help-0

[coral pagoda]

You're still talking about this problem right?

[rich basin]

yes

I was wondering why isn't my answer correct

And what operators do i require to obtain the right answer and for what reasons do i need to use that oeprator for

[coral pagoda]

Okay, well we know there are 8C4 different ways to seperate coats into two piles

You got that down good

Now we need to consider the total number of possobilities

[rich basin]

Like wouldn't that be 2^8 -2

[coral pagoda]

Our initial thought would be to just add 8C1+8C2+...+8C8, but there is one tiny problem: [ \binom{n}{k}=\binom{n}{n-k}.]

[ocean seal]

dackid (jump king +)

[rich basin]

The only problem here is that you can have duplicates

But that was when i thought of dividing 2^8 by 2

[coral pagoda]

So in regards to this problem, choosing to have 2 coats in the left pile and 6 coats in the right is the same as having 6 coats in the left pile and 2 in the right

[rich basin]

,w solve ((8 choose 4))/ (2^8/2 -2)

[ocean seal]

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[rich basin]

Which still isn't the right answer

Yeah choose 2 on the left is the same as choose 6 on the left

[coral pagoda]

Please be patient and let me explain

Okay, well dividing by 2 does seem like it would get you there, but there is a problem: there are exactly 9 different types of combinations if you have 8 items.
8C0,8C1,8C2,8C3,8C4,8C5,8C6,8C7,8C8.

So just dividing by two isn't going to give you 8C0 through 8C4 (which is what we want)

[rich basin]

yeah

I don't think 8C0 to counts, because that wouldn't really be dividing

[coral pagoda]

That all depends. Can we have 1 pile empty in this problem?

Also, 8C0 is 1, not 0

There are no division issues here

[rich basin]

,w solve (8 choose 4) divide ((2^8-2)*(4/7))

[ocean seal]

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[coral pagoda]

You done trying random stuff?

[rich basin]

Okay

[coral pagoda]

Thank you. Let us assume we can have an empty pile (that is still two piles).
So we end up with the following probability [ \frac{\binom{8}{4}}{\binom{8}{0}+\binom{8}{1}+\dots+\binom{8}{4}}.]

[ocean seal]

dackid (jump king +)

[coral pagoda]

And that will get you your result.

[rich basin]

let me try that

[coral pagoda]

If you can't have an empty pile, then just omit 8 choose 0

[rich basin]

,w solve (8 choose 4) divide ( + (8 choose 1) + (8 choose 2) + (8 choose 3) + (8 choose 4))

[ocean seal]

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[rich basin]

Was wondering why can't you use 2^8 -2 but then add like some constrains

[coral pagoda]

Well, this isn't 2^8-2 for one. Second off, why are you getting that in the first place?

I understand where you are getting 2^8 (which we have addressed has duplicates), but where you get -2 is beyond me.

[rich basin]

becasue 2^8 includes the casess such as 8 choose 0 and 8 choose 8)

,w solve (8 choose 0) + (8 choose 1) + (8 choose 2) +(8 choose 3) + (8 choose 4) + (8 choose 5) + (8 choose 6) + (8 choose 7) + (8 choose 8)

[coral pagoda]

Ah, okay. Well there are more duplicates than 2.

[rich basin]

,w solve 2^8

[ocean seal]

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[coral pagoda]

I know that the sum of the combinations is 2^{number of items)}

I am aware of this

But we have already addressed there are many duplicates in here, so this is clearly not right.

[rich basin]

Okay thanks

[coral pagoda]

Happy to help

[alpine sable]

Hey, doing this quick probem for my homework

I'm not quite sure how to find the coordinate points for this.

Would very much appreciate some guidance here

I know how to find the terminal angle but not the coordinates

[dark granite]

isn't that just the unit circle?

or am I reading that graph incorrectly?

[alpine sable]

No it is the unit circle but

it'

is not one of the points that's on the unit circle explicitly

the question is asking me to calculate the coordinates idk how to

[dark granite]

For starters, I'd use x^2+y^2=1

that'll give you coordinates *on * the edge of the unit circle.

but it's kind of unclear what coordinates you were asked to find

[alpine sable]

the coordinates at this reference angle

in radians btw

[dark granite]

oh

I get it now

give me a sec

so the coordinates is (cos(pi-2.7),sin(pi-2.7))

[alpine sable]

wait you can do that

wait youre right

holy shit im stupid

i forgot how to do thsi LOL

[dark granite]

we sure can!!

Note that those are coordinates on the unit circle

[alpine sable]

yea

[dark granite]

if your teacher was asking for points on the line, then there's more work to be done, but sounds like you got it from here

[alpine sable]

idk i was

looking online for how to do this i forgot that

yea.

thanks

[dark granite]

you're welcome!!

[somber osprey]

whats 1+1?

oh its 2

nvm

[ancient creek]

https://tenor.com/view/not-funny-didnt-laugh-gif-14688388

[zenith hemlock]

How do i continue?

I use
dy/dx=[ f(x+h)-f(x) ]/ h
Formula (first principle)

[karmic dew]

Someone pls help me understand z-scores

[neat mesa]

Sorry I wish I could but idk what that is

does anyone know how to solve this??

#3 and #4

[wanton turtle]

Rationalize the numerator

Multiply and divide by sqrt(x+h) + sqrt(x)

You'll be left with h in the numerator which cancels out with the h in the denominator

After which you can substitute 0 as the indeterminacy has been removed

[slow silo]

Mathematical induction

[dark granite]

do you want to prove this for all integers n>0?

[slow silo]

yea i did but i solved it

thanks anyways

[dark granite]

you're welcome

[thorn kindle]

49^n + 24^(n-1)

[dark granite]

yeah showing $25|49^n+24^{n-1}$ for all integers $n>0$ is equivalent to showing the statement @slow silo wanted to prove

[ocean seal]

logician_pdx

[cobalt ledge]

What about it are you having trouble understanding

[oblique goblet]

Whats an angle sector?

[gentle flame]

Can anyone help with how you’ll complete this with fractional powers 🤷‍♂️

[cobalt ledge]

By that you mean simplify?

[noble crypt]

try grouping the terms and then cancelling the powers

[cobalt ledge]

(27x^-2)^2/3 = 27x^-4/3 = 1 / 27x^4/3 no?

[noble crypt]

for example if you have $(25x^2)^\frac{1}{2}\implies(5^2x^2)^\frac{1}{2}$

[ocean seal]

わたし

[noble crypt]

then you can get $5^2$ and $x^2$ together and cancel the 1/2 power

[ocean seal]

わたし

[noble crypt]

so in the end you remain with 5x

[noble crypt]

let them try first don't give the answer directly

[cobalt ledge]

Eh fine

Not used to giving help yet lol

[noble crypt]

no problem

[hollow pelican]

guys how to do 3b?

is my working wrong?

[ionic jewel]

,w sqrt(3)sin(x)+2cos(x) = 1

[ocean seal]

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[ionic jewel]

the answer is a bit less than 2, so yes

[hollow pelican]

but i dont rly know which part of it is wrong

[rigid smelt]

a^2 != 3^2 to start with

[hollow pelican]

ans is still wrong tho

[shrewd otter]

The previous question hasn't been solved, this chat is occupied.

[quasi flame]

sorry

[rigid smelt]

no, you are going in the right direction

your answer is correct

tho, thats not the general solution to sin(phi + theta)=1/sqrt(7)

[hollow pelican]

this is the correct ans

i only got 1 of the ans right

[clear rampart]

In a packet of spaghetti, one-third of the strands of spaghetti are intact, but the rest have been snapped into two pieces. of all the pieces of spaghetti from the packet (broken and whole), what is the largest fraction guaranteed to be at least as long as half an unbroken strand?

can anyone help me?

[rigid smelt]

oh you are solving for theta in [0,2pi]

then you still need the general solution

to figure it out

[shrewd otter]

This chat is occupied, the previous question hasn't been solved.

[rigid smelt]

like i said tho, you are going in the right direction

[hollow pelican]

which general solution?

[clear rampart]

ok

[rigid smelt]

sin(x)=a for -1<=a<=1

do you know the general solution to this equation?

[shrewd otter]

Since x is in [0, 2pi>, why do we need a general solution?

[rigid smelt]

to figure out the solutions in the interval?

[shrewd otter]

Right, but there are finitely many, it seems kind of redundant.

[rigid smelt]

i mean you could also get two terminal angles and then add 2pi periods to it

either way is fine

[hollow pelican]

i am confuse

[shrewd otter]

We can probably use the fact that sin and cos are injective on this interval.

[latent tundra]

can know how to do this???

can i

[shrewd otter]

Calculate the surface area of everything but the slope and multiply by two.

[latent tundra]

do i need to calculate the slant height???

[rigid smelt]

that doesnt really work, either way you would still be adding 2pi to the solution you get to figure out the appropriate solution

[hollow pelican]

u mean to find the reference angle first?

[rigid smelt]

yes

well not exactly

but yes

a reference angle by which you can add the periods to, to get the solutions in the interval

its inevitable whatever way you do it

[hollow pelican]

but isnt my ref angle 0.3875

[rigid smelt]

no....

thats arcsin(1/sqrt(7))

[hollow pelican]

ohh thats not the working for ref angle?

[rigid smelt]

do you remember that sin(x) = a for -1<=a<=1 has two solutions?

[hollow pelican]

yea

[rigid smelt]

those two solutions are x=a and x=pi-a

this is me not referring to the general solution btw

for now just take them as your reference angle

also next time, dont approximate your answer till the very end

we'd like to have the least error in calculation

[hollow pelican]

ok

my 1st ans is still wrong

[rigid smelt]

you are still not getting my point

you are supposed to take the reference angle and add 2pi to them

until you exceed 2pi

the angles you get during the calculation that are in [0,2pi] are the accepted ones

[vale wigeon]

good question

what does this mysterious acronym stand for?

[dark granite]

I’m not sure

[vale wigeon]

[feral owl]

Anybody can solve this?

[coral cosmos]

Woah mate, atleast some of these lol

[feral owl]

send answers priv

[coral cosmos]

1st) substitute 3 in place of x , if you get 0 then that function is divisible by (x-3)

[shrewd otter]

Wait, hold on.

Why should we send the answers privately?

This is kinda sketchy.

[feral owl]

Send it here

[coral cosmos]

I can tell you how to do it, won't send the answer 🙂

You gotta try mate, otherwise you won't learn

[shrewd otter]

This isn't an exam, is it?

[coral cosmos]

Seems so

[hollow swan]

isnt this just a) x = 5 and b) x = 6

[vale wigeon]

yes

[hollow swan]

bruh

[coral cosmos]

He's having an exam lol

I prefer you to not help him now, not being mean or something... it's for his own benefit

[hollow swan]

most of the questions arent that hard

[coral cosmos]

Yep

[hollow swan]

my point wasnt to help him

it was to say

how tf do u not know the answers to those quesitons

i mean not judging

[coral cosmos]

Oh lmao, I get it now

[hollow swan]

but... grade 11

[coral cosmos]

Wait he isn't in grade 11

Is he?

[hollow swan]

i think that means grd 11 idk

[coral cosmos]

Hmm but on the contradiction the questions are too easy

I am in grade 11 myself

and I used to get these questions in exams when I was in grade 8th 😅

[hollow swan]

i j finished grade 9 and ik more than half of these

[dry thunder]

yep

[upper notch]

Can someone explain me derivatives of function in easy language?

[vale wigeon]

how familiar are you with basic physics?

[shrewd otter]

Derivative at a point or the derivative in general?

The derivative at a point (x, f(x)) is the rate of change of the function f at that point.

Big number => function grows quickly.

Small number => function grows slowly.

Big negative number => function falls quickly

Small negative number => function falls slowly.

Zero => function does not change.

[woeful pulsar]

the derivative is basically the best linear map that approximates the function input around x mapping to the output around f(x)

[shrewd otter]

I believe OP asked for a description in easy language.

[woeful pulsar]

well this is pretty easy considering the context in multivariable calculus

the op didn't mention if the function is a single variable function

[plucky crow]

i can teach you how to complete these questions (long division), however i do not see what gain anyone gets if i do them for you

if you wanna learn yourself what youll need to know is: factor theorem, remainder theorem, polynomial long division

[wanton spoke]

are a and b parallel? what proofs can I input to justify my answer?

[feral pier]

Yes they are both 180 degrees

[wanton spoke]

is there, like, a proof for that? a theorem perhaps?

[feral pier]

I forget what the angle is called

[wanton spoke]

these proofs are the only ones that are given to us

and I don't see anything that fits

[feral pier]

We know it's 180-69 so it it 111

[wanton spoke]

but that doesn't prove anything, does it?

[feral pier]

It's basically the Converse Of The Alternate Angles Theorem

[wanton spoke]

alternate what

exterior?

[feral pier]

Interior

[wanton spoke]

what the

no it isn't.

[feral pier]

Both would work right

You have four interior and exterior angles

[wanton spoke]

but for it to be "alternate interior", both angles should not be adjacent, right?

and they're not even.. interior angles.

do you really know the topic

[feral pier]

Ok

I was wrong about the interior bit

But they are parrrrl

If the angles remain the same

The lines will

[wanton spoke]

wdym remains the same

[feral pier]

Since we have the line intersecting the alternate angles then we know the angles are the same

[wanton spoke]

yo not to be rude but

the things you're saying,, doesn't make sense

i mean, it's good that you're helping me but

don't just answer to questions that you don't really know

some kid might believe you immediately without asking for any reasons lol

and that could result to confusions

[wanton spoke]

<@&286206848099549185> can someone help me w this

i'll just post the image again so u don't have to scroll up.... someone answered and just made me confused lol

"are a and b parallel? what proofs can I input to justify my answer?"

[glass lichen]

Not sure how you can reason stuff about line b without assuming b is parallel, since FCZ patterns require them to be parallel

[wanton spoke]

hm

[wanton spoke]

i think we just need to prove that a is parallel to b and vice versa using these proofs. but since i don't see anything that fits, do you think it means that they're not parallel?

[glass lichen]

no they're clearly parallel.

[wanton spoke]

why do you think they're parallel?

i mean a might be 1 degree slanted towards right

like, the main task is to determine whether they're parallel or not

and we didn't tackle about FCZ patterns so that might.. not be it

[glass lichen]

Im aware it is...

however like I said, FCZ stuff requires they be parallel

[wanton spoke]

is it, like, the only way to prove that they're parallel? the FCZ stuff?

[glass lichen]

Not sure, I only know FCZ patterns for angle congruence

[wanton spoke]

hm

oh wait.

this satisfies one of the proofs now

i used the vertical angle and alternate interior theorems

what do you think

since the two lines are intersected by a transversal, and the alternate interior angles are congruent, then they are parallel?? bc of Converse fo the Alternate Interior Angle Theorem??

not sure lol idk what im doing

[glass lichen]

no clue what alternate interior angles are

but yes, those agree with FCZ

[shrewd otter]

How do you know this is true without assuming the lines are parallel?

[wanton spoke]

oop- wait... that's true..

hm

[glass lichen]

Yeah, you cant deduce anything about b's relation to a from only knowing stuff about a

[wanton spoke]

dlkfjdal it's an error maybe, i'll ask my teacher tom... im tired wanna sleep :()

[shrewd otter]

That sounds like a good idea.

[neat mesa]

Yeah I got the same thing

[agile compass]

express x in terms of p, given the fact that p = ln(x), do the same for y

[quaint trout]

Need to keep applying log rules

Specifically there is one about products and one about powers

Apply the product one first, then the power one

What is I?

Please send a picture of your steps

It looks like you are assuming it's equal to 0. This is an expression you are simplifying. Not an equation.

[upper notch]

I understood it thank you.

[shrewd otter]

ln(1) is not 1.

[quaint trout]

ln(1) - 13ln(x) - 16ln(y). Very good. But, where does the equals sign come from??

Okay

And you can simplify ln(1)

Then you are done

[neat merlin]

What is your favorite geometry channel on YouTube?

[tame elm]

i tried looking at the answer but i dont understand it, can someone help?

[woeful pulsar]

the assumption here is that a and b are vectors in general, which means they can potentially be non-parallel

[tame elm]

oh, okay(?

cause i tried solving by the rule of, if they are multiples of the same vector then i could find k but, uh, didnt work-

[vale wigeon]

can you show the answer you looked at & point out the part you had trouble understanding?

[tame elm]

i dont understand where the 5/8 comes from

[vale wigeon]

it's to make the a components match up

[coral cosmos]

5/8 = k/2

[vale wigeon]

one of the vectors is a scalar multiple of the other

@coral cosmos this does not answer linglingbee's question

[coral cosmos]

oh

[tame elm]

so it would be 5a + kb = 5a + 2b?

[vale wigeon]

no

[coral cosmos]

Ok yes, two vectors are parallel means the vector 2 is some multiple of vector 1
so a1 + b1 = x(a1 + b1)
= xa1 + xb1

If you match components then
a / xa1 = b / xb1 = 1/x comes out to be constant

[vale wigeon]

if you scale a vector by 5/8 you scale the whole vector by 5/8, not just one component

[smoky relic]

8.795 - 2.485 : 35 = 8.724
Because We divide it first
Is that true?

[smoky relic]

Sorry, Is that okay if I'm asking my question like this?

[coral cosmos]

also I think what Ann was saying that
8a is some multiple of 5a
you need to find the multiple {which in this case is 5/8} and then multiply it with 2

[coral cosmos]

yep

[tame elm]

oh i see

thanks!

[smoky relic]

Thank you

[coral cosmos]

No prob : )

[coral cosmos]

No prob : )

[smoky relic]

I have 5 1/2 🍎 and 6 3/4 🍏
After few days 1/7 from both apple had Rotten
It's mean
5 1/2 + 6 3/4 - 1/7
Or ➗ 1/7?

[vale wigeon]

what do you want to find? how many apples have rotted, or how many apples didn't rot?

[smoky relic]

Ohh
Sorry,How many Apples didn't rot?

[vale wigeon]

then that'll be $\frac{6}{7} \times \left( 5 \frac{1}{2} + 6 \frac{3}{4} \right)$.

[ocean seal]

Ann

[smoky relic]

Wait
I Will write my answer

[vale wigeon]

...is english not your native language, by the way? you sound like you're struggling.

[smoky relic]

Yes, sorry 🙏😂

[vale wigeon]

i know it's unlikely but it may be worth trying anyway: what is your native language?

(if you don't want to answer, you don't have to)

[smoky relic]

Indonesia

[vale wigeon]

okay nevermind

[smoky relic]

I want to fall in love with math and try to do some elementary school question and i have forgot a lot.
Then want to ask someone to ensure my answers

[vale wigeon]

you want someone to check your answers?

[smoky relic]

Yes

[vale wigeon]

okay, post the problems and your answers here and people can check them

if possible, you could upload a picture

[smoky relic]

Is that okay?
thank you sm

[vale wigeon]

yes, that's how this server works

you post a problem, you show what you've done so far, and people check it to see if you made any mistakes, and point you in the right direction or highlight your mistakes (as appropriate)

[smoky relic]

Awesome

[covert berry]

$$f: \real \to \real$$
f is a continuous function. Find functions f such that:
$$f(xy) + f(x + y) = f(xy + x) + f(y)$$

[woeful pulsar]

what substitutions have you tried

[ocean seal]

Qun

Qun

[woeful pulsar]

substituting y with 1 might be useful for calculating f on integers

can you perhaps find enough relations to calculate f on integers?

like spam lots of small numbers to see if you can force a system of equations

[covert berry]

But how will it help me on reals?

[woeful pulsar]

if you can solve it on integers, you may be able to extend it to rationals

[strong furnace]

displace to get f(x+y)-f(y)=f(x+xy)-f(xy) this should help probabl

you can get a differential from here ()

[covert berry]

My fundamentals are really weak, sorry. My teacher is really bad at explaining. Everyone except a few gifted people could understand it.

[woeful pulsar]

if you set x to be a large integer while y to be a+k/x you might be able to do something to lift integers to rationals

[covert berry]

;-;

[woeful pulsar]

though it's not symmetric hmm
so you might want to swap x and y and see what you get

left hand side is symmetric but right isn't

[strong furnace]

to expand on this if you take y to be the derivative variable which tends to 0 you get a differential equation
lim h-> 0 (f(x+h)-f(h))/h=x(f(x+xh)-f(xh))/hx
f'(x)=xf'(x)

[strong furnace]

is this about my differential form thing?

[woeful pulsar]

more like the original functional equation given

[alpine sable]

Why is part (c) not just the integral of x from 0 to 4?

[woeful pulsar]

integral of velocity only gives displacement, you need to integrate |v|

and it doesn't really make sense to integrate position

[alpine sable]

I'm integrating position though

Why not?

Is there a way to do this without computing $\int_0^2 x' - \int_2^4 x'$?

[ocean seal]

n/c

[jaunty crane]

It wants me to draw straight line

Any solution?

I dont understand it

[alpine sable]

For y>10?

[jaunty crane]

Yea one of them

Can u please show me

[alpine sable]

I can

For any value x, y will be anything greater than 10

[jaunty crane]

I dont understand can you please draw one of it for me

It says we need to draw straight line

[alpine sable]

Shaded region is what y cannot be

Anything above the line drawn is a good solution for y

[jaunty crane]

Owhhh OK thank you

[alpine sable]

So on the y axis is where you look

y values above 10

Shaded region is values below 10

[jaunty crane]

Oh I understand can

[alpine sable]

Makes sense? Do the next one and I will check for you

[jaunty crane]

The question ask about straight line

Should i just draw the straight line

And should I color the part below y

[alpine sable]

I dont know what convention you use

An altenative way can be this

The idea is to show the 10 is not included

But all values above are

However, I like the first way more. Because it shows that we can only look at the values above 10 regardless of x

[jaunty crane]

Oh I understand now thank you so much

[alpine sable]

Ultimately depends on what your professor says

Yeah no problem :)

[plucky crow]

counting from 19-30

youre actually counting 31-19 terms right

[alpine sable]

A jumbo jet needs to reach a speed of 360 km/h (􏰁 224 mi/h) on the runway for takeoff. Assuming a constant acceleration and a runway 1.8 km (􏰁 1.1 mi) long, what minimum accel- eration from rest is required?

Please check my working: The jet has at most 1.8/360 hours, so y'(1.8/360) = a_x * 1.8/360 = 360, and so a_x = 72000

But the correct answer is supposed to be 36000, where would I need to divide by 2?

I started with y''(t) = a_x, and so y'(t) = a_x t + y'(0), and y(t) = a_x t^2/2 + y'(0) t + y(0)

So It should be right, but I am getting 72k, not 36k

[dusk smelt]

ee

ew

[hazy dome]

I think you need to use physics to solve this problem

By using a kinematic equation

[alpine sable]

@hazy dome But that's what I am doing?

I have y''(t) = a_x, and then I integrate to get y'(t)

Since it is from rest, y'(0) = 0

So we are left with y'(t) = a_x t

[hazy dome]

Try using (final velocity)^2=(initial velocity)^2 +2ad

Idk where ur getting derivatives from

[alpine sable]

What about my working though?

[hazy dome]

But where did you get derivatives from?

[alpine sable]

What do you mean?

[hazy dome]

Your work above is just derivative stuff

But it won’t help in answering the question

[alpine sable]

How will it not? I am calculating the velocity at the last possible second

[hazy dome]

Hmm

Your method is confusing to me

Try kinematic equations and see what you get

[alpine sable]

Where did your formula come from

Can you show me how to derive it?

[hazy dome]

The physics reference table

[alpine sable]

lol

[hazy dome]

I don’t have the ability to prove it, it’s just a kinematic equation

[alpine sable]

We're supposed to derive the equations we need to use

Like I am doing above

[hazy dome]

Hmm

Well you kinda stated the elementary concepts of rectilinear motion above

But that won’t lead you anywhere

You said that the second derivative of the position function is acceleration, which is true, but doesn’t help because we aren’t given a position function

We have enough info to use a kinematic equation though

[alpine sable]

What do you mean?

Our position function is y = a_x t^2/2

[hazy dome]

Hmm

Can you please send a pic of the original problem?

I think that will clear things up

[neat mesa]

Hi, can someone please check my work??

[glass lichen]

channel in use.

[hazy dome]

Yea no you’re not given a position function

[alpine sable]

I built one..

[hazy dome]

Doesn’t work in this case because you lack the info

[alpine sable]

What info do I lack?

[hazy dome]

You need to use physics

[neat mesa]

??

[hazy dome]

Data points

[glass lichen]

the channel is in use, #❓how-to-get-help

[hazy dome]

Positions at certain times

[neat mesa]

Alright thank uuu

[alpine sable]

Like which?

It's at 0 at t = 0, and supposedly at 1.8 km at t = 1.8/360

[hazy dome]

Well you’re only given the length of the runway and the final velocity

You don’t even know how long it’s gonna take for the airplane to reach the end

[alpine sable]

Of course I do, it's 1.8/360

[hazy dome]

That’s not true

[alpine sable]

And why not?

[glass lichen]

$x=1800m \ v_i = 0 \ v_f = 100m/s \ a=?$

[ocean seal]

Mosh

[hazy dome]

Look to the above

You HAVE to use physics

There’s no other way

[alpine sable]

I am using physics lol.

[glass lichen]

so what kinematics equation are you using?

[leaden lily]

Hey guys I have a function that goes from R ---> R
how can I draw a non motonic function ?

[alpine sable]

@glass lichen You agree with me that y''(t) = a_x, right?

[glass lichen]

sure

[alpine sable]

So y'(t) (acceleration) = a_x t + y'(0)

But y'(0) = 0 since it is from rest

So we're left with y'(t) = a_x t

[glass lichen]

ok but how do you find the time?

[hazy dome]

Use one of these

These are kinematic equations

[dusk smelt]

time is relative, so just write down any answer

[glass lichen]

it's not

[alpine sable]

@glass lichen Why not 1.8/360 hours?

[dusk smelt]

it is

[glass lichen]

it's not since the speeds are well below .1c before relativisitc correction is even needed

[hazy dome]

Because that’s distance divided by final velocity

[glass lichen]

anyway

[alpine sable]

Which is... time

[dusk smelt]

depends on the observer

[glass lichen]

ill be blunt, shut up if you dont plan on helping.

[dusk smelt]

no u

[hazy dome]

Ok so we have time... now what???

We now know how long it takes the plane to reach the end

[alpine sable]

So now we just solve y'(1.8/360) = 360

[hazy dome]

But we don’t even know y

[alpine sable]

Yes we do...

[hazy dome]

You can’t derive something you don’t even know

[alpine sable]

y'(t) = a_x t

What you're saying doesn't make sense

I start with acceleration and then I integrate to get velocity

I am deriving the velocity equation

[hazy dome]

Ok cool... but now what?

[glass lichen]

what n/c is correct, but it's not really using physics persay, just calculus

[alpine sable]

What do you mean now what???

It comes out to a_x = 72000

But the correct answer is 36000

I'm asking why

[hazy dome]

Yea but it feels like n/c is kinda restating what we already knew

[alpine sable]

@hazy dome You can't derive your formula

[hazy dome]

Using kinematics, I got 2.7777777

[alpine sable]

You have to be able to derive it

[glass lichen]

You can derive it

[hazy dome]

M/s^2

[alpine sable]

@glass lichen I meant he can't

Not that it can't be derived, in general

[glass lichen]

ok, who gives a shit if he cant

[hazy dome]

Bro I just finished my first physics course XD

Chill

[alpine sable]

Because we haven't learned how to derive it

[hazy dome]

I just know what they teach me

[alpine sable]

So I shouldn't be using something we haven't learned how to derive, just because I got it from Discord

[hazy dome]

Here let’s think about this logically: if the acceleration is 72000, do you know how fast the plane would be moving???

[alpine sable]

Yes, twice as fast as it should be.

[hazy dome]

Because acceleration is the rate of change of velocity

[alpine sable]

So that's what I am asking, where do I need to divide by 2?

[hazy dome]

We’re gonna assume that this acceleration is in m/s^2, that’s WAYYYYY too fast for any airplane

[dusk smelt]

guys, everything is relative, theres no wrong answer here

[alpine sable]

@hazy dome You're wrong.

[hazy dome]

Yes there is. Just stop

[hazy dome]

Write out your full work and send it in this chat

Via a pic

[alpine sable]

I already did, but I will do it again

[dire pilot]

would this be equal to 8f + 4g or do you not multiply the 2 by the 4 and 2

[hazy dome]

8f +4g is correct

[glass lichen]

it isnt

[alpine sable]

$y'' = a_x \implies y' = a_x t + y'(0)$, however we know that $y'(0) = 0$ as it is from rest. So then $y'(t) = a_x t$, and we wish that $y'(1.8/360) = 360$ as that is the final velocity and the most amount of time we have, so $y'(1.8/360) = a_x \cdot 1.8/360 = 360 \implies a_x = 72000$

[ocean seal]

n/c

[hazy dome]

Except it’s actually 4fg

[leaden lily]

depends if f is a function or just a variable

[dire pilot]

varibale

variable*

[leaden lily]

you multiply 4 by 2f and 2g by 2f

[alpine sable]

<@&286206848099549185> I wrote the original question like 20 minutes ago so I will ping now

[glass lichen]

where are you getting 1.8/360?

[alpine sable]

1.8 km/360 km/h

[glass lichen]

yeah but why are you doing that?

[alpine sable]

1.8 km is as far as we can go

[glass lichen]

yeah

[alpine sable]

Why wouldn't I do that?

[dire pilot]

are you sure tho because wouldnt you only multiply the number not the variable

[alpine sable]

We want the minimum acceleration

[glass lichen]

cause it's wrong

[leaden lily]

you multiply everything

[hazy dome]

I’m telling you you gotta use physics

[glass lichen]

it means the vehicle is travelling at 360 for the whole 1.8

[alpine sable]

Correct

[dire pilot]

bro

[hazy dome]

THATS IT

[leaden lily]

@dire pilot replace the variable by a random number like 2 and it might make it clearer for you if you have real numbers instead of letters

[dire pilot]

😭

[glass lichen]

@leaden lily @dire pilot the channel is in use, stop posting

[hazy dome]

That’s what I was forgetting

[dire pilot]

sorry

[hazy dome]

Ok @alpine sable so where you went wrong is by dividing 360 by 1.8. By doing that, you assume that the plane is traveling constantly at 360 km/h the whole time, but that’s not true at all. It’s accelerating, the speed is always increasing

[glass lichen]

IN USE

[hazy dome]

I appreciate your effort @alpine sable , but the only way to solve this problem is by physics

[alpine sable]

@alpine sable I got 2.78 m/s^2

[hazy dome]

Same

[alpine sable]

You are both getting 36k

In km/h^2

Okay, so what should I do?

[hazy dome]

Have you taken physics yet?

[alpine sable]

Yes, this is from the second chapter of a physics book

[hazy dome]

Perfect

So what you need to do is write down the givens and then consider the 3 kinematic equations

Only one of those equations will assist you in getting the correct answer

[alpine sable]

What 3 equations?

Position, acceleration and velocity?

[hazy dome]

No

[alpine sable]

Hello.

[hazy dome]

These 3

[alpine sable]

I don't know how to read those

[hazy dome]

I think your main issue is you’re staying centered on Calculus

Which is fine, but it won’t always help

[alpine sable]

I've decided to create my own mathematical theory or mathematical model which will describe geometrical objects and nature. Is there anyone who'd be interested in this?

[hazy dome]

Ok here are the variables: vf is final velocity, vi is initial velocity, a is accel, d is distance, t is time

Also deal with SI units only, so that means meters, seconds, and meters per second

Otherwise you will get an incorrect answer

[alpine sable]

So v_f is just y'(t) = y'(0) + a_x t, like I was saying

And distance is simply y = y'(0)t + a_x t^2/2

Also like I was saying

[hazy dome]

Yea, but don’t think about it through a Calculus lense

[alpine sable]

You're not making any sense

Where do you think they come from?

[hazy dome]

No you’re right, but I think you’re attempting to apply TOO MUCH Calculus to this problem. Just think about substitution

[alpine sable]

Anyway, the last equation we have not derived yet

[hazy dome]

Yes these problems are derived from Calculus but they need to be used algebraically

[alpine sable]

So we can't use it

[hazy dome]

You derive it from the first 2

Via direct substitution

[smoky relic]

Excuse me,
3 × 14/4
Am I could multiply immediately or Should i simplify it first ?

[hazy dome]

Simplify 14/4 then go from there

It makes the multiplication easier

[alpine sable]

So what you're saying is I could've used calculus this whole time

All I needed to do was solve for t

You saying not to use Calculus was entirely wrong...

[hazy dome]

I’m saying to use physics equations derived from Calculus

Also to be a little more open-minded

[alpine sable]

What you are saying does not make sense

I was using the physics equations derived from calculus

[hazy dome]

Physics and Calculus overlap but there are problems that lie exclusively in their own fields

[alpine sable]

I was deriving them in front of you

[hazy dome]

I’m not saying that’s wrong

[alpine sable]

That. Does. Not. Make. Sense.

I was deriving the acceleration, position and velocity equations

[hazy dome]

Look, why are we even arguing about this?

[alpine sable]

They cannot be different

[hazy dome]

What about you spend some more time in your physics class until you get to kinematics

So that you can learn it from an actual qualified individual instead of some stranger in Discord

[alpine sable]

I am reading about that, but we need to derive every equation we use

Instead of using a "physics reference table"

Like you told me to

[hazy dome]

I encourage you to wait and learn for yourself

Wait for a professional to introduce these topics

[alpine sable]

lol

We've been going over kinematics

But like I've said 20 times now, we can't use random formulas without showing their complete derivation

[hazy dome]

Look, the 3rd one is derived from the first 2, which we’ve already proven to be true

Try it out via direct substitution

[smoky relic]

Wrong ask

[alpine sable]

I know?

My point is you kept saying not to use Calculus

Even though I solved the problem without any reference tables

[hazy dome]

But your solution was incorrect

[alpine sable]

The problem was I didn't realize I was assuming the velocity to be a constant 360 km/h

[hazy dome]

Because you assumed the speed was constant

[alpine sable]

Right, but that has nothing to do with calculus

Nor does it have anything to do with deriving formulas using calculus

Which is what you were arguing against doing

[hazy dome]

<@&286206848099549185> umm a little help please...

[alpine sable]

Anyway, it's simple to solve now: y'(t)/y''(t) = t, and so 1.8 = y'(t)^2/y''(t) * 1/2 implies y''(t) = 360^2/3.6 = 36000

km/h^2

[lavish cypress]

[alpine sable]

Notice how I didn't assume a single formula

I derived them all myself

This dude confusing

[lavish cypress]

You did assume a formula

[alpine sable]

Which?

[lavish cypress]

That v = d/dt x

[alpine sable]

No, that's how we're taught. If we define y(t) to be the position at time t

Then y'(t), is, by definition, the change in position at time t

[alpine sable]

How do I apply for tutor in homework help server

[lavish cypress]

What

Why are you asking about another server in this one

[alpine sable]

good question

[alpine sable]

Check dms

[hazy dome]

Oh dear

That looks painful

[floral jungle]

yeahh ;-;

[smoky relic]

It's could use for all numbers in fraction?

I mean, the answer will still same?

[hazy dome]

Yea

Because it’s just multiplication and division

They’re interchangeable in terms of order

[smoky relic]

Great,
Thank you!

[hazy dome]

You’re welcome!

[still steeple]

I finished everything in the practice test but i'm not sure what they are asking me to do in 1. b)

[hazy dome]

Basically substitute k into f(x) then do a little algebra

[still steeple]

what does it mean like -2f(k)

so is it -2(k^2-2k-9) = 2?

[cobalt ledge]

Write f as a function of k instead of x, and multiply the entire function by -2, then set it equal to 2

Yes

[still steeple]

oh ok

thank u

[cobalt ledge]

Np

[alpine sable]

How is the domain of this graph [0, inf)? what about at x = 3?

[marble comet]

it's bc it drops down

jump discontinuity

but u can see that at (3, 2) it has an open hole

but at (3, .5) it has a closed hole

indicating that the function drops from 3, 2 to 3, .5

so technically 3 is part of the domain

closed circle indicates it includes that point

and open circle means it doesn't

[ancient creek]

yeah g(x) is still defined at x = 3

[gusty hinge]

can anyone tell me how to proceed with this type question, I am new to probability

[vale wigeon]

@gusty hinge is this your first intro to formal probability theory, with formal arguments involving measures and all that fun stuff? or is this your first introduction to probability in general?

or to put this another way, have you taken any basic probability classes such as those which would have you compute probabilities for dice or card games?

[gusty hinge]

I know just very basic probabilty

[lavish cypress]

Interestingly enough I've seen this question like 3 times in the past couple of days

[gusty hinge]

how we take example for p(Aintersectionb)=p(A).p(B)

[vale wigeon]

that's only true when A and B are independent...

[gusty hinge]

how to take such example

wouldn't it be just hint and try

[vale wigeon]

well you can start by drawing some pictures

both parts 1 and 2 have many different possible answers

so you can try making pictures to represent the sets you're choosing for your events

[alpine sable]

A world’s land speed record was set by Colonel John P. Stapp when, on March 19, 1954, he rode a rocket-propelled sled that moved down a track at 1020 km/h. He and the sled were brought to a stop in 1.4 s; see Fig. 2-28. What acceleration did he experience? Express your answer in terms of g (􏰁 9.8 m/s2), the acceleration due to gravity. (Note that his body acts as an accelerometer, not a speedometer.)

How do I find the acceleration he experienced?

I found that -202 m/s^2 is the acceleration of the sled (I think)

But how do I find his acceleration?

[ionic jewel]

he's literally riding the sled

so it's the same

[alpine sable]

But what does it mean to express in terms of g?

[ionic jewel]

g = 9.8m/s^2

2g = 2(9.8m/s^2)

divide your answer by 9.8 and slap a g on the end

[alpine sable]

oh Hahahahahahaha

[ionic jewel]

,calc 202/9.8

[ocean seal]

Result:

20.612244897959

[alpine sable]

Lmao, okay thanks

[ionic jewel]

about -20.6g

[vale ridge]

can anyone help me with this question. Its
2x+5y=7
x-3y=-2
I have to like solve for y and x so I can get a coordinate. Thanks guys.

[copper summit]

x=3y-2 @vale ridge

now put in the first equation as x

[neat mesa]

Can someone help me w this?

Number 14

[copper summit]

,rotate

[copper summit]

trigo

[neat mesa]

??

[small galleon]

what is 9+10

[sleek elbow]

21

[small galleon]

https://tenor.com/view/akash-chhabria-evil-akash-akash-megamind-smile-hands-gif-17703505

[neat mesa]

<@&286206848099549185>

[queen wigeon]

use the fact that if the base angles of a triangle are congruent, then it is an isoceles triangle

[neat mesa]

Alright thank you, but I have to find the x value and when I equal them to each other the answer isn’t right

[queen wigeon]

what value of x are you getting?

[neat mesa]

4.6

[queen wigeon]

RS = RT, so 9x - 13 = 4x + 2, use that to solve for x

[neat mesa]

Alright thank you sooo much!!

[queen wigeon]

np

[trail hamlet]

hello im trying to understand how to check if a specific matrix is in the span of other matrices

i have those 3 and im trying to see if the bottom M_1 is in the span of the other 3

i found a video that explained it slightly, i put the vectors side by side and did guassian elimination

im just trying to understand if this is what im supposed to do?

[royal fulcrum]

What does it mean to be in the span?

[mossy geyser]

for M_1 to be in the span it should be expressible as a linear combination of A, B, and C

so for each entry of M1 you have a three variable equation

three variables four equations

[glass lichen]

they got help already...

[whole prairie]

Can you simplify 2xy + 2 = 6y dy/dx -2x dy/dx?

[mossy geyser]

bruh how am i supposed to know

[sudden crater]

I’m not sure what you mean, but if you want to find dy/dx just factor out the RHS and then divide

[brisk tree]

Can someone help?

[whole prairie]

RHS?

[sudden crater]

Right hand side

[whole prairie]

Gotcha

So how would I factor it out? Just divide by those two terms?

[sudden crater]

6ydy/dx -2xdy/dx=

dy/dx (6y-2x)

then now that you have it factored just divide by 6y-2x on both sides to get dy/dx isolated

[whole prairie]

So it would then be:dy/dx = 2xy+2/6y-2x?

[lavish cypress]

Try applying ibp as well as the integral of the inverse theorem.

[sudden crater]

Does anyone know how to do 12?

[thorn kindle]

discriminant of a quartic

[vale sapphire]

... how about no?

i mean

i guess it's the only way, but if it really is that that's bullshit

[lavish cypress]

I guess you can also do it using calculus

Find the local maxima and minima, and then set k appropriately

[brisk tree]

For using Integral of inverse theorem I need to know the antiderivative of f

[sudden crater]

Idk if that’s allowed because this problem came under the factor theorem/remainder theorem chapter

[thorn kindle]

or do polynomial division

[sudden crater]

But anyway after finding the local extrema what would have to be done?

[sudden crater]

how would it work in this case

[random pelican]

what is 2 times x, is it 3x or 2x?

[sudden crater]

5x

[random pelican]

what?

[thorn kindle]

2*x = 2x

[random pelican]

ok, ty

[thorn kindle]

why would it be 3x lmao

[sudden crater]

it’s very likely they’re trolling

[random pelican]

because im stuck in a problem and im breaking my head to see what am doing wrong

[thorn kindle]

go to a different channel i can help you in a bit

[random pelican]

ok

[thorn kindle]

ohh i see. make sure that the maxima are greater than 0 and the minima are less than 0

[lavish cypress]

Finding k such that the values at the local extrema alternate from negative to positive to negative

[thorn kindle]

yes

[warped phoenix]

$\frac{2x^2}{\sqrt[4]{5}}$

[ocean seal]

TheMane3

[warped phoenix]

can someone help me figure out how I would get the radical out of the denominator?

[thorn kindle]

12x^3 + 12x^2 - 24x = 0

[thorn kindle]

the nth root of z is z^(1/n)

[sudden crater]

x(12x^2+12x-24)= 0

x=0, 1, -2

what to do then?

actually

then I should just find the maxima/minima

[thorn kindle]

yes

[arctic wren]

Which one is the correct derivative?

[sudden crater]

-5 is a minimum, 0 is a maximum,

-32 is also a minimum

@thorn kindle what would I do now?

[lavish cypress]

Then you need 2 negative minimums and one positive maximum, which gives you -5 < k < 0.

[warped phoenix]

@thorn kindle i was told to do something like this: $\frac{2x^2}{\sqrt[4]{5}}\cdot \frac{\sqrt[4]{5^3}}{\sqrt[4]{5^3}}$

[ocean seal]

TheMane3

[warped phoenix]

im not sure why...or how that would work\

because if i cross cancel all it does is leave me with had i originally had, except the 5 is cubed

<@&286206848099549185>

?

[undone dock]

4throot(5) times 4throot(5)^3 = 4throot(5)^4

[slow monolith]

is thi lane open

[alpine sable]

asking a question rn lol

[thorn kindle]

you got your signs mixed up

0<k<5

[rocky silo]

Hey, a quick question. What if the end of pi were to be found. Would it be rational and would it change any complex operation, afaik people just use it up to the 20th digit.

[nocturne mirage]

it has been proven that pi is irrational

so you cant find any last non zero digit of pi

it's litteraly impossible

[lavish cypress]

When doing numerical computations, perhaps people use 20 digits or so. However, when people use it within math, they usually use the exact value.

[warped phoenix]

@nocturne mirage i mean regardless hes asking what if

in some alternate universe where it could be found, would it have any impacts like he asked

[rocky silo]

Exact, as in?

[elfin snow]

exact value means without decimals

it has stuff like pi and square roots and other constants

[lavish cypress]

The exact value of pi, as a real number.

[elfin snow]

essentially, no approximations/rounding

3.14 is an approximation of pi but π is the exact value

0.142857... is an approx for 1/7 but 1/7 is the exact value

[rocky silo]

Ah I see

Thanks

[warped phoenix]

Can someone explain to me how $x^{\frac{1}{5}}y^{\frac{1}{5}}=\sqrt[5]{xy}$

[ocean seal]

TheMane3

[winter bay]

What part don't you get?

@warped phoenix

[warped phoenix]

ik that $x^{\frac{1}{5}}=\sqrt[5]{x}$

[ocean seal]

TheMane3

[warped phoenix]

but does the y in there not change anything?

like wouldnt the y also make it $\sqrt[25]{xy}$

[ocean seal]

TheMane3

dackid (jump king +)

[warped phoenix]

ohhhhhhhh

i see

[ocean seal]

dackid (jump king +)

[warped phoenix]

ahhhh

🤦‍♂️

[coral pagoda]

Happens to the best of us :)

[winter bay]

@warped phoenix it's kind of like how $n(x+y) = nx + ny$

[ocean seal]

visual of Petter's ascendance

[warped phoenix]

riiiiiiiiight

i see now

yikes

i need to memorize these rules better

[coral pagoda]

I don't think this particular exponent rule is one of the typical ones you see when doing exponent laws.

So don't beat yourself up too much

[warped phoenix]

ah ok ty ❤️

[lofty terrace]

How do I get started solving either the vector $\bar{a}$ or $\bar{b}$ from the equation $\bar{a}\cdot\bar{b}=|\bar{a}||\bar{b}|cos\theta$? I know both sides are equivalent as that's just a dot product, but if I only treat $\theta$ as the variable and solve for b, I'd expect two answers, but I can't get either of the vectors out of the dot product 😕

[ocean seal]

jetp250

[lofty terrace]

Oops, that's small text

[glass lichen]

so you want to reconstruct a and b given the dot product?

[lofty terrace]

I have either a or b and want the other vector given the angle, the lengths of both vectors and the other vector

[glass lichen]

Ok so you can get a generic b vector using the other definition of dot product

then scale it up to be the correct length

since any vector on span(b) will give the same dot w/ a, you just need the one with correct norm

actually I think you can only know a plane of vectors, then get a circle as a subset of said plane

$b=\begin{bmatrix}x\y\z \end{bmatrix}\implies a\cdot b = a_xx+a_yy+a_zz$

[ocean seal]

Mosh

[glass lichen]

or whatever co-ordinate space you're working in

[plucky crow]

,w

bruh

,w solve

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Syphax#3869

[glass lichen]

you can use the website you know...

instead of spamming a help channel

[lofty terrace]

I'm doing this in 2D to keep it simple, but my initial attempt was to break down the vector into its components and solve for each dimension separately

[glass lichen]

ok so yeah, $a\cdot b=a_xx+a_yy$

[ocean seal]

Mosh

[lofty terrace]

that is an inadequate explanation, but I don't see why I have to re-scale it, and I'm not getting two results so it's probably not right to begin with

[glass lichen]

$a_xx+a_yy=\norm{a}\norm{b}\cos(t)$ is a linear equation, so you can get a vector whose span is the line

[ocean seal]

Mosh

[lofty terrace]

Seems like having actual linear algebra classes could be handy, I'm not even familiar with spans 😅 Maybe I'll do some Googling on that and it seems like I could be able to solve it

[glass lichen]

span of a vector is the set of scalar multiples

[lofty terrace]

The equation is not hugely complex anyways and now that's a scalar form already

[glass lichen]

span of a set of vectors is the set of linear combinations of the vectors

[lofty terrace]

Yeah I'm hitting a total wall with terminology. It's better I look up all the terms and try again

[plucky crow]

can i post?

[lofty terrace]

Fine by me

[plucky crow]

,w solve (1/2)(n)(n+1)(n^2+n+1)=(100)(1/6)(n)(n+1)(2n+1)-(1/2)(n)(n+1)

[ocean seal]

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Requested by Syphax#3869

[plucky crow]

why cant i cancel the factor of (1/2)(n)(n+1)

so im left with just a quadratic

if i do that then i get the bottom two solutions but not the top two

i was just wondering why i cant cancel the common factor

(as in divide both sides by it)

[oak chasm]

@plucky crow You can, but if you divide by something, going on past that assumes that what you divided by wasn't zero.

[plucky crow]

oh

[oak chasm]

So, you can divide by n and n + 1, but then you have three cases:

• The case where those are divided out.
• The case where n = 0.
• The case where n + 1 = 0.

[plucky crow]

so do i sub n = 0 and n = -1

to find other solutions

[oak chasm]

No.

They're different, completely separate cases.

[plucky crow]

oh

[oak chasm]

You handle all three cases separately.

You find all the solutions.

You check whether each one makes the original equation true.

Just because you divide by something doesn't necessarily make what you divided by equal to zero a solution to the original equation.

That's why you have to check each solution.

[plucky crow]

im a bit confused

so what do i do with the information that n=0 or n+1 = 0

to find a solution

[oak chasm]

You solve those equations for n as well.

[plucky crow]

what does check mean

[oak chasm]

Then you check them in the original equation.

[plucky crow]

oh so i sub n=0 in the originak

[oak chasm]

Yes.

[plucky crow]

and n=-1

[oak chasm]

See if both sides end up equal.

Also the two with radicals.

[plucky crow]

well 0 it is yes

yeahhh i think it may be easier instead of plugging the radicals into that massive eq

to just

not divide by those things

lol

[oak chasm]

Then you have to find the roots of a quartic.

[plucky crow]

yep ill just factor

lol

ty for the help anyway

[oak chasm]

You should be checking your solutions anyway.

No problem.

[wanton spoke]

yeah. but then again, how can we know that this is true without assuming that the liens are parallel right

[pulsar fractal]

if the first derivative of a function is abs(x), would 0 be considered a minimum

[glass lichen]

no because the derivative would never change sign

[pulsar fractal]

wait doesn't the slope change from -1 to 1

[glass lichen]

you said the derivative is |x|

[pulsar fractal]

yea

[glass lichen]

|x|>=0 for all x in R

since we use abs value to denote distance

[pulsar fractal]

oh i see

does a "sharp turn" on a derivative mean anything

[glass lichen]

it means the 2nd derivative isnt defined there if it's a corner

[pulsar fractal]

ok that makes sense

thank you

[sleek elbow]

you need to bring all the w's to one side @worldly coyote

[slender thorn]

6w-2w=-16-36
4w = -51
w= -51/4 = -12.75

[surreal merlin]

why do people still have school

[arctic wren]

My book asks me to take the first 5 derivatives of f(x) = x²e^x and then find a formula for the derivative of number N of the above function. Here is my demo, is it correct?

[hazy dome]

Looks good to me

Nice job

[alpine sable]

help please???

[hazy dome]

Assign a variable to represent the number

[arctic wren]

A number X that divided by X+6 = 10/11, X/(X+6)= 10/11 -> 11x= 10x+60-> x=60

[hazy dome]

Then go from there

[arctic wren]

When you read try to write the equation as you are reading

[alpine sable]

okay thanks

[warped phoenix]

$y=\sqrt[3]{x-1}+7$

[ocean seal]

TheMane3

[warped phoenix]

The domain would be all real numbers greater than 0, and the range is all real numbers

for the above function

right?

[arctic wren]

No, all real numbers

[alpine sable]

What is one property that cubes have that squares don't?

[warped phoenix]

ah....

right

LOL

[ocean seal]

TheMane3

TheMane3

[warped phoenix]

if we were to graph these two, they would never intersect, right?

[dusk smelt]

right

[flat tundra]

I'm not sure if I got it right

If one of the sides shown is head there are 3 possible cases
A) hh coin, it gives H
B) hh coin, it gives H
C) ht coin , it gives T

The probability of getting H is 2/3 = 66.66666...%. But I'm not familiar with calculating probabilities

This conceptually makes sense , but I might be wrong

[ionic jewel]

i vaguely think this is one of those ambiguous problems

nah nvm i just ran out of brainpower today

[flat tundra]

It's more about comprehending the text than math , so maybe this is not the right server to post it