help-38

[serene crane]

im just asking if that 1 is a pivot or not

[ionic pendant]

in which matrix?

[serene crane]

sorry shouldve said

[ionic pendant]

the first 3 columns are pivot columns

[ionic pendant]

only the augmented column is not

[serene crane]

so since EVERY column is a pivot, theres one solution

[ionic pendant]

as long as every column except the augmented column has a pivot, yes

[serene crane]

for #1, every column has a pivot, but theres a row entry on the last row that makes it inconsistent so thats the problem

oh wait

last column is pivot

i see isee

And for #3, the last column (before the augmented one), isnt a pivot, and theres another row that isnt a pivot. makes it an infinite solution.

Would -2, 3, and 4 all be free variables?

[ionic pendant]

no

[serene crane]

ah

[ionic pendant]

only the non-augmented columns without pivots are free columns (corresponding to free variables)

[serene crane]

So which would be a free variable

x4 is augmented onto the other matrix right?

so would -2 be the free varaible?

[ionic pendant]

no, x4 is not augmented

[serene crane]

oh boy

2 steps forward, 10 back

Okay explain to me one more time what an augmented column is, and what would be the non-augmented coulmns

please

oh wait

the augmented coulmn is the last one including 1 and -1. as that was put onto the matrix?

[ionic pendant]

yes

it's the column separated by a bar

[serene crane]

ok ok

[ionic pendant]

the text just calls it the "last column" but i don't find that very descriptive

[serene crane]

now the non-aug column is 3, and 4 as it doesnt hae a pivot in it?

[ionic pendant]

the non-augmented columns are every other column

[serene crane]

oh i see

i see i see

Now how do I go about figuring out waht the free variable is from that?

The free coulmns are the ones without pivots

Can I think that if theyre a free coulmn, each variable in that coulmn is free?

[ionic pendant]

each nonaugmented column corresponds to one variable

[serene crane]

mhm

so 3,4 is one variable

[ionic pendant]

so column 1 corresponds to x1, column 2 corresponds to x2, etc

[serene crane]

mhm

x2 and x4 are free as they arent pivots

So does that mean each entry in the variables x2 and x4 are free variables?

[ionic pendant]

x2 and x4 are free variables as they correspond to free columns. the numbers in the column aren't variables, they're the coefficients of that variable

[serene crane]

i see i see

So if someone asked, what are the free variables in this

And by definition, a free variable (or coulmn) is a column with no pivot

Would I say, x2 and x4 are my free variables

[ionic pendant]

columns 2 and 4 are your free columns, x2 and x4 are your free variables

[serene crane]

ah

[ionic pendant]

free columns correspond to free variables

[serene crane]

i see

also when they said, "The last column is not a pivot column, and some other column is not a pivot column either.". did they mean the augmented column is not a pivot column

i think i was mixing it up with x4 when they were saying last

[ionic pendant]

whenever this text says "last column" they mean augmented column

[serene crane]

ok

everything has clicked, thank you so much

I'm about to go attempt my homework, do I have your permission to ping you in that channel if I come across a question, as your explainations are really good? If not thats okay also, i know its busy

Im gonna close this channel

Also is there anyway to like download the transcript of this channel?

[trim jolt]

@serene crane Has your question been resolved?

Channel closed

Closed by @serene crane

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pseudo fossil]

Anyone know where I can start for this?

[nova spire]

looks like De Morgan's law

think about how the Right hand side can be reexpressed using De Morgan's

[dull temple]

ugh start by picking better symbols

[trim jolt]

@pseudo fossil Has your question been resolved?

[pseudo fossil]

but I need to show that the left is equal to a bunch of the things on the right that eventually leads to what they want

[limpid dawn]

You can start from either side

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pseudo fossil]

.reopen

[trim jolt]

✅

[pseudo fossil]

oh!

[limpid dawn]

but it's usually easier to simplify the right side then to think of what to do on the left side, so to get to the right

[pseudo fossil]

I'm not sure what the first simplification step is

[limpid dawn]

Do you know the De Morgan distributive law?

[pseudo fossil]

Yes but the not sign is throwing me off

ϕ ∧ (ψ ∨ ¬ψ) is it this?

[solid kiln]

anti-algebraist 𝔸dωn𝓲²s

[limpid dawn]

yes!

Now notice what can you say about (ψ ∨ ¬ψ)

[pseudo fossil]

hmm

um

just true?

[limpid dawn]

yes

it's a tautology

so you can write ϕ ∧ T

[pseudo fossil]

okay yaa

hmm

and then just ϕ?

[limpid dawn]

What can you say further

yes

[pseudo fossil]

why can we just say that?

[limpid dawn]

T is always true so it has no impact basically

you can do a table

A T A ∧ T
0 1
1 1
what happens?

[pseudo fossil]

T T

[limpid dawn]

T T?

[pseudo fossil]

true true?

[limpid dawn]

first row

true and false results to?

[pseudo fossil]

false

[limpid dawn]

second row

true and trwu

[pseudo fossil]

true

[limpid dawn]

A T A ∧ T
0 1 0
1 1 1

So you get this

[pseudo fossil]

okay ya

[limpid dawn]

A and A ∧ T are here logically equivalent

[pseudo fossil]

ohh ok

that makes sense

thank you so much!

[limpid dawn]

you could see

A T A ∨ T
0 1
1 1

what here happens

as an exercise

[pseudo fossil]

ya

what is the best way

to

write this proof out then?

start with right side

[limpid dawn]

yea

[pseudo fossil]

and show it ends up being ϕ

[limpid dawn]

yea

it's like whether you have x = 2 or 2 = x situation

preferably you could still start from the left and just proceed to do it backwards

up to you

[pseudo fossil]

yaa that's what I thought

[limpid dawn]

if you know from right to left you also know from left to right

[pseudo fossil]

oh true

we could say

ϕ≡ ϕ∧True
≡ ϕ∧(ψ∨¬ψ)
≡ (ϕ∧ψ)∨(ϕ∧¬ψ)

as required.

[limpid dawn]

as we speak.

[pseudo fossil]

so that's correct then?

[limpid dawn]

yes

[pseudo fossil]

cool cool

How did u know to look at demorgan's first?

just intuition?

[limpid dawn]

because I knew de morgan's distributive law

it resembled that, so why not start with that

it's essentially as x²+4x = 0 why not factor here x(x+4) = 0

we basically "factored"

[pseudo fossil]

gotcha

Thank you so much! You are very helpful!

I really appreciate it!

[limpid dawn]

np!

[pseudo fossil]

.close

[trim jolt]

Channel closed

Closed by @pseudo fossil

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[atomic shoal]

need help solving this by completing the square

[restive vortex]

can you use derivative

if you cant we could complete the square

[atomic shoal]

what u mean derivative

gr11 functions btw

[restive vortex]

alr

we could complete the square to finish the equation

-4.9t^2+28t+2

[atomic shoal]

yeah

[restive vortex]

could you complete the square btw

[atomic shoal]

i did

thats where i got the issue

it aint working out

i factor out -4.9 from the first 2 numbers correct?

[restive vortex]

could you show me the work you did

yeah

[atomic shoal]

ok sure

here

u see where i got stuck

[restive vortex]

i couldnt even see

alr alr

let me work it out here

[atomic shoal]

u see i factored it out

oh shit i dont think i devided b by 2 and squared it

i devided it by 4.9

thats prolly where i went wrong

[restive vortex]

maybe

[atomic shoal]

csn u stil solgve it

[restive vortex]

alr

-4.9(t^2-40/7-20/49)

[restive vortex]

complete this square @atomic shoal

[lucid sinew]

-4.9t^2 +28t+2
factor out -4.9
= -4.9(t^2 + 23.1t) +2

oh

nvm

also work

[atomic shoal]

wait

im almost done solving

it

ill send apic

[restive vortex]

wait

[atomic shoal]

got it

boom

im crazy smart

[restive vortex]

nice

w

[atomic shoal]

max height 42m at 2.9s

[trim jolt]

@atomic shoal Has your question been resolved?

Channel closed

Closed by @atomic shoal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wraith hinge]

HALP

[wraith hinge]

how to solve

i still don't get it

because when i tried setting 9x^2+2 not equal to 0

it kinda gave me an imaginary number

meaning square root of -2/3

how can it be - infinity positive infinity

[limpid dawn]

you dont have restrictions because of that

[wraith hinge]

wait

[west sleet]

Since 9x^2+2=0 has no real solutions

[wraith hinge]

yep

[west sleet]

That means there's no real x such that 9x^2+2=0

[wraith hinge]

ah i get it

[west sleet]

So the domain is just the entire set of real numbers ye

[wraith hinge]

ah tysm

[wraith hinge]

u too

i mean logically that makes sene

sense

but i cannot trust my gut feeling in math

[trim jolt]

@wraith hinge Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dense linden]

Combinatorics
Find the possible combination of variables
problem 1
x+y+z=6 x,y,z are whole number greater than or equal to 1
I create 6 sticks , then I have to fill up 5 spaces with 2 stars
the answer is (5*4)or(5C1x4C1) ie 20. but I cannot use 5C2

problem 2
x+y+z+a=12 x,y,z,a are whole number greater than or equal to 1
use same concept of markers the answer is 11C3. but not 11x10x9.

I CANNOT UNDERSTAND THE DIFFERENCE

note:the answer 20 for first problem and 165 for second problem are strictly correct

[dense linden]

.close

[trim jolt]

Channel closed

Closed by @dense linden

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[boreal apex]

What you just said wasn't comprehensible. Could you rephrase what you mean by this?

[empty tulip]

sorry

[trim jolt]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[empty tulip]

How do i solve this using excel, graphs

.open

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dull thorn]

Given that we have 3 points A B and C that don't form a straight line: M is the point where MA+MB-MC=0 (all of these are vectors)
Prove that vector V (defined by V=NA+NB-2NC) (all of these are vectors) is independent of N. Construct vector V
No other information has been given

[vernal palm]

did you switch between M and N?

[dull thorn]

No I did not

I made sure I wrote everything correctly

We have a point M and an unknown point N

Just so my English won't disappoint me again lol

[vernal palm]

so you're trying to prove that if you take 3 points who are not on the same line no matter what other point N you take NA+NB-2NC is independent of N?

[dull thorn]

Yes

[vernal palm]

I'm not sure if that is correct

[dull thorn]

It's in french but I'm sure I copied that correctly

[vernal palm]

ok

!status

[trim jolt]

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

[vernal palm]

@dull thorn

[dull thorn]

I am done I have solved it (sorry I forgot I put my phone on DND 😭)

.close

[trim jolt]

Channel closed

Closed by @dull thorn

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[left sierra]

how would i factorise this is there any method for it

[summer bluff]

it follows the format
Ax² + Bx + C

multiply A and C, then list the possible factor pairs (include negative factors like -2 times -5)

figure out which pair adds up to B (in which case, -11)

[trim jolt]

@left sierra Has your question been resolved?

Channel closed

Closed by @left sierra

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wet rune]

I believe he wants us to prove it using intermediate value theorem, but how would i prove that the function is continous first

[zinc ginkgo]

you can probably cite that products and sums of continuous functions are continuous

[trim jolt]

@wet rune Has your question been resolved?

Channel closed

Closed by @wet rune

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[covert loom]

Find the last two digits of the number $2^{3^{2024}}$

[solid kiln]

alex <3

[covert loom]

Can someone tell me how does one solve questions like these?

This is for a math competition btw, and I'm trying to atleast do better this time than last time.

[zinc ginkgo]

do you know modular arithmetic

[covert loom]

i never understood it

maybe i can with a little side help though, if that's the only way to solving this?

[zinc ginkgo]

yea i don't know how to do this without modular arithmetic

[covert loom]

could you explain to me then?

i am familiar with modular arithmetic as we've covered it before but i just never understood how to do it, we just went through it in a breeze

[zinc ginkgo]

https://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction

[covert loom]

So, to solve this, to find the last two digits, I would use mod(100)?

[zinc ginkgo]

yes

[covert loom]

okay ig

ty

.close

[trim jolt]

Channel closed

Closed by @covert loom

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[smoky marsh]

can someone help me solve this

[kindred pier]

!status'

[trim jolt]

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

[smoky marsh]

1

[empty orchid]

$\ln(a^b)=b\ln(a)$

[solid kiln]

;(

[empty orchid]

$\sqrt{x}=x^{1/2}$

[solid kiln]

;(

[smoky marsh]

ok so 1/2lnx

[empty orchid]

yep 👍

do you know how to integrate ln(x)?

[smoky marsh]

wait hold on

you know photomath?

[empty orchid]

i would rather you not use it, but yes, i know what it is.

[smoky marsh]

when i plug in this it shows me the answer "(lnx*x-x)/2"

[empty orchid]

yes, it is.

[smoky marsh]

but when i plug in integral of 1/2lnx it shows me the answer of the integral i solved myself using ibp method

so that would be ((lnx*x)/2) - (1/2)x

[empty orchid]

yes.

[smoky marsh]

wait what

[empty orchid]

$\frac{\ln(x)\cdot x-x}{2}=\frac{\ln(x)\cdot x}{2}-\frac12 x$.

[solid kiln]

;(

[smoky marsh]

oh

[empty orchid]

you quite literally just split the fractino.

[smoky marsh]

so i solved it correctly

[empty orchid]

yes.

[smoky marsh]

omg

thanks then

.close

[trim jolt]

Channel closed

Closed by @smoky marsh

Use .reopen if this was a mistake.

[empty orchid]

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sudden lagoon]

True or false: the intersection of linear hyper planes is always nonempty

[sudden lagoon]

I believe the answer is true because linear hyperplanes always go through the origin so any two given hyper lanes must have at least the origin in their intersection

I would appreciate any feedback on this

[grim sparrow]

what is your definition of a hyperplane?

[sudden lagoon]

We define a subset of Rn of the form H = { x in Rn s.t a^T x = 0 (vector)} for a fixed nonzero vector a in Rn

[grim sparrow]

okay, but importantly, this definition says that 0 is in H, yeah?

so in that case, every hyperplane contains 0, and so I agree with you

[sudden lagoon]

Of course yes you’re right

Thank you very much @grim sparrow

[grim sparrow]

no problem

[sudden lagoon]

.close

[trim jolt]

Channel closed

Closed by @sudden lagoon

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wraith hinge]

\int 1/2 ln x
1/2 \int ln x
1/2 x + c

[wraith hinge]

.close

[trim jolt]

Channel closed

Closed by @stoic crater

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[smoky marsh]

is the answer x*(e^2θ)*sin^3θ correct?

[zinc ginkgo]

no

use integration by parts twice

[smoky marsh]

why does sin 3θ have to switch places with e^2θ

[zinc ginkgo]

no idea what you mean "switch places"

[smoky marsh]

commutative property

[zinc ginkgo]

it doesn't have to?

[smoky marsh]

oh

[zinc ginkgo]

why do you think so

[smoky marsh]

i just looked it up on photomath

[zinc ginkgo]

there's more than one way to do this problem

[smoky marsh]

is this the right path or am i completely wrong with this answer

[zinc ginkgo]

but i think the intention at the moment all solutions involve double integration by parts.

[smoky marsh]

so am i on the right tracks do i integrate by parts the "answer" or no

[zinc ginkgo]

i really have no idea what you mean

[smoky marsh]

u said double ibp

[zinc ginkgo]

yes

[zinc ginkgo]

i don't know what "answer" you're referring to

[smoky marsh]

so the first ibp i got x(e^2θ)sin^3θ

[zinc ginkgo]

nah

show your full steps

[smoky marsh]

ok

u=e^2θ
du=0dx
v=x*sin3θ
dv=sin3θdθ

uv-∫vdu

ik where i messed up

[smoky marsh]

ok so is ((xe)^2θ)*sin3θ-sin3θx is this better

[zinc ginkgo]

you should not have x anywhere

[smoky marsh]

oh damn

[zinc ginkgo]

this tells you the variable you're integrating is theta, not x

[smoky marsh]

ok

so basically thats where im messing up

[smoky marsh]

-(((e^2θ)*cos3θ)/3)+((sin3θ)^2)/18 better?

[zinc ginkgo]

what?

if you just want to check your answer you can do

,w int e^(2x) cos(3x) dx

[solid kiln]

Results provided by WolframAlpha

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

Requested by rie.mann

[smoky marsh]

but how do i do it

[zinc ginkgo]

should just show your full steps instead of the last one

[smoky marsh]

ok

[zinc ginkgo]

can't find your mistake from one wrong answer

[smoky marsh]

u=e^2θ
du=0dθ
v=-cos3θ/3
dv=sin3θdθ

uv-∫vdu

(e^2θ)*(-cos3θ/3) - ∫ (-cos3θ/3) sin3θ

from this we get -(((e^2θ)*cos3θ)/3)+((sin3θ)^2)/18

im so sorry i gtg

.close

[trim jolt]

Channel closed

Closed by @smoky marsh

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[molten comet]

Hello

[molten comet]

Does anyone know where -2x is coming from and why we can't use ≠ f(y)

[empty orchid]

it’s what that monster expression is equal to.

try to factor a 2x term from the numerator and see what you get.

[bright quarry]

$\frac{N_x - M_y}{M} = \frac{-6x^3y^2 - 8xy}{2xy^3 -2x^3y^3 - 4xy^2 + 2x}$

[solid kiln]

knief

[bright quarry]

since this isnt purely a function of y we cant use this in finding an integrating factor to make it an exact DE

[molten comet]

wdym this isn't purely a function of y?

[bright quarry]

there are terms with x in it

you learned the integrating factor method right?

if its not exact

how to convert it

$\rho(x) = e^{\int f(x) \dd{x}}$

[solid kiln]

knief

[bright quarry]

$f(x) = \frac{M_y - N_x}{N}$

[solid kiln]

knief

[bright quarry]

if this condition is met

and for the other case

we can check if $\frac{M_y - N_x}{M} = g(y)$

[solid kiln]

knief

[bright quarry]

in which case youd use $\rho(y) = e^{-\int g(y) \dd{y}}$

[solid kiln]

knief

[trim jolt]

@molten comet Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tepid hamlet]

you can directly post your question

[zinc ginkgo]

!done

[trim jolt]

If you are done with this channel, please mark your problem as solved by typing .close

[tepid hamlet]

didn't realize my suggestion was so controversial :p

[zinc ginkgo]

.close

[trim jolt]

Channel closed

Closed by @zinc ginkgo

Use .reopen if this was a mistake.

[zinc ginkgo]

don't troll

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pure oak]

Need a hint for this problem

[kindred pier]

Polar form of a vector:
$$\vec{u}=\norm{u}(\cos\theta\hat{i}+\sin\theta\hat{j})$$

[solid kiln]

SWR

[pure oak]

Instead of 60 degrees can I use pi/3

[trim jolt]

@pure oak Has your question been resolved?

Channel closed

Closed by @pure oak

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[novel anvil]

Can someone help me figure this out please?

[stuck plover]

Do you know what the equation for a circle looks like?

With radius r and center (a, b)

[novel anvil]

is it x^2 + a + y^2 - b = r?

[stuck plover]

No

Because then you could move the a and b to the right to get x^2 + y^2 = (r - a + b)

So it wouldn't be well defined

Okay easier question

Do you know what the equation for a circle of radius r and centre (0,0) is?

Work it out using pythagoras

[novel anvil]

i dont know what pythagoras is actually

never heard of that term

[stuck plover]

Okay 1 sec

This is pythagoras' theorem

[novel anvil]

oh

well i would call it pythagorean theorem

[stuck plover]

Normally taught in middle school I think so you've probably heard of it

Yeah fair enough it can be called either

Named after a guy called pythagoras

Anyway

Can you use that theorem to work out the equation of the circle?

[novel anvil]

isnt it just 0?

im prob wrong

[stuck plover]

No, 0 is just the equation for the origin

Does this help?

[novel anvil]

no i have no idea

[stuck plover]

Okay

[stuck plover]

This diagram represents every point on the circle

For each one of them, you can draw a right angled triangle like that

Do you know what the side lengths are of that triangle?

Say if a point (x,y) is on that circle, what can you say about x, y, and r?

[novel anvil]

3 4 and 5?

[stuck plover]

No

Where did that come from?

If r = 5, then the point (3,4) would be on the circle, and the triangle could be a 3 4 5 triangle

But that top right vertex could be any point on the circle

[novel anvil]

i refrenced this a while ago

[stuck plover]

Here are another couple for clarity

Yeah so 3 4 5 is just one possible right angled triangle

It's "common" because they're low numbers, and 3^2 + 4^2 = 5^2

But mathematically it's not anything special

[novel anvil]

alright

[stuck plover]

Does that make sense?

[novel anvil]

i think so

i gotta head to bed any way so

[stuck plover]

Okay

Can you work out what the base and height lengths of that triangle are?

Given that the middle of the graph is (0,0) and the top right corner is (x,y)

[novel anvil]

can i try tomorrow

or do i have to rn

[stuck plover]

Your choice

[novel anvil]

yeah i gotta sleep

[stuck plover]

You're 1 conceptual leap away from getting the whole thing

But yeah come back to it in the morning

[novel anvil]

alright thanks

[trim jolt]

@novel anvil Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glad pumice]

Can someone please help me on this question

[glad pumice]

please help

<@&286206848099549185>

[trim jolt]

@glad pumice Has your question been resolved?

[glad pumice]

<@&286206848099549185> please help

bruh

.close

[trim jolt]

Channel closed

Closed by @glad pumice

Use .reopen if this was a mistake.

[past widget]

Still stuck?

[glad pumice]

i moved on to a diff q

[past widget]

Alr

Btw this was a one liner ._.

Look up Menelaus lol

No need to beat yourself up

$\frac{BE}{ET}\cdot \frac{TA}{AD}\cdot \frac{DC}{CB} = 1$

[solid kiln]

Arya

[glad pumice]

ok thanks

..clsoe

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[storm widget]

Hi im having trouble with this math question for geometry, were doing trig and im stuck on where to go from here.

[dull temple]

,rccw

[storm widget]

heres the blank one

[round thorn]

!status

[trim jolt]

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

[storm widget]

3

[past widget]

Label the vertices in this figure and repost

[past widget]

Where's the labelling?

[trim jolt]

@storm widget Has your question been resolved?

[storm widget]

I lied i did it

[zinc ginkgo]

!done

[trim jolt]

If you are done with this channel, please mark your problem as solved by typing .close

[trim jolt]

@storm widget Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stark drum]

i am not sure where to start here

[past widget]

Area of a ||gm = 2wice the area of either triangle cut by the diagonal

[stark drum]

oh

[past widget]

^^

[stark drum]

i was trying to visualize a 3d object and it was tripping me up

thanks

[past widget]

You know how to find area for ABC right? 0.5 |a x b| ?

[median jasper]

is this linear algebra?

[stark drum]

calc 3

[median jasper]

i was gonna say, is it possible to use determinant

[atomic seal]

you can also find diagonals d1 and d2 and do d1 x d2 /2

[past widget]

why ping?

[stark drum]

oh if thats the area than this should be simple ig

[atomic seal]

my bad idk that setting turns on all the time

[stark drum]

ok ill try it then

[past widget]

btw the a and b are side vectors AB, AC or AB, BC, any of those

Alr

[stark drum]

oh wait so the area of the parallelagram is |a x b|

[past widget]

|AB x AC| to be precise

[stark drum]

yeah, cuz a and b in the context of the problem are points

yay i got it!!!!

.close

[trim jolt]

Channel closed

Closed by @stark drum

Use .reopen if this was a mistake.

[stark drum]

.reopen

[trim jolt]

✅

[stark drum]

uh

[past widget]

Lol XD

[stark drum]

that one looks like what i thought the other one was

3d

:<

i guess i should find 3 vectors first?

[past widget]

Do you know what the quantity |(a x b) . c| gives you?

or what it even is?

[stark drum]

that?

idk what it represents tho

[past widget]

https://youtu.be/6NeAK0rJwlk?si=jJ7emnD2fqL6_Kec

there, that'd add to your set of 3D visualization skills :p

[stark drum]

great, thanks!

ooooh

i dont even have to watch the video to understand what's going on here

did it!

tysm @past widget and gn

.close

[trim jolt]

Channel closed

Closed by @stark drum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dense linden]

Theorem 2
Let Dom(Circle m k) denote the number of ways to place
k indistinguishable and non -overlapping dominos on a circular sequence
of numbers 1 ,2,...,m, where each domino covers two numbers Then,

Dom(Circle m, $k)=\frac {m}{m-k}(\begin{matrix} m-k\ k\end{matrix} )$

Proof:
The strategy adopted here in enumerating the number of place-
ments works by counting the number of placements in classes of placements
which are both disjoint and exhaustive.The total number of placements is
therefore be the sum of the number of placements calculated over the entire
set of these disjoint (and exhaustive)classes.
Consider the following two classes of placements:

(i) the class of place-
ments where the number 1 is covered by a domino and

(ii)the class of
placements where the number 1 is not covered by a domino.

These two
classes are disjoint and exhaustive and we use them here to evaluate Dom
(Circle m. $k$
The number of placements in which m and 1 are covered by a single
domino (as shown above) is clearly given by Dom $(Linem-2,k-1)$ . By
the same token.the number of placements in which 1 and 2 are covered
by a single domino is Dom(Line $m-2,k-1)$ The number of placements
in which 1 is not covered by any domino is clearly given by Dom(Line
$m-1,k)$ Summing the number of placements in the two classes gives:
$Dom(Circlem,k)=2Dom(Linem-2,k-1)+Dom(Linem-1,k)$
$
=2(\begin{matrix} m-k-1\ k-1\end{matrix} )+(\begin{matrix} m-k-1\ k\end{matrix} )$
$
=\frac {2(m-k-1)!}{(m-k-1-(k-1))!(k-1)!}+\frac {(m-k-1)!}{(m-2k-1)!k!}$
$=\frac {(m-k)!}{(m-2k)!k!}(\frac {2k}{m-k}+\frac {m-2k}{m-k})$
$=\frac {(m-k)!}{(m-2k)!k!}\cdot \frac {m}{m-k}=\frac {m}{m-k}(\begin{matrix} m-k\ k\end{matrix} )$

my alternative method
let 1 be number not covered by domino,
let 2 replace the number covered by domino,
circular permutation=(m-k-1)!,
repeated 2 = k!,
repeated 1= (m-2k)!,
final answer is
(m-k-1)!/(k!(m-2k)!)
my logical answer is missing multiplication by m to be correct what logic did I miss

[solid kiln]

Alex

[past widget]

Does your method only count the cases specific for (1, 2) in a circular setting? Cause then counting the same for {(1, 2), (2, 3), ..., (m - 1, m), (m , 1)} gives you m times this count [cause for each setting one number does not have a domino covering it so each cases are disjoint]

[dense linden]

did not understand sir

[trim jolt]

@dense linden Has your question been resolved?

[dense linden]

<@&286206848099549185>

[dense linden]

<@&286206848099549185>

[trim jolt]

@dense linden Has your question been resolved?

Channel closed

Closed by @dense linden

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brave rock]

hello i’m confused on how to do this

[brave rock]

all i know is it’s probably either B or D?

because it should:
have one y value correspond to one x value
must fail horizontal line test somewhere

but how do i know if it’s B or d?

[limpid dawn]

When you look at D

Can you find in (-oo, 0) two x values with the same same output?

Ok maybe even easier, does the function in D pass the horizontal line test in (-oo, 0)?

[brave rock]

No

it doesn’t

[limpid dawn]

So that makes the function in D not one-to-one in (-oo, 0)

[brave rock]

ohhhhh

[limpid dawn]

leaving you with only one option

[brave rock]

and for B it does pass it

[limpid dawn]

yes

[brave rock]

so answer D

[limpid dawn]

no

[brave rock]

oh

wait

shouldn’t it fail the HLT?

[limpid dawn]

which one

[brave rock]

like

in regard to the

question

shouldn’t it fail the HLT?

[limpid dawn]

which one

[brave rock]

the answer

[limpid dawn]

what is the answer?

[brave rock]

B?

[limpid dawn]

See there is a difference

when you consider the function in B on a specific interval like (-oo, 0)

then it actually passes the horizontal line test

cover the right half with your hand and see

but on the whole interval (-oo, oo) it fails the test, yes and which it is supposed to

[brave rock]

ohhhhhhh

[limpid dawn]

so on (-oo, oo) it is not one-to-one which you want, but (-oo, 0) it is

that is the criteria you were looking for

[brave rock]

i see i see i see

thank u sm

i’ll pay attention to the intervals

in further questions

.close

[trim jolt]

Channel closed

Closed by @brave rock

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[civic crypt]

Hi, I don't know what question 22 means about "gained a mark. could someone help me out

[past cargo]

it translates to "how many students had scores b/w 43 and 64"

43 is one standard deviation below the mean

and 64 is two standard deviations above the mean

you'd use this

[civic crypt]

b/w?

[past cargo]

between

[civic crypt]

ohh

is gained meant to mean like

"received"?

[past cargo]

yeah

[civic crypt]

Ohh

ok thx

.close

[trim jolt]

Channel closed

Closed by @civic crypt

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rough heron]

I have no idea how to solve it. Can I get help?

[naive otter]

Yeah

Sub 1+ x³ = u

[rough heron]

@naive otter Don’t I start with geometric series expansion?

[naive otter]

Nah

[naive otter]

You first integrate

To get an easy function

it will be of the form kln(1+x^n)

And you already know the expansion of ln(1+x) so you can expand it !

[wanton rune]

you can use geometric series expansion alternatively as you said

start with 1/(1-r), let r=-x^3

[trim jolt]

@rough heron Has your question been resolved?

Channel closed

Closed by @rough heron

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[smoky marsh]

is ln(2)*(1/2)+3/2 the correct answer?

[trim musk]

please send your working

[empty orchid]

!show

[trim jolt]

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

[smoky marsh]

ok

so first i found the integral

[trim musk]

I’m getting something like -1/2 -1/2ln(1/2) not sure though I don’t have paper or a pen

[empty orchid]

no way!

[smoky marsh]

ikr

amazing

[trim musk]

Cosx = t and integral of Lnx right

[empty orchid]

$\int_{\frac12}^1 \ln(u)du$, right?

[solid kiln]

;(

[empty orchid]

or am i tripping

[smoky marsh]

u=ln(cosx)
du=(1/cosx)(-sinx)dx
v=-cosx
dv=sinxdx

ln(cosx)(-cosx)-∫-cosx*(1/cosx)(-sinx)dx
=ln(cosx)-cosx-∫sinxdx
=ln(cosx)-cosx-(-cosx)
=-ln(cosx)cosx+cosx

[empty orchid]

my brudda in christ

[smoky marsh]

now we just plug in pi/3 and 0

[empty orchid]

why did you not do u-sub first 😭

[smoky marsh]

well

is this correct

[empty orchid]

uh yeah...

[empty orchid]

but this is better imo...

[smoky marsh]

-ln(cosπ/3)(cosπ/3)+(cosπ/3)-ln(cos0)cos0+cos0
=-ln(1/2)(1/2)+(1/2)-ln11+1
=-ln(2^-1)(1/2)+3/2
=-(-ln(2))(1/2)+3/2
=ln(2)(1/2)+3/2

[smoky marsh]

so how u do this

[empty orchid]

le tme see

$u\ln(u)-u\big\vert_{\frac12}^1$

[solid kiln]

;(

[empty orchid]

yeah ur answer isn't correct

[smoky marsh]

why

[empty orchid]

let me see

[smoky marsh]

did u see it

[empty orchid]

no

[smoky marsh]

oh

[empty orchid]

😔

[smoky marsh]

so are u going to see it?

[empty orchid]

i can't find it

it must be somwhere in between plugging in and the derivation

oh i see now

[smoky marsh]

is the integration done correctly?

[empty orchid]

you didn't distribute the negative on that last cos(0) term

yeah that fixes it

[smoky marsh]

wait where

i dont get it

[smoky marsh]

can you please tell me where exactly and what i did wrong please

[empty orchid]

$-\ln(\cos(\frac{\pi}{3}))\cos(\frac{\pi}{3})+\cos(\frac{\pi}{3})-(-\ln(\cos(0))\cos(0)+\cos(0))$

[solid kiln]

;(

[smoky marsh]

oh ok

yeah

ok thanks

.close

[trim jolt]

Channel closed

Closed by @smoky marsh

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[half marsh]

Someone please help these series make my brain explode

[empty orchid]

$S_n-S_{n-1}=a_n$

[solid kiln]

;(

[half marsh]

oooh ye

[empty orchid]

$\sum_{n=1}^{\infty} a_n=\lim_{n\to\infty}S_n$

[solid kiln]

;(

[half marsh]

Sn= a1+a2+a3+...+an-1+an
Sn-1= a1+a2+a3+...+an-1 right?

thats how u get it

[empty orchid]

yep

[half marsh]

and sn is also sommation n=1 infinite an?

just for notation

i know the steps now tho

[empty orchid]

yes

[empty orchid]

👍

[half marsh]

great thank you

[empty orchid]

well, $S_n=\sum_{k=1}^n a_k$

[half marsh]

Can you also help with this one?

oh so a finite?

[solid kiln]

;(

[empty orchid]

you don't know whether the last term is 1 or -1

therefore you cannot do that grouping

QED

[silver glade]

there is no last term

[half marsh]

ye that is what i was thinking

so my brain

just stops working

[empty orchid]

[half marsh]

not the clash royale emote

💀

[silver glade]

we define it by the limit of partial sums
but if you change parentheses, you change the partial sums, so you also change the limit

[half marsh]

Ahaaaa

gotta love series

Can you also help with this one :-:

[silver glade]

try a_n = n and b_n = -n

[half marsh]

Sommation of 0 is 0 aaah

[silver glade]

1, 2, 3, 4, 5...
-1, -2, -3, -4, -5...

[half marsh]

i want to go back to just normal limits

[empty orchid]

you can't necessarily conclude, because of the nature of sequences

[half marsh]

and i hated normal limits already

[empty orchid]

nope

[half marsh]

alright that was it for now probably get back here in like 10 minutes

thank you guys

.close

[trim jolt]

Channel closed

Closed by @half marsh

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fair forge]

for m>=2 is this even defined?

[trim jolt]

Please don't occupy multiple help channels.

[marble wharf]

the binomial coefficient is just zero if the bottom number is bigger than the top number

[trim jolt]

@fair forge Has your question been resolved?

[fair forge]

and (0.5 choose n) ?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[round walrus]

Im not sure how to evaluate this

[robust wigeon]

Easiest method is probably using substitution

Do you know how to do that?

[round walrus]

no im not sure what you mean

[robust wigeon]

You need to make a substitution and change the variable you are integrating with respects to, so in this case you'd do u=2-5x => du/dx = -5

If you don't know about this method I'd recommend looking it up on youtube or the internet, just search "u-substitution"

[round walrus]

i dont think im allowed to do it that way

is there another way

[robust wigeon]

Strange, this problem looks like it was made to teach you that method. What class are you in?

[round walrus]

this is supposed to teach "indefinite linear composition"

i can do this same problem without the 8 exponent

thats the problem

i would just do the natural log of |2-5x| times -1/5

thats what i tried and it doesnt work

if you absolutely have to use the u substitution then idk maybe its not disallowed

[robust wigeon]

I never heard of this method before and just looked it up, it essentially achieves the same thing as u-substitution it's just less powerful

[robust wigeon]

I think you did it correctly give me one moment to check

[round walrus]

i just looked and the next topic is about u substitution so i guess they are just trying to teach us multiple ways even if one is really better

i know how to get the integral of (2-5x)^8 and i can get the whole fraction without the exponent but together im not sure how to make it work

[robust wigeon]

This indefinite linear composition method seems seems kinda stupid to me. I wouldn't put much time into it if you're learning u sub next topic.
After integrating I got -24/35 * (2-5x)^(-7) + C

You need to use the power rule when you have an exponent

This one but backwards

[round walrus]

yeah im just not sure when to do that

because its in the bottom

[robust wigeon]

Whenever you need to integrate something of the form x^n where n is a constant

It works the same way when it's at the bottom

It just becomes negative

If you know your exponent rules

[round walrus]

oh my god

lol it makes so much sense now

[robust wigeon]

yay

[round walrus]

idk how i didnt see that thank you

[robust wigeon]

you're welcome, good luck

[round walrus]

.close

[trim jolt]

Channel closed

Closed by @round walrus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[graceful trail]

how do i find the second part

[umbral onyx]

$c^2 = a^2 + b^2 - 2abcosC$

forgot what thats called

[graceful trail]

pythagoras??

[umbral onyx]

noo

[plush vigil]

cosine rule

[graceful trail]

ngl i dont understand this

[solid kiln]

Nyxzore

[graceful trail]

what values do put for each letter

[umbral onyx]

so c is the side opposite to the angle you want and a and b are adjacent

[plush vigil]

its basically the big brother of pythagoras

[umbral onyx]

yep but works for all trirangles

[graceful trail]

thbut this is like a pyramind on top of a cubiod

for my ai i got 20.67890835

was this correct?

[umbral onyx]

so 20.... is the length of ai?

[graceful trail]

the number above mb

[umbral onyx]

you use pythag for that?

[graceful trail]

ye

[umbral onyx]

19^2 + diagofbase/2^2 = Ai^2

,w sqrt(4^2 + 3.5^2)

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

19^2 + 5.31507^2 = Ai^2

,w sqrt(19^2 + 5.31507^2)

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

ummm mr Nagi

[graceful trail]

ye?

[umbral onyx]

thats what i just got for length of AI

[graceful trail]

20.67890835

[umbral onyx]

...

thats because im stupid

[graceful trail]

💀

[umbral onyx]

,w sqrt(4^2 + 7^2)/2

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

,w sqrt(19^2 + 4.03112887414^2)

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

okay mr nagi im pretty sure thats ai lenth

[graceful trail]

ight thx

[umbral onyx]

werent you asking about the angle...

[graceful trail]

19.4 (to 1 d.p)

ye

[umbral onyx]

im saying ans for question 1 is 19.4

concur?

[graceful trail]

cooncur?

[umbral onyx]

agree

do you agree>

[graceful trail]

i have to put the answer for the angle before it checks

but i agree

[umbral onyx]

$15^2 = 19.422922^2 + EI^2 = EI(19.422922)cosx$

[solid kiln]

Nyxzore

[umbral onyx]

,w sqrt((sqrt(4^2 + 7^2)/2)^2 + 4^2)

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

did you get that for EI?

[graceful trail]

ye

i did

[umbral onyx]

,w arccos((15^2 - (19.422922^2 + 5.678908^2))/((5.678908)(19.422922)))

,w arccos((15^2 - (19.422922^2 + 5.678908^2))/(-(5.678908)(19.422922))) in degrees

[solid kiln]

Results provided by WolframAlpha

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

Requested by nyxzore

[umbral onyx]

bro lemme just grab a calculator woldram is tiring

[graceful trail]

kk

[umbral onyx]

$15^2 = 19.4^2 + 5.7^2 - 2(19.4)(5.7)cosx$

[solid kiln]

Nyxzore

[umbral onyx]

I got 33.8 degrees

didnt you get something else?

[graceful trail]

should i put it into the thing?

i coulndt do the anlge

it was 33.2 for the angle

the line one was correct

but we gotta redo cus the pass mark is 95% and 4makrs would cost me too much

i hate the question reset tho

😭

ima send all 3 wich one do you think is easiest

[umbral onyx]

is this a test then?

[graceful trail]

nah homework

put our tracher is realy strict cus we top set matsh

ima just put if on the chat thingy again

respond if you have enought time

.close

[trim jolt]

Channel closed

Closed by @graceful trail

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[keen panther]

how do i solve this iwthout useing euler's form

[trim jolt]

@keen panther Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mint lily]

Differential equations: Possibly stupid question, I'm able to solve the integral as arctanx but unsure what to do with the 0 and y limits

[mint lily]

like will it literally just be arctan(y) - arctan (0)

oh ok i was way overthinking thank you so much

.close

[trim jolt]

Channel closed

Closed by @mint lily

Use .reopen if this was a mistake.

[kindred pier]

If $x=\tan t$, and say $x_{\text{lower}}$ is the lower bound, then the relation is just $x_{\text{lower}}=\tan (t_{\text{lower}})$. Same idea with upper bound.

[solid kiln]

SWR

[mint lily]

Oh wait lemme look to make sure I get it

OHH yep that's what I was forgetting yep thanks so much

.reopen

[trim jolt]

✅

[mint lily]

@kindred pier sorry for the tag, just want to clarify -- so then lower limit is still 0 but upper limit is tan(y). Evaluating integral gives arctan(tan(y)), is this a normal form of answer?

Like normally something like that would set off alarm bells but is that to be expected for diff eq

[kindred pier]

$x_{\text{upper}}$ is the upper bound of your integral with respect to $x$. If you change your integrating variable to $t$, then your new upper bound must be $t_{\text{upper}}$. You can use $x_{\text{upper}}=\tan(t_{\text{upper}})$ to find
$$t_{\text{upper}}=\arctan(x_{\text{upper}})=\arctan y$$
So, $\arctan y$ would be the upper bound of your integral when it is with respect to $t$.

[solid kiln]

SWR

[mint lily]

Ahh yeah I was just doing tan(xupper) instead of tan(xlower)

So then that leaves me with arctan(arctan(y))

as the evaluated integral

[kindred pier]

hope that helps

[trim jolt]

@mint lily Has your question been resolved?

Channel closed

Closed by @mint lily

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[high hawk]

Let’s say, I get €15,97 of interest rates on my savings account on that month. The interest rate is 7,90% in a year scale, and the money is given out every month.

The tax is 22% so minus €3,52.

And I get €12,45 in total.

Now. How much do I get realistically if we count the inflation? The inflation now is 4,8%.

[trim jolt]

Please don't occupy multiple help channels.

[kindred pier]

@high hawk, please stop spamming channels. I get that you've been trying to get help for a while now, but if no one is helping, it's probably because not many helpers here deal with finance questions

[zinc ginkgo]

.close

[trim jolt]

Channel closed

Closed by @zinc ginkgo

Use .reopen if this was a mistake.

[past widget]

btw it's really interesting you got to 12.45 monthly earning after adjusting the taxes and the interest. did you perhaps try adjusting for inflation and still not match the answer?

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stuck narwhal]

z1 = 1 - i, z2 = 4i
calculate |z1 + z1 * z2|
I don't understand what happened in the first step, that is, from |z1 + z1 * z2| --> |z1 * (1 + z2)|

[covert loom]

you put z1 in front

z1 + z1 * z2 = z1 ( 1+z2)

[empty orchid]

its just factored, lol

[stuck narwhal]

OH

OMG

TY

[empty orchid]

$a+ab=a(1+b)$

[solid kiln]

;(

[stuck narwhal]

thank you i aa

.close

[trim jolt]

Channel closed

Closed by @stuck narwhal

Use .reopen if this was a mistake.

[empty orchid]

👍

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[orchid drift]

x^2 - 8x + (8/2^2) + 5 = (8/2^2)
(x + (8/2))^2 + 5 = (8/2^2)
(x + (8/2))^2 = (8/2)^2 - 5
x + 8/2  = 8/2 - sqrt5
x  = 8/2 + 8/2 - sqrt5
x = 8 - 2.23
x = 5.78 OR 5.8 rounded```

• Where is the error?

[trim jolt]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[clear cloud]

Ah

[orchid drift]

NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

https://tenor.com/view/we-do-a-little-trolling-trolling-shockwave-nuke-nuclear-explosion-gif-21948424

[orchid drift]

do you know?

[clear cloud]

Let me read

[orchid drift]

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

[clear cloud]

So -2ab = -8 implies that a = 1 and b = 4 right ?

[knotty oriole]

Seems fine?

[clear cloud]

Why not adding +16 so that its b²

[orchid drift]

?

wdym

[clear cloud]

You wrote 8/2²

[knotty oriole]

Oh wait maybe I did not read closely

[red mountain]

you need to pull that ^2 out of the brackets

(8/2)^2

[orchid drift]

(8/2)^2

[clear cloud]

In that case yes

[orchid drift]

so i did not make an error?

[clear cloud]

Which is 4 also

[clear cloud]

Parentheses written wrong

[orchid drift]

but the answer, was that correct?

how is 5.8 wrong

[orchid drift]

but i think i still considered that as having it

which line?

[clear cloud]

Just telling

[knotty oriole]

Seems like a sign error has to be in there somewhere

Expand (x+8/2)^2

You won't end up with a minus sign

[clear cloud]

Before before last line its - not +

[red mountain]

you need to be more precise in your writing
(x+(8/2))^2=(8/2)^2-5
x+8/2=sqrt((8/2)^2-5)

[orchid drift]

bc this answer means its rather lower than 4 or greater than 7

[red mountain]

also, this channel is going to close soon

be careful

[orchid drift]

https://tenor.com/view/we-do-a-little-trolling-trolling-shockwave-nuke-nuclear-explosion-gif-21948424