture it

So how can the subset of R^2 be two lines?

Are they just points making the lines

I'm assuming

[mighty drift]

you can take a set like (1, 0)R U (0, 1) R

basically the two axis lines

[crimson sedge]

Yeah

So because of by adding a point from one of the lines with the point on another of the lines creates a point outside this set, it is therefore not stable under linearity hence why it isn't a subspace* yeah?

[mighty drift]

correct. The subspace they span is R²

[crimson sedge]

Ok perfect thank you

I have another question

How would it work the other way

[mighty drift]

you can use a similar idea thinking about lines

[crimson sedge]

What does it mean by an additive inverse?

[mighty drift]

it's written in the parentheses

have you not done basic group theory ?

[crimson sedge]

I don't think so

Set of integers would work yeah?

[mighty drift]

that's usually when you first learn of these terms when studying algebra. But nowadays people do linalg before alg

[mighty drift]

yes

[crimson sedge]

Ok my understanding is much better now

Thank you appreciate it

[mighty drift]

the idea is to have some gaps that you can't fill in, but that scalar multiplication can

[crimson sedge]

I should have done it before I think

But I am revising backwards for some reason

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[regal sapphire]

help

[regal sapphire]

IS x=1 and y=9 ???

[sick ruin]

you have x + y = 10, and you want to choose x and y to minimize 2x^2 + xy

@regal sapphire do you know calculus

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[wanton elk]

How do I find the final answer for this problem?

[wanton elk]

What is K?

[obsidian coral]

I don't think you can get help with this

[wanton elk]

Ah man

It’s ok I understand

!close

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[obsidian coral]

It does say something about violation of academic integrity that's why

[wanton elk]

Ok that’s fine I just wanted to get hint towards the right direction but if you can’t help that’s fine

[cedar kiln]

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[crimson sedge]

how would I re-index a summation to 0

[crimson sedge]

from 1 to 0

cant I just do: re-written summation at 0 - the first term

= summation indexed at 1

[mighty drift]

$\sum_{k=1}^n f(k) = \sum_{k=0}^{n-1} f(k+1)$

[wraith dagger]

themateo713

[mighty drift]

the sum is the same in both cases

if you look term by term

[crimson sedge]

is $\sum_{k=1}^\infty \frac{x^{3k}}{k!} = \sum_{k=0}^\infty \frac{x^{3k}}{k!}} - 1$

[wraith dagger]

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

[crimson sedge]

@mighty drift

[mighty drift]

also true

[crimson sedge]

it is?

[mighty drift]

add and subtract the zeroth term, one you put in the sum, the other you leave outside

[crimson sedge]

?

add and subtract?

[mighty drift]

how to prove it

[crimson sedge]

I only subtracted

the zeroth term from the summation indexed at 1

[mighty drift]

how would you prove it ? by adding and subtracting the term corresponding to k=0, i.e. the zeroth term

[crimson sedge]

ok

so what I did is correct right?

[mighty drift]

yes

[crimson sedge]

thanks.

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[crimson sedge]

.reopen

[cedar kiln]

✅

[crimson sedge]

jose

so I've got the summation as

$\sum_{k=0}^{\infty} \frac{x^{3k}}{k!} - 1$\

[wraith dagger]

Joseph Fourier

[crimson sedge]

I cant quite wrap my head around how the substitution of the known summation works

or is my approach wrong here

[mighty drift]

x^3k = (x^3)^k

[crimson sedge]

...

my brain just doesnt work today

thank you

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[crimson sedge]

.reopen

[cedar kiln]

✅

[crimson sedge]

Wait sorry one more think

So from what I understood here it would lead to e^3x

But the power series representation for e^3x is a bit different

@mighty drift

[mighty drift]

yes

it is different

e^3x = (e^x)^3

which the cube of the sum, bad stuff

it's e^(x^3)

[crimson sedge]

ok im gonna think of this and get back to you

[cedar kiln]

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[modern sparrow]

do you know how to multiply out brackets? for example (a+b)(c+d)?

[dark mason]

Yeah

[modern sparrow]

okay do you know what squaring is?

[dark mason]

Yeah

[modern sparrow]

okay so then do you know how to re-write (c+sqrt[d])^2 in the form of 2 brackets and multiply out?

[dark mason]

I'm not sure

Is it (c+d) (c+d)

[upper garnet]

that's (c+d)^2

[upper abyss]

Instead you want
(c + √d)² = (c + √d)(c + √d)

[dark mason]

Oh yeah I get it

Is C times √D = C √D

[modern sparrow]

yes

another example is 2 times √2, which is just 2√2

[dark mason]

So is the final answer c²+C²√d+D

Would c√d + c√d add up to 2c√d

If so pls tell me how

[upbeat meadow]

the final answer would be c^2 +2c sqrtd +d

[upbeat meadow]

yes

[upper garnet]

say sqrt(d) is a

ca+ca is 2ca right?

[cedar kiln]

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[dire hazel]

im not sure how to make an example out of this

[upper abyss]

Let's say it starts at $100. How much is it after the increase? How much after the decrease?

[dire hazel]

would i have to use the equation for future value?

[upper abyss]

Ye

[dire hazel]

like FV=PV(1+i)^n

pv=100(1+.010)^5?

@upper abyss

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[crimson sedge]

Hi! What is the answer? I believe it is 2 but I am not sure

[livid hound]

show work/reasoning

[crimson sedge]

oh it's not two

i believe it's 3 since it would be 3 6 18 54

oh i just figured it out my self

thank you

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[calm geode]

how do I I fill in the other boxes?

[cedar kiln]

@calm geode Has your question been resolved?

[cedar kiln]

@calm geode Has your question been resolved?

[cedar kiln]

@calm geode Has your question been resolved?

[flint plinth]

what are Q1 Q2 and Q3? Part of the problem seems to be missing

[sick ruin]

@calm geode

[calm geode]

all it gives me is the numbers

[south juniper]

I believe Q1,Q2,Q3 stand for the lower quartile, medium quartile(median) and the upper quartile respectively.

@calm geode idk the formulas for q1,q2,q3 but if you look them up, you can find them easily

[calm geode]

but what go in the second boxes??

[south juniper]

The value of Q1,Q2,Q3

Which you will get from the formulas

If lets say Q1 is indeed 3, then the position of Q1 is 2nd, since 3 is the 2nd number in the sequence

[calm geode]

im sorry bro, im lost

[south juniper]

Formula for position of Q1 is (N+1) * (1/4). We have N = 7, so position of Q1 = (7+1) * (1/4) = 8/4 = 2. That means Q1 is the 2nd term of the sequence.

And on the right side, you will write Q1 = 3(This is the value of Q1 which is 3 because it is the second number in the sequence)

@calm geode

[sick ruin]

You don’t even need the formulas

Q2 is just the median, which is 12

Q1 is the median of the numbers from the beginning to Q2, which are 1,3,9,12, and the median of these is (3+9)/2 = 6. So now we have Q1 = 6.

@calm geode are you following this

[calm geode]

yeah, thank you guys

[sick ruin]

Remember to close

[south juniper]

.close

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[timid ice]

is it justifiable to think of matrices as functions?

[fair geyser]

why not

i guess i mean thinking in a certain way is always fine

free thought

[timid ice]

our teacher only defined it as "a grid with columns and rows"

[timid ice]

what would be the correct definition?

[fair geyser]

i agree with your teacher's definition

it's a rectangle of numbers

[timid ice]

whats its purpose?

[cedar kiln]

@timid ice Has your question been resolved?

[crimson sedge]

I think that's a great way to think of matrices

[marble bone]

I would recommend thinking of it as transformation rather

Something which rotates space by some angle

And streches it by a factor

[cedar kiln]

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[hollow glen]

I am trying to solve for y using logarithmic functions.

2log_3(x)-log_3(y)=2

I end up with
log_3(x^2/y)=2, but I am not sure how to isolate y from here.

[dense oriole]

@hollow glen Have you seen this before?

[hollow glen]

would that apply to both terms?

oh wait

so it would be log_3(x^2/3^2) =log_3(y) after adding it to both sides i think, then log_3 would cancel to give x^2/9=y I think

[cedar kiln]

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[hollow glen]

<@&286206848099549185>

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[sand yacht]

The amount of time spent by ABC college students on study per day is normally distributed with mean of 6
hours and a standard deviation of 1.5 hours
Find the probability that in a random sample of 6 students all study for less than 5 hours per day.

[cedar kiln]

@sand yacht Has your question been resolved?

[sand yacht]

Hi?

[elfin hemlock]

what have you tried?

[sand yacht]

i tried to put p=(p(x<5))^6

however i dont know it is correct or not

[elfin hemlock]

bad notation but sounds like the right idea

[sand yacht]

😦

[cedar kiln]

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[crimson sedge]

im doing practice problems

how do i integrade this?

what do i assign to be u

or dv

i know how to do it if it were sinxcosx

but the x in front is throwing me odff

[elfin hemlock]

Know any trig identities?

[crimson sedge]

yeah

i know them all

well not all

but the ones i were shown in class

dont know what applies here?

[elfin hemlock]

There is one for sin(x)cos(x)

[crimson sedge]

ohh snap

which one?

wtf

sinx(2x) = 2sinxcosx

this is the closest i know lol

[elfin hemlock]

Yes indeed

Divide both sides by 2

[crimson sedge]

ohhh shoot

so sin(2x) / 2

right?

[elfin hemlock]

Yes

[crimson sedge]

okay i see where i can go now

thank u

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[crimson sedge]

.reopen

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✅

[crimson sedge]

i dont know how to type this into wolfram

but i got -pi / 4

could someone double check with me?

[dark yarrow]

so the integrand is equal to (x*sin2x)/2

so you can take the half to the outside of the integral

so you are just integrating x*sin2x

[crimson sedge]

1/2 on the outside

of integral

[dark yarrow]

yee

[crimson sedge]

i did the work

just needa check my answer

• (pi / 4)

never hurts to double check ya know?

[dark yarrow]

true true

[crimson sedge]

u know how to put this in wolfram alpha?

or double check this baddie?

[dark yarrow]

I'll try one sec

[crimson sedge]

ahh kk thanks

if u get same answer

good enough for me

[dark yarrow]

well If I had paper I'd try do it myself but I'll use Wolfram alpha

[crimson sedge]

kk

[dark yarrow]

here you go

[crimson sedge]

ahhh

i got it right

good sign

great things comin

thank u

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[fickle thicket]

hi, i need help
The graph shows a polynomial function of the third degree. Write the polynomial on the form ax ^3 + bx ^2 + cx + d .

[marble bone]

Ok then?

[stiff zenith]

oh

[stiff zenith]

like gettings the polynomials formula ig

[fickle thicket]

I solved it. But the answer in the book is 2x^3 -2x^2 -4x

I don't understand why?

[marble bone]

How did I got the result?

[fickle thicket]

?

[marble bone]

Like how did u got ur answer

The method and stuff

I can't understand the picture much other than the part where u used distributive property

[fickle thicket]

It's from the graph

[marble bone]

U said u solved it

So

Umm where is your answer

[fickle thicket]

.

[marble bone]

Which u found wrong

[fickle thicket]

Not wrong. The answer is dubbeled. Look at the picture a sent

[fickle thicket]

This

[marble bone]

I did but I am unable to understand the steps before u applied distributive property

Like the things written

I can't read it

[fickle thicket]

Ok we see in the graph. That we have -1, 0, 2 as solutions to the equation . So I wrote it in factorized form

X(X+1)(X-2)

The I multiplied them all together and got an answer

[modern sparrow]

but it could also be a stretch in the y-direction

so i could have 2x(x+1)(x-2) or 3x(x+1)(x-2) and that would have the same roots too

@fickle thicket you will need to find the turning points as well and use those to check

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[cedar kiln]

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[livid shadow]

.closed

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[cedar kiln]

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[livid crystal]

help please

[cosmic steppe]

Is this a test

[livid crystal]

actually its hw

[modern sparrow]

you can either do double product-rule, or expand (x+1)e^x and split fractions then use quotient rule, but the second method you'll need to factorise at the end so more time-consuming but easier to understand imo

[cedar kiln]

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[mint igloo]

How exactly does 1/cosx x cos^2x simplify to cosx? Or another way to put it, how does cos^2x/cosx = cosx? I feel like an idiot, but I need this explained step by step like I’m 5. Thank you!!!!

[modern sparrow]

erm, cos2x/cosx doesn't equal cosx

[mint igloo]

Hold on, let me take a picture I think I wrote it wrong

[modern sparrow]

that's not cos2x

that's (cosx)^2

[mint igloo]

Sorry

[modern sparrow]

no worries

so

do you know what x^2 divided by x =?

[mint igloo]

X

I see 😦

[modern sparrow]

yh

[mint igloo]

Yep, I think my brain is fried. Thank you very much :))

[modern sparrow]

[elfin hemlock]

(he wrote cos^2x which can only be read as what he sent a picture of)

[modern sparrow]

oh yeah fair, I read my brain just ignored the ^ for some reason

[cedar kiln]

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[crimson sedge]

I'm extremely behind in math and haven't been in a classroom for 8 months. I have absolutely no idea what any of this means. Can someone please give me a step by step explanation on what is going on in this problem?

[cerulean star]

Does the problem begin at the top of the left page or does it start in the form on the bottom of the left page?

[crimson sedge]

I think it starts on the right

[cerulean star]

Then just divide by 8 and use a calculator.

[crimson sedge]

Do I divide 8,262 by 8?

[cerulean star]

You divide the entire left and right side by 8 to isolate k

Division is not going to affect what is happening inside the logarithm

[twin scroll]

Problem is the right answer isn’t given, unless I’m being dumb, but I’m getting 0.039988

Oh wait

Nvm, it’s rounded to the nearest ten thousands

Do you know where the ln button is on your calculator

[crimson sedge]

I don't

I'm using the windows calculator right now

[twin scroll]

Ok, well if you have a graphing calculator chances are it’s 2 buttons above the on button

[crimson sedge]

Oh I found it

[twin scroll]

Yeah

[crimson sedge]

What do I do from the start to solve the problem

[twin scroll]

I’d advise to divide first to avoid error

The 8262 by 6000

[crimson sedge]

oh okay

I got 1.377

[twin scroll]

Yep

Then click the ln button

[crimson sedge]

I got this

[twin scroll]

And hit 2nd then (-), this will pull up the previous answer

Well that works too

[cerulean star]

I'm pretty sure this math problem was supposed to "start" at the top left and all but the last step was done for her

[twin scroll]

Yeah true, although it’s put together in a strange manner but I’ll do my best to explain the left hand side

[crimson sedge]

these two right

[twin scroll]

So on the left hand side we are given 8262 = 6000e^(k-8)

[twin scroll]

No it should be the one to the right of the decimal point

It should say ans in blue above the button

[crimson sedge]

This is how my calculator looks like

Should I buy a real one

[twin scroll]

Oh ok, well it depends if you plan on doing a lot of math in the future but that’s not necessary, it just gives you more precise answers

[twin scroll]

What you got however was correct

Do you think you can solve it from here?

You have

0.3199072197 = 8k

[crimson sedge]

I don't think I can sorry

[crimson sedge]

Do I divide both sides by 8?

[twin scroll]

Yep : )

[crimson sedge]

Which means it's k = 0.0400 right? :)

[twin scroll]

And that would get you your answer, remember it’s rounded to the nearest thousandths place

[crimson sedge]

Thank you so much that makes a lot more sense now!

[twin scroll]

Yeah no problem : )

[crimson sedge]

.close

[cedar kiln]

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[worldly vigil]

HOW?

[worldly vigil]

I know we have to use by parts but i still cant prove it

so can anybody completely break it down

[still barn]

Just do integration by parts on the second integral with dv = x

[cedar kiln]

@worldly vigil Has your question been resolved?

[worldly vigil]

can you please write and show me the steps pls pls....

[still barn]

It's a one step problem, you do that then simplify.

Which you would have immediately seen if you even tried

[worldly vigil]

oo now i see it

bruh

thnx

.close

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[worldly vigil]

.reopen

[cedar kiln]

✅

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[slow sparrow]

How would I do b). ?

[cedar kiln]

@slow sparrow Has your question been resolved?

[tight herald]

After the transformations, where is P

P' I should say

We saw a vertical compression, horizontal expansion, and a translation

See if you can find where P' is

Using your answer from A

[slow sparrow]

(5pi/4, 0)?

Wait no

I’m confused

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[crimson sedge]

Hey, could anyone help me solve this?

$$0.75 = {1/x}e^{-1000x}$$

[wraith dagger]

edders

[crimson sedge]

I cant figure out how to get rid of the natural log 😦

[dire geode]

Need the W Lambert function if you want all solutions

[crimson sedge]

I saw that when i tried to solve it with a online calculator, doesnt ring a bell

ill try that thanks!

.solved

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[honest stag]

Sir we could have used e^1000x expansion upto 3 terms since the value of expression is very small compared to the entire expansion and then divide it by x and equate it 3/4 and solve for x right?? Can we do it this way

[cedar kiln]

@honest stag Has your question been resolved?

[dire geode]

Sure? Nothing stopping you from getting an approximate solution

[honest stag]

Oh thank you

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[unkempt loom]

The fifth term of an arithmetic series is -5. The sum of the first 14 terms is 35. work out the 12th term

[unkempt loom]

hi

<@&286206848099549185>

[flint hazel]

help

[west dome]

Don't post in other people's channels

[west dome]

What work have you done

[cedar kiln]

@unkempt loom Has your question been resolved?

[cedar kiln]

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[nimble linden]

Help

[faint dirge]

[nimble linden]

This question

I have been thinking about it for an hour

[faint dirge]

are those red circles yours?

[nimble linden]

Yep

[faint dirge]

where did you get this from?

[nimble linden]

From my teacher

But she took it from a website

[faint dirge]

I'm afraid both that this is not my strong suit and regardless, I have no idea.

Somebody'll hopefully be along who knows how to help

[nimble linden]

Ooh ok thank you

[red crater]

what kind of math is this

[nimble linden]

Iq test

[red crater]

bruh ur asking for help on an IQ test?

[nimble linden]

Ye

[red crater]

IQ test is suppose to test ur intelligence

not somebody elses

[nimble linden]

Ik

But ot just a question from my teacher, not from a real test

[clear garnet]

3 5 4
5 4 3
4 3 ?

[red crater]

ahh i see

[clear garnet]

At least i think that's what this means lmao

[nimble linden]

Ye

[clear garnet]

That only elimantes like 1 tho

[nimble linden]

Yep

[faint dirge]

which is about where I gave up

[red crater]

is ur teacher going to give u the answer?

[nimble linden]

nope

she didnt even give a single hint

[red crater]

mine gave me this problem

you have to go over every bridge and go into each land area (the capital letters)

where you start is where you end

and you must cross each bridge only once

[nimble linden]

its impossible

all lands have odds number

of bridges

[red crater]

yEpp...

[nimble linden]

you need even number of bridges to enter and exit the land

[red crater]

yrah.. she gave us an impossible problem :/

[nimble linden]

i think no one gonna help me

.close

[cedar kiln]

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[balmy apex]

can the mantissa length be 0?

[kindred storm]

@balmy apex Is this about floating point numbers?

[balmy apex]

yes

[kindred storm]

If you only want to store a 1 as the mantissa, yes.

Then you'd only get powers of two or whatever base you use with the exponent.

[balmy apex]

so it's $m \in \mathbb{N}_0$?

[wraith dagger]

illuminator3

[kindred storm]

No, m ∈ { 1 }.

[balmy apex]

what

[kindred storm]

The mantissa would be 1.

[balmy apex]

m represents the mantissa length

[kindred storm]

Oh, I thought you meant the mantissa itself.

Yes, though 0 isn't very useful.

[balmy apex]

rip

this breaks my proof for something

well

ty

.close