help-0

[toxic dust]

This system has no solution. The planes do not intersect with one another, there are no points that lie on all three planes as there are no points that lie in all three planes.

Does this make sense for the 1st one

[viral patio]

yes

[toxic dust]

i just repeated the sentence twice 😄

@viral patio I dont get this one

[viral patio]

hmmm this one's a bit tougher
before we continue, can i ask - are you familiar with matrices?

[toxic dust]

Umm no

[viral patio]

okay, don't worry about that then

[ionic jewel]

why do they even give problems like this preLA

what's wrong with 2 var eqns smh

[toxic dust]

Unsure man... Its Chapter 8 and 9 on the last week of school

I just want this to end 😭

[viral patio]

i have a really hard time justifying this in words but can you see that the planes might all intersect?

[toxic dust]

Umm yeah when i move to the other side

It does look like it

Eq2 intersects with all 2 @viral patio

[viral patio]

okay, well if you're satisfied that all three equations intersect, in what way? one single point, or an infinite line/plane?

[toxic dust]

I am thinking... Unsure

it looks like Eq2 does intersect

but i think it would be infinite line no?

[viral patio]

ah okay, i think i can see it:
so if you look at the top parts, there's one place that goes top-left-to-bottom-right (i'm calling that plane A)
there's also a plane to the top-left half of the image (plane B), and a plane to the top-right half of the image (plane C)
are you okay with my labellings?

[toxic dust]

https://tenor.com/view/agt-americas-got-talent-mel-b-confused-unsure-gif-4502135

[viral patio]

sorry, give me a sec

@toxic dust

how's that?

[toxic dust]

Yeah that makes sense

[viral patio]

now A and B intersect at a line (D)
B and C intersect at another line (E)
and the lines D and E should intersect at a point

[toxic dust]

Okay....

I get where u getting

@viral patio

[viral patio]

yes?

[toxic dust]

So from what u saying it would be One unique solution?

[viral patio]

yes

[toxic dust]

umm i think u did try to explain here but whats the reason for that?

Its cause Plane A and B will form a line and B and C will form another line which will in fact cross?

[viral patio]

yes, so there's one point that is the intersection of all three planes

[toxic dust]

i see

[woeful lion]

the parabola $$y=a(x+b)^{2}-8$$ has tangent $$y=2x$$ at the point Q(4, 8). Find the values of a and b.

[ocean seal]

Proxy

[woeful lion]

to find the gradient i can get the derivative of y=2x?

[viral patio]

y = 2x is the equation of a tangent already, so what should you differentiate instead?

[woeful lion]

can i also do $$m=\frac{0-4}{0-8}$$

[ocean seal]

Proxy

[woeful lion]

to find the gradient

@viral patio

does $$m=\frac{0-4}{0-8}$$ always work?

[ocean seal]

Proxy

[viral patio]

why do you want to differentiate the tangent?

[woeful lion]

i know that I have to differentiate the parabola and use simultaneous equations to find a and b

[viral patio]

oh, then do that?

[woeful lion]

yes but

i dont understand the gradient part

the gradient is 2

[thorn kindle]

gradient is the rate of change

did you know?

[woeful lion]

yes

is it the rate of change at (4, 8)

yeah i understand this

how do i flag as solved

[viral patio]

this room is now free

[crystal lodge]

b) The number of bacteria on a plate viewed under a microscope follows a Poisson distribution with mean 75. A plate is rejected if less than 55 bacteria are found.
i) Approximate the probability of the rejected bacteria. [5 marks]
ii) If 2000 such plates are viewed, how many will be rejected? [1 mark]
iii) Approximate the probability that there are between 60 and 80 bacteria (inclusive both) on a plate. [2 marks]

im struggling with this question my teacher gave as hw. cant figure out how to do it

[alpine sable]

could someone guide me through the next few steps

[crystal lodge]

<@&286206848099549185>

[alpine sable]

i think ive done it wrong

[abstract totem]

i think its my computer but the image is super blurry

[alpine sable]

i messed up a step last time

[viral patio]

if 12a + 20b = 31/5
what should the next line be?

[alpine sable]

ye ye i know i did it wrong

[alpine sable]

this is ok i think?

[viral patio]

60a + 40b = 31?

[alpine sable]

yes, thats what i did

[viral patio]

double check this calculation

[alpine sable]

ahh

im so dumb

[viral patio]

the great thing about simultaneous equations is that you can check your answers, so at least you know something was wrong

but yes, be careful

[alpine sable]

60a+100b=31

right?

[viral patio]

yes

[alpine sable]

could u tell me the next steps

[icy jetty]

Anyone free to help with algebra 1 in vc

It's just simplifying rational expressions

[alpine sable]

@viral patio after this?

[viral patio]

so the idea with simultaneous equations is that you want to multiply one (or both) equations, so that when you add (or subtract) the two equations, you'll cancel out all of the a's or all of the b's

[alpine sable]

its not cancelling

[alpine sable]

this is why i dont know what to do

it always cancelled before

[viral patio]

sorry i wasn't clear, let me say slightly differently:
the idea with simultaneous equations is that you want to multiply one (or both) equations by some constant number, so that when you add (or subtract) the two equations, you'll cancel out all of the a's or all of the b's

[alpine sable]

OMFGGGG THANKS A LOT

[viral patio]

oh okay, if that works let me know

[alpine sable]

u helped me alot man thanks

[viral patio]

all good?

[alpine sable]

i just need to know do i multiply before or after adding?

[viral patio]

before
if you try after adding you won't cancel anything out

[alpine sable]

so i do it before?

[viral patio]

yes

[alpine sable]

do both equations need to be multiplied by the number

?

[viral patio]

in some cases you might need to multiply both equations by some number (if you do, they'll be different numbers)

[silk coral]

Hey could I possibly get some help on this

[viral patio]

we're still using this room, please post your question in an empty room

[silk coral]

Sorry

[alpine sable]

have i done it correctly so far

@viral patio

[viral patio]

it's a bit hard to follow what you're doing

why did you decide on multiplying both by 1/2?

[alpine sable]

it divides the most numbers

?

[viral patio]

the purpose of multiplying is to that the coefficient of both the a's or the coefficient of both the b's will cancel out when you add (or subtract) the two equations

[alpine sable]

what number would that be in this case

i think 1/2 is the one?

?

[viral patio]

i think you need should go through some simultaneous questions lessons on khan academy, this is the kind of thing where having someone explain it in a video and going through lots of simple questions is better than just one person going through one example

[alpine sable]

umm

i just need to know what “a number that will cancel out both b’s”

is

[viral patio]

you might not have one number that works for both
you might need to pick different numbers for each equation

plus, if you tried to use the same number on both equations, you haven't changed your situation at all

[alpine sable]

i see

so it can be different

[viral patio]

it usually is

[icy jetty]

Can someone help

me

Wait

There

I just need to simplify

And solve

[viral patio]

sure, which one? what have you tried

[icy jetty]

So for the first one I cancelled out the x-2 and x-8 ones

And I ended up with 1 + 2x = x/2

[viral patio]

okay so you can't quite "cancel out" like that

what you need to do is multiply the WHOLE equation (every part) by (x-2), and the simplify any fractions. then do the same for (x-8). does that make sense? want to try?

[icy jetty]

I see

Sure

[viral patio]

(also if you reply to my messages, i get ping'd)
let me know what you get

[icy jetty]

Alright

1 + 2x/x-8 = x/2(x-8)(x-2)

@viral patio

[viral patio]

ooh almost, let me run you through the (x-2) part:

[icy jetty]

Okay

[viral patio]

$$\frac{1}{x-2} + \frac{2x}{(x-2)(x-8)} = \frac{x}{2(x-8)}$$

[ocean seal]

ZainAK283

[viral patio]

that's what your question is, correct? @icy jetty

[icy jetty]

Yes @viral patio

[viral patio]

now i'm going to multiply EVERY fraction by (x-2):

$$\frac{x-2}{x-2} + \frac{2x(x-2)}{(x-2)(x-8)} = \frac{x(x-2)}{2(x-8)}$$

[ocean seal]

ZainAK283

[viral patio]

do you see how i got that? @icy jetty

[icy jetty]

Yes

[viral patio]

can you simply each fraction for me? if it can't be simplified, just say so

[icy jetty]

1 + 2x/x-8=x(x-2)/2(x-8)

[viral patio]

perfect! my only small thing is to put an extra pair of brackets:
1 + 2x/(x-8)=x(x-2)/2(x-8)

[icy jetty]

Alright

[viral patio]

can you now do the same thing that i did but with (x-8)?

[icy jetty]

Yes

[viral patio]

go ahead 🙂

[icy jetty]

(x-8)1+(x-8)((2x/(x-8))=(x(x-2)/2(x-8))*(x-8)

@viral patio

[viral patio]

great, can you simplify?

[icy jetty]

(x-8)1+2x=((x(x-2))/(2))

[viral patio]

exactly! but you can simplify a few things - for example:
(x-8)1 = x-8
because multiplying by 1 does nothing, and you can drop the brackets now

what do you think you should do next?

[icy jetty]

Multiply everything by 2?

[viral patio]

yup, go for it

[icy jetty]

2(x-8)+2x=x(x-2)

@viral patio

[lusty pewter]

The average of all possible five-digit numbers that can be formed by using each of the digits 4, 8, 1, 7, and 6 exactly once is ???

[ionic jewel]

wow multiple peopole interrupting at the same time thats pretty cool

[lusty pewter]

The average of all possible five-digit numbers that can be formed by using each of the digits 4, 8, 1, 7, and 6 exactly once is ???

[ionic jewel]

try finding a new channel

wow this guy doesnt even stop

[lusty pewter]

ok soz

[ionic jewel]

man posts twice

[lusty pewter]

lmao

[icy jetty]

Lol

[viral patio]

ooh almost, try again

[icy jetty]

Aaaa

Idk

[ionic jewel]

i know its in the context of the problem but this hurts my soul

[lusty pewter]

The average of all possible five-digit numbers that can be formed by using each of the digits 4, 8, 1, 7, and 6 exactly once is ???

[viral patio]

this channel is still being used. there are other channels which say "this channel is free". ask your question there.

[viral patio]

(x-8)+2x=(x(x-2))/2
try one more time

[harsh acorn]

Hi is this correct? Prove that raising an even number to an odd power gives an even number. Proof: Let 2k be an even number and let 2p+1 be an odd number, 2k²ᵖ+¹ = 2k x 2k x 2k x 2k = (2p+1 lots of 2k) = 2(k x 2k x 2k x 2k) the expression in brackets is an integer and since it is multiplied by 2 it must be even

[ocean seal]

Chai T. Rex

[oak chasm]

@harsh acorn Something more along these lines ^

[harsh acorn]

= 4p + 2 + 2kp + 1k ?

[oak chasm]

That's not how powers work.

[ocean seal]

Chai T. Rex

[harsh acorn]

Is that the final answer?

[oak chasm]

Is what the final answer?

[oak chasm]

That's a correction to what you wrote.

[harsh acorn]

So is it the final answer?

[oak chasm]

No.

[harsh acorn]

So how do I find the final answer?

[oak chasm]

@harsh acorn You need to understand how powers work first.

[harsh acorn]

Can you explain please

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[harsh acorn]

What about if k is in algebra form only

[oak chasm]

It's the same.

You just don't know how many times 2 is multiplied by itself as a number.

[ocean seal]

Chai T. Rex

[harsh acorn]

What answer would you give for this?

[oak chasm]

Do you see how I got the first part?

[harsh acorn]

Yeah

By multiplying 2 by 2p+1 then k by 2p+1

[oak chasm]

No.

It's not multiplication.

[harsh acorn]

Sorry, making it the power of

[oak chasm]

You have 2p + 1 copies of 2k.

That's like 2k2k2k2k2k2k2k... all multiplied together.

You can rearrange it to have the 2s in front and the ks in back.

You have 2p + 1 copies of 2k multiplied together, that's the same as 2p + 1 copies of 2 multiplied by 2p + 1 copies of k.

Does that make sense?

Yes.

[harsh acorn]

so you did 2²ᵖ+¹ and k²ᵖ+¹ = 2²ᵖ+¹k²ᵖ+¹

[oak chasm]

Yes.

Let's do it with a number like 7.

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

See how I'm just rearranging?

[harsh acorn]

Yeah

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

Does that make sense?

[harsh acorn]

Yeah

[oak chasm]

OK, so we don't have 7, we have 2p + 1.

[ocean seal]

Chai T. Rex

[oak chasm]

Now, what's the form of an even number?

[harsh acorn]

2k

[oak chasm]

So, we take off one of the 2s we have all multiplied together.

[ocean seal]

Chai T. Rex

[oak chasm]

See what I did there?

[harsh acorn]

No

[oak chasm]

OK, let's show that.

Let's go back to the power of 7.

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

See how I just separated one of them off?

[harsh acorn]

Yeah

[oak chasm]

Oh, wait.

[harsh acorn]

6 2's?

[ocean seal]

Chai T. Rex

[oak chasm]

There.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[harsh acorn]

Yeah

[ocean seal]

Chai T. Rex

[oak chasm]

So, we can take out one of the 2s.

And then there will be six 2s still together.

Does that make sense? We start with seven 2s, we separate one out, we have six 2s left stuck together?

[harsh acorn]

Yeah, makes sense

[ocean seal]

Chai T. Rex

[oak chasm]

We separated one of the 2s out.

We have 2p 2s left.

Does that make sense?

[gleaming obsidian]

so there is something very nice about 2 * 2^n = 2^n+1

But I dont know if you guys would understand it

[ionic jewel]

[ionic jewel]

shoot, im interested

[gleaming obsidian]

nice

[oak chasm]

@harsh acorn Does it make sense what I've done there?

[gleaming obsidian]

okay so, you know about groups?

[ionic jewel]

yes, but send it in one message to not distract this convo please

[harsh acorn]

Where did the +1 go on 2p+1?

[oak chasm]

@harsh acorn Remember how we separated out one 2 from 2^7?

[gleaming obsidian]

Okay here wait:

[oak chasm]

And we got 2 times 2^6?

[harsh acorn]

Yeah

[oak chasm]

Well, if we separate out one 2 from 2^(2p + 1), we have 2^(2p) stuck together, right? One less?

[harsh acorn]

Yeah

[oak chasm]

OK, so does it make sense what I did?

[harsh acorn]

No

I dont know where the +1 went

[oak chasm]

If we have 2p + 1 copies of 2 stuck together, and we separate one out, we have 1 copy of 2 and 2p copies of 2.

The 2p + 1 turns into 2p because you moved 1 of the 2s out.

So, you subtract 1.

[ocean seal]

Chai T. Rex

[oak chasm]

Did that part make sense?

[gleaming obsidian]

okay freagh it i tried writing it out and there is just too many visuals but here is a link to what I was going to talk about: https://www.youtube.com/watch?v=XPF5fe1WdKY

I will say though that by the end of this video you should understand why e^(n+m) = e^n * e^m

because there is a homomorphism between the two groups e^n or whatever e^ x

[oak chasm]

@gleaming obsidian Sorry, can you please do this elsewhere?

[gleaming obsidian]

and the additive group

oh sorry I was actually just explaining to bunny before you showed up actually

[oak chasm]

No, I was here before that.

[gleaming obsidian]

but sure

look man I dont care go ahead

[oak chasm]

@harsh acorn When you have a bunch of copies of a number multiplied together, you can count the copies, right?

[harsh acorn]

Yeah

[oak chasm]

OK, so let's say we have 7 copies of 2.

[ocean seal]

Chai T. Rex

[oak chasm]

Now, we can separate them into groups.

[ocean seal]

Chai T. Rex

[oak chasm]

See how we still have seven 2s?

[harsh acorn]

Yeah

[oak chasm]

But they're broken into two groups. One has three 2s. One has four 2s.

Does that make sense?

[harsh acorn]

Yeah

[oak chasm]

OK, so the three 2s plus the four 2s gives us the original seven 2s.

3 + 4 = 7

[harsh acorn]

Yeah

[oak chasm]

So, the number of 2s should stay the same when they're all added up.

[ocean seal]

Chai T. Rex

[oak chasm]

Now, we have 2p + 1 copies of 2 on the left side, right?

[harsh acorn]

Yeah

[oak chasm]

We have 1 copy and then 2p copies on the right side, right?

[harsh acorn]

Yeah

[oak chasm]

That adds up to 2p + 1 copies like we had on the left, right?

[harsh acorn]

Yeah

[oak chasm]

OK, so let's go back to our problem.

[ocean seal]

Chai T. Rex

[oak chasm]

So, let's go through it step by step.

We have 2p + 1 copies of 2k.

That's what we start with.

That can be separated into 2p + 1 copies of 2 and 2p + 1 copies of k.

Does that make sense?

[harsh acorn]

Yeah

[oak chasm]

OK, and let's look at the last part.

There's:

• 1 copy of 2
• 2p copies of 2
• 2p + 1 copies of k

[harsh acorn]

Yeah

[oak chasm]

How many copies of 2 does that add up to?

[harsh acorn]

1

sorry 3

1 copy of 2 and 1 2p copy of 2

[oak chasm]

Well, there's:

• 1 copy of 2
• 2p copies of 2
• 2p + 1 copies of k

So, we add the 1 copy and the 2p copies.

We get 2p + 1 copies of 2 all put together, right?

[harsh acorn]

Yeah

[oak chasm]

So, that's why it's equal to what came before.

The number of copies of 2 didn't change (it used to be 2p + 1). The number of copies of k didn't change.

Does that make sense?

[harsh acorn]

Yeah

[ocean seal]

Chai T. Rex

[oak chasm]

See how I just surrounded part with parentheses?

[harsh acorn]

Yeah

[ocean seal]

Chai T. Rex

[oak chasm]

So, what's the form of an even number?

It's 2 times something, right?

[harsh acorn]

2k

[oak chasm]

Right, so 2 times an integer.

And the part inside parentheses is an integer, right?

[harsh acorn]

Yeah

[oak chasm]

So, it's an even number.

So, an even number to the power of an odd number is an even number.

Does it make sense why it's an even number at the end?

[harsh acorn]

because an even number to the power of an odd number is an even number

[oak chasm]

Right, but I mean because you have 2 times an integer at the end, so you have an even number at the end.

So, you start out with an even number to the power of an odd number.

You end up with an even number.

So, you've proven what you wanted to.

An even number to the power of an odd number is an even number.

[ionic jewel]

thanks

maybe this will further broaden my understanding of e^(ix) witchcraft

but probably not

[harsh acorn]

So, Prove that raising an even number to an odd power gives an even number: Proof: let k be any integer and let p be any integer, so 2k²ᵖ+¹ = an even number because an even number to the power of an odd number is an even number

[oak chasm]

No, not because.

You saw the work I did, right?

You start with (2k)^(2p + 1). You go through finding what it's equal to.

At the end, it's equal to an even number.

That's why.

[harsh acorn]

So I have to show the calcualtion of 2k²ᵖ+¹ ?

[oak chasm]

Yes.

Don't forget the parentheses.

[harsh acorn]

Oh yeah

[oak chasm]

You have to show that that's equal to something else, which is equal to something else, which eventually is equal to an even number.

So because everything is equal to each other, you have what you started with equal to an even number.

So, because it's equal to an even number, it is an even number.

Does that make sense?

[harsh acorn]

Yeah

[oak chasm]

@harsh acorn Here are some exponent rules to make things easier: https://mathworld.wolfram.com/ExponentLaws.html.

I used the 4th one and the 1st one.

[fallen orbit]

what is the answer for this

its very confusing

[alpine sable]

How can I find the surface area of this?

[ionic jewel]

it has 6 sides, fine the AREA of each and add em

thank you autocorrect very cool

[torn patio]

guys can u explain dis 4 me pls idk how to do dis

[viral patio]

you already posted this in another channel, don't double post

[wheat prawn]

is this answer wrong

how did he reduce 30

it is not possible

how did he get 3

[viral patio]

simplify $$\frac{\sqrt3}{\sqrt10}$$

[torn patio]

no one anwered it tho

[viral patio]

you literally waited two minutes

[wheat prawn]

how did he get 3

[torn patio]

bruv im in a rush

[wheat prawn]

@viral patio what did he do?

[torn patio]

i poseted

in two chats

[viral patio]

sorry, i meant:

[torn patio]

like its not that deep bruh

[viral patio]

simplify $$\frac{\sqrt30}{\sqrt10}$$

[ocean seal]

ZainAK283

[wheat prawn]

did he reduce the 2 radicals?

by dividing by 10

oh yeaa its not a binomial i forgot

[viral patio]

$$=\sqrt{\frac{30}{10}}$$

[wheat prawn]

you can do that to monomials

[ocean seal]

ZainAK283

[strong furnace]

does the question imply the restriction on the function makes the function a monotonic increasing curve or is the domain of this function range of a monotonic increasing curve

first one would make more sense

[viral patio]

move to #help-6 please

[torn patio]

first one

[strong furnace]

sure

[torn patio]

ok bruh

[little wadi]

helo, i made this question by looking at a carpet and i want to know if it's possible. the question is "given a value for theta in degrees or radians, find a value for x for which A = B

and also the two angled ones are parallel

[viral patio]

this seems like a nice puzzle 👍

[little wadi]

yeah, i played around and i couldnt find any definite answers

[viral patio]

hmmm i think i'm going to redraw your diagram a bit...

[vale wigeon]

are the lines labeled A and X perpendicular to each other

[little wadi]

yes

[vale wigeon]

..............

don't call me sir.

[little wadi]

apologies

[viral patio]

that might look a bit more helpful

[vale wigeon]

it sounds like you want the red and green triangles to be congruent

[little wadi]

Mhm

[vale wigeon]

you would thus have this, where phi = pi/4 - theta/2

[little wadi]

Mhm

[vale wigeon]

well $x = a \tan(\varphi)$ isn't it

[ocean seal]

Ann

[ocean seal]

BelowAveragePlayer02

[nova dune]

How do we determine f(1)?

[strange fern]

if I squareroot 4x^2, does that become 2x or 4x?

[viral patio]

the equality holds for all x, so in particular it holds at x = 1

[nova dune]

2x

is f(x) just -|x|?

[rigid smelt]

not really

use the equation they gave you

[nova dune]

oh ofc

[viral patio]

it's some function that satisfies a given equation
all you need to do is use the fact that the equality holds for all x, including x = 1

[nova dune]

sorry, my brain ain't working

I understand now

Chur

[viral patio]

have any other questions?

[nova dune]

Nah

Thanks

[viral patio]

this room is now free

[dreamy wharf]

"For an infinite product to have a finite value, the general term must converge to 1 as you approach infinity". Is this statement true?

Or are there exceptions

[viral patio]

my brain is a bit low on juice
can you write that as "if ___ then ___"?

[vale wigeon]

@dreamy wharf infinite products may diverge to zero

when you have terms between 0 and 1, say

and they don't approach 1 quickly enough, or at all

[viral patio]

i haven't really dealt with infinite products - do we say that they "diverge to zero"? not "converge to zero"?

[vale wigeon]

such products behave more like divergent than convergent products

[dreamy wharf]

I meant finite non zero value here

Then is my statement true

[vale wigeon]

yes

[dreamy wharf]

[daring kindle]

Does anyone here know how to make a x bit binary array from 0 to N in python?

[languid grotto]

The log of a product (so the sum of the logs of the terms of the product) diverging to zero will diverge to -infinity also justifying the name a bit

[ivory otter]

we use the dot product

im confused by the question

maths makes me angry

[drowsy garnet]

The bold "i" is the vector (1, 0) (or whatever the proper notation is, I forgot)

The bold "j" is the vector (0, 1)

Does that help?

[ivory otter]

ye, but how can they tell what the angle is

[drowsy garnet]

Draw the vectors on the XY plane

(I'm assuming you're working with 2D vectors, not 3D)

[ivory otter]

ah shit wait the angle between i and j is always 90

isnt it

lol

[fallow jasper]

Yeah

[ivory otter]

or no not always

but for unit vectors

[drowsy garnet]

i and j are always unit vectors

[ivory otter]

i just realised that

[drowsy garnet]

i is defined to be (1, 0)

j is defined to be (0, 1)

[ivory otter]

3i isnt

?

[drowsy garnet]

I'm not sure what you're talking about.

[ivory otter]

ye i ask dumb questions when im confused

but i understand now i think

[native temple]

Is my graph Right and my equation right?

[native temple]

<@&286206848099549185>

[sinful quiver]

How do I determine where b is?

R, L, and N are known. a to b is perpendicular to R to L and b to N

[alpine sable]

plz help

wait

let me show answer and tell me if its right

1. do the answer is 682.2592?

2. do the answer is 82.525?

3. do the answer is 127.18?

plz answer i need to pass it on 1h

Can someone teach me question 1a and c.

<@&286206848099549185>

[zinc maple]

Help me

[merry salmon]

the length and the midpoint of the chord $2x+y-5=0$ wrt the circle $x^2+y^2=9$

[ocean seal]

PhysicsEnthusiast1618

[merry salmon]

I've tried to get the value y from the line equation and substituted to circle equation, but felt lil too long

[tough hatch]

also don't post questions in multiple channels @alpine sable @zinc maple

[simple pond]

1. 217.28/2=108.64 is the circumference of the field. 108.64/2pi= 17.29. Pi(17.29) ^2= 939.16 is the answer

[alpine sable]

the big line is in c a/b//c

c it's x-1 its hard but i wouldn't surrender

there's no way it will equal 0/0

[merry salmon]

wdym? i didnt get you

were you replying to me?

[alpine sable]

lim goes to 1

or approach to 1

[rigid smelt]

try to do one sided limit

see if they equal

channel might be busy, you should move

[upper fjord]

okay

[simple pond]

Send it to #help-6

[upper fjord]

okay ı did

[alpine sable]

Do / is divide

[neat dome]

i need some help with this question ;-;

[rigid smelt]

can you determine the second derivative first?

[neat dome]

aight gimme a sec

12rx^2+6sx

[rigid smelt]

btw, is there any restrictions on r and s?

[neat dome]

not any are given

[rigid smelt]

this is wrong

its almost correct

[neat dome]

dang

[rigid smelt]

try to do it slowly

hmm strange tho

there should be some restrictions on r and s

[neat dome]

i mean there arent any in the question

[rigid smelt]

can you post the whole question?

[neat dome]

i did

that was the whole question

[rigid smelt]

weird

because f(x) have two points of inflections only if r*s<0

[neat dome]

well maybe the question wanted me to like, figure out when it makes the function prove the requirements?

idk man

[rigid smelt]

doesnt seem like so

ask your teacher about it

it clearly states that it wants you to prove that f(x) has two inflection points, which is false

[neat dome]

yeah i checked on desmos and i only see one inflection point at (0,0)

[rigid smelt]

well r and s have to have different sign for the graph to have two inflections

or mathematically expressed, rs<0

[neat dome]

hmm

[rigid smelt]

well i guess you can change the subject of the question and instead prove the inequality above

and then ask your teacher if the question has some errors or sth

[neat dome]

umm okok

is desmos wrong or something

[rigid smelt]

no

again, the question is wrong

f(x) has two inflections point only if rs<0

[neat dome]

is it possible to see it on a graph? I have trouble visualizing these things ;w;

[rigid smelt]

so now the question is are you interested in proving that

[rigid smelt]

https://www.desmos.com/calculator/rquv5oigli

try playing around with the slider

if both of them are positive or negative, the graph either concave up or down

if not, they have points of inflections

[neat dome]

okok

wait do these two dots count as an inflection point?

[rigid smelt]

no

oh wait oops yes

they are the two inflection points

[neat dome]

oh okok

wait but this graph is ax^4+bx^2

the one in the questions is to the power of 3

and i couldnt find anything for that graph

[rigid smelt]

which one is a 3?

oh the second term

jesus

alright then

ok so your second derivative is correct

now how do you find the point of inflections?

[neat dome]

uhhhhh set it to 0?

[rigid smelt]

yes

so 12rx^2 + 6sx =0

can you factor this?

or you can also prove that the discriminant is always positive

but factoring is faster

[neat dome]

ok lemme try

[tight sphinx]

Someone explain pls

I don't understand

[pearl marlin]

So it is 75% empty of 96

[nova dune]

Me neither. Can u convert this into text?

[tight sphinx]

Ohhhh

Ty

[silk willow]

I have a question about polynomials.
I have two polynomials in Z19[x]
p(x) = 13ax^2 + 2x + 5
q(x) = 2x + 18

GCD(p(x),q(x)) = x + 9
How do I find the value of a so that the remainder of the polynomial division is 0?

[alpine sable]

solve equations

[daring chasm]

factor out the x, x(12rx+6s)=0, and at that point it should be pretty trivial

[silk willow]

How?

[daring chasm]

and nvm im an idiot and didnt realise you were answering, yeay

[pearl marlin]

Is answer is 4?

[alpine sable]

like what does it mean to give the remainder 0 homie

set up some equations

[silk willow]

Let me check

[tight sphinx]

@pearl marlin the answer book says 24 gigalitres, but idk how to get to it, my working is 75/100x96/1

nvm'

[loud talon]

It only has 25% of its capacity

That would be

25/100 *96

25% ‘’full’’

[tight sphinx]

ohhhhh

wait

but isnt it

96/100*25

[silk willow]

Yes. How did you do it?

[alpine sable]

homie tell me what it means to give reaminder 0

[tight sphinx]

because when i done 96/100*25 it got me to 24GL which was the right answer

[alpine sable]

and you will solve it

[pearl marlin]

I read question wrongly ,my apology

[alpine sable]

step bys tep

[tight sphinx]

no worries haha

[loud talon]

Put x as -9

[loud talon]

U are wrong as

The answer is right

What does 25% represent

[tight sphinx]

how much there is inside the tank?

[loud talon]

=>25/100

The capacity of tank

[tight sphinx]

mhm

[loud talon]

=>96

[pearl marlin]

Here gcd is x+9 so x=-9 or we can say x=10 (because of mod 19)

Now here x=10 is root (because x+9 was gcd means divide the polynomial)

Put X=10 and try to find a

[loud talon]

The question says it’s 25 % full
So it has 25% of its capacity.
Multiple 25/100 to 96(capacity

[tight sphinx]

mhm

oh

[silk willow]

Ow, ty a lot❤️

[raven path]

can we calculate the nth prime number using reimann's conjecture ?

[alpine sable]

why not just do p=aq and solve easily

..

[raven path]

what is p = aq?

[alpine sable]

not to you

[raven path]

oh, my bad

[alpine sable]

nth prime is n/logn

jk

this tells you how many primes there are up to n

[raven path]

yeah

[alpine sable]

what's reimann conjecture

[raven path]

https://en.wikipedia.org/wiki/Riemann_hypothesis

[alpine sable]

lol

reimann =/= riemann

conjecture =/= hypothesis

[raven path]

lol my bad

[alpine sable]

but yeah assuming riemann hypothesis you can predict nth prime

[raven path]

hmm how?

[alpine sable]

it gives a formula $\int_{2}^{p_n} \frac{dt}{lnt} = n + O( \sqrt{n ln^3 n})$

[ocean seal]

Ledog

[raven path]

hmmm can you provide a source to read about this?

[alpine sable]

theres Tao's lecture about it

wait

https://www.youtube.com/watch?v=PtsrAw1LR3E&t=

[raven path]

ohk thanks

[neat dome]

help :ccc

[scenic wind]

Can someone tell me how i would work this out from my understanding i would write it twice?

[glass lichen]

$(a+b)^2=a^2+2ab+b^2$

[ocean seal]

Mosh

[pearl marlin]

Derivative can help you here

[neat dome]

yeah but i dont know where to go from there

f'(x)=-2x^3+3x^2+36x-8

f"(x)=-6x^2+6x+36

[steel gulch]

for points of inflection

solve the second derivative

this is known as the second derivative test

[neat dome]

i got -3 and 2 but when i checked desmos it didnt look right ;w;

[steel gulch]

the answer u get will be the x values for which there is a point of infleciton in your funciton

check the second derivative

if it intercepts the x axis at those values

[pearl marlin]

Can you find where it is postive and negative?

[steel gulch]

ur POIs are correct

[neat dome]

okok

[neat dome]

as in concavity?

[pearl marlin]

Yes

[neat dome]

umm i just take values from the left and right of -3 and 2 and like, solve for x right? thatll tell me whether they are pos or neg?

[neat dome]

oh wait do i need to solve the first derivative first

for the intervals of increase and decrease

[pearl marlin]

Yes

[neat dome]

i think that was wat i was stuck on ;w; i didnt know how to solve for x in the first derivative

[pearl marlin]

Use desmos ,he can give you idea , write this -6X^2+6x+36> 0 ,he will tell you intervel

[neat dome]

but i need to do it algebraically so...

i dont know how to factor this AHHHHHHHH

[pearl marlin]

-6x^2+6x+36>0

-6(x^2-x-6)>0

X^2 -x -6<0

Can you solve now

[neat dome]

oh why do u use <> symbol rather than =

[neat dome]

wait thats for the second derivative no? I thought you need the first derivative to find the intervals

[pearl marlin]

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/03%3A_The_Graphical_Behavior_of_Functions/3.04%3A_Concavity_and_the_Second_Derivative

[steel gulch]

i can use cross product for this right

[glass lichen]

yes, cross product gives mutually orthogonal R3 vectors

[pearl marlin]

Yes

[steel gulch]

and check my answer with dot product

what about this

[glass lichen]

use the projection formula

[steel gulch]

how do i do this?

i know i ened the dot product

with i can find by doing a dot b

what is the formula

[glass lichen]

that's b onto a iirc

[steel gulch]

there is a formula for this as well i beleive

u dot v/magnitude of u * magnitude of v cos 60 ?

[glass lichen]

expand the dot product

[steel gulch]

how so

[glass lichen]

dot product is distributive

[lapis seal]

hi

basically i got this big exam tommorow and i know all the formulas but somehow still can t resolve some problems

[steel gulch]

i see

like this

i found a similar solution in my notes

[glass lichen]

yes

$(a+b)\cdot(c+d)$ expands how you think it expands with FOIL

[ocean seal]

Mosh

[steel gulch]

ok i see

that makes sense

whoops

"and is moving at a rate of 1 m/s"

[undone scroll]

help

[outer moon]

can someone please check my answer about proving triangle similarity?

this too, please?

thank u smmm

[alpine sable]

What do we call that

Thing

[pearl marlin]

Delta y

[alpine sable]

Ok thanks

[glass lichen]

$\delta$

[ocean seal]

Mosh

[alpine sable]

I was trying to show in $\mathbb{H}$ -Poincaré half-plane model- that hypercycles defined for a given line $l$ and a given $a$ in $\mathbb{R}$ as $$H(l)={z \in \mathbb{H} : d_{\mathbb{H}}(z,l)=a } $$
are not lines.

To prove something I tryed to argue that given that $Mob(\mathbb{H})$ acts transitvely on the lines of $\mathbb{H}$ I can find the hypercycles of the imaginary axis and via the $\gamma \in Mob(\mathbb{H})$ that maps my line in the imaginary axis i can state $$H(l)=\gamma^{-1}(H(\gamma(l))$$

Where I'm using the fact that a Möbius transformations preserves distances. At this point I defined [already here i have doubts] $d_{\mathbb{H}}(z,l)$ for a given $z \in \mathbb{H}$ and a line $l$ as the inf of the distances $d_{\mathbb{H}}(z,w)$ with $w \in l$.

Given this and the general assumption $z=a+bi$ and $w=ki$ i'm left with trying to calculate the inf of $$arccosh(1+\frac{|a+(b-k)i|^{2}}{2bk})$$.

Is any of this correct? There is any "distance from a given point to a given line" standard formula in hyperbolic geometry? Thanks for any help and hint.

[ocean seal]

Stephen

[vale wigeon]

@alpine sable i think you may want to move to #point-set-topology, a channel that is far less hectic, unless you're okay with your question getting completely buried

oh you multiposted

[ornate quest]

Hello,

I have a stack of 10'000 pieces that I want to releas in a logaritmic ways during 84 months.

So I expect the first release to have a higher numbers of pieces than the lasts. Here is an example :

Month 1 : 50 pieces. Total : 50
Month 2 : 48 pieces. Total : 98
...
Month 83 : 1.2 pièce. Total : 9'998.9
Month 84 : 1.1 piece. Total : 10'000

Does someone could help me 🙂

Thank you

Have a good day

[violet swift]

nyonkne know

[viscid basalt]

if p=np does that mean p is 0

[vale wigeon]

no, it could also be that n = 1.

[vague coral]

isnt P=NP some computer science problem ?

[viscid basalt]

yes, but no

[tribal yarrow]

Hi, can I ask about calculus problem here?

[vague coral]

yes

[tribal yarrow]

I want to prove this limit exist on (x,y) -> (0,0)

I was wondering how would you apply squeeze theorem into this..

[pearl marlin]

Try using poler coordinates

[tribal yarrow]

I already did, my problem is that they want me to solve it with squeeze theorem

the problem is don't know why did they select 0 and 1 for the bounds

[pearl marlin]

I think because they use polar coordinates
Sin^4 theta/ sin^4 theta+ cos^4 theta

Have maximum value 1 and minimum 0

[tribal yarrow]

alright, i'll ponder on it thanks

[steel gulch]

can i get some help on my question

[summer crow]

the way I see it, 0 and 1 are the easiest bounds you can think of where you're sure that both functions have limits that do exist.

We are sure that g(x, y) is a positive-valued function since the exponents are even, thus it is bounded below by 0. Also, since the numerator is smaller than the denominator, it is a proper function, thus bounded above by 1.

Try and check this by using a graphing calculator and see that the graph is bounded by 0 and 1.

[paper bay]

is the chat open?

I have a question

If p(x) is a polynomial of at least degree one and p(k)=0 then K is known as

[alpine sable]

Me needs help

[alpine sable]

Zero of that polynomial

[paper bay]

can u explain pls

[summer crow]

zeroes of p(x)

because if you substitute all x's in p(x) with k, it returns 0. Mathematically, p(k) =0

[alpine sable]

Put the values in the formula for Compound Interest

[alpine sable]

I guess baitxh has explained...
if you have some other prob just DM me I'll try to explain

[paper bay]

I didnt understand anything tho

[alpine sable]

i need help with finding p for this

[alpine sable]

You are having prob with which part??

[pearl marlin]

Where is p?

[paper bay]

with my whole question

[alpine sable]

idk thats all they gave me

[alpine sable]

It's pretty clear I guess Like if p(x) is a polynomial let's say x+1= 0 for instance

Then the values of x for which poly satisfy

Will be the zero of polynomial

@paper bay

[paper bay]

That confused me more

[alpine sable]

Ohh lemme clear things up a bit

[alpine sable]

Like In this case -1 is the possible value of x for which the poly satisfies...

Therefore the zero of the poly is -1

[summer crow]

I think @paper bay is misunderstanding "zero" as 0, not Zero as in what you call those numbers that return 0?

[alpine sable]

I think so

[paper bay]

no the thing is
I am unable to understand what the question even means

[summer crow]

hmmm... the question asks for the thing you call to numbers that return 0 when you insert it in a function

[alpine sable]

@summer crow I think he/she just don't wanna learn and want to put all the blames on our education system

[paper bay]

a) I am he
b) Its education system fault
c) Maths is senseless

[normal lance]

$f(f(x)^2+f(y))=xf(x)+y$

[ocean seal]

Mad dron Matrix

[normal lance]

Find F of R all functions

[elder stratus]

mhm

Bruh

This is fisic

[elder stratus]

Here result

[simple pond]

6x8=48. 6(8)+24(9)

=264

[glass lichen]

dont crosspost / spam your question

[ebon temple]

its different

[glass lichen]

it's the exact same problem with different numbers

[ebon temple]

ok

[summer crow]

compute for the area of the side triangles first using A=1/2 (bh), where b=8 and h=6
now, the area of the rectangle at the back, A=lw, where l=9 and h=6
area of slanted rectangle, A=lw where l=9 and w=10
and area of bottom rectangle A=lw too where l=9 and w=8

add these up

[simple pond]

https://youtu.be/TycP9snLk1E look at this video. It will teach u. Its only 4minutes

[ebon temple]

thx

[alpine sable]

how do you turn log(3-x) to log(x-3)?

[vague coral]

you cant I think

[ocean seal]

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

[alpine sable]

there has to be some sort of connection

[pearl marlin]

Zoom it ,

[vague coral]

zoom again

[pearl marlin]

Can you see them intersecting

[alpine sable]

yes

[frail siren]

hey this isnt really related to anything but i have a 15sq ft box right how would i write out a formula to fill it with 1cm objects

there are 50 of those 1 cm objects in a packet that is worth 50cents how much money would it take to fill

the box is 10 inches deep

[remote heron]

do you mean like to figure out how many objects you can fit into a box?

[frail siren]

yes and how much money it would be if the packet of objects was 50 cents

there are 50 of those objects

per pack

[remote heron]

if youre doing this for a real world thing youre gonna wanna figure out how many whole cm you can get from each dimension of the box

assuming that you cant cut them into pieces

its probably gonna be smaller than the dimensions of the box by a little bit

so just use a converter and truncate each of the three answers

[frail siren]

im trying to fill an entire box with seeds to the brim each seed is 1cm the box is 15² ft and 10 inches deep the seeds come in a 50cent pack there are 50 seeds per pack

[remote heron]

whats the dimensions of the seeds

you mean like 1cm high?

[frail siren]

1x1cm

[remote heron]

should be one more dimension

[frail siren]

i dont know they are circular but they are roughly 1cm all round

[remote heron]

its hard to say it sounds like youre describing a cube

or a cylinder

you can just divide the volume of the box by the volume of the packet of seeds

that will give you a good estimate if each packet of seeds is very small in comparison to the box

if you want to get an exact answer youll need to do the fancier truncation thing i was talking about

if you do the approximation thing, just make sure the units match (so convert the seeds to inches, or the box to cm)

[ebon temple]

Help pls

[remote heron]

@ebon temple please stop posting across multiple channels lol

[ebon temple]

I just need help

[glass lichen]

then follow the rules

[ebon temple]

dam my bad

[alpine sable]

i'll post it here again

but don't crosspost problems please
just take all the sides and calculate the sum of those and then add them all

wasn't referring to your problem sorry

[summer pecan]

Hi, I need someone to explain this concept to me. Thanks

[rain sparrow]

Hi, would I use present value or future value for this?

[sleek elbow]

channel is occupied

[rain sparrow]

Oh, okay

[pearl marlin]

What is An here

[glass lichen]

There's no "final" natural number, so no matter what m you pick, m will not be in the next A

this holds because we're intersecting the infinite number of A_n, if it was a finite intersection, then the set would not be empty, it'd be the next A after where you end

[summer pecan]

OuO! thanks for you explaination! I understand! arigatogozaimasu

[glass lichen]

m in the big intersection means m is in every A_n, which is impossible since N is countably infinite

m would have to be the final value in the set N, which doesnt exist

You could also do a very loose inductive-esque proof on the upper bound of the big intersection

$\lim_{m\to\infty}\cap_{n=1}^m A_n =\emptyset$

[ocean seal]

Mosh

[glass lichen]

which makes sense cause we're removing elements as m gets bigger, but the explanation in the picture is much better

[summer pecan]

Lol, i still don't understand what is it talking about until you explain it to me 🤣

[bitter kite]

Is anyone online?

[summer pecan]

Well, Thank for your help, Mosh🤣

[bitter kite]

Whats the server id, i need it now im on my phone

[winged smelt]

268882317391429632

[bitter kite]

Ok thanks

[icy jetty]

The second term is 4x

[alpine sable]

Are you asking me

[glass lichen]

Google it

ok then keep searching, you asked a question which you can google.. do your own work

[dark zenith]

In this type of problem, should I take 2 integrals, one from 0 to pi/2 and one from pi/2 to pi..? I'm not sure if this is cosine or sin half series how do i know which one I need to follow... (sint is odd, so should I go for sin series, if in second range it is an even function, what do i need to do)

[charred flint]

hey awake

@dark zenith it should be 1 integral on the full interval, and either sine or cosine are fine

[alpine sable]

Can someone explain how 1-(1/2sqrt(x)) = (2sqrt(x)-1)/2sqrt(x)

[charred flint]

I'd guess sine is easier though

[dark zenith]

What?.. Can u tell how. M

[charred flint]

by reading

[dark zenith]

Sooo can i take half sin series and function in series as sin(t)

[dark zenith]

What should be limits

[charred flint]

the interval

[final crag]

How would I get the coefficient matrix?

Would it just be ```py
2 3 4
4 3 1
3 1 2

[glass lichen]

yes, that's the co-efficient

$\begin{bmatrix}2&3&4\4&3&1\3&1&2\end{bmatrix}$

[ocean seal]

Mosh

[alpine sable]

Help with this pls

[final crag]

Would the augmented matrix just add the last column?

[glass lichen]

it'd augment the constant vector, yes

[final crag]

So ```py
2 3 4 1
4 3 1 6
3 1 2 2

[glass lichen]

yes

[final crag]

kk thanks

do you know anything about pivots?

how do i determine if theres a pivot in a matrix?

[glass lichen]

pivot is 1 in 1 entry of the column, 0 else

[final crag]

oh so like ```py
1 0 0
0 1 0
0 0 1

3 pivots?

[glass lichen]

yes

[final crag]

<@&268886789983436800>

[sly mantle]

b&

[wraith cairn]

bampersand.

[final crag]

Is row reduction called row echelon form?

[ionic jewel]

row reduction is the process

ref/rref is the result

[final crag]

oh okay

i think row echelon form is like ```py
1 0 0
0 1 0
0 0 1

[glass lichen]

that's RREF specifically

[final crag]

row reduction gets to row echelon form eventually

like thats the goal with row reduction

to get in to that form?

[glass lichen]

Gauss-Jordan is to get the system into RREF, yes

[final crag]

2 3 4 1
4 3 1 6
3 1 2 2

for something like this, would you start off by diving r1 by 2?

[glass lichen]

yeah, you want first column to be 1 0 0 (top to bottom)

[jagged trout]

@final crag you also can do r2 - r3 and r3 - r1

[torpid stump]

Help please? Whats the answer to the DE dp/dy = -Kp?

I have ln p = -Kh + c is this correct?

[glass lichen]

$\dv{p}{y}=-kp \implies \ln{\abs{p}}=-ky+c$

[ocean seal]

Mosh

[torpid stump]

sorry typed it wrong

its dp/dh no dp/dy

[glass lichen]

ok then yeah, just replace what I wrote y's to h's

[torpid stump]

oh ok thanks

[final crag]

how would i know if the soluttion to the system is unique?

i gott x1 = 1, x2 = 1, and x3 = -1

is that unique?

[glass lichen]

yes

that's a unique R3 vector..

[final crag]

can you explain why please?

[glass lichen]

cause it's no other R3 vector

[final crag]

there are no free variables?

[glass lichen]

[1,1,-1] is clearly unique

[final crag]

and theres a pivot in every column?

[glass lichen]

yes, it's full rank so Ax=b has a unique solution

[final crag]

i'm trying to understand what pivot means

[glass lichen]

you get $x_n=c$ for some n

[ocean seal]

Mosh

[glass lichen]

or, like I've said already, the column is 1 in 1 entry and 0 else

[final crag]

so basically 1 in each column

means it has a pivot?

so ```py
1 0 0
0 1 0
0 0 0

but ```py
1 0 0
0 1 0
0 0 1

[glass lichen]

the 1st has 2 pivots

the 2nd has 3

[final crag]

ah

1 0 0 1
0 1 0 1 
0 0 1 -1
``` would have 3 pivots?

[glass lichen]

yes

[final crag]

ah okay i think i get this now

ty

[glass lichen]

you have x=1 y=1 z=-1 which is a unique solution to Ax=b

[final crag]

so ```py
1 0 0
0 0 0
0 0 0

1 pivot?

[glass lichen]

yes

you'd have x=something, and y and z be free variables

[final crag]

ah okay got it

thanks!

[flat gust]

Can someone help me out

[ionic jewel]

write any function such that it takes 1.75 hours to go 13.1 miles

that's literally the only criteria

oh and 0 time = 0 miles

[flat gust]

How did u get 13.1 miles

[ionic jewel]

26.2/2

[glass lichen]

half-way time

[ionic jewel]

^

I'm guessing this is a lesson on lines and they want a line, but id guess marathon runners slow down at the end

so a log function or something probably would be more accurate

[glass lichen]

Running as a sine wave \s

[ionic jewel]

cursed

[glass lichen]

POV you're a particle between 2 springs with the same spring constant

[ionic jewel]

because it's not

what kind of explanation do you want

pi is defined as a constant 3.14... which is not 4

lemme guess you saw that stupid square "proof"

the answer is because it never turns into a circle

theres plenty of videos online debunking it

... sure

[fast wave]

this is right?

[ionic jewel]

sure, but you could also just find a video online that says the same thing but with cooler visuals

you too

[ionic jewel]

think so

yea

looks right

[fast wave]

this?

@ionic jewel

[ionic jewel]

uh

yea

wait

f(f^(-1)(x)) = x