help-28

[wispy flare]

no

no

[orchid iris]

oh sry

[wispy flare]

(-4w+w-17)/m

sorry

z

but wait

[orchid iris]

ok

[wispy flare]

wait

i messed up

[orchid iris]

oh

its ok

so what is it?

[wispy flare]

gimme a sec

[orchid iris]

k

@wispy flare ru back yet?

[wispy flare]

yes

so, now,

multiply the coefficent

which u already did

[orchid iris]

here?

[wispy flare]

and got -4w+wz

= mz+17

[orchid iris]

this?

[wispy flare]

now, you take the -4w to the to the other side

[wispy flare]

no

write your answer

[orchid iris]

there are =

from withc equation

[wispy flare]

??

[orchid iris]

wat equation do i use?

[wispy flare]

k

let me give u

wz = mz+17+4w

[orchid iris]

-4w + zw -17 = mz
?

oh

[wispy flare]

nah

[orchid iris]

when did we get that?

[wispy flare]

k, so now take mz to the other side

[wispy flare]

when we take -4w in the eq to the other side

[orchid iris]

oh I get it now

[orchid iris]

ok so, wz -mz = 17 + 4w

[wispy flare]

yes

[orchid iris]

ok

[wispy flare]

so, now what it the left side simplified?

factor out the "z"

[orchid iris]

W x Z - M x Z = 17 + 4w

[wispy flare]

yes

so now what happens when you factor it?

[orchid iris]

is that possible

[wispy flare]

yes

it becomes z(w-m)

[orchid iris]

2z x w -m?

[orchid iris]

oh

ok

[wispy flare]

k, so now isolate z

how do u do that?

let me write it out

z(w-m) = 17+4w

[orchid iris]

isolate it by moving w and m

[wispy flare]

yes

so write it out in terms of z=

[orchid iris]

Z = 17 + 4w + w - m?

[wispy flare]

no

let me put it in these terms

if wx=zx

then won't w=z?

so how do we get this, we divide both sides by x

so, divide both sides by (w-m)

do u want the solution?

u these?

there?

[orchid iris]

yes

sry

ok

[wispy flare]

k

did u get the solution?

z= what

[orchid iris]

how is this wrong?

[wispy flare]

because z is being multiplied by w-m, so you can't subtract it

[orchid iris]

oh

[wispy flare]

so, divide both sides by (w-m)

[orchid iris]

ohh

z(w-m) = 17+4w

z = 17 + 3 / m

[wispy flare]

the answer is z = (17+4w)/(w-m)

im gonna leave now

gn

[orchid iris]

gn

friend me

thank you!

<@&286206848099549185> can anyone explain it more?

mostly the last step

[torn jolt]

youre just dividing the whole thing by w-m

(17+4w)/(w-m)

[orchid iris]

so thats how I do it

its seams kinna weird ru sure

[torn jolt]

certain

[orchid iris]

I kept the aswer its right

i mosly inderstna it

TYSM @torn jolt, and @wispy flare !

I mostly got it

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[thick hedge]

first, I would start by finding the limits at $\infty$

[glossy valve]

ƒ(Why am. I here)=I don't know

[thick hedge]

and $-\infty$

[glossy valve]

ƒ(Why am. I here)=I don't know

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@winter latch Has your question been resolved?

[winter latch]

of discriminant?

the method my teacher taught was

let the f(X)=y

then cross multiply

and find interval of D accordingly

but theres way too many variables here

[thick hedge]

no, of the function

and the limit at a,b,c, too

[winter latch]

ohh

how

[thick hedge]

divide the numerator and denominator by x

[winter latch]

why

[thick hedge]

to find the limit at $\infty$

[glossy valve]

ƒ(Why am. I here)=I don't know

[winter latch]

i tried doing this

[thick hedge]

what do you not understand here?

[winter latch]

this

[thick hedge]

what does it mean for $D>0$

[glossy valve]

ƒ(Why am. I here)=I don't know

[winter latch]

two real roots

[thick hedge]

yes

anywhere on the coordinate axis

[winter latch]

yes

[thick hedge]

now this curve has 3 asymptotes, which means it will cut the coordinate axis atleast twice, right?

two towards $-\infty$

[glossy valve]

ƒ(Why am. I here)=I don't know

[thick hedge]

actually beyond this, I'm not too sure myself

https://math.stackexchange.com/questions/2786727/if-x-in-r-and-fracx-ax-cx-b-can-assume-any-real-value-then-whi?noredirect=1

see this

[winter latch]

😭 youre making it complicated

[thick hedge]

I know

sorry

ignore me

I'm not sure myself as I said earlier

sorry

[winter latch]

the option he said is wrong

its jee pyq

[thick hedge]

as I said, I'm not sure, sorry

ping helpers

[winter latch]

i got it dw

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[atomic vortex]

I do not understand how P(X >= x) = (1-p)^x

I was thinking that P(X >= x) 1 - (p * sum_{x=0}^x (1-p^x)) but that will equal 1 - 1 = 0 right

idk how go get P(X >= x) = (1-p)^x

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[open quail]

Hi, this is a kinematics question

so

vt = 41

and instead of +- change it to +

I know LHS = 41arctan(v/41)+C

but what do I do with the RHS?

[thick hedge]

$\int dx?$

[glossy valve]

ƒ(Why am. I here)=I don't know

[thick hedge]

what is that

[open quail]

I have no idea

I'll just ask the physics server because I guess this isn't a math thing

[thick hedge]

it's x

so what is $\int dt$

[glossy valve]

ƒ(Why am. I here)=I don't know

[open quail]

oh

just t+c

?

[thick hedge]

yes

[open quail]

oh

Ok

alright thanks

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[thick hedge]

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[torn jolt]

i tried do pit. and got d=sqrt(3^2 + 3^2)=3 * sqrt(2)

and used v = (3*sqrt(2))/t+0.5

but, v equals to 3/t too

so i got this expression

[spiral vigil]

hang on

[torn jolt]

and v in this expression equals to 2.484

[spiral vigil]

speed = distance / time

you know your distance

and you know how much time it took

[torn jolt]

the time is 0.5 + t

[spiral vigil]

why is the time 0.5 + t

what's t

[torn jolt]

t + 0.5: time to travel from the center of the pool to the sides and additional 0.5 seconds to travel from the sides to the vertices.

[spiral vigil]

oh i see i didn't notice the "after hitting the edges" in the question

okay, well this seems reasonable then. you can check by using your speed and calculating the time the wave hits the edge, and the time the wave hits the vertices

[torn jolt]

yes

but, 2.484 = aprox 2.5, not 2.4

so, its wrong, not?

[spiral vigil]

did you do that check? what did you get

[torn jolt]

give me a sec.

[stuck storm]

pretty confident that this is correct

did it tell you that answer c was incorrect?

or are you doubting

because you can (kinda) say that 2.48 is approx 2.4

[torn jolt]

doubting

[spiral vigil]

if they did it with crappy precision (√2 = 1.4) then i could see it being off by that much

[stuck storm]

yeah precisely actually

id be quite happy with c

[torn jolt]

ok, i undetstood.
Thank you guys so much

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[limpid monolith]

Why are they equal to 0 ?

[kindred grove]

idk

What are f and k even ?

@limpid monolith

[limpid monolith]

When I try to solve a Fourier transform of the partial derivative Uxx(x,t)

I need to write it down

Why are they equal to 0 in the circle part ?

[vestal meadow]

I believe it is a common assumption/behaviour that u(x,t) vanishes at +- infinity

https://math.stackexchange.com/questions/803814/behavior-of-solutions-to-the-heat-equation-at-infinity

this seems like a proof to it but the proof is more advanced

[full forum]

@limpid monolith Has your question been resolved?

[limpid monolith]

Thank you so much, but this confuses me the most

[scarlet comet]

this is some advanced stuff i cant help :)

though i would like to learn it

[limpid monolith]

UwU

[scarlet comet]

what is that supposed to mean

[limpid monolith]

Maths is so difficult :((

[scarlet comet]

sometimes yes

but it's fun too :) and learning new stuff is fun too :D

are u a college student, or is this high school maths

[limpid monolith]

College

I know how to prove the solution for the heat equation but I don't know why lim ux(x,t)=0 and lim u(x,t) =0 because it's very weird

[scarlet comet]

it's weirder for me :)

[limpid monolith]

Sorry 😔

[scarlet comet]

eh ima learn it someday

[limpid monolith]

Yeaaa partial differential equations is a fun course

[scarlet comet]

agreed

[limpid monolith]

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[drowsy finch]

pls where go the -3 in this inequation

[torn jolt]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

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[naive hamlet]

Hi guys, I have a little problem with the Riesz representation theorem in the case of metric spaces (not especially Hilbertian).

Let E be a metric space of finite dimension n, then,
∀y∗ ∈ E∗; ∃!y ∈ E | [x, y∗] = y∗(x) = <x, y> ∀x ∈ E

y* being a linear form on E, Dim(Ker(y*)) = n-1. Let N = Ker(y*). And let us concider M, the orthogonal complement of N.

Let x ∈ N, then [x, y*] = 0.

So by the theorem, ∃!y ∈ E | <x, y>=0. But since <x, y>=0, this means that x and y are orthogonal, so the relation is true ∀ y ∈ M. Except that ∃!y ∈ E | <x, y>=0.

I'm probably missing something, but it seems really strange to me.

[naive hamlet]

No, ok, it's fine

My bad

I misunderstood the theorem, I understood

∀x ∈ E,∃!y ∈ E | [x, y∗] = y∗(x) = <x, y>

But it doesn't make any sens

[kindred grove]

What is <x,y> supposed to mean if E is not Hilbert anyway ?

[naive hamlet]

Just a scalar product

the dot product

[kindred grove]

So you have a scalar product then ?

[kindred grove]

Ok so what's your problem with it then ?

[naive hamlet]

We're assuming we're working in a metric space, so yes

[naive hamlet]

Nothing, I understood by myself, my bad x)

There are no problem

Thank you x)

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[toxic hawk]

I would like help in understanding this question and formula and lead me to the right answer

[fair oracle]

The question asks you find a formula, so that when you input Fahrenheit it gives you a Celsius value as an output.

$F = \frac{9}{5} C + 32$

[glossy valve]

.doc

[fair oracle]

Notice in this formula you plug in a Celsius to get the Fahrenheit (which is other way around)

@toxic hawk

[toxic hawk]

yes

[fair oracle]

Do you understand the question ?

[toxic hawk]

Im a little confused with the wording but yes

[fair oracle]

in my writing or in the question ?

[toxic hawk]

writing but i get it now

[fair oracle]

Essentially you need to change the subject of the equation to C instead of F

[toxic hawk]

Ok i get it now thank you

[fair oracle]

maybe give it a try and share your attempt ?

[toxic hawk]

alright

I think i mightve messed up

[spiral vigil]

show your steps

[toxic hawk]

F=9/5c+32
-32 -32
-32+f=9/5c
divide 9/5 which flips it and i get that answer

i totally messed up

[shrewd hamlet]

heres the thing

when u divide both sides by 9/5

every term on both sides gets divided by 9/5

so u had

$F - 32 = \frac 95 C$

[shrewd hamlet]

now when u divide both sides by 9/5, you get

$\frac {F - 32}{\frac 95} = C$

[shrewd hamlet]

see if u can figure out what to do from here

remember that

$\frac {a+b}{c} = \frac ac + \frac bc$

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@toxic hawk Has your question been resolved?

[toxic hawk]

still workingon it

5/9 (f-32)=c ?

@shrewd hamlet sorry if im not allowed to ping you didnt know

[shrewd hamlet]

Yea this is right

Now what will u do

[toxic hawk]

distribute?

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@toxic hawk Has your question been resolved?

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[ember idol]

find the number of solutions to this equation:
(x1 + x2 + x3 + x4)(x5 + x6 + x7) = 63

[ember idol]

such that all the Xi's are naturals

[verbal mantle]

are those x^1 etc or what

[ember idol]

no theyre different variables

numberes X's

[verbal mantle]

then

[ember idol]

so the way i did it was split into cases

[verbal mantle]

wait are x positive or also negative

[ember idol]

21 * 3 and 9 * 7

but thats too long

[verbal mantle]

yep that's right

[ember idol]

im wondering if theres a shorter way

[verbal mantle]

can they be negative though?

[ember idol]

theyre natural numbers

[verbal mantle]

okok

so no

so your first process was right

[ember idol]

yeah but its too long

[verbal mantle]

either 213 or 321

[ember idol]

what

[verbal mantle]

oh this stupid formatting

sorry

[ember idol]

lol

[verbal mantle]

21x3 or 3x21

[ember idol]

` avoids formatting

[verbal mantle]

and then 9x7 or 7x9

[ember idol]

yeah

[verbal mantle]

can x equal 0

[ember idol]

yes

[verbal mantle]

ok

you see, the first case is easy

[ember idol]

yeah i solved it

im wondering if theres another solution

[verbal mantle]

ok good

[ember idol]

thats shorter than spliting into cases like this

[verbal mantle]

oh not really if you are asking for this

but then there are simple ways to count the number of ways the xs can arrange

[ember idol]

yeah thats not an issue

[verbal mantle]

then yeah you're done

there are no easier ways

[ember idol]

alright then

thanks

[verbal mantle]

this was quite simple already wasnt it

np

[ember idol]

yeah

cheers

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[nocturne trench]

How to solve $$ \int{sin^{-1} x dx} $$

[glossy valve]

Nerdy_Coder

[nocturne trench]

Here is my most recent attempt

[spice orchid]

if you already have an answer you can just check it yourself using calculators

,w int arcsin(x)

[glossy valve]

Results provided by WolframAlpha

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

Requested by icaird

[spice orchid]

note that $\frac{1}{\sqrt{u}} \neq u^{\frac12}$

[glossy valve]

ΣAC

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[visual pebble]

i need help with this.The lest two digits of my number are 82

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[sterile cloak]

.reopen

[rapid agate]

how do i solve this

i know that i have to do something with times the denominator but idk what

[sterile cloak]

first
x ≠ 0
x ≠ -2
x ≠ -1

put all sides ^-1

then we got

x/2 + (x+2)/4 = (x+1)/6
multiply by 2
x + (x+2)/2 = (x+1)/3
now multiply by 6
6x + 3(x+2) = 2(x+1)
6x + 3x + 6 = 2x + 2
-2 both sides
6x + 3x + 4 = 2x
-2x both sides
4x + 3x + 4 = 0
7x + 4 = 0
-4 both sides
7x = -4
divide
x = -4/7

[viral jasper]

!nosols

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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[sterile cloak]

its step by step

[cursive furnace]

this is wrong either way

raising both sides to -1 does not do that

[sterile cloak]

oh fr

[viral jasper]

step by step solutions can absolutely be copied as a homework solution. step by step or not, do not share solutions please

[sterile cloak]

hmmmm

[cursive furnace]

$\left(\frac{2}{x}+\frac{4}{x+2}\right)^{-1}\neq \left(\frac{2}{x}\right)^{-1}+\left(\frac{4}{x+2}\right)^{-1}$

[glossy valve]

Daniel

[sterile cloak]

try multiply by a commom therm of x, x+2 and x+1

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[rapid agate]

(x+1) * log5 --> xlog5 + log5 right?

oh nvm

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[rapid agate]

could u explain

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[nocturne root]

integrate (3-5x)/(1-x)

[nocturne root]

I got 5x-2ln(1-x)+c

but the answer is 5x+2ln(1-x)+c

idk why

i first divided using long division

[haughty wren]

you probably forgot a chain rule sign or something somewhere

[nocturne root]

idk, but when i divide it, it becomes 5 -2/1-x

and integrate that equals what i said above

[dusty scaffold]

ah yeah i see the issue

what's the derivative of ln(1-x)?

@nocturne root

[nocturne root]

1/1-x

[dusty scaffold]

nope

[nocturne root]

wait

-1/1-x

[dusty scaffold]

there you go

so do you see the issue with your answer to the integral?

[nocturne root]

oh

now i see

thanks

.close

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[finite gulch]

when a set, for example S, comprises of all positive integers in base 10 comprising of only 0's and 1's (e.g. 11, 101, 1100, etc.)
how would someone find all the constructions of a number such as 1298 or something through addition of digits in S?
(e.g. adding up '1' 1298 times, or doing 1100+100+10+10+10+10+10+10+10+10+10+1+1+1+1+1+1+1+1)
is there a specific method, code or equation to do this

what i have done so far (the actual question isnt 1298 btw i just want to know the method to achieve)
i put a restriction on it being only 4 digits number in the set S
which would be 1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111
as the biggest 4 digit number in this set is 1111, smaller than 1298
and 5 digits are invalid ofc
therefore its only a combination of those numbers that can add up to 1298

you exclude leading 0's, standalone 0's which is also how i got the 15 values written above
(otherwise you can add up an arbitrary amount of 0's)

but thats how far ive gone, unsure of how to solve
sorry for confusing wording, i can elaborate

[full forum]

@finite gulch Has your question been resolved?

[finite gulch]

<@&286206848099549185>

[reef oyster]

hmmm

say

what do you need?

[finite gulch]

the amount of combinations that add up to 1298

using numbers from S

[wild sleet]

what's this from?

[finite gulch]

a research challenge thing my school gave

[coarse chasm]

Isn't the point for you to do it then

I feel like it kinda defeats the purpose for us to do it for you (and help seems possibly questionable?)

[finite gulch]

i just needed some guidance and this is unmarked but if not then all g lol

thanks

[wild sleet]

i would tell if i knew

but i can't see any way

other than just let computer do it

[finite gulch]

thanks haha im not sure how to let computer do though

[wild sleet]

for example we have 99
we can subtract 1, 10, 11
(99 into 1,10,11) = (98 into 1, 10, 11) + (89 into 10, 11) + (88 into 11)
so if we used 10 at any point, we never use 1 again
this way the constructions come out sorted

so they are all unique, and the problem is solved

[finite gulch]

hmm ok

i'll take it into consideration thanks

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@finite gulch Has your question been resolved?

[full forum]

@finite gulch Has your question been resolved?

[full forum]

@finite gulch Has your question been resolved?

[full forum]

@finite gulch Has your question been resolved?

[visual pebble]

<@&286206848099549185>

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[austere cove]

@finite gulch a term for you to search, this is called a "restricted partition" of an integer.

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

This is explicitly not an easy problem.

my gut instinct has perhaps a workable approach is to ignore all values that aren't a multiple of 10, and find the ways of constructing the number using only those, and then use combinatorics to find the total number of ways.

that seems doable

but in the spirit of not giving away the answer, I'll leave that work to you.

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[austere cove]

!showwork

[full forum]

Show your work, and if possible, explain where you are stuck.

[bright panther]

im stuck at how to get AB

in the answer schemes its weird

i can see how you get PB even without finding AB with it being

PO + OB

then it would be -6x+4y

But how do you get AB

[austere cove]

Is AB asked for?

I don't see where it's asking for AB

[bright panther]

you can get PB by PA+AB

and either way you needa find for AB

[austere cove]

that is a very strange way of notating that

[bright panther]

for OQ = OB+BQ

[austere cove]

I would have assumed PB to be the straight line distance across the interior of the triangle

[bright panther]

you can do that too but this is easier

[austere cove]

OQ to be the straight line distance across the interior of the triangle through point R

[austere cove]

No, those two approaches give different values

[bright panther]

but we dont know point R

[bright panther]

yes but it equates to the same

same way PA+AB is also correct

as the other approach

its different approaches but they testing for concept

[austere cove]

Unless you are using a very specific metric space, then no, they would give very different values.

and if you don't know what a metric space is, you aren't using a special one.

[bright panther]

this is more for concept

[austere cove]

I don't know how to answer your question then, because it doesn't seem to be proper plane geometry, and I don't know the rules of this strange system.

It's probably more likely that you've misinterpreted something you've been taught

[bright panther]

the rule is using the given information to determine an equation that suits da question

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@bright panther Has your question been resolved?

[bright panther]

<@&286206848099549185>

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[full forum]

@bright panther Has your question been resolved?

[bright panther]

<@&286206848099549185>

[modest inlet]

could you maybe translate or say where are you stuck

[bright panther]

(A)

wym translate

its in english

[modest inlet]

oh its also translated

you can find the area bwtween the upper function and the x and also between the lower and the x axis

[bright panther]

how would you do that?

[modest inlet]

using integration

[hollow delta]

,tex $\int_{0}^{2}(6x-x^2-2x^2)dx$

[glossy valve]

Marquis de Plas

[bright panther]

ahh i see so the top and bottom are the roots?

[modest inlet]

wdym by roots

[bright panther]

how do you get the limit

as 0 and 2

[modest inlet]

oh

yeah the roots of the diffrence bewtween them

[hollow delta]

It's the beginning and the ending of the shaded area on x

[modest inlet]

or just because the ends of the area you are looking for

[bright panther]

ahh so based on the x coords?

das how we write derive

[hollow delta]

Yes like "basic integration"

[bright panther]

so in order to find the are we just substitute?

[hollow delta]

Can you reformulate please ?

[bright panther]

do we do it like normal as in substite 0 in one and 2 in another then minus?

[hollow delta]

Yes that's it, so here you can reduce, it gives us :

,tex $\int_{0}^{2}(6x-3x^2)dx$

[glossy valve]

Marquis de Plas

[bright panther]

so then (6(0)-3(0)^2)-(6(2)-3(2)^2)

[modest inlet]

nah, you need to integrate first not just put it in

[hollow delta]

No, you must take primitives first

Do we say primitives ?

[bright panther]

so then 6x^2 is what we left with

if we integrate

[modest inlet]

use this

[bright panther]

oh yea x+1

so 6x^2-6x^3?

[hollow delta]

,tex So if f(x)=6x-3x^2, F(x)=\frac{6x^2}{2}-\frac{3x^3}{3}

[glossy valve]

Marquis de Plas
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[modest inlet]

not exactly

yeah what he said

[bright panther]

oh yes then we divide

2x^2-x^3 den we subs?

[hollow delta]

,tex That's it $F(2)-F(0)$

[glossy valve]

Marquis de Plas

[modest inlet]

3x^2

[bright panther]

why ^2

oh wait

ah yes

3x^2-x^3

[modest inlet]

no I mean the left term is the coefficient is 3 not 2

[bright panther]

yes ur right

[bright panther]

so now we substitute?

[modest inlet]

yeah

[bright panther]

so (3(0)^2-(0)^3)-(3(2)^2-(2)^3)?

[modest inlet]

the other way around

F(2)-F(0)

[bright panther]

oh so its positive?

[modest inlet]

should be

area is positive

[bright panther]

then just slap a modulus on it

[modest inlet]

I think in the first place we put it the other way around, but its right just need to take the abs value

[bright panther]

yus its 4

[bright panther]

now what about b?

[modest inlet]

now idea how to do that

[bright panther]

💀

[bright panther]

ikr its so weird

i mean i do have the answer scheme

i cud send it to you

[modest inlet]

I know its a thing we just dont go over it

[bright panther]

its so weird

[hollow delta]

Perhaps Geogebra can help you to view ?

[modest inlet]

what is the answer?

[bright panther]

128/5

pi

[modest inlet]

for sure?

[bright panther]

YES

according

to answer

sorry cap

[modest inlet]

im getting something else 🙂

[bright panther]

accident

[bright panther]

check this out

[modest inlet]

oh I didnt get that they wanted the area only of this curve

[bright panther]

its so weird

[modest inlet]

that is the formula

for a function rotated around the x-axis between x=a;x=b

[bright panther]

tf

theres a formulas

[hollow delta]

If you can imagine it, you can do it

[bright panther]

really?

[hollow delta]

In maths

Yes

[bright panther]

im tryign to grasp math logic instead of becoming a memoriser

any tips/

[hollow delta]

Math Logic like logical proposition or how maths works ?

[modest inlet]

if how maths works, you can find intuition for a lot of things in books/videos. but be careful with that cause sometime you can picture something as true but it won't necessarily be

[hollow delta]

I think it comes with training and searching by yourself yes

[modest inlet]

also a good teacher would be really helpful

[hollow delta]

A teacher that explain well and from different manners

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[ember idol]

prove using a combinatorical argument

[ember idol]

which means by making up a problem that can be solved by both sides of the identity

like this

[rare dock]

what does the right side count?

[ember idol]

i dont know

[rare dock]

well that one is simpler than the left side, so maybe start there

[ember idol]

what could it count?

[rare dock]

find what it counts and then try to think of why the left side counts the same thing

probably plenty of different things. one example is # ways to roll two 1 sided dice + # ways to roll two 2 sided dice + … + # ways to roll two n sided dice

whether that particular example is amenable to counting by the left side is another question

[ember idol]

why is the number of ways to roll an n sided dice n*n?

[rare dock]

edited. is that better?

[ember idol]

uh what did you change?

oh two

[rare dock]

added the word ‘two’ in 2 places

[ember idol]

well ive been staring at this for 2 hours and my brain is fried

could i get a bigger hint? lol thanks

[rare dock]

i haven’t done the problem yet so i don’t have much of a bigger hint

[ember idol]

fair lol

[rare dock]

this might work but having trouble verifying my idea

[ember idol]

i wont have time to finish this

thanks for the help tho

.close

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[rare dock]

[ember idol]

:(

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[gilded thorn]

why does the entire term thing turn to zero? https://youtu.be/6rXByMcuAyI?si=pXgFfgAt7yBcMn5J&t=1846

[gilded thorn]

in (Cx+D)(x+1)(x-1)

i assumed the 0 would fizzle out?

[coarse chasm]

Can you give a little bit more context

[gilded thorn]

30:29 he does x = 1 and says that the entire (Cx+D)(x+1)(x-1) turns to zero cus of x-1?

[grave lynx]

Hi

[gilded thorn]

yo

[grave lynx]

How does po shen lo metod works?

[gilded thorn]

this session is occupied

[woeful inlet]

#❓how-to-get-help

[grave lynx]

Thanks

[coarse chasm]

If x=1, then (Cx+D)(x+1)(x-1)=(C+D)(1+1)(1-1)=(C+D)(2)(0)=0

[gilded thorn]

i did not know that 0 stayed

[coarse chasm]

What do you mean by that

It's part of the expression, why wouldn't it?

[gilded thorn]

oh, i just thought when somthing equaled 0 in something that wasnt a fraction it stopped existing, like if I had 0(2x-2) it would equal 0? im just surprised i never came across this before

[coarse chasm]

0 times any number is 0

[gilded thorn]

oh

nvm later

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[craggy tapir]

Given $y = f(x)$ continuous on $\mathbb{R}$ such that [
2f(x)=\int_0^x\sqrt[4]{2[f'(t)]^4+8[f'(t)]^2 + 1}\dd t, \forall x\ge0
]
Let $D$ be the area of the region confined by $y=f(x)$, $y=0$, $x=1$. Rotate $D$ around the $x$-axis, we obtain a solid with a volume of $V=\frac{8+\sqrt{a}}b\pi$. Calculate $a-b$

[craggy tapir]

not sure how to approach the ODE

hmm, the thing inside the root looks a bit like a quadratic though

[granite torrent]

you can find f that works

[craggy tapir]

hm, someone suggested that i differentiate both sides

$\dv{x}\int_0^xf(t)\dd t= f(x)$

[craggy tapir]

is this true?

[granite torrent]

yes that's how you find f

[craggy tapir]

would i need a +C for this?

[craggy tapir]

im referring to this

[granite torrent]

go C for urself

what happens when u try

(normally i would answer the q but i am fairly confident u will figure out what goes on here after the differentiate both sides suggestion)

[craggy tapir]

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[void root]

when a set, for example S, comprises of all positive integers in base 10 comprising of only 0's and 1's (e.g. 11, 101, 1100, etc.)
how would someone find all the constructions of a number such as 1298 or something through addition of digits in S?
(e.g. adding up '1' 1298 times, or doing 1100+100+10+10+10+10+10+10+10+10+10+1+1+1+1+1+1+1+1)
is there a specific method, code or equation to do this

what i have done so far (the actual question isnt 1298 btw i just want to know the method to achieve)
i put a restriction on it being only 4 digits number in the set S
which would be 1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111
as the biggest 4 digit number in this set is 1111, smaller than 1298
and 5 digits are invalid ofc
therefore its only a combination of those numbers that can add up to 1298

you exclude leading 0's, standalone 0's which is also how i got the 15 values written above
(otherwise you can add up an arbitrary amount of 0's)

but thats how far ive gone, unsure of how to solve
sorry for confusing wording, i can elaborate

[rare dock]

does ‘find all’ mean enumerate them all or count how many there are?

if you just want to count, you could do this with generating functions

[full forum]

@void root Has your question been resolved?

[rare dock]

in addition to this can you detail the problem parameters more? what exactly are you asked for? a program? what numbers does it need to be able to handle? should it be built around handling just one query, or all numbers in a range, or what?

and ideally just post the source of the problem

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[spiral cedar]

A-Level trig

[spiral cedar]

havent got a clue with any of these

nope

just gotta try solve them from what we learnt in lessons

My question 2 I tried

[robust slate]

The perimeter of the sector also included the two radii on the sides

Not just the arc length

[spiral cedar]

ah so plus 8 aswell?

[robust slate]

Yeah

[spiral cedar]

any idea on these?

[glossy valve]

Civil Service Pigeon

[tidal citrus]

I think...I think the answer is ||pi||

||(Theta/2)r^2 = 2pi*r

theta = 4pi/r||

[robust slate]

? Why are you putting the entire circumference

[tidal citrus]

From the given. It said that the area of the sector is equal to the perimeter (circumference)

[tidal citrus]

Oh poop

Yes I just noticed

||(Theta/2)r^2 = 2r+r*theta

(Theta/2)r - 2 = theta||

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[vapid pawn]

The table shows 3 values of x and their corresponding values of y, where y=f(x)+4 and f is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y =f(x) in the xy-plane?

[full forum]

@vapid pawn Has your question been resolved?

[hazy lance]

!status

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vapid pawn]

7

I did not understand how to solve it

[hazy lance]

f(x) is a quadratic function right so you have $f(x) = ax^2 + bx + c$

[glossy valve]

esca (@ with reply)

[vapid pawn]

Yea

[hazy lance]

then you plug in values of x and y

[vapid pawn]

Okay

[hazy lance]

$-8 = a(21)^2 + b(21) + c + 4$

$8 = a(23)^2 + b(23) + c + 4$

[glossy valve]

esca (@ with reply)

[hazy lance]

so on

you can also identify that x=23 is the vertex of the parabola

[vapid pawn]

Why

[hazy lance]

because 21 and 25 are the same distance from 23, -8 and -8 are the same distance from 8, and you can see that 23 is a local maximum

[vapid pawn]

Okay

But they should be the same distance away from each other right?

Like the 21 and 5 and - 8 and - 8

[hazy lance]

yeah

like basically its symmetric around (23, 8) you can tell that its your vertex

[vapid pawn]

Okay

Thank you

So what's next 😊

[hazy lance]

so you have $y = a(x-h) + k$ where (h, k) is the vertex

[glossy valve]

esca (@ with reply)

[hazy lance]

so y = a(x-23) + 8

now just plug in eithrr of the other values to obtain a

you can verify your solution by making sure it agrees with the other pair

[full forum]

@vapid pawn Has your question been resolved?

[vapid pawn]

It doesn't work

I'll try again and update you

Thank you so much for your time 🥰🥰

I will close the ticket 😅😁

.close

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[hazy lance]

uhh sorry i forgot a square

[hazy lance]

it should be $y = a(x-23)^2 + 8$

[glossy valve]

esca (@ with reply)

[hazy lance]

.close

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[vapid pawn]

Okay thank you sir 🥰🥰🙏

[hazy lance]

npnp

[vapid pawn]

🥰

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[versed crow]

how could i go about getting to the finish line from the black line following the yellow line within 400m Each unit on the graph = 1 km
https://www.desmos.com/calculator/n8zmakx4wq

[full forum]

@versed crow Has your question been resolved?

[rustic frigate]

What exactly do you mean by that?

Like what is the finish line even supposed to mean? Give a more thorough explanation; we can’t read your mind

[versed crow]

If you look at the attatched link you'll see what I mean.

[pale oriole]

the link doesnt explain anything at all

[fallen hull]

do you want the line to follow the yellow line?

[pale oriole]

but your question still makes no sense

[versed crow]

dosent have too

as long as its within 400m

Each unit on the graph = 1 km

[rustic frigate]

So the trouble is that last bit to the Finish?

Making it within 400m?

[versed crow]

Let me simplify this, say the end of the black line is point A, and the finish line is point B (located at (0.5 0)

[rustic frigate]

My first question would be, how did you do the rest?

[versed crow]

Had help from a friend

But all the equations I used are

There

[rustic frigate]

Are you allowed to use splines?

This becomes a piece of cake

[versed crow]

I can only use these:

[rustic frigate]

I see

Not even a line? Lol

[pale oriole]

a line is just a parabola without the quadratic term

[versed crow]

Lines are fine

[rustic frigate]

Yes, but it says parabola, not quadratics. So that’s not obvious

[pale oriole]

and a (finite) line is a circle squished down to width 0

[rustic frigate]

It could imply that they mean through an algebraic geometric sense

[pale oriole]

im just wondering why you would do this in desmos

[versed crow]

thats just what the task is idk

[pale oriole]

wouldnt it be simpler to place some points that the path must go through, and then create lines from point to point?

[versed crow]

TLDR just need a line from point A to B

and idk how to do that

maybe i could use a parabola so its more accurate to the line

but

dosent matter

[rustic frigate]

Yes, just do linear interpolation. That is what Flappie says

[pale oriole]

get the coordinates from point A and B and draw a straight line through it

[versed crow]

ok how do i do that 😭 is the quesiton '

[pale oriole]

aha

why didnt you ask that in the first place without this weird other stuff

[versed crow]

idk

i havent slept in like 26 hours cause ive been doing

comp sci shit

ok after i do the line thingy, i need to justify

the shit ive used

but that

shouldnt be hard

[pale oriole]

https://www.groundwatersoftware.com/calculator_2_linear_interpolation.htm#:~:text=Linear interpolation determines%2C from two,at another given point x. plug in the coordinates of A and B in here

and you get your answer

[versed crow]

• You need to provide the coordinates of each point where the drone switches from following one function to another.

• You need to state the range or domain of the functions you are using
Task 2
• Describe how you chose each function and show any calculations you did to decide upon the values in your equations. If you needed to adjust any of these values to improve the fit, briefly explain what you had to do, and why.

• State the key features of your final functions.

[pale oriole]

(hint: i googled linear interpolation two points and clicked on the first link)

[rustic frigate]

Start simple. So given two points A and B, you want to find a line that passes through it

[versed crow]

needs 3 coordinates we have 2 here

[rustic frigate]

What would for example a line in general look like?

[versed crow]

uh

a line idk

usually straight or vertical

[rustic frigate]

What grade is this?

[versed crow]

yr 12 so

idk what grade that is

[rustic frigate]

Have you gone over slope of lines etc?

[versed crow]

Could I just get one of you guys to figure out what I need to plug in, I might be actually braindead or smth

[pale oriole]

general form of a line is y=ax+b

you fill in your two points $$y_1=ax_1+b\y_2=ax_2+b$$ so that you get two equations with two unknowns

[glossy valve]

Flappie

[pale oriole]

then you can solve for a and b

[versed crow]

idk how to do allat rn 😭

oh its just

y=2.266x-1.133\left{0.5<x<1\right}

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[full forum]

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[rigid perch]

(Stats and prob) ive been doing my hws and noticed that a lot of solutions are using formula 2 to find sample stdev rather than 1. Are they equivalent expressions?

[full forum]

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@rigid perch Has your question been resolved?

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[static basalt]

I need help

[static basalt]

I have a Math 9 PAT tommorow

And I need help studying

[brisk obsidian]

Good luck on your test. ☘️

[static basalt]

thank you

but could u help me

[brisk obsidian]

You should just ask your questions then.

[brisk obsidian]

The line is divided into 1/8th segments, that should help a bit

If you convert each of the blue squares into fractions with an 8 in the denominator, the answers should be apparent.

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[static basalt]

GUYS HELP

[static basalt]

ASASP

[viral jasper]

!status

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[coral spire]

The top line shows when a number is less than 1

n < 1

The bottom line shows when a number is greater than or equal to -1

n >= -1

So when does n satisfy both cases?

This when n is both less than 1 and greater than or equal to -1

-1 <= n < 1

[austere cove]

!nosols

[full forum]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[austere cove]

@coral spire ^

[static basalt]

1

[coral spire]

😬

[static basalt]

could u draw it out for me

I understand visually

[austere cove]

!show

[full forum]

Show your work, and if possible, explain where you are stuck.

[static basalt]

I don;t understand what the question is asking

I don't know how to read the numberline

[austere cove]

Do you understand what a number line is though?

[static basalt]

yes

judt now how to read this one

[austere cove]

So if you have a point on the number line at the location labeled 3, the value indicated by that point is?

[static basalt]

huh?

what did u say?

[austere cove]

It's a question about your understanding of the number line

This is the image that can accompany the question above. What number am I indicating?

@static basalt I'm not trying to be obtuse or anything, just trying to figure out where your disconnect on this topic is, and because you've not been terribly helpful with exactly what you're confused about, I'm having to start with the most basic of basics, and almost insultingly easy questions.

I have had students who have been confused about this, so if you are, that's totally fine and normal

But I'm going to need a little bit of investment from you in order to help you learn this.

After all, learning is fundamentally a two way street, I literally can't do the learning for you

[full forum]

@static basalt Has your question been resolved?

[static basalt]

sorry im not really on the smart side of things

[austere cove]

Don't be sorry for being who you are, and don't put yourself down.

You're fine, just I need some engagement

[static basalt]

im so stupid

I can't solve this

I can't even understand it

im doing a 55 question practice exam

[austere cove]

That's fine, can you tell me in your own words what a number line is?

[static basalt]

and im struggling in the simiplist of things

[static basalt]

where numbers are arranged in a line?

[austere cove]

Yes, and are the numbers in order or can they be out of order?

[static basalt]

in order?

im only in grade 9

my friend is so smart at these things

[austere cove]

Yes in order

[static basalt]

but everytime I ask him he gets more and more annoyed

[austere cove]

Don't mind him

[austere cove]

So I have this drawing

[static basalt]

yes

[austere cove]

And I have a dot on the number labeled 3.

[static basalt]

yes

[austere cove]

What value am I representing with that dot?

[static basalt]

3

[austere cove]

Exactly

What if I moved that dot to the 0?

[static basalt]

0

[austere cove]

Yeah, super easy

Ok, now what if I moved the dot halfway between the 1 and the 2?

[static basalt]

so 1.5

are we taking baby steps to solve this equation?

[austere cove]

Yeah

We are

So this bold line

What do you imagine it is supposed to be?

The one on the top and bottom line

If you don't know, feel free to guess

[static basalt]

idk

I don't even have a guess

[austere cove]

Ok, so what if I want to represent every point between 0 and 1

I could put a dot over every number

If I do that, what would the result look like?

[static basalt]

u lost me

summarize those words

Im not good with big words

[austere cove]

Let's say any number between 0 and 1, so 0.5, 0.23, 0.747292... and so on. I want to mark on my number line

So I can put down a dot for each of these, but there are a lot of numbers between 0 and 1

So what can I do instead?

[static basalt]

but thsi numberline doesn't have any dots inbetween

[static basalt]

put it on top

of the whole number instead??

[austere cove]

If you imagine I put down infinite dots wouldn't it just look like a solid bold line?

[static basalt]

yeah

[austere cove]

So the bold line indicates that all of the numbers in that area are included

So let's look at the top number line

Is the number 3 included?

[static basalt]

idk

yes?

if it is please ecplain

[austere cove]

So is there a dot at 3 on the top line?

[full forum]

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[spice rose]

How would I solve an equation like this?

[spice rose]

,rotate

[spice rose]

everything other than eta is known here. But how do I rearrange this further?

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[full forum]

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[full forum]

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[edgy imp]

I cannot understand "This linearly independent list cannot be longer than
any spanning list of 𝑉 (by 2.22). Thus the process eventually terminates, which
means that 𝑈 is finite-dimensional."

Why does it terminates

[zinc chasm]

Do you understand (or agree with) 2.22 ?

[edgy imp]

yes

[zinc chasm]

Do you also agree that at each step (k), the family {u1, ..., uk} is linearly independant ?

[edgy imp]

that is contrapositive of this lemma, right?

[zinc chasm]

Yes

So, since at each step you are constructing a bigger linearly independant family and, in the same time, since the dimension of the vector space is finite the maximal size of such a family is bounded, the number of steps you can make is also bounded/finite

Does it make sense ?

[edgy imp]

i cannot understand this part: since the dimension of the vector space is finite the maximal size of such a family is bounded