help-10

[obtuse pebble]

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[woeful light]

[discrete-math] Finding four piles of rocks on a trail, we decided to rearrange them into five piles. Show that at least two rocks finished in smaller piles.

[woeful light]

I was thinking that this one would be easy. But I'm not finding the way to make the proof. The pigeonhole principle is enough?

Like, the number of rocks dont grow, but the number of piles do. So its obvious that some piles will have less rocks then others

But I dont think that this argument will suffice

<@&286206848099549185>

[obtuse pebble]

@woeful light Has your question been resolved?

[obtuse pebble]

@woeful light Has your question been resolved?

[obtuse pebble]

@woeful light Has your question been resolved?

[swift marsh]

Sorry for the long wait

Idk if you’re still on this problem

But if you are, one way to approach it is to think about labelling the piles, and then you can work with inequalities to establish the result

It’s also good to order them

If you want a bit more help: ||you could consider summing the largest (some number) piles, up until the sum for the first pile is larger than that of the second one (which must occur at some point)||

[woeful light]

Relax, you're not obliged. You're doing me a favor to come in here and helping and I'm grateful for this

[woeful light]

Like, sum the largest piles to the first and second one to find and prove the inequality between them?

assuming that they are the smaller piles

[swift marsh]

Yeah

So if you let the first piles be p_1 up to p_4 and the second q_1 up to q_5

At some point p_1 + … + p_n > q_1 + … + q_n and it’s a useful result

It’s quite an intuitive thing, the proof probably less so though

I’d be interested in a proof in plain english or a really elegant one

I should say p_1 > p_2 > … and similarly for q

[woeful light]

Unfortunately I need to write this in portuguese

haha

But thanks man, helped a lot

.close

[obtuse pebble]

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[obtuse pebble]

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[onyx dust]

hey could someone please walk me through this?

<@&286206848099549185>

.close

[obtuse pebble]

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[graceful sparrow]

$1/4x^2-x$

[warm shale]

dani el bruh

[graceful sparrow]

i need help converting this to vertex form

[obtuse pebble]

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[graceful sparrow]

did it not go through?

[graceful sparrow]

oh there we go

[graceful sparrow]

.

[long sinew]

I think the \ thing on discord is stopping me

Do you mean 1/(4x^2) - x?

Or 1/4 * x^2

@graceful sparrow

[graceful sparrow]

no

[graceful sparrow]

.

[long sinew]

1/4 * x^2?

[short spruce]

the way you wrote it can be interpreted in different ways, and a lot of people make parenthesis mistakes here

[graceful sparrow]

$4(y+1)=(x-2)^2$

[warm shale]

dani el bruh

[short spruce]

that's what breezi is trying to clarify

either way, complete the square

[graceful sparrow]

this is the orignal equation

[long sinew]

...

[graceful sparrow]

and i need to find the vertex, directrix and focus

and the first equation i put was the simplied equation i got

[long sinew]

Well thats different than what you asked for

[graceful sparrow]

i mean to get the vertex, i need to convert it to vertex form, no?

[long sinew]

Not necessarily lol

-b/(2a) works just fine

Then plug that in for x

[graceful sparrow]

$-b/(2a)$

[warm shale]

dani el bruh

[long sinew]

@short spruce Do you know how to fix the issue with the frac\ command, whenever I use the curly braces {} it stops working

[short spruce]

\frac{}{}

not frac\

[long sinew]

Oh

I am a moron :)

I somehow forgot how to use a simple latex thingy

(I literally used this like 15 minutes ago wtf)

$\frac{-b}{2a} = x$

[warm shale]

Breeziboi

[long sinew]

But if you want focus of the parabola then yes vertex form

Tho I guess it's not necessary if you get the vertex with -b/2a = x, but whatever thats how I learned it 🤷

¯_(ツ)_/¯

[graceful sparrow]

well i also have to draw the parabola in that problem too

but i know how to do it

i just forgot the process of getting it using formulas

[graceful sparrow]

so thats the vertex equation?

[long sinew]

For the x coordinate or axis of symmetry

Then you plug in whatever you get for the x coord into the original equation

[graceful sparrow]

alrighty

then what about the focus and directrix

[fickle bramble]

Is the roster notation of {2xϵZ+|x≤4} 2,4,6,8 or 2,4 only?

[graceful sparrow]

not to sound rude but this channel is already occupied

[fickle bramble]

ow sorry I clicked the wrong one

[long sinew]

Alright lets do this by vertex form of a parabola

y = a(x - h)^2 + k
Focus: a = 1/(4p)

By finding p, it's pretty simple to find the focus and directrix

Since the distance from the vertex and the focus is p

As well as the distance from the vertex to the directrix

We know a = 1/4 from the standard form equation
1/4 = 1/(4p)
4 = 4p
p = 1

[graceful sparrow]

i see

but my main question is

$y=\frac{1}{4}x^2-x$

[warm shale]

dani el bruh

[graceful sparrow]

how do i turn this into a(x-h)^2+k

[obtuse pebble]

@graceful sparrow Has your question been resolved?

[raw horizon]

by completing the square

[obtuse pebble]

@graceful sparrow Has your question been resolved?

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

[timid silo]

Algebra 2 eliminations

This is wrong apparently

This is wrong as well

[civic zealot]

how are you eliminating x?

[timid silo]

Its equations

Its X & Y as well its algebra 2

[civic zealot]

i understand that. I'm asking what you did to eliminate x in the equations you have

[timid silo]

Oooh

First i added both equations as the help video told me

Ended up with 2 + 14 = 52 and idk wtf i did with the x put im pretty sure it goes away

Delta math what my teacher uses says the equation even the app came up with is wrong

[civic zealot]

if you add them directly you have (2x+7) +(x+7y) = 20+32

nothing goes away

[timid silo]

No the X from the 2’s

I feel l like putting in a fake answer to get the real one and see where I went wrong then I can get a better grasp

Did it

The final answer was 4 & 4

Lemme send u it so u can help me with the next problem please

Why does this shit gotta be so damn complicated 😭

Imma write this out to get a better understanding

Then ill send u the next problem and i’d like u to help me work through it to get it correct

Do u know why it works like this? I don’t understand it

Actually i do kind of understand it just messed up the process

[civic zealot]

you're adding two equations and combining like terms

you want something to go away, you multiply one of the equations by a constant so one of the variables will add to 0

[timid silo]

Which switches the sign right?

[civic zealot]

the multiplication can switch the sign if you need it to, yes

[timid silo]

Also step 3 why do you add 8 to both sides?

[civic zealot]

to solve for y

[timid silo]

But how do i know when to do it

When its like that?

Cuz its the opposite of the other 8 oh shit

To get rid of it

[civic zealot]

once you sub 4 in for x, you have -8+7y = 20

[timid silo]

And u gotta do that to the other side

[civic zealot]

this is a linear equation, so you're solving for y

[timid silo]

And X

But yeah

[sacred oak]

Its an equality

If u add something in one side

[timid silo]

U add it to the other or subtract ye

[sacred oak]

You gotta do the same on the other side

[timid silo]

Remembered that after ive done fuck all in math for years really behind 😭

U can tell but yk im tryna get serious about it again better off than giving up

[sacred oak]

And its great mate

Keep it up

[timid silo]

Thanks

[sacred oak]

Find good resources on yt or books

[timid silo]

Mh

[sacred oak]

And just solve

[timid silo]

Ok gonna try this one now

Hows this (i fixed the 3 to a negative)

Thats following the same process as the other now i need Y

So this is wrong where’d i go wrong

@bold meadow

[civic zealot]

what is 9y+9y?

[timid silo]

Ur supposed to cancel it out per the other equation

[civic zealot]

yes, you're supposed to cancel them out by multiplying something so when you add them they cancel

[timid silo]

That has no place in the equation for x correct? Or minimal? If so what do i do to the 18

[civic zealot]

they don't just cancel because you added them

[timid silo]

Ah but it does go away at the end of the day correct?

So that i did right thanks for letting me know why but where did i go wrong cuz its wrong

[civic zealot]

no....you added 9y+9y and got 0

[timid silo]

Yes to get rid of it

I did that

[civic zealot]

what is 9+9?

[timid silo]

18

[civic zealot]

so how is 9y+9y = 0?

[timid silo]

I thought I was eliminating it

I know it’s not 0

[civic zealot]

so multiply the second equation by -1

[timid silo]

So what am i supposed to do with that 18

[civic zealot]

that will give you a -9y

[timid silo]

Wait lemme rewrite that now

Now -5 + 18y = -36

[civic zealot]

do you?

[timid silo]

-5x* which i am solving for the X first

So now i get rid of the 18 y right?

[civic zealot]

you should have 9y-9y

[timid silo]

??????

You add or subtract this whole problem first oh fuck i forgot that

Ok its -5x + 18y = 15

[civic zealot]

is it?

[timid silo]

Now wtf do i do cuz i am supposed to get rid of the y first as thats now what i solve first as shown in the first ss’s im showing

I don’t think I’m supposed to add on the first omg wtf am I doing man I’m so confused 😭

[civic zealot]

you should get -8x - (-3x)

9y-9y

-21-(-36)

[timid silo]

Man how’d u even get that

[civic zealot]

first equation - second equation

[timid silo]

I still have -5x + 18y = 15 written down and don’t know if that’s what I should he doing

Lemme look at an example

[civic zealot]

what is this?

[timid silo]

Equations

Elimations****

[civic zealot]

what is 9-9?

[timid silo]

0

[civic zealot]

so what is 9y-9y?

[timid silo]

0

[civic zealot]

so why do you have 18y when you do 9y-9y?

[timid silo]

Or y

Cuz u told me not to add it

[civic zealot]

because you had 9y+9y = 0

[timid silo]

I just got rid of it

It was wrong as well tho

Maybe I am supposed to add since I subtracted and it was wrong

This is an example

Weird one lemme find another

[nocturne minnow]

What exactly do you mean by this?

[timid silo]

I don’t even fuckin know I’m out of it this is algebra 2 eliminations

You are supposed to subtract first tho

For x

The first step of it

[nocturne minnow]

Elimination means you want to cancel out one of the variables in the equation. You need to have equal but opposite coefficients to do so

[timid silo]

So Y correct? I cancel it out?

[nocturne minnow]

For the examples, you are demonstrated, it's eliminating y, because in both equation, they have the same coefficient

[timid silo]

Then i get -3 same answer as before

[nocturne minnow]

The only difference is that, they are both positive and as I mentioned, you want equal but opposite coefficients so you take the first equation and subtract the second equation from it

[timid silo]

Yes

So ive done this correct so far right?

[nocturne minnow]

Basically, you are just flipping the signs in the second equation and then adding it to the first

[timid silo]

Why

[nocturne minnow]

Because, for example, 5 - 6 is the same as 5 + -6, right?

Flipping the sign of the second part and then adding it to the first

[timid silo]

Thank u for trying to help me if my brother was not screaming and if it was not almost 12 at night I think i’d be doing better ill be back tmr I cant do this tmr

this rn*

[nocturne minnow]

Maybe this will help out
https://www.youtube.com/watch?v=T-b9GbfO9Eg&ab_channel=TheOrganicChemistryTutor

[timid silo]

Thanks I’ll come sci here and look at it tmr when I’m not tired and all

Dk where the sci came from 😭

If u want help u need to @ then say help for it sum will come

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[timid silo]

Tmr

[obtuse pebble]

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[wild forge]

find dy/dx of e^y=x

[wild forge]

y=lnx
then answer is 1/x ?

is that correct

.close

[obtuse pebble]

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[obtuse pebble]

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[woeful shale]

need help

[teal prawn]

are you allowed to use a calc to find sin(27°)?

[woeful shale]

nop

[tardy epoch]

Why not

[woeful shale]

idk teacher doesnt want me to use a calc

[tardy epoch]

Is it in the instructions with the problem?

[woeful shale]

no its not

so sin27 is 0.956

[obtuse pebble]

@woeful shale Has your question been resolved?

[tardy epoch]

,calc sin(27 deg)

[warm shale]

Result:

0.45399049973955

[tardy epoch]

Check your units

[obtuse pebble]

@woeful shale Has your question been resolved?

[wary coyote]

?

[obtuse pebble]

@woeful shale Has your question been resolved?

[obtuse pebble]

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[unkempt sapphire]

is this linear transformation invertible?
f(v, minV, maxV) = (v + minV) / (maxV - minV)

[last basalt]

An invertible linear transformation is injective and surjective

Can you find an instance where this is not injective

[unkempt sapphire]

nope

actually i don't think it's possible to invert (i.e given x = f(v, minV, maxV) recover the original v from x)

if i also knew minV maxV when recovering, it should be possible

altho i suppose i could figure out minV maxV too since i know how these were generated

[last basalt]

What happens if you use an arbitrary vector like [2,2,3]

Then a multiple of it

[unkempt sapphire]

as an input to the function?

[last basalt]

Yes

[unkempt sapphire]

it gives identical results

i.e f(2, 2, 3) = f(6, 6, 9)

[last basalt]

Yes

not unique

Thus not one-to-one

So you can't recover the original vector

[unkempt sapphire]

i only want to recover one component tho

[last basalt]

If it's a multiple of some other vector

[last basalt]

What do you mean

[unkempt sapphire]

i don't know the mathematical definition of it

the first domain?

what i mean is the first component of the vector

f(v, minV, maxV) = (v + minV) / (maxV - minV)
so in this case i'd just want to recover v

[last basalt]

Oh I assumed v was a vector

[unkempt sapphire]

nope

it's 3 scalars

v minV maxV are all scalars

[last basalt]

It's the same case tho

Either way

Like if you take [1,2,3] and [2,4,6] the function is 1 (using v as 1 and 2)

For both

It's not unique

[unkempt sapphire]

can i find all possible solutions tho?

and then just pick one

[last basalt]

There's infinite solutions that will result in 1

[unkempt sapphire]

well i just want an arbitrary one

[last basalt]

What is this for

It's not an invertible function

In a mathematical sense

[unkempt sapphire]

i'd explain but it'd get fairly complicated so idk if there's a point, but basically it's related to texture mapping and generating a texture atlas from a set of textures

fairly complicated because it's related to computer graphics and not math in general, so i'd have to explain all the terms etc

[last basalt]

I don't see how you can recover an accurate v component based on the input V vector

Unless you are logging the min and max but then you still know the vector V anyway

[unkempt sapphire]

even if i knew the original minV, maxV used to construct the result?

[last basalt]

If you knew the originals then you know the vector

What dimension is it

[unkempt sapphire]

i do know minV and maxV the only one i don't know is v

2D i guess?

actually 1D

[last basalt]

How can there be min and max of 1D vector

[unkempt sapphire]

well v basically means height in my case

[last basalt]

Yes so the entire vector

[unkempt sapphire]

it's the vertical axis in an image

[last basalt]

Is it 3d

[x,y,z]

[unkempt sapphire]

well if u consider (v, minV, maxV) as a vector then yes it's a 3D vector?

but it's not a vector in my case

it's 3 floats/scalars/real numbers, w.e u wanna call them

[last basalt]

What is V

I guess it doesn't matter

[unkempt sapphire]

a float

same with minV, maxV

[last basalt]

Do you know the output

Of the function

[unkempt sapphire]

yes

[last basalt]

Then it's just v = ouput* max - (output + 1) min

[unkempt sapphire]

what i want to achieve is:
v = f2(f1(v, minV, maxV))

[unkempt sapphire]

alright ill try that

yea that works perfectly

[last basalt]

Nice!

[unkempt sapphire]

how does it work

[last basalt]

What do you mean

[unkempt sapphire]

like why is it v + 1

well i don't understand how the solution works right now

[last basalt]

I just solved the equation

[warm shale]

Skid

[last basalt]

For x

Where y is min z is max and c is output

[unkempt sapphire]

alright i see

wolframalpha tells me the same thing

solve c = (x + y) / (z - y) gives x = c z - (c + 1) y and y != z

[last basalt]

Yeah your max never equals min right

y!=z

[unkempt sapphire]

ye it doesn't

[last basalt]

Will be dividing by 0

Ok cool

[unkempt sapphire]

thanks

[last basalt]

Np

[unkempt sapphire]

idk how to free this channel, i rarely use this discord

/free

[last basalt]

Do .close

[unkempt sapphire]

.close

[obtuse pebble]

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[full verge]

<@&286206848099549185>

[full verge]

Idk where to start integrating this

Could someone give some hint?

[obtuse pebble]

@full verge Has your question been resolved?

[royal basin]

write the 1/sinh(t/2) in terms of exponentials?

[full verge]

In then integrate by parts?

[obtuse pebble]

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[full verge]

I was looking for special functions related to this i thought that you could write e^(-t/2)/e^(t/2)-e^(-t/2) as some form of series like from n=1 to infty of e^(something)

[full verge]

.reopen

[obtuse pebble]

@full verge Has your question been resolved?

[versed turret]

e^(-t/2)/(e^(t/2) - e^(-t/2))?

[obtuse pebble]

@full verge Has your question been resolved?

[obtuse pebble]

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[last tangle]

polynomial degree of this

[last tangle]

is it 12?

options ^

[pine sail]

12 it is.

[last tangle]

thank you

!close

.close

[obtuse pebble]

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[sacred orchid]

Does this question contain a mistake? for example if K = Q, consider X^2 + 1: this is irreducible over Q but it is (X+i)(X-i) over Q(i)

[worthy comet]

Your "counterexample" doesn't work: i is not a second root of unity over Q

[timid silo]

<@&286206848099549185>

Where’d i go wrong in this the first one is the check

[worthy comet]

@timid silo read #❓how-to-get-help and use and unoccupied channel from the "Math Help (Available)" section

[timid silo]

(For the first one u have 2)

Ok

[sacred orchid]

@worthy comet apologies but I still don't see it. My understanding of primitive root of unity is a zeta such that zeta^n = 1 and zeta^k is not 1 for any positive k < n

In this definition I don't see a dependence on Q anywhere

[worthy comet]

yes, and i^2=-1

[sacred orchid]

Well, I am actually dumb.

Thank you very much!

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[timid silo]

Hi, how can I calculate, in how many combinations there is a certain element?
My problem is related to discrete math. I have a K_20 and I'm looking how many paths of length 8 are there that contain element A. The correct answer from my materials is this. And i don't know what the 9 means.
I get that in the parentheses I am counting all possible paths of length 8, but idk how does the 9 help me with my question.

[brave bramble]

I'm not an expert in graph theory. However, whatever they are counting in the parenthesis, there must be 9 different ways to count that. So, we multiply by 9. Does that make sense in the context of the question?

[timid silo]

yes, ive figured it right now 🙂 9 possible ways where the certain element can be, and for the rest there is the parentheses. Thank for making me certain though 🙂

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[woven parcel]

Why is it 8C2 not 8P2? I thought the order matters here

[sacred orchid]

Order doesn't matter because the A's are indistinguishable from one another

[obtuse pebble]

@woven parcel Has your question been resolved?

[woven parcel]

I see... Noted, thanks

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[valid raft]

Hey

[timid silo]

hi

[valid raft]

i struggle to get the f('x) of it

would like to get some help

what i did was

2x-2/2√x^2 * x^2 - 2x√x^2-2x and all of that / to (x^2)^2

i don't manage to continue from there

[robust sleet]

combination of croissant rule and chain rule

[valid raft]

but somehow i still cant get the right answer

[robust sleet]

latex it

maybe the answer is a simplified form of your answer

[valid raft]

uhm

i'm not sure how to latex it

[robust sleet]

write it on paper and send pic

[valid raft]

oh

i thought you wanted me to do it with the commands here

[robust sleet]

yes if u could latex

[robust sleet]

let me solve it wuick

quick

u can simplify numerator left term

[valid raft]

i tried

i still dont get the right answer

my x'es are 0 and -2

(that i get)

[robust sleet]

afterwards

put numerator in common denominator

then u can factorize both num and denum by x^2

then u get

$\frac{-x+3}{x^{2}\sqrt{x^{2}-2x}}$

is that the answer

[warm shale]

Ugu'yaränikeri'u

[robust sleet]

,w derivative of ((sqrt(x^2 - 2x)/(x^2))

[warm shale]

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[robust sleet]

yep

I would rate this derivative difficulty 3 out of 5

[valid raft]

can you send the way you solved it

[robust sleet]

did u put numerator in common denumerator?

[obtuse pebble]

@valid raft Has your question been resolved?

[obtuse pebble]

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[sacred root]

Hi

[sacred root]

$\frac{a^2}{(a-x)^x} - \frac{2a}{(a-x)^{x-1}}$

How do I simplify this

??

[warm shale]

बाशुदेव

[minor pilot]

Make the denominator the same on the right

making it 2a(a-x)/(a-x)^x

then u combine them to get a^2 - 2a(a-x) divided all my a-x to the power of x

[sacred root]

Ok

[minor pilot]

At least thats how I think its done

[sacred root]

Ok

Let me give it a try

[minor pilot]

kk then we can do the next step together

[sacred root]

Ok

Got the answer

It's

$\frac{-a(a-2x^2)}{(a-x)^x}$

[warm shale]

बाशुदेव

[minor pilot]

hm

2a(a-x) gives 2a^2 - 2ax

So when u combine the 2 on the top u should a^2 - 2a^2 + 2ax over a-x to the power of x

So i think the x^2 part is a bit off but otherwise well done!

[obtuse pebble]

@sacred root Has your question been resolved?

[obtuse pebble]

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[solid mirage]

.

[solid mirage]

.close

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[rocky cosmos]

You must create a password that begins with four letters (either uppercase or lowercase) and ends with two digits. You can choose from 26 capital letters, 26 lowercase letters and 10 numbers. How many combinations of codes can you choose from?

[rocky cosmos]

Since the password begins with four letters that are either uppercase or lowercase, we have 26+26.

But I don't know how to proceed from here.

[high lily]

be more specific on what

we have 26+26
is supposed to be

[lusty cedar]

52P4

for selecting the alphabets

[rocky cosmos]

You must make six choices, one for each character in the password. For the first four choices, we have 26 + 26 = 52 possibilities for each character.

[high lily]

and what about the last two characters?

[rocky cosmos]

52+2?

[lusty cedar]

nope

[rocky cosmos]

No wait

[lusty cedar]

you deal separately and multiply

[rocky cosmos]

52^4 * 10^2?

,calc 52^4 * 10^2

[warm shale]

Result:

7.311616e+8

[lusty cedar]

wth why 52^4

[rocky cosmos]

The answer seems to be right

[high lily]

52^4 * 10^2?
yes

[lusty cedar]

why?

[civic zealot]

your solution assumes no repetition which isn't stated

[lusty cedar]

godammit

my bad

[rocky cosmos]

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[obtuse pebble]

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[hazy linden]

could i have help with this question

[woven parcel]

First, write an equation in term of X

[T Only] + [B only] + [Both B and T] + [Neither B or T] = Total Stamps

[hazy linden]

ok

what do you mean by equation in term of x

[woven parcel]

You have X in the equation and you want to find its value

[hazy linden]

ok

[woven parcel]

Show me your entire equation when you got it

[hazy linden]

ok

do i add the values and thats my equation

[woven parcel]

Yes

But show me first before you add it

I wanted to see if there're any mistakes or not

[hazy linden]

so is it x^2-2x=80

oh ok

[woven parcel]

And then, solve for X

[hazy linden]

i am really confused

[woven parcel]

Hold up, nvm, this one is correct, i thought the numbers beside the x in the middle includes B and T

[hazy linden]

oh ok

[woven parcel]

Now solve for X

What is X

[hazy linden]

i dont know how to find x

because theres x^2 and 2x

[woven parcel]

Move everything to the left side

and solve the quadratic equation

Do you know how to solve quadratics?

[hazy linden]

No

[woven parcel]

...

[hazy linden]

we havent learnt this

[woven parcel]

God

[woven parcel]

https://www.mathsisfun.com/algebra/quadratic-equation.html Read this for a sec

[hazy linden]

ok

[woven parcel]

Go to the "How to Solve Them" section, those are the important stuffs

[hazy linden]

Okay

ohh i see

[woven parcel]

You have 3 methods to solve quadratics

Quadratics formula, factoring, completing the square

For you rght now, the easiest one would be factoring

[hazy linden]

the quadratic is x^2-2x-80=0 and then we work this out using the quadratic equation

[woven parcel]

Yeah, you can use the formula as well

[hazy linden]

oh ok

[woven parcel]

Do you know how to factor quadratics btw?

[hazy linden]

yes

[woven parcel]

Oh good

Then itll be easy

Just factor the equation first

Dont use the formula, this one is much simpler

[hazy linden]

oh ok

[woven parcel]

So what's the factor of x^2 - 2x - 80 = 0

[hazy linden]

i think i have forgot how to do it...

i dont remember

i apologise for being so annoying right now...

[woven parcel]

What times what becomes -80
and also adds up to -2

[hazy linden]

I am not sure

[woven parcel]

its 8 and -10

[hazy linden]

ohh

[woven parcel]

(8) x (-10) = -80
8 + (- 10) = -2

So the factor is?

[hazy linden]

(x-80)(x+2)

[woven parcel]

No

(x+8)(x-10)

[hazy linden]

ojh

[woven parcel]

Thats why we;re finding what times what

[hazy linden]

my bad

sorry

[woven parcel]

Now we equate it to 0

(x+8)(x-10) = 0

[hazy linden]

yes

[woven parcel]

How to make a number becomes 0 by multipying

[hazy linden]

What

x0

[woven parcel]

You multiply it by 0, because 0 times any number is 0, understand?

[hazy linden]

Yes

[woven parcel]

So that means, either x+8 or x-10 should be 0

got it?

[hazy linden]

Ohh okay

yeah

[woven parcel]

so we have 2 answers

x+8 = 0
x -10 = 0

Find x this way

[hazy linden]

x= -8 x= 10

[woven parcel]

Good

[hazy linden]

Is that the answer

[woven parcel]

Not yet, our goal is to find the probability of getting stamp T

[hazy linden]

OK

[woven parcel]

Now since we have 2 answers for X, find what is [Amount of Stamp T]

Remember, That is everything that have stamp T

This includes the one on the middle as well

so its x(x-5) + x

[hazy linden]

so just substitute -8 and 10 in??

[woven parcel]

Yes

And then whatever your answers are, you'll be dividing it by the total amount of stamps

[T Stamps] / [Total Stamps]

Remember that you should've 2 different answers

[hazy linden]

ok

i did t stamps and got 1.2

[woven parcel]

Answers || answers are 96/100 and 60/100||
I'll be heading out first, its kinda late here, mb

[hazy linden]

ohh ok

[woven parcel]

I hope you learned sth thanks

[hazy linden]

thank you so much

for the help

and sorry for being such a hassle

.close

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[silent kindle]

I need help with limit of this.

[silent kindle]

I think I'm going in the right direction by doing this but I don't know what to do next

[obtuse pebble]

@silent kindle Has your question been resolved?

[silent kindle]

nvmd got it myslelf

.close

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[vagrant dawn]

Can someone give me a hint for this?

[vagrant dawn]

it says f is a differentiable function and is defined on the real set of numbers

The answer is 7 but idk how that's the case

[tardy epoch]

show what you've tried

[vagrant dawn]

first i thought since there a limit exists, the limit must be in the form of 0/0 so I found f(0)=0

so i input x=1 and y=0

but the one cancels out leaving only f(0)=0 again

so im lost on how to find f(1)

I tried manipulating all sort of ways but still didnt find anything

im also not sure how to differentiate the function, do i use implicit differentiation or do i treat y as a constant as the question never stated that f(x)=y

@tardy epoch

Do i treat y as a function of x or is it a constant?

[tardy epoch]

tricky problem.

f(0) = 0 follows from the definition with x=y=0. f(0+0) = f(0) = f(0) + f(0) + 0 and subtract f(0) from both sides

Yea 7 is the right answer. You have to look at $f'(1) = \lim_{h\ra 0}\frac{f(1+h) - f(1)}{h}$.

[warm shale]

riemann

[tardy epoch]

you don't need to

[tardy epoch]

nope, just do the limit

[vagrant dawn]

oooh i think i get it

ok ill try that

ooh

thanks a lot

[tardy epoch]

fun problem

[vagrant dawn]

the solution was a lot simpler then i thought

.close

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[glass palm]

why is sin^-1(sin(x)) not always equal x

[brave bramble]

sin(x) doesn't have an inverse. This can be seen with a horizontal line test

[robust sleet]

,w arcsin(sin((2)) and arcsin(sin(1))

[brave bramble]

But if we cut some of the function away, we can create a different version of sin that does have an inverse!

,w graph sin(x) between -π/2 and π/2

[warm shale]

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[brave bramble]

That clipped sin is invertible. We choose to call its inverse sin^-1

arcsin doesn't correctly invert any value of x that's outside of that range, and needs to be "fixed" if you are using such an x.

[glass palm]

i dont understand this part

i understand why we did the restricted domain so we can have a one to one function but i dont rlly understand why sin^-1(sin(x)) after the domain restriction is not equal to x all of the time

an example when sin^-1(sin(x)) dose not equal x would help

[robust sleet]

range of sinx is [-1,1] you cannot get any y values out of that range in real numbers, sinx=2 doesn't exist in R, the inverse of sin of x, with x any value outside of the range will not equal to x

for example arcsin(sin(2)) no equal to 2

[brave bramble]

Let's work in degrees, so we can be more clear.
The restriction is between (-90,90). sin^-1 will always assume that a value comes from this range.

So, for example,
sin^-1(sin(150°))
= sin^-1(1/2)
= 30°

Because the only input, in that range, which outputs 1/2, is 30°

[obtuse pebble]

@glass palm Has your question been resolved?

[glass palm]

alrrrr tysm

[obtuse pebble]

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[proven shard]

need help with this

just started learning it today and am very confused

[quiet wadi]

When solving a limit, your first step is to check if the function can actually just be evaluated at that point (ie. just plug in the number and see if it is defined)

[proven shard]

so i would plug in 3 for x and get 9-2 which would be 2

correct?

[quiet wadi]

9-7, but yes

correct

[proven shard]

square root of 2 doesnt work does it

[quiet wadi]

Yes, it does

sqrt(2) is a number

The places where it "doesn't work" are when you get an "indeterminate form"

[proven shard]

ah okay

so ive tested and it works

where would i go from here

[quiet wadi]

You're done

[proven shard]

wait what

[quiet wadi]

The limit of a continuous function is just its value at that point

[proven shard]

so the answer is square root of 2?

[quiet wadi]

Yes

[proven shard]

wow i way overthought that okay

[quiet wadi]

Most questions will be harder, but occasionally it will just be something like this

Sort of a trick question

[proven shard]

yea i was looking at the other examples and they are much harder

alright welp that was pretty easy to understand thank you

and also for the answer i would just use square root of 2 because its easier than doing the math and getting a decimal correct?

[lapis pine]

boobz

[obtuse pebble]

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[silk moat]

So I found cot(t) which is sqrt2 / 4

And then I'm using csc^2t = cot^2t + 1 to find csc(t)

But I'm getting 3/2 somehow and I know it's wrong from the answer key

[cedar lichen]

Try drawing a picture. The cos of an angle is -1/3, and we know where that angle is. We can draw a triangle to find the other trig identities

[silk moat]

something like this?

@cedar lichen

[cedar lichen]

The angle t is the angle at the origin, not that point off to the side

It's the angle the ray makes with the x axis

[silk moat]

ohh

okay so how can I use that?

to find the cosecanrt

[cedar lichen]

Well, you can use the pythagorean theorem to find the third side, taking care to use the right sign given the quadrant

Then you can find the others geometrically. Sin is opposite/hypotenuse, tangent is opposite/adjacent, etc etc

[silk moat]

hmm okay yeah that checks out with the answer key

the problem is we were taught to use the pythagorean identity thing

and my math is somehow not getting the correct value..

[cedar lichen]

Can you show your work?

[silk moat]

when I plug the stuff into the bottom formula

[silk moat]

yeah I sent it here

[cedar lichen]

18/16 = 9/4?

[silk moat]

LOL whoops

alright got it

csc(t) = -3sqrt2 / 4

thanks man

.close

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[serene hatch]

how do i do this

plz help

<@&286206848099549185>

[obtuse pebble]

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[heavy shuttle]

how is this solved

also this

[obtuse pebble]

@heavy shuttle Has your question been resolved?

[obtuse pebble]

@heavy shuttle Has your question been resolved?

[noble oriole]

hi do u still need help?

[obtuse pebble]

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[timid silo]

D is 13

so is it 132 base 16?

[nocturne minnow]

You can use a base 16 to decimal converter

And also, you don't concatenate

[timid silo]

?

what

[nocturne minnow]

Google "base 16 to decimal converter" and you can convert numbers in base 16 to base 10

[timid silo]

is there another way

without that converter online

[nocturne minnow]

You can do it by hand then check your answer, using the converter

That's why I'm suggesting it

As a method of checking

[timid silo]

.close

[obtuse pebble]

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[slow forge]

How many different 4 digit numbers contain exactly 2 digits of 3?

[slow forge]

Ok so there was this combination question that asked How many different 4-digit numbers contained at least one digit of 3 and that got me wondering about this

If this is a bad question/doesn't have a nice solution to it/has to be brute forced just let me know I'll close this channel asap, not homework help just genuinely curious

I thought about it for like half an hour and my head is messed up

[obtuse pebble]

@slow forge Has your question been resolved?

[obtuse pebble]

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[fading musk]

guys I know the equation is 350x+150y=225(x+y) but I don't know why is it 225(x+y)

nvm I know now

[obtuse pebble]

@fading musk Has your question been resolved?

[obtuse pebble]

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[fading musk]

hi

...

I'm grade 7

no

[plain owl]

What’s your age

[fading musk]

13

no

??

mo

[obsidian isle]

[fading musk]

mo

no

you ain't controlling

[obsidian isle]

Who cares lmao

[fading musk]

I'm 13

1231

year 2008

just tell me what is it

[nocturne minnow]

No need to be hostile

[fading musk]

why not

we are trying to help you

I'm 13

I learnt some basics of calc

how old are you then

bet you are grade 10

[nocturne minnow]

No one likes a bragger

[fading musk]

and I'm not 12

[nocturne minnow]

https://www.youtube.com/watch?v=58dVDrrvTCw&ab_channel=BrianMcLogan
See if that helps

[obtuse pebble]

@timid silo Has your question been resolved?

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[keen bobcat]

So I'm a Finance student and I'm taking an elective about Urban Economics. I don't really understand where to start on this assignment so if someone can point me in the right direction that would be great

[obtuse pebble]

@keen bobcat Has your question been resolved?

[keen bobcat]

I feel like I'm. It doing this right because I keep getting 1

<@&286206848099549185>

[obtuse pebble]

@keen bobcat Has your question been resolved?

[obtuse pebble]

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[magic siren]

can anyone tell me if this is correct?

[obtuse pebble]

@magic siren Has your question been resolved?

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[obtuse pebble]

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[tidal pelican]

Can someone explain how you can tell if it’s infinity or zero?

[tidal pelican]

Also these ones, do you apply the same thing with these questions?

<@&286206848099549185>

[cinder ivy]

Just imagine "plugin infinity in" Plug a huge Number hin. In this exercise you either have ^x or ^-x . You have to know how to rewrite ^-x, this will help you

[tidal pelican]

ok thanks!

.close

[obtuse pebble]

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[dull plume]

Q) Y is directly proportional to x. Y is 7 when x is 14. Find:

1. Y when x = 25
2. x when y = 23

Stuck on the 2nd part i solved it like this (2nd pic) but i rly dont think this is the asnwer. (Sorry if im making some basic mistake or smth rly bad at math lol)

[obtuse pebble]

@dull plume Has your question been resolved?

[dull plume]

Pls ping when someone is here dont wanna do @.helper since the question is pretty stupid

Nvm

.close

[obtuse pebble]

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[warm pine]

hey guys

[warm pine]

what's $\sigma$

[warm shale]

陽火　四つ葉

[royal basin]

a greek letter

[warm pine]

standard deviation I mean

how, and why do we need to use it

[royal basin]

well if you want to ask about standard deviation then ask about standard deviation lol

loosely speaking, st dev measures the spread of your dataset (or random variable) around its mean. the higher your standard deviation, the more broadly the data points are spread

if you know that your data follow a normal distribution, you can also estimate what range a big percentage of your data lies in using the 68-95-99.7 rule

is this what you were looking for?

@warm pine

[stiff minnow]

it measures the average (mean) squared distance from the mean. since that distance is squared it's very sensitive to outliers, so use it in non-skewed datasets, generally

[royal basin]

you're thinking of variance. stdev is the square root of that.

[warm pine]

thx

.close

[obtuse pebble]

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[timid silo]

thats my question

[timid silo]

ive got as far as

3n/(3^2)^n-1

which is equal to

3n/3^2n-2

but i dunno where to go from there

[scarlet locust]

do you know what $\frac{a^m}{a^n}$ is?

[warm shale]

Swas.py

[timid silo]

no

what is that ?

[scarlet locust]

ok so it is $\frac{a^m}{a^n} = a^(m-n)$

a^(m-n)

so you should be able to do it now

[timid silo]

wait rlly ?

ok lemme try

so would it be 3^(n-2n-2)= 3^n-2

[scarlet locust]

no

you forgot ()

[timid silo]

ok lemme try again

wait i forgot the brackets where

[scarlet locust]

n-(2n-2)

[timid silo]

-n+2

well

3^-n+2

[scarlet locust]

yes

[timid silo]

LETS GOOOOOOO

tysm dude

.close

[obtuse pebble]

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[full verge]

<@&286206848099549185>

[warm pine]

what

.reopen

[obtuse pebble]

✅

[warm pine]

reopen it for u first

[full verge]

.close

[warm pine]

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[inland blade]

Can you help me

[obtuse pebble]

@inland blade Has your question been resolved?

[royal basin]

@inland blade do you still need help with this?

[obtuse pebble]

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[forest snow]

um what formula am i supposed to use ty

[forest snow]

.close

[obtuse pebble]

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[timid silo]

how do I find the angle for 5?

[scarlet locust]

what all angles do you know currently

[timid silo]

supplementary, vertical, complementary, alternate, cointeror, and corresponding

[scarlet locust]

no I meant

have you found some angles in this question already?

[timid silo]

oh

[scarlet locust]

or have you found none

[timid silo]

I found 1, 2, 3, 4 so far

[scarlet locust]

if you know 4 then you should be able to use the fact that the angles in a triangle add up to 180 deg to find 5

[timid silo]

but they aren't parallel

[scarlet locust]

Wdym?

[timid silo]

what do you mean by angles in a triangle?

[scarlet locust]

do you know the angle sum property?

[timid silo]

oh we didn't learn that in class

is that the only way to solve for 5?

[timid silo]

we only learned about some angle properties

[torn locust]

Yes. You know the other two angles, so solve for the final one

[timid silo]

yeah I know how to solve it but I'm asking if this is the only way to solve it

because we didn't learn the angle sum property yet

[obtuse pebble]

@timid silo Has your question been resolved?

[jade hornet]

Judging by your assigment, I think they expect you to know that the angles of a triangle add up to 180 degrees

[timid silo]

ah ok

thanks

.close

[obtuse pebble]

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[slim leaf]

cos(A) = adj/hyp = sqrt(1-x^2) / 1 = sqrt(1-x^2).

sec(A) = 1/sqrt(1-x^2)

[obtuse pebble]

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[shell heart]

Hey

[obtuse pebble]

Please don't occupy multiple help channels.

[shell heart]

Where was mine then?

[vagrant gale]

I saw a problem recently while doing math comp problems, and its been bugging me. I couldn't figure out the exact answer, but I wrote some Python code that approximated it. The problem was:

a and b are positive real numbers that satisfy the equation [(a/b) • ((a/b)+2)] + [(b/a) • ((b/a)+2)] = 2022.

Find n if sqrt(a/b) + sqrt(b/a) = sqrt(n).

The code I wrote solved the equation for values in between a certain range that I hand tested to see if it was close to 2022 by seeing if the floor of the function and the ceiling function were equal to 2022. With these values, it found the n, which floated around 45.99 and 46.01.

Here is the pastebin for the code: https://pastebin.com/MjJVBNUT

The approximation I got was 46, but I'm not sure if this is the answer. Would anybody walk through how to solve it normally, and verify my answer? Sorry if I cant respond to questions promptly

[obtuse pebble]

@shell heart Has your question been resolved?

[finite vector]

try taking a/b as 't' n see if it helps

[obtuse pebble]

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[devout anvil]

Hey, ik this is very abstract but can anyone tell me how can i create some function that gives me this function?

[devout anvil]

i think its necessary to use two functions

Use another channel, and delete your comment

@timid silo same plz

[brave bramble]

Almost looks like a piecewise between a 1/x and a linear function

[devout anvil]

yeah i got it!

thx

@brave bramble do you know how can i make this here?

[brave bramble]

Bend down a little faster? Perhaps 1/x² instead

[devout anvil]

hm

[devout anvil]

i have -(1/x²) btw