help-10

[warm shale]

Ansh

[grave thistle]

nice

[raven spire]

nvm smh, it's probably something to do with GCD(1+x1 , 1-x1) = (1+x1, 2) = {1, 2}

[grave thistle]

yes yes

absolutely

[raven spire]

=.= you're mocking me

[grave thistle]

sry

im just so lost

omgoodnees

i think i might have found a way

[raven spire]

DID YOU SOLVE IT?

AAAAAAA

[grave thistle]

IDK

AAAAA

[raven spire]

TELL MEEEE

[grave thistle]

WAIT

I COULD JUST BE MISTAKEN

LEMME CHECK

i have no idea how to verify this

lemme try a smaller example with only x1 and x2

OMG

I THINK IT IS

[raven spire]

WHAT

[grave thistle]

for the smaller case at least

[raven spire]

P = 1?

[grave thistle]

AAAAAH

idk

[raven spire]

tell me already

[grave thistle]

if i reduce the problem down to (1+x1)(1+x2)=(1-x1)(1-x2)=x

i can prove that x1=-x2

[raven spire]

yes

ofc

obv

so? what next

[grave thistle]

oh no

NOOOO

damnit

i got to x1^2 = x2^2

aaaaaaa

buuut that still satisfies x1 = -x2

[raven spire]

You don't mean x1 = -x9, x2 = -x8, x3 = -x7, x4 = -x6?

and that'd imply x5 = 0?

or something like that?

[grave thistle]

yeah

maybe

aaaaaaa

oh dear

[raven spire]

,w solve (1+a)(1+b)(1+c)(1+d)(1+e) = (1-a)(1-b)(1-c)(1-d)(1-e) over integers

[warm shale]

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

Requested by Ansh#3502

[grave thistle]

AAAA

[raven spire]

,w solve (1+a)(1+b)(1+c) = (1-a)(1-b)(1-c) over integers

[warm shale]

Results provided by WolframAlpha

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

Requested by Ansh#3502

[grave thistle]

ohh woow

[raven spire]

bad choice... at least keep an odd number of variables

[grave thistle]

yeah

i was gonna

[raven spire]

(1+x1)(1+x2)(1+x3) = (1-x1)(1-x2)(1-x3) hmmm

[grave thistle]

hmmmm

[raven spire]

and prove x2 must be zero or smth

[grave thistle]

yeaaah

[stable rose]

first of all, x1, x2 and x3 can't all have the same sign........

[raven spire]

WAIT

[grave thistle]

IM WAITING

[raven spire]

YOUR QUESTION MAKES ABSOLUTELY NO SENSE

=_=

[grave thistle]

IDK

DID YOU FIND A COUNTEREXAMPLE

[raven spire]

x1 = 1, xn = -1 satisfies the question

and x =0

so P = 0

aaaaaaaa but then again it's a particular case ;-;

how to prove for geeeneral

[grave thistle]

aaaaaaaaaaaaa

[stable rose]

oof

[raven spire]

help 🥺

[grave thistle]

cant believe this was for 9th grade exam takers

t_t

[stable rose]

i'm trying......... i also don't know the answer

[raven spire]

they can just put in the values smh

[stable rose]

but you can see that all the x1, x2,.... can't all have the same sign

[raven spire]

since it's true for all integers that follow the equation

[stable rose]

e.g. if they were all positive, then the absolute value of the product of (1+x1) etc is strictly larger than the absolute value of the product of (1-x1) etc

so you can split up the x_i : some are positive, and some are negative..........

i'm trying to see if there's some argument which makes the number of positive ones equal to the number of negative ones

hmm, also the number of x_i which are negative has to be even

[grave thistle]

fine

im looking up the solution

[stable rose]

go for it xD

[raven spire]

I'm getting the polynomial vibes smh

[grave thistle]

ok

the ans was 0

heh

[stable rose]

actually, @grave thistle , in the case of two variables, how did you conclude that x1 = -x2 ?

[grave thistle]

oh

just

[raven spire]

obv 😂 aren't we trying to prove?

[grave thistle]

swap it out

or you could do some

[stable rose]

if you managed to do that, then you might be able to apply some kind of induction argument

[grave thistle]

algebra stuff

woah

i think the ans is abt induction

wait

oh i forgot we have the least rigorous maths around here

[stable rose]

lol it's okay

i'm not fond of rigor myself........

as long as it makes sense to me i'm good

[grave thistle]

they had split it into 2 cases

1st case is assume x1=x2=…=x9=0

gosh i love this country

[stable rose]

lol

right, easy case covered. Next case?

[grave thistle]

i have no idea

ooh

i get it

[stable rose]

oohh I get it!!

LOL

[grave thistle]

woah

were twins

[stable rose]

IKR

so with an odd number of x_i, if none of them are zero, then x^2 would be < 0

cool

[grave thistle]

t^t

[stable rose]

now I can relax xD

[grave thistle]

what a weird contradiction

.close

[obtuse pebble]

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[amber plaza]

If we have this, what is x/y equal to then?

[spiral maple]

unknown

[amber plaza]

There isn't a specific rule so I can express the sin x / sin y ?

[high lily]

nope

there isn't anything meaningful you can do with it

[amber plaza]

k, ty

[raven spire]

Oh I get it!

You were right about multiplying with conjugate smh, should've divided by x^2 instead of (conjugate)^2 = 1

[grave thistle]

🥲

[obtuse pebble]

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[obtuse pebble]

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[worthy glacier]

help

[worthy glacier]

can someone explain this to me

this is the answer

but i dont really know

[scarlet gale]

@worthy glacier When you see A = πr², each of the letters there is a variable. Variables are numbers we might not know just yet.

[worthy glacier]

this in the question

[scarlet gale]

So, A is the number that stands for the area the inside of the circle covers. r is the number that stands for the radius of the circle.

Does that make sense so far?

[worthy glacier]

yeah

i think so

[scarlet gale]

OK, so if we know the radius is 2, then we know that r is 2, since r is the number that's how big the radius is.

If r is 2, we can replace it with 2.

[worthy glacier]

so it would be

[scarlet gale]

Any time we know that a variable is equal to something else, we can replace it with that something else.

[worthy glacier]

π2²

[drifting flax]

$4\pi$

[scarlet gale]

A = πr²
A = π(2)²

[scarlet gale]

Exactly.

It's π times 2².

Which is 4π.

Does it make sense how we got there?

[worthy glacier]

what would π mean

[royal basin]

pi is pi

[drifting flax]

$\pi = 3.14......$

[scarlet gale]

π is a special number called pi, pronounced like the pie that you eat.

[worthy glacier]

alr

ok

[scarlet gale]

It starts off with 3.14 and goes on with a bunch more digits.

[balmy mortar]

its roughly 3.14

thats all u need to know for now probably

[scarlet gale]

So, it's about 4 times 3.14.

[worthy glacier]

i just figured it out

ty

thanks so much

[scarlet gale]

You're welcome.

No problem.

[worthy glacier]

wait

so @scarlet gale

would i just have to mulyiply 3.14 by the r

[scarlet gale]

Almost.

[worthy glacier]

twice?

[scarlet gale]

Yes, exactly.

r² has the exponent 2.

That means r multiplied by itself 2 times.

r² = r × r
r³ = r × r × r
r¹⁰ = r × r × r × r × r × r × r × r × r × r

[worthy glacier]

wait

[scarlet gale]

The exponent tells how many times to multiply the base by itself.

[worthy glacier]

how would i do this

[scarlet gale]

OK, so first you write the formula for circle area.

A = πr²

[worthy glacier]

there is no circle

[scarlet gale]

There is in the words there. It's just not drawn maybe.

[worthy glacier]

ok

would 6 milimetres be the same as how i did before

[scarlet gale]

Yes.

A = πr²

The radius is 6mm long, and r is the number that's how long the radius is, so we fill in r with 6mm.

A = π(6mm)²

[worthy glacier]

i understandd it now omg

[scarlet gale]

Now, there's a bit of a hard thing here.

The 6 gets squared AND the millimeters gets squared.

Because you're squaring the entire r number.

So, you get:

A = 36 · 3.14 mm²

And you get some number of square millimeters.

mm² is said out loud "square millimeters".

[worthy glacier]

ohhhh ok

how would i do

i understand r

[scarlet gale]

OK, now you need to know a little geometry to do that.

[worthy glacier]

how would i do d

[worthy glacier]

oh no

[scarlet gale]

D is the diameter.

The diameter is just twice the radius.

Like the radius goes halfway through the circle.

The diameter goes ALL the way through the circle (through its center).

So, the diameter is twice as long because it's like two radiuses stuck together, one going one way from the center and one going the other way from the center.

[worthy glacier]

oh ok

[scarlet gale]

You can see that in the picture. There are two radiuses that start at the center and go to the edge of the circle stuck together to make that diameter.

So, we can say that the diameter is 2 times the radius in a formula.

D = 2r

Then we just fill in D.

And we can use algebra to get r.

[worthy glacier]

thr r would be

17?

[scarlet gale]

Right, but 17 cm.

Now you know r and you can use that to get A.

A = πr²
A = π(17 cm)²

[worthy glacier]

so how would i calculate the answer

[scarlet gale]

Well, you would do the squaring.

What do you get from that?

[worthy glacier]

squaring

?

[scarlet gale]

That means the ² there.

[worthy glacier]

oh

[worthy glacier]

34cm

[scarlet gale]

² can be said "to the second power" or "squared".
³ can be said "cubed".
There are no other nice names for powers, they're just "to the whatever number power".

Almost.

Squaring doesn't mean multiplying by 2.

When you have an exponent, here's how you do it.

17²

So, you write 17 two times because the exponent is 2.

17 · 17

If it was 17¹⁰⁰, you'd write 17 a hundred times and multiply all those together.

But it's only 17² here, so you only write it twice.

17 · 17

And then you multiply them together.

Does that make sense?

[worthy glacier]

oh yeah

the answer would be 901.18?

[scarlet gale]

Almost.

How did you get 901.18?

[worthy glacier]

wait

i think i calcd it wrong

[obtuse pebble]

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[crimson kiln]

Am I right? I think it is wrong though I am thinking if the input should be B0(no button press), P0(No presence of people), B1(button pressed) and P1(presence of people).

[obtuse pebble]

@crimson kiln Has your question been resolved?

[shy cedar]

help me

[crimson kiln]

em this channel is occupied

[shy cedar]

oh, umm ok

[crimson kiln]

go to channel help 13 i will help you there

<@&286206848099549185>

[obtuse pebble]

@crimson kiln Has your question been resolved?

[obtuse pebble]

@crimson kiln Has your question been resolved?

[obtuse pebble]

@crimson kiln Has your question been resolved?

[obtuse pebble]

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[grand depot]

can anyone help setting up the bounds for this integral?

im clueless for this one

[tardy epoch]

draw a picture?

[grand depot]

i know its an upward cone

with radius 1

and height 1

but stil

[tardy epoch]

not a cone

have you set up an integral?

[obtuse pebble]

@grand depot Has your question been resolved?

[grand depot]

no because i dont even know where to start

[tardy epoch]

https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/double-integrals-a/a/double-integrals-beyond-volume

[obtuse pebble]

@grand depot Has your question been resolved?

[obtuse pebble]

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[tulip plinth]

can somebody help me with this

[short spruce]

note that $a^b\cdot a^c=a^{b+c}$

[warm shale]

a disappointing son

[tulip plinth]

what

[short spruce]

exponent rule

apply it

[tulip plinth]

ok i wrote it

ty for nothing

.close

[obtuse pebble]

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[short spruce]

lmfao

if you expect someone to do it for you, not the server for that

[obtuse pebble]

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[noble jetty]

Am I aloud to get help on like 10-15 homework questions

[unique solstice]

I mean you should be able to figure out the rest if youre learning from 1 or 2 problems

Unless theyre all completely different

[obtuse pebble]

@noble jetty Has your question been resolved?

[noble jetty]

I mean I wouldn’t say they are all completely different problems but they are definitely not the same

[high lily]

perhaps start by posting one of the problems

[noble jetty]

Oh ok

Is it ok if I start sending them in like 30 minutes

[spiral maple]

why did you ask now then?

but sure, just close the channel

[noble jetty]

Bc I was gonna close the channel but can’t only the bot close the channel when you react to it which is like every 30 min

[high lily]

why the delay though

supposedly you already had the questions 30 minutes ago

[noble jetty]

I got in the middle of something

And plus I assumed the answer would have been no

[high lily]

you can close the channel with
.close

[noble jetty]

Alr

.close

[obtuse pebble]

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[tawdry vortex]

i need help

[tawdry vortex]

ik what to do for the first derivative but dont know the second

[clear sonnet]

Correct me if im wrong, but basicly you should state if the pitch of the graph y(x) is positiv or negativ. Or if its uphil or downhill.

do you say pitch?

[tawdry vortex]

havnt heard anyone say that but idk

[tawdry vortex]

but yea for examplpe b is positive , c is zero, and d is negative

for the first derivative

[clear sonnet]

exactly

[tawdry vortex]

since thats the gradient

but idk about the second derivative

[clear sonnet]

Oh ok, so what you do is, you try to map the y'(x) graph. It doesnt matter where exactly to put the points on the y coordinates but at the same x coordinate. You try to do it relative to the other gradients. If you do that you will be able to map the second graph and itll be easy for you to also state its gradients.

[tawdry vortex]

let me try drawing it

Like this?

[clear sonnet]

Well yeah but try to make curves as the gradient doesnt just switches.

like this:

but wait. did you try to draw the first derivate from the task ?

[tawdry vortex]

i didnt cause it doesnt mention to draw it in the question

[clear sonnet]

ok good.

so the "pitch" of the graph doesnt just change as it rounds itself out. if you know what i mean.

[tawdry vortex]

ah ok

[high lily]

consider concavity and inflection points for the sign of the second derivative

[tawdry vortex]

oh i think i got it

for point a since its shaped like a positive parabola, it second derivative will be a diagonal line

making it a positive

right?

[clear sonnet]

i am not entirely sure but if i get what ur saying yes

[clear sonnet]

if you compare to parabola, yes but that wont work for the other points. So what you do by drawing the first derivative, you will be able to just see the 2nd derivative.

[tawdry vortex]

First derivative sketch, is it right?

[clear sonnet]

mines the same :)

[tawdry vortex]

Nice, so what about the second derivative

Wait nvm

That’s the only sketch u need

[clear sonnet]

Exactly

[tawdry vortex]

Alr I got it

[clear sonnet]

Lets say y'(x)=f(x) then y''(x)=f'(x)

Same thing again

[tawdry vortex]

So if a normal function is a cubic

It’s first Derivative will be a parabola

And it’s second is just a line

Thanks for ur help!

.close

[obtuse pebble]

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[jolly reef]

I need help with some problomes sorry!

I think it's C but am not sure.

<@&286206848099549185>

[obtuse pebble]

@jolly reef Has your question been resolved?

[gritty musk]

I am pretty sure its d

sounds rather simple

[balmy mortar]

Pretty sure you explain why

[gritty musk]

So

[balmy mortar]

rather than giving the answer

[gritty musk]

alright, i am quite new here, ty for helping me out

lets have an example

x(y+z)

by "distributing" the x or multiply the x times y and z you will get xy+xz

this should help:

if anything

https://www.khanacademy.org/math/4th-grade-foundations-engageny/4th-m3-engage-ny-foundations/4th-m3-te-foundations/a/distributive-property-explained

[jolly reef]

I don't care to be honest I am so thankfull for the help!

[gritty musk]

lol alr thats what i thought

then the guy told me to explain.-,

anyways have a good day/night

❤️

peace

[jolly reef]

.close

[obtuse pebble]

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[balmy mortar]

This isn't the place to ask if you just want answers.

[obtuse pebble]

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[cerulean bear]

When factoring perfect squares, why use the perfect square method in place of the product sum method when both yield the same answer when factoring?

[nocturne minnow]

The perfect square method is a shortcut

You can do product sum, but if you can identify that it's a perfect square, then you just do $$\left(\sqrt{a} + \sqrt{c}\right)^2$$

[warm shale]

dldh06

[obtuse pebble]

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[mighty ether]

can someone confirm for me that raising a fraction to a negative power is the same as raising its reciprocal to the positive version of the power ?

[pulsar grail]

Today in 8th grade math my teacher said that the sqaure root of 0.4 repeating wasn't 0.2 repeating how???

it really hurts my brain

[spiral maple]

(a/b)^(-n)=(b/a)^n

just a^-n=1/a^n

[obtuse pebble]

@mighty ether Has your question been resolved?

[urban frigate]

think about this

whats 2 times 0.5?

its obviously one

remember, if u multiply some number x by a number less than one and more than 0, you are actually making x smaller

0.2 repeating times 2 is .4 repeating

0.2 repeating times 0.2 repeating is NOT .4 repeating

its closer to 0.049382716

the square root of .4 repeating is .6 repeating, since when u multiply by .6 repeating you get 1 third, and 1 third of .6 repeating is obviously .4 repeating

[obtuse pebble]

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[timid silo]

Hello , I need help with this question

[timid silo]

Q7

Here’s what I tried so far

[brave bramble]

(a,b) meaning gcd?

[timid silo]

I started with assuming (a+bx,c) = d for some d>1

Yes

@brave bramble should I post a picture of what I tried so far

This is what I did so far

Leading from my assumption (d,b)=1

But how to proceed from there I’m not so sure

I used Bezouts theorem here

But I don’t think it’s a generalised case

X here is any integer

[brave bramble]

No x merely exists. Most choices don't work.

[junior inlet]

there exists an x, so, well, i think you just need to choose one? (welp, just assumed a and c are coprime)

[brave bramble]

With that in mind, you can put any rules on x you want, as long as such an x exists by the end

[timid silo]

Hmm

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Hi

[timid silo]

i need help with polynomials

[brittle swan]

do you know what degree 5 means

[timid silo]

no not really

or wait

would it be 5x5y3?

would the answer be 5?

[brittle swan]

do you know the difference between coeffcient and variable?

[timid silo]

yes

[brittle swan]

alright so

lets talk about degree of a term

basically, we add the exponents of all the variables of a term together

to get degree of a term

for example, $6x^2y^3$

[warm shale]

Chromium

[brittle swan]

its degree is 5, because the variables are x and y, and adding their powers tgt we get 5

[timid silo]

ohhhhhh

so it would be 2?

[brittle swan]

polynomials are just sums of multiple terms

those terms have different degrees

deg of a polynomial is just the biggest of them

[brittle swan]

so, yea

[timid silo]

could you help with another one please?

[brittle swan]

sure

[brittle swan]

standard form means descending power

so $x + x^2$ is not standard form

[warm shale]

Chromium

[brittle swan]

and $x^3 + xy + 1$ is

[warm shale]

Chromium

[timid silo]

oh wait

[brittle swan]

sorry

[timid silo]

so i thought the answer would be $6^3$

[warm shale]

TheG3

[timid silo]

but that cant be right

im so confused

[brittle swan]

do you understand this

[timid silo]

no

[brittle swan]

a polynomial is in standard form

if and only if

all terms are arranged in descending order of power

[brittle swan]

so here, the power order is 1, 2

which is not desending

[brittle swan]

here, it's 3, 2, 0

which is indeed descending

[timid silo]

ok

[brittle swan]

so you check which one is arranged in descending orders of power

which is standard form

[timid silo]

and how is this decending

[brittle swan]

.

3, 2, 0 sorry

now constants have order 0

and $x^3, xy$ have orders $3, 2$ respectively

[warm shale]

Chromium

[brittle swan]

do you understadnd?

[timid silo]

oh ok

yes

i thought it would be the first option but it says thats wrong

so would it be the second one?

or no it would be the 3rd one

<@&286206848099549185>

@brittle swan

<@&286206848099549185>

[brittle swan]

dont tag helpers twice

[timid silo]

ok sorry

so would it be the 3rd option?

[brittle swan]

no

[timid silo]

im still confused then

.close

[obtuse pebble]

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[obtuse pebble]

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[jagged mango]

How do I write an exponential function for a graph that passes through the points (2,16),(3,32)?

[tardy epoch]

do you know the general formula for an exponential function?

[jagged mango]

No

[tardy epoch]

How To Find Exponential Functions
https://www.studypug.com/algebra-help/find-an-exponential-function-given-its-graph

[vast wren]

f(x)=a^x

[tardy epoch]

Example 1 is the closest to your problem

[obtuse pebble]

@jagged mango Has your question been resolved?

[obtuse pebble]

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[final citrus]

why is it +1?

[final citrus]

im thinking that u=e^x

[ionic heart]

Because in the original qn there's a +1

[final citrus]

oh wait no

[final citrus]

wdym?

shouldnt it be 1/u then

because u*1/u = 1

[ionic heart]

No I think there shouldn't be a u before the brackets

[final citrus]

oh i get it now. du = udx so dx = du/u

nvm thanks anyway

[ionic heart]

Ooh I've seen it

[final citrus]

.close

[obtuse pebble]

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[wooden solstice]

they said its supposed to be on standard form

but i did something else

[junior inlet]

i think it's supposed to be like ax^2+bx+c

not vertex form

[wooden solstice]

yeahh thats what they said

how can i change it to standard tho

[junior inlet]

from their given equations, you can move the term with y to RHS (x for c and d)

and divide by y's coefficient

[wooden solstice]

how

[tardy epoch]

The unfortunate thing is it's closer to standard form in the start than your answers.

For a, maybe it's better to start all over so that you can more easily solve for y

[obtuse pebble]

@wooden solstice Has your question been resolved?

[wooden solstice]

can you help me with that

cause i have to pass my hw like at 5 hours from now

[tardy epoch]

Can you move the term with y to the other side?

[wooden solstice]

i guess

[tardy epoch]

And can you multiply or divide by a number to make y by itself?

[raven spire]

what's going on

[obtuse pebble]

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[raven spire]

No that's not it ...

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

[high lily]

the image is too small and blurry

[ruby finch]

$\frac{\sqrt{52.29} - \sqrt{5.29}}{\sqrt{52.29} + \sqrt{5.29}}$

[warm shale]

kirby your mom

[timid silo]

yeah

[ruby finch]

Rationalisation would be the first thing to do here

[timid silo]

what would it be I actually gotta check my answer

[ruby finch]

Use a calculator?

[timid silo]

.close

[obtuse pebble]

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[stable heron]

Just a little dumb question: Is the value of 1/1 + 4/9 + 5/90 rounded up or down?

[brave bramble]

1.5 is rounded up.

[stable heron]

Sure, but technically it's 1.499... you know

Is there a rule to that?

[brave bramble]

1.4999... = 1.5

If you work out the fractions algebraically, you'll get 3/2

(I fell for this too, thinking 1.4999... should be rounded down. Caught my error and deleted the message to avoid confusion)

[stable heron]

thanks bro

.close

[obtuse pebble]

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[pseudo cargo]

Can anyone provide an example of a function that is a bijection such that f(x) != x but f^n(x) = x where f^n is function composition

[obtuse pebble]

@pseudo cargo Has your question been resolved?

[pseudo cargo]

<@&286206848099549185> ?

And f must be from an infinite set to the same infinite set

[royal basin]

$f: \bR \to \bR$ given by $f(x) = \begin{cases} x+1 & x \in {0, 1, \dots, n-2} \ 0 & x = n-1 \ x & \text{otherwise}\end{cases}$

[warm shale]

Ann

[pseudo cargo]

Kinda trivial, but thanks

.close

[obtuse pebble]

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[hexed wadi]

Can I convert kVArh to kWh?

[royal basin]

what's kVArh?

[hexed wadi]

https://acronyms.thefreedictionary.com/KVARH

[obtuse pebble]

@hexed wadi Has your question been resolved?

[nocturne minnow]

Google can answer this question

[unique solstice]

Kvar is ideal reactive power

So you could I guess

[obtuse pebble]

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[unique solstice]

If you knew the efficiency

[obtuse pebble]

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[fleet harness]

These polygons are so confusing

[short spruce]

seems like a quiz

[obtuse pebble]

@fleet harness Has your question been resolved?

[obtuse pebble]

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[frozen cave]

Krista launches her model rocket in a completion. Currently the record to beat is 125m in height reached by the rocket. Krista's rocket launch can be modelled by the equation

h(t) = -4t2 + 12t + 112.

Where h(t) is he height in meters, of the rocket and t is the time, in seconds.

a. Does Krista win the rocket launch completion?

b. After how long does Krista's rocket reach maximum height?

c. In order to land safely, the rocket must land within 8 seconds. Krista said the rocket was successful because it landed in 7 seconds. Prove mathematically that Krista's rocket landed in 7 seconds.

[frozen cave]

need help wit it

[pallid sun]

Does it not give you any time?

[nocturne minnow]

You can solve for t

[pallid sun]

That’s true

[nocturne minnow]

Find the maximum of that equation, and that relates to the highest it travels

[obtuse pebble]

@frozen cave Has your question been resolved?

[obtuse pebble]

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[timid silo]

hi

[timid silo]

i need help

what the fuck i hate proofs so much

[sage geode]

That's one of the simplest proves they could ask you for tho

[leaden ibex]

what are the options for the dropdown

[sage geode]

Post your question in an available help channel

[leaden ibex]

Before we move any further

[high lily]

the majority of the work has already
been set up for you

[placid hollow]

sorry he posted it before i was typing it

[timid silo]

oh im sorry

[high lily]

what's your issue with it

[leaden ibex]

Well this is very easy then.

[timid silo]

i do not like proofs.

and it hurts my brain.

because this class is hard and i hate the hw.

[leaden ibex]

That's geometry

But besides that

what is the issue

What do you not understand specifically

[timid silo]

all of it ;-;

i got the first one

[high lily]

that's not all of it

[timid silo]

okay

[high lily]

don't exaggerate

don't make me ask you whether you understand things one word/object at a time

did you get the second one?

[leaden ibex]

silence

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

hi there, this is about chemistry. I'm simply trying to understand the idea of solute concentration in a solution. Specifically w/w w/v v/v

[timid silo]

from what I understand, you have your solute in either grams of weight/mass or the volume ml

same goes for the solution

and some % of that solution is made up of said solute

now how do I properly calculate this myself

say we have

msolution = 160g
msolute = 40g

if it's gonna be a % then the number 100 is involved so we either multiply or divide by it somewhere

I could use some help

[tiny rivet]

Is this saying there is 40g of solute dissolved in 160g of solution?

[timid silo]

yes

[tiny rivet]

So total mass is 200g?

[timid silo]

yes

[tiny rivet]

Isn’t solute concentration defined as the amount of solute in a volume ?

[timid silo]

how much of that solute exists in a certain amount of the solution

[tiny rivet]

So it would seem to be something like 40/200?

That is the mass is solute/ total mass of solution

[timid silo]

so i just divide the solute into the solution?

nothing else needed?

[tiny rivet]

I don’t do chemistry so I’m not totally sure

If you had the concentration

[timid silo]

yeah Jesse, we cannot cook like this

[tiny rivet]

Could you then use it to find the amount of solute in 5G of the solution or something

[timid silo]

this is going to be a mess

[tiny rivet]

It seems like from a google that solute concentration refers to the mass of a solute dissolved in a volume of solution

[timid silo]

to find a percentage you would need to divide or multiply it with 100 somehow though

otherwise you would get unstable results

[tiny rivet]

Yes a percentage is times 100

[timid silo]

(100*40)/200 lol idk

[unique solstice]

I think there's actually 160g total

[timid silo]

well you could see it that way too

and 40g of that is the solute

[unique solstice]

msolution = 160 g
msolute = 40 g
msolvent 120 g

Unless it's mislabeled

[timid silo]

no that's about right

could you enlighten me?

[unique solstice]

The solution represents everything

Solute and solvent

So you'd divide by 160 g

The solute is already a part of the 160 g if it's labeled right

[timid silo]

well it is labeled right, now

it's not a real problem, i just came up with it on the spot

[unique solstice]

Oh

[timid silo]

okay, I'm supposed to divide the solute by the solution then

[unique solstice]

Ye

[timid silo]

so 160/40

[unique solstice]

Other way

[timid silo]

oh

[unique solstice]

Because you want a number less than 1

[timid silo]

so you get floating point

[unique solstice]

Ye

[timid silo]

but why

oh wait

[unique solstice]

Because you can't have a solution that's 120% solute

[timid silo]

i get it

how much of the whole solution fits in the solute

that's what is being said here

and it's always going to be the part of the solution which is the solute

you can't have anything else

that's perfect, thank you

does anything change once we move on from grams to volume?

like if the solution or maybe the solute was in ml instead of g

[unique solstice]

Wait actually

All of this would depend on how you wanna measure concentration

I think typically you'd measure it using moles

Though ig you could use percent by mass or volume

So it'd all depend

[timid silo]

im trying to do that rn

[unique solstice]

If it's still just percent it's the same

[timid silo]

%w/w %w/v and %v/v

they're the easier ones to start with

[unique solstice]

Is w representing mass?

[timid silo]

yes

weight/mass

in chemistry it's used interchangeably as far as i know

so you're supposed to calculate concentration with both volume and mass

[unique solstice]

Yeah that'd be the molar way I think

[timid silo]

huh

[unique solstice]

Since molar concentration is moles per liter

I guess it's not technically mass but it's close enough

[timid silo]

oh no Jesse

[unique solstice]

I've never liked chemistry

[timid silo]

i mean it's not bad

it's just taught boringly

you could make sugar rockets with... well, sugar and potassium nitrate

super powerful and explosive and anti-finger

either way im not making any sense through this

thanks but rip

.close

[obtuse pebble]

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[unique merlin]

Why is an empty set the subset of all sets?

Most of the proofs I have looked at utilise the concept of vacuous truth, a concept that I haven't been able to grasp yet.

One proof I looked at went along the lines of:
"You have 5 objects and take it way, then you are left with nothing/it is empty, you have zero objects which is what an empty set is. A|A=Empty set "

By that resemblence of numbers and sets, we don't say that "Every number contains no number/has zero"
Also, when you say something is a subset of something else, then that subset is present within the other set ie. A{x-> Positive integer set, x>=5} ={Empty set,0,1,2,3,4,5}
So if you removed a set from itself, you would be removing the "empty set" itself, which is nonsensical.

[spiral maple]

suppose the empty set isn't a subset of A for any set A

then that means there exists an element in {} not in A

Contradiction.

[balmy mortar]

Definition of subset:

$$A\subseteq B:= (\forall a\in A)(a\in B)$$

[spiral maple]

Was waiting for them to respond.

[warm shale]

Shuri2060

[obtuse pebble]

@unique merlin Has your question been resolved?

[unique merlin]

I have seen this proof and it's still confusing

Let us take a random set A

[spiral maple]

random non-empty set A*

[unique merlin]

When we assume that the empty set is not a subset, this means that the content of the empty set is not in A

[balmy mortar]

'there is something in the empty set that is not in A'

[spiral maple]

If we assume {} is not a subset, then that means {} has something not in A

[unique merlin]

But doesn't the empty set not have any element is the first place, akin to saying that A does not contain "no element" ?

[spiral maple]

ie {} is non-empty

For example:

{1,2} is a subset of {1,2,3} cause every element of the 1st is in the 2nd

However, {1,2,3} is not a subset of {1,2} because 3 is in the 1st but not in the 2nd

[unique merlin]

But doesn't the empty set have no elements in the first place?

I don't think I understand what an empty set means in the first place then.

[balmy mortar]

Yes. And this is a contradiction.

You assumed {} is not a subset of A
And reached a contradiction.

[spiral maple]

it's the set with no elements

In our universe of discourse, {} is either a subset or a superset of A

we assumed not a subset, so we suppose {} is a superset of A

to which bullshit b/c A is not a subset of {}

[unique merlin]

Still nothing

Example. A={1,2,3}
For {} to not be a subset, it must have an element which is not in A
But if {} has no elements in the first place, how can it be a subset?

Taking the opposite, let {} not be a subset of A
This means that {} has an element that is not in A
But since {} has no elements, it's impossible for the above assumption to hold, hence proven.

It seems that the contradiction forces the axiom to be true, without stating why it should be so.

[balmy mortar]

@unique merlin
'But if {} has no elements in the first place, how can it be a subset?'

Where are you coming from with this.

Perhaps we should agree on the definition of 'subset' first

before going any further

'If A is a subset of B, then for each element x of A, x is an element of B'

Also, what axiom are you referring to?

[spiral maple]

For {} to not be a subset, it must have an element which is not in A
Yes, that's the point

[obtuse pebble]

@unique merlin Has your question been resolved?

[obtuse pebble]

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[twin sentinel]

i'm just.. totally lost. help appreciated!

[obtuse pebble]

@twin sentinel Has your question been resolved?

[twin sentinel]

.close

[obtuse pebble]

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[teal sleet]

I want to calculate the dimension of U
however the triplet (u1, u2, u3) is not a basis, because they are linearly dependent
Could someone give me input on this?

[teal sleet]

V = Q^4 (Q = fractions)

I've calculated rref:
1 2 3
0 0 0
0 0 0
0 0 0

[hazy marlin]

(rationals would be more appropriate)

[hazy marlin]

Okay so.. you've put your vectors as columns in a matrix?

[teal sleet]

yes

[hazy marlin]

great, so the vector corresponding to the first column, will form a basis to U

In general, when you're looking for a basis , and you align your spanning vectors in columns then once you've achieved the rref form, then your pivots will indicate which of the vectors will form a basis

however .. are you sure about your result?

it seems to me that there are 2 vectors here that form a bsis

since u3 is linearly dependant on u1 and u2 (check 2*u2-u1)

[teal sleet]

1 3 5
0 4 8
1 2 3
2 1 0
----------- 1-3, 4-3
0 1 2
0 4 8
1 2 3
0 -3 - 6
----------- 2+4
0 1 2
0 4 8
1 2 3
0 1 2

[hazy marlin]

that will give you 2 pivots

+1 for the effort of writing that out lol

[teal sleet]

so V is dim 4 and U is dim 2?

[hazy marlin]

yea

[teal sleet]

gotcha

[hazy marlin]

do you understand how to pick your basis tho

[teal sleet]

mom

[hazy marlin]

[teal sleet]

@hazy marlin
v1 = 1, -1, 1, 0
v2 = 0 0 0 1

[hazy marlin]

?

@teal sleet

[teal sleet]

x1= x3
x2 = -2x3

x3
-2x3
x3

a *(1, -2, 1)

[hazy marlin]

i think I lost you bruv

what are you attempting to do now?

[teal sleet]

this.
I have two pivots, x1 and x2
and x3 is free
1 0 -1 => x1 -x3 = 0 => x1 = x3
0 1 2 => x2 +2x3 = 0 => x2 = -2x3
and x3 =x3

[hazy marlin]

and your final result ?

your final result is the solution vector (1,-2,1) ?

[teal sleet]

---

x3
-2x3
x3

a *(1, -2, 1)

[hazy marlin]

so this right?

okay

what does the final result tell you?

[teal sleet]

that the dimension is 1 not 2?

since dimK (V ) = dim(V ) := n ?

with (v1 , . . . , vn) basis of V

[hazy marlin]

Okay First of

When you're trying to find a basis out of spanning vectors

you're not solving a linear map

you're performing row reduction on them to see if they're linearly independent

the solution vector you found is some random kernel for some linear transformation defined by the column vectors u1,u2,u3 which has no relevance to the question

[hazy marlin]

What you did here is very much correct

all you had to do , is find out which columns have pivots, and pick the vectors corresponding to those columns

say you got a pivot in first column and you placed u1 in that column, u1 will be in your basis

the other approach, was to align your vectors as rows , bringing your matrix to it's rref , and thus discovering a set of linear independent vectors that will form a basis to your subspace

@teal sleet

[teal sleet]

was to align your vectors as rows oh

[hazy marlin]

?

No it doesn't really matter

either method works

it's just the conclusion from the methods are different

[teal sleet]

ok thanks

[hazy marlin]

sure

but do you understand the difference?

[teal sleet]

yeah 1) taking trivial vectors out
or 2) calculate a new set

[hazy marlin]

yea pretty much

column alignment lets you know which vectors to take out and which to take in

row alignment gives you a new set of vectors that form basis

:)

[teal sleet]

Alright
thanks again
.close

.close

[obtuse pebble]

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[elfin ferry]

need help with 7. A ball is shot into the air. Its height h, in metres, after t seconds is modeled by .
h= -4.9t^2 + 30t + 1.6
a) How long will it take the ball to reach a height of 35 m?

[tardy epoch]

do you know how to evaluate functions?

[elfin ferry]

well this is what i have so far

35=-4.9T^2 + 30 t + 1.6
0= -4.9T^2 + 30 t + 1.6 – 35
0= -4.9t^2 + 30t -33.4 -4.9 √’-4.9^2 – 4 (30)(-33.4) / 2 (30)

can you let me know if thats right?

<@&286206848099549185>

[tardy epoch]

looks like the right method, but i'm not gonna check your algebra

[nocturne minnow]

-4.9 √’-4.9^2 – 4 (30)(-33.4) / 2 (30)
Is that line using the quadratic formula?

[elfin ferry]

yea

[nocturne minnow]

That's wrong

You know the quadratic equation is $$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

[warm shale]

dldh06

[elfin ferry]

yes

4.9 +-√’-4.9^2 – 4 (30)(-33.4) / 2 (30)

this is wrong?

[nocturne minnow]

Yes

What is the a term, b term, and c term in that equation you have?

[elfin ferry]

wait b is suppose to be 30

and a -4.9

[nocturne minnow]

So if a = -4.9 then why is your 2a, 2(-4.9)?

[elfin ferry]

i dont really know hwat you mean sorry

[nocturne minnow]

You plugged in the numbers wrong

$$\frac{4.9 \pm \sqrt{-4.9^{2} – 4 (30)(-33.4) }}{2 (30)}$$

That is your statement there

[warm shale]

dldh06

[nocturne minnow]

So your denominator is 2a, according to the formula, meaning that you said a = 30

Do you see the mistake I am pointing out?

[elfin ferry]

yes

[nocturne minnow]

So then that means you need to fix that and write the proper equation

[elfin ferry]

but 30 is supose to be <b> ??

[nocturne minnow]

Yes b = 30

But as I said, you did 2(30)

Meaning you said a = 30

[elfin ferry]

ohhhh yesss ok

so it should be like 30 √’-30 – 4 (-4.9)(-33.4) / 2 (-4.9)

[nocturne minnow]

Still didn't apply the formula correctly

$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

[warm shale]

dldh06

[nocturne minnow]

Here is the formula again, plug in a, b, and c

[elfin ferry]

x = -30 +-√ 30 - 4 (-4.9) (-33.4) / 2 (-4.9) i dont know man i think tahts still wrong,....

[nocturne minnow]

That's right, you just need the squared part

Because b^2

b^2 - 4ac

[elfin ferry]

oh yes ok

so once i have that forrmular then what would i do?

to find how long will it take the ball to reach a height of 35 m

[nocturne minnow]

You do math

Simplify that

$$x_{1,2}=\frac{-30 \pm \sqrt{30^{2} - 4 (-4.9)(-33.4) }}{2 (-4.9)}$$

[warm shale]

dldh06

[obtuse pebble]

@elfin ferry Has your question been resolved?

[obtuse pebble]

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[shrewd flame]

A number consists of 3 digits. The sum of the digits is 15. The sum of the outer digits is double the middle one. The difference of that number with that number read in reverse is 396. Find that number.

[shrewd flame]

I need to solve this questian with the gauss jordan method but i am stuck because i cant seem to figure out where to start

This is what i have understood but i dont think that the last equation is linear

The teacher also the answer which should be 753

But that is not given in the problem

<@&286206848099549185>

<@&286206848099549185>

.close

[obtuse pebble]

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[lost siren]

how can i get the quotient?

[brave bramble]

https://www.cuemath.com/numbers/division-of-complex-numbers/

[obtuse pebble]

@lost siren Has your question been resolved?

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[hushed harbor]

Hi there, I'm stuck on this problem. I have utterly no idea how to solve it. Its the very last question. Underneath the graphs

Honestly, this isn't even my hw problem. I'm just trying to figure it out, and idk how to maximize dimensions. I never learned that in pre-calc. I got the function to be f(x)=x^2(72-4x)

Since x is between 0 and 18, would it just be 9? Since f(9)=max val

The textbook offers no help whatsoever, it labels this as geometry and thats it. I would super appreciate the help

<@&286206848099549185>

[obtuse pebble]

@hushed harbor Has your question been resolved?

[hushed harbor]

<@&286206848099549185>

[obtuse pebble]

@hushed harbor Has your question been resolved?

[obtuse pebble]

@hushed harbor Has your question been resolved?

[obtuse pebble]

@hushed harbor Has your question been resolved?

[hexed plank]

waht type of graph is it? Volume vs 'wut'

[obtuse pebble]

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[vapid knot]

I'm doing this google foobar challenge and at the end I need to reduce multiple fractions that all have the same denumerator. After reducing the fractions should have the same smaller denumerator as well. Example: 6/28, 4/28, 18/28. becomes 3/14, 2/14, 9/14. I know how to reduce a single fraction say 4/28 becomes 1/7. But I'm stumped trying to reduce more than one because 4/28 in this case would need to be 2/14. How do I do this?

[obtuse pebble]

@vapid knot Has your question been resolved?

[vapid knot]

Oh I get it. I have to calculate the gcd of all the numerators + denumerator

[obtuse pebble]

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[tall flint]

help pls

[tall flint]

probability (A) = 0.6
probability (B) = 0.8
probability (A & B) = ?

how do dis

[raven spire]

Is there anything else said about events A and B that you know?

If not, there's not enough info to find P(A & B)

[timid silo]

Can't we multiply both of them.

If they are exclusive events that is.

[tall flint]

wait lemme foto the whole question then

This @raven spire

[timid silo]

P(B|A)xP(A)

[tall flint]

Question 3

[raven spire]

Yeah so $P(B|A)$ given here right

[warm shale]

Ansh

[raven spire]

Use the formula for P(B|A) to determine the answer

[tall flint]

What is that formula

[timid silo]

^. Because you can use the conditional probability formula.

P(B|A)=P(A and B)/P(A).

[tall flint]

Me no understand that formula

[raven spire]

Check your textbook

and maybe the articles surrounding the formula as well.. Would help