help-0

[wintry ice]

rip i have no idea what this i s

[wet fulcrum]

ok so for each integral given we have to take its limits and find the area of the graph in that range

for example for first one find the value of area of the shape between x=0 and x=3

@wary stream is the first one 5.5

im just gonna tell the first answer to confirm method not others

[wary stream]

Not what I got

[wet fulcrum]

hmmm

[wet fulcrum]

6.5?

[wary stream]

Yes

What I got

[wet fulcrum]

oh i made a silly mistake

[sturdy glen]

when solving a system of linear equations using gaussian elimination, what happens if two of the rows end up the same. does that mean it's inconsistent?

[wary stream]

Depends on the amount of rows you have

[sturdy glen]

i have 3 rows

[wary stream]

It's consistent

Inconsistent is no solution

[sturdy glen]

alright, thank you

preciate the help

[vast geyser]

Can you have a homomorphism over a different field? For example, from C[2]z -> R[2] , or does C[2]z have to be over R then, so (1,i,z,iz,z^2,iz^2)?

[haughty bronze]

help?

[alpine sable]

<@&286206848099549185>

[haughty bronze]

<@&286206848099549185>

[limpid spade]

what

why did u ping Andreas

[haughty bronze]

maybe if you read above u would know why

[limpid spade]

andreas only message is helpers tag

he just tagged helpers for no reason lol

[haughty bronze]

he tagged you guys for me

[limpid spade]

then why did u tag helpers again

if he did for y

you

[hard salmon]

@haughty bronze B

[haughty bronze]

are you sure?

[hard salmon]

@haughty bronze u wanna c poof

[haughty bronze]

huh?

u mean u wanna see proof?

sure

[vast geyser]

<@&286206848099549185>

[vast geyser]

.

[sly mantle]

no we only talk of homomorphisms of vector spaces over the same field

[timid flint]

Hi, HOW do i change 2,67 to HOUR and min?

[pine pawn]

2,67, its 2 hours + 67% of 60 min's

[alpine sable]

some one help me out

[restive bobcat]

An investor pays $170,000 for a mine that will produce level annual revenue for 25 years. What should the level annual revenue be (received at the end of each year) if the investor is to receive 4% annual return on the investment while recovering the principal in a sinking fund earning 2.5% per year?

anyone can help out

math finance

[alpine sable]

oh fuck no

[restive bobcat]

rip

[alpine sable]

Any1?

[tropic blaze]

Guys, if you DM me, i have a C#3GG bot

[mystic sinew]

quick question ~(P v Q) = ~(P ^ Q)

right?

[tropic blaze]

can i post my invite link here, without getting banned or smth

[mystic sinew]

#rules

bro this is for questions

[native dawn]

I don't think so, If I get you, the rule should be ~(P or Q) = (~P and ~Q)

[mystic sinew]

:tinfoil:

(~P ^ ~Q) = ~(P ^ Q)

right

[native dawn]

@mystic sinew this should help you

[mystic sinew]

I understand the laws I just want to know that if not p and not q = not ( p and q)

that can't be true right since if it was then p and q = p or q which is false

[wary stream]

$$\neg(P \land Q) = (\neg P \lor \neg Q)$$

[ocean seal]

dldh06

[mystic sinew]

bro just me this

that's the real question

[wary stream]

No, it should be not (p or q)

[mystic sinew]

I am not asking you about demorgans laws just tell me if it's true or false bro

it's false right

[wary stream]

If you know De Morgan's Laws, you should know the answer

[winter flare]

<@&286206848099549185>

[wary stream]

I'm pretty sure that the equation $$r = acos(\theta) + bsin(\theta)$$ then $$r = \sqrt{a^2 + b ^2}$$ but I could be wrong

[ocean seal]

dldh06

[winter flare]

that

[wary stream]

?

[winter flare]

it's 16+4 in the final

so 2 square 5

what do you think?

[atomic glade]

isn't it 4*sqrt(5) ?

sqrt(8^2 + 4^2) = sqrt(64 + 16) = sqrt(80) = sqrt(5*4*4)

[winter flare]

why?

can you explain me?

PLEASEEEE @atomic glade

@wary stream

<@&286206848099549185>

[harsh bone]

Anyone here speaks French

[scarlet spire]

oui bien sure

sur

[harsh bone]

Oh ok

Tu peux me aider ?

Si possible

[winter flare]

noooooooooo

help me

the channel is in use

[harsh bone]

Ah

[winter flare]

use another one

[harsh bone]

Ok cya

[scarlet spire]

dms @harsh bone

[harsh bone]

Oki

[sturdy glen]

how would i use one augmented matrix to solve two systems of linear equations

like these

[atomic glade]

you want a solution to both at the same time, or what?

[sturdy glen]

i've been asked to find an augmented matrix that can solve both

[atomic glade]

what is augmented

[sturdy glen]

wdu mean

[atomic glade]

okay google told me

just solve it one at a time

do you know how to use a matrix to solve a system?

[sturdy glen]

yes i do

i dont know how to make one for two different systems

[gray isle]

add an extra augmented column

[sturdy glen]

ohhh you can add two augmented columns?

did not know that

ty

[small helm]

I'm not sure of the actual numbers of the question, but lets say player A has a 30% chance to win a game, player B has a 40% chance to win the game and they have a 30% chance to draw. After ten rounds, what is the probability that player B wins?

[atomic glade]

wins = wins more than the other player?

[small helm]

My brother got this for his grade 6 math homework and I feel like this question is really hard, so either I'm really dumb or his teacher is dumb for giving this question

yeah

[atomic glade]

if the odds for A and B are the same then this question is a lot easier

[small helm]

yes, but a part of the question is the chance that player B wins each round is slightly higher

[atomic glade]

huh idk with 6th grade math

[polar kindle]

Hey, how can I write this =N on LaTeX?

[misty roost]

?

like $tg \alpha = N$

I'm confused

[ocean seal]

Lagrange the Multifarious

[polar kindle]

No is more like =^n

In portuguese this mean "numerically equal"

[gray isle]

$\overset{N}=$

[ocean seal]

ℝamonov

[polar kindle]

Oh, thanks

[atomic glade]

my results show 58%

now how do we prove it

[small helm]

wait how did you solve it?

oh did you just

[atomic glade]

i ran simulations

[small helm]

do the game 10 times

ok

[atomic glade]

i did it 100,000 times but yeah

[misty roost]

P(B wins 6 times) + P(B wins 7 times) + ... works

[atomic glade]

it's about 57.75% for B winning, 28.5% for A winning, and 13.75% for a draw

[small helm]

wait but

B doesn't ened to win a majority of times to actually win

[atomic glade]

what about P(B wins 1 time, A wins 0 times, draw 9 times)

[small helm]

like if there's 1 B win and 9 Draws

oh

lol

[misty roost]

wait actually right I didn't see it can draw

you can probably just write some really ugly expression and sum everything up for an exact answer

[small helm]

I can't even think of an equation

[atomic glade]

let's start with the equal odds

then calculate odds of a draw

[small helm]

cause they way they were taught in class was to draw it out and show all the possibilities, but you can't even begin to do that here

[atomic glade]

its not super hard with combinatorics

but they dont have that

[misty roost]

how would you do it with combinatorics

[haughty bronze]

jsut wondering with the equation y=mx+b what would cause it to be y=mx-b

[small helm]

if b was a negative number

[atomic glade]

go over all possibilities and multiply by the ways to order them

[fading rover]

If b ends up being negative the equation would look like y = mx + (-b). Adding a negative number is the same as subtracting.

[misty roost]

I mean it still seems somewhat tedious

[atomic glade]

we know win + lose + draw = 10 and win > lose so we can go over win = 1..10 and lose = 0..min(win-1, 10-win)

we can split to avoid the min: for win = 1..5 we get lose = 0..win-1, and for win = 6..10 we get lose = 0..(10-win)

we want to sum p(win)^win * p(lose)^lose * p(draw)^(10 - win - lose) * 10! / (lose! win! (10 - win - lose)! )

[misty roost]

right, but that still seems like a lot of things to add up

[atomic glade]

= ((p(win)/p(draw))^win / win!) * ((p(lose)/p(draw))^lose / lose!) * (p(draw)^10 * 10!/(10-(win+lose))!)

[misty roost]

I mean yeah those look right

[atomic glade]

idk i cant get anything better

[misty roost]

for each win = 1...10 you still need to add up a bunch of things

and then add up all those answers

it's still simpler than brute forcing the whole thing, but it doesn't seem by any means elegant

[atomic glade]

the math answer is 57.8267...%

similar to what my simulation showed

for 3 games this is $w^3 - 3w^2 +3w +6w^2 l + 3l^2 w - 6lw$

[ocean seal]

NotWearingPants

[atomic glade]

where w is the probability of winning and l is for losing

[final crag]

How did they get 14.243?

[carmine ermine]

If you're calculating a definite integral

isn't the "A" already included in the definite integral calculation?

why am I adding a constant after the DI calculation

[clever tapir]

help me out

[late tundra]

just equate them

[carmine ermine]

Just graph them :/

well

u can just put

the quadratic equation (remove the y)

[glass lichen]

graphing isnt algebra

[carmine ermine]

on one side

and put the 8 on the other

so it becomes

Oh wait

Nvm

3(x-2)^2 - 3 = -2(x+2)^2 + 8

[alpine sable]

(x-2)^2 = 11/5?

[carmine ermine]

Solve for that

Huh?

[glass lichen]

dont solve the question for them

[clever tapir]

O like substitute it

bet that up

[glass lichen]

yes, set them equal

[carmine ermine]

^^^^

[carmine ermine]

^^^^^

:/

[clever tapir]

So essantially if I get imaginary numbers they wont meet

[alpine sable]

You should equate the two graphs, and then use how many answers(?) are in that graph to determine how many points it intersects in

Sorry i'm confused with english ill go somewhere else

[carmine ermine]

it says do it algebraically

[glass lichen]

yes, if you get complex roots then there are no real values in which they are equal

[glass lichen]

I mean your first answer was graph them

[carmine ermine]

Jeez didn't I change it?

[glass lichen]

well you did in a long spam of messages

then just repeated what mathlover had said

[carmine ermine]

Did I tell them how to do it algebraically? yes I did

I get what ur saying but it's abt if I answered his question correctly

[carmine ermine]

Yeah they won't

[clever tapir]

NOO THEY WONT MY DISCRIMINANT IS IMAGINARY

[glass lichen]

discriminant is strictly real

since the functions have real co-efficients

[clever tapir]

oh no like its imaginary cause

you need to square root the negative

cause I got -164 as the discrimnant

[glass lichen]

then yes you'd have complex intersection points which dont exist in R2

[final crag]

Could someone please help me with this prooblem?

[minor dagger]

<@&286206848099549185> can someone please help me

[alpine sable]

Whats 4x2?

[late tundra]

it's (0,4)

[late tundra]

DIY

[alpine sable]

?

Huh?

[late tundra]

u don't know what 4×2 is?

[alpine sable]

No

Thats why im asking

[late tundra]

how old r u

[alpine sable]

7 im on my brothers acc😁

[late tundra]

4×2 means you get 4 candies twice so how many candies do u have ?

[alpine sable]

8

[muted raft]

discord is supposed to be 13+

[late tundra]

yes

[alpine sable]

I didnt know

Sorry

[small sundial]

I need help here

How do I solve this I’m so confused

[left robin]

solve for g(-2) first

then plug it into f

[minor dagger]

i. also need help with. the max and minumum

ive been stuck on this assignment for hours-

[left robin]

@minor dagger u entered it in wrong

[small sundial]

I don’t exactly understand how to do that @left robin

[left robin]

@small sundial ok look at the table it says g(-2) right, so when x = -2 what is G(x) on that table

[small sundial]

Ah

Then what do I do after that

[left robin]

so you got that g(-2) = -1 right?

[small sundial]

Yeh

[left robin]

so whats f(-1)

[small sundial]

5?

-5?

[left robin]

so when x = -1 what is f(x) on that table

[small sundial]

2.5

[left robin]

there is no 2.5

[small sundial]

Oh wait

[left robin]

its 2

[small sundial]

I dint see the right part

So is that it?

That’s all it was asking?

[minor dagger]

can you help m e

[left robin]

local max should be 0,4

[flat turtle]

pls

help

i know that the left triangle is an equilateral triangle now i dont know what to do

[scarlet spire]

what are you trying to find

@flat turtle

[flat turtle]

oh wait

im trying to find g

i know that vertically opposite thing

i just need to find the middle triangle then im good

[alpine sable]

so...

you should use the attributes that a Isosceles triangle has

[flat turtle]

wdym

[minor dagger]

i need help. on decreasing

[alpine sable]

that's a hint

[flat turtle]

oh

so 180 - 120 = 180 - 2a?

[alpine sable]

yes

you solved it

[flat turtle]

how did you get 30

oh

[alpine sable]

wait

nooo 😦

180 - 120 = 180-( 180 - 2a)

it's supposed to be like this

[hidden horizon]

Bruh stop confusing

What u can't understand @flat turtle

[flat turtle]

i didnt know what to do when i got the first triangle

this one

[minor dagger]

<@&286206848099549185> can someone please help. me with the increase and decrease

[alpine sable]

so, the 3 angles added would be 180 degrees

[hidden horizon]

Channel occupied go other channel pls

[alpine sable]

the remaining angle must be 180-60-60=60

[celest void]

y is increasing means derivative is positive

[flat turtle]

yeah

[hidden horizon]

Do u know exterior angle property ?

Exterior angles of a triangle is equal to the sum of opp interior angles

[flat turtle]

oh

so how did you get 30 degrees

oh yeah right

the 30 is equal to the top side

120 + 30 + 30 = 180

[hidden horizon]

Isoscles triangle

[alpine sable]

mhm

[flat turtle]

oh ok

i get it now

thanks

[hidden horizon]

Cool

[sly stream]

confused on how to sketch this function since it's not expanded

[alpine sable]

i would group it by u and just do everything else literally

[mossy stream]

Is there anyone who could help me with some differential calc problems. Some of the stuff i need some help with are eigen values, equilibrium and recurrence relations.

[undone geyser]

hey everyone

i have a calc question

just a basic integration rules question

if :

find:

if anyone replies kindly ping me

[late tundra]

-12

[undone geyser]

hmmmm may i know how ?

i used the integration by parts rule

didn't yield anthing tho

i feel i messed up smthng

[floral crest]

Can someone help me with this one? It is just for fun, but I have tried to use algebra to solve this but it is getting me nowhere. With that said, I can't seem to find other ways other than guess and check, which probably is not the right way 😀 .

[stuck plaza]

i think everyone is asleep

[royal shard]

Are you sure the derivative exists?

the derivative of f I mean

[undone geyser]

ummmmmm how do i check .....

[oak chasm]

@floral crest Sorry, channel is busy.

[royal shard]

I think there is a more straighforward way to solve for f(1)

[undone geyser]

which is ?

[royal shard]

What's the meaning of the symbol $\int$ ?

[ocean seal]

b2unit

[undone geyser]

integrals

calc

i am fam with integrals

[royal shard]

yes, but, for example, what does this $\int x^2 dx$ means to you?

[ocean seal]

b2unit

[undone geyser]

the antiderivative of the function f(x)

[celest void]

area of the function x^2

[undone geyser]

that's definite integrals

[royal shard]

great, but what's an antiderivative?

[undone geyser]

the "original function" of the derivative

[celest void]

What do you mean that's definite integrals? Is it not true for indefinite integrals then?

[mossy stream]

take the derivative of the whole thing factor out an x and you are left with f(x)=?

[undone geyser]

the one that if which u differentiate will yield whatever expression we have in the question

[celest void]

I mean one has bounds and the other one doesn't?

[undone geyser]

oh

[royal shard]

perfect, now apply that thought to \int xf(x) dx

[undone geyser]

so i just take the derivative of both sides ?

[mossy stream]

taking the derivative of an integral does what?

[undone geyser]

xf(x) = 4x^3 -16x

[undone geyser]

just leaves the funv

c*

[mossy stream]

now its just algebra

[undone geyser]

yeah

tysm @royal shard and @mossy stream

appreciate the help 💟

[crystal quest]

can someone help me how to do this?

[mossy stream]

can eigen values and eigen vectors be used to solve an individual ODE?

[royal shard]

what do you mean by individual ode?

[mossy stream]

like a single equation

[royal shard]

oo

[mossy stream]

I know they can be used to solve systems of ODEs but i dont recall anything about just one

[royal shard]

Try to express that LHS operation as a application of the differential operator in this form $(D - \lambda I)$, where $\lambda \in R$ amd I is the identity operator,

[ocean seal]

b2unit

[royal shard]

$\lambda \in C$, sorry

[ocean seal]

b2unit

[royal shard]

that way, you will be able to find the eigenvalues easily, (you can also use the characteristic polynomial, but I'm not too good at that)

the point of finding the eigenvalues is that, with the eigenvalues, you can find solutions to the ODE

[mossy stream]

The characteristic polynomial is the $D^3-2D^2-D+2=0$ right?

[ocean seal]

Raymon

[royal shard]

yeah

(although using D as the variable for the polynomial is not the best thing lol)

[mossy stream]

yeah im really good at those and its way simpler than eigen values because its is factor able and homogeneous

[royal shard]

after that you can try finding the eigenvectors, as those will be solutions since they will give 0 when put on the respective form of $D - \lambda I$

[ocean seal]

b2unit

[royal shard]

but, at least in my ode class, the eigenvectors were known depending on the eigenvalue, I don't know if that's the same for yours

[mossy stream]

can you explain $D - \lambda I$ more, im not really familiar with it

[ocean seal]

Raymon

[royal shard]

Sure, Recall that an eigenvector $v \in V$ of a linear transformation T: V -> V, and its corresponding eigenvalue $\lambda$, fulfills $Tv = \lambda v$

[ocean seal]

b2unit

[royal shard]

you can write this last equality as $Tv - \lambda v = 0$, $(T - \lambda I)v = 0$, where I is the identity operator

[ocean seal]

b2unit

[royal shard]

now, if you are able to express your ODE as containing a form like $D - \lambda I$, then a solution to your (homogenoous) ODE will be a eigenvector which correspond to the eigen value $\lambda$, since this pair fulfills the equality said in the last message

[ocean seal]

b2unit

[mossy stream]

Im a lot better at understanding through examples rather than general theory. Could you walk me through an example. It doesnt need to be the problem i posted it can be another example.

[royal shard]

Consider the ODE $y'' - 2y' + y = 0$, this ODE can be written as $(D^2 - 2D + I)y = 0$

[ocean seal]

b2unit

[mossy stream]

now here why would I not equal 1?

[royal shard]

which can also be written as $(D-I)(D-I)y = 0$ (you can find this factorisation using characteristic if thats easier for you)

[ocean seal]

b2unit

[royal shard]

Those are operators, not numbers, but if you understand the difference there's not really any problem with writing 1

[royal shard]

Now, if we are able to find eigenvectors for the eigenvalue 1, we would have a solution for this ODE

[mossy stream]

2 questions. How would we know to try 1? and how would we go about using the I operator is the differntail equation factored to something like $(D-3)(D+2)$

[ocean seal]

Raymon

[royal shard]

nice, recall that we want $(D- \lambda I)y = 0$ (we want this to be zero, so that all the others term cancel and we are left with 0 = 0 in the ode), this is the same as asking for $D(y) - \lambda I(y) =0$, $D(y)=\lambda I(y)$, $D(y) = \lambda y$, which is the same as asking for an eigenvector of the eigenvalue $\lambda$

[ocean seal]

b2unit

[royal shard]

the last one should be like $(D-3I)(D+2I)$

[ocean seal]

b2unit

[wet fulcrum]

can someone do sin ( 120c) = 45/41

[mossy stream]

So $x'''-2x''-x'+2x=0$ turns into $(D^2-3I)(D-4I)x=0$?

[ocean seal]

Raymon

[royal shard]

,w factor x^3 - 2x^2 - x + 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by b2unit#9282

[royal shard]

It should be of the form $(D-2I)(D-1I)(D+1I)y = 0$

[royal shard]

Try expanding what you have on the left, you won't end with the original ODE

[ocean seal]

b2unit

[mossy stream]

$D^2-1=(D-1)(D+1)$

[ocean seal]

Raymon

[quiet cloud]

Does anyone know what the height, width and length of a 30,000 litre cube would be?

[mossy stream]

oops looked at the wrong work on my paper. Meant $(D^2-1)(D-2)$

[ocean seal]

Raymon

[mossy stream]

cube means height, width and length are the same, therefore $V(x)=x^3$ so the dimensions would be $30,000^\dfrac{1}{3}$

[royal shard]

that's also correct,

the main point of doing all this is to easily see what are the eigenvalues of the whole operator

[ocean seal]

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

[royal shard]

for example, in this case the eigenvalues are 2, 1 and -1

you can take this approach, or you can solve the characteristic polynomial to find the eigenvalues, those approaches are the same,

now, we have half of the question done, we need to find the eigenvectors as those will be solutions of the ODE

[mossy stream]

so solving the characteristic equation is essentially using eigenvalues and eigenvectors?

[royal shard]

Solving the characteristic polynomial of an operator is the same as finding the eigenvalues, since the zeros of the characteristic polynomials are the eigenvalues of the operator

[mossy stream]

so now that we know $\lambda_1= 1, \lambda_2=-1, \lambda_3 = 2$, how would i find the eigenvectors?

[ocean seal]

Raymon

[mossy stream]

would they just be the oppisites of the eigenvalues

[royal shard]

great question, I don't know how they taught you this on your side, but at least on my part, we proved a theorem that gives the eigenvectors for a certain eigenvalue

for example, see how the derivative of $e^x$ is $e^x$, then that means that $e^x$ is an eigenvector of 1

[ocean seal]

b2unit

[royal shard]

,another example, see how the derivative of $e^{-5x}$ is $-5e^{-5x}$?, that means that $e^{-5x}$ is an eigenvector of -5

[mossy stream]

eigenvalue or eigenvector?

[ocean seal]

b2unit

[royal shard]

my bad sorry

[mossy stream]

ah okay

[royal shard]

see the pattern?

[mossy stream]

so to find the eigenvector I take the derivative of $e^{-\lambda x}$ and the eigenvector is the coefficient of the derivative?

[royal shard]

mmm the eigenvalue is already found, what you want to find now is an eigenvector

[ocean seal]

Raymon

[mossy stream]

my bad typo

[royal shard]

yeah kinda like that, if you already know the result beforehand, it's not necessary to take the derivative,

what im trying to say is that if you have an eigenvalue of $\lambda \in R$, then the corresponding eigenvector is $e^{\lambda x}$

[ocean seal]

b2unit

[mossy stream]

ohhhh the eigenvector is our solution

[royal shard]

(although this is sufficient to solve your ODE, this is not the whole theory, there are some cases, like what happens if $\lambda$ is complex?, or what happens if the ODE has the same eigenvalue repeated twice?)

[ocean seal]

b2unit

[royal shard]

Yes

[royal shard]

I would recommend you the check those out if you are interested, right now I don't think I have the time to explain it all :8

now lets find the solution for your ODE ok?

[royal shard]

Which numbers where the eigenvalues again?

(i always confuse the words lol sorry)

[mossy stream]

yeah you would use the multiple roots, $t^ne^{-\lambda t}$ with n increasing for each root. And you can use Euler's identity to convert complex eigenvectors into sin and cos

[ocean seal]

Raymon

[mossy stream]

The eigenvalues were 1,-1,-2

[royal shard]

So the corresponding eigenvectors would be?

[mossy stream]

So the eigenvectors would be $e^{1t},e^{-1t},e^{2t}$

[ocean seal]

Raymon

[royal shard]

good, so each of those is a solution to your ODE, and they are linearly independent (you can check this if you want), so a general solution would be?

[mossy stream]

and then i sum then and multiply each by a different arbitrary constant $c_n$

[ocean seal]

Raymon

[royal shard]

exactly

that's it

[mossy stream]

okay thank you

[arctic zephyr]

i have already solved 8, 9, and 10
i'm having trouble with the last two

there are choices for this exercise, and the choices i have left are:
39 674 880, and 241 920

i've tried to solve number 11 and i only came up with
9! multiplied by 3! which is 2 177 280 but that isn't in the choices :(
so i'm stumped on how to get the correct answer

[alpine sable]

Do you mean 10!3!

@arctic zephyr

[arctic zephyr]

is it 10!3! ?

[alpine sable]

Edz rac and car is 1 group, the rest 9 people are 9 group

[arctic zephyr]

yeah
so 10 units, circular permutation is (10-1)! right

[alpine sable]

Oh it's a circle

Haven't thought

Give a sec

It would be the same imo?

[arctic zephyr]

o what do you mean?

[alpine sable]

I think it's 10!3!

I don't see how circle permutation makes it different here?

[arctic zephyr]

my book says the formula is (n-1)! though, and there's 10 units

[alpine sable]

Oh

Well would you just check 10!3! On the answer?

[arctic zephyr]

okay

21 772 800, which isn't in the choices either

im starting to think the choices are wrong

[alpine sable]

Hmm

[arctic zephyr]

wait, 8!3! is 241 920
which is in the choices

but i don't see how we're gonna get 8!3! if there's ten units 🤔

[alpine sable]

Yes

Quite weird

[arctic zephyr]

i'll just put a correction for the choices then

i'll talk to my teacher also

[alpine sable]

Sure

[arctic zephyr]

thanks for the help! :P

[placid stone]

can someone help me with logarithm

[alpine sable]

Put laptop as 1500 x (0.92)^n

Put necklace as 800 x (1.06)^n

[placid stone]

@alpine sable can u explain the steps

[alpine sable]

Problems in my country have a specific (log x = ....)

Since we don't use calculator

[placid stone]

ok

uh

[placid stone]

i'm not sure how you got that

[alpine sable]

But it ususlly goes like this

[placid stone]

could u flip the photo

[alpine sable]

Oh do you not undersrand this

[placid stone]

yea I'm not sure

how you get that

[alpine sable]

Well since the base price is 1500

And in depreciates 8p per month

It also can be said

That it retains (100-8)/100 of its value

Which is 0.92

If 1 month passes, it retains 0.92 of its value

[placid stone]

so

for this

Put laptop as 1500 x (0.92)^n

means

[alpine sable]

If 2 month passes it retains 0.92^2 of value

[placid stone]

let the cost of the laptop be represented

by

1500 x (0.92)^n

[alpine sable]

Month as n

Mhm

[placid stone]

okk

[alpine sable]

Same for necklace except it adds

Then everything else would be smooth

Take log position on both sides of the < >

And use the fact that log a^n = n * log a

[placid stone]

ok

so the equation is
log15+ nlog0.92 < log8+nlog1.06
?

[alpine sable]

Yes

[placid stone]

ok

[alpine sable]

Wait

Nlog0.92

Not log0.92

[placid stone]

ok

this is

a multply symbol right

@alpine sable

[alpine sable]

Yes

As you know log xy = log x + log y

That's honestly the hardest part of log tbh

[lethal vortex]

Given −7 is one of the roots of the quadratic equation

(x + k)^2 = 16, where k is a constant, find the values of k.

any clue on how to find k

[upper kayak]

take the square root of both sides

$\sqrt{(x+k)^2} = \pm\sqrt{16}$

[ocean seal]

gang

[upper kayak]

$x + k = \pm4$

move 4 to the left

and you know x = -7 makes the equation 0

so

$-7 + k \mp 4 = 0$

[ocean seal]

gang

gang

[upper kayak]

now solve

or, you could do it this way

if that makes it easier to think about

$(x+k)^2 = 16$

[ocean seal]

gang

[upper kayak]

$$(x+k)^2 - 16 = 0$$
Sub x = -7
$$(k - 7)^2 - 16=0$$
$$k^2-14k+49-16=0$$
$$k^2-14k + 33=0$$

[ocean seal]

gang

[upper kayak]

now solve this quadratic

you can factor it

[lethal vortex]

with 3 and 11

so

(k - 3)(k - 11)

[upper kayak]

yeah those are the values of k

[lethal vortex]

thank you so much @upper kayak

ima re read it hehehe

[upper kayak]

👍

[alpine sable]

how do i take the partial of this implicit equation $$2x^2 + 5y^2 + z^2 - 23 = 0$$

[ocean seal]

ajuze

[alpine sable]

<@&286206848099549185>

[dry plover]

whats wrong?

nvm

[dawn thicket]

Hi guys , how can i solve these ?
A- d) and the rest . I need just a example or 2

Not english right there

[daring mountain]

<@&286206848099549185>

[upper kayak]

that looks like an exam

[dry plover]

help

nvm

[alpine sable]

lmao

imagine giving exam on google forms

[upper kayak]

plenty of people do

my siblings have exams on google forms

[upbeat maple]

could someone do this and tell me what answer they get for the volume

i wanna cross check with mine

i got (243/5)pi

[mossy stream]

can anyone help with this?

[versed talon]

Any hint to solve this?

[alpine sable]

Do you know how to calculate the mean ?

[raven valve]

what does average mean @versed talon

[versed talon]

Sum of all the values/ no of values

[raven valve]

so, apply that to the question

[alpine sable]

yes, exactly. So try applying the formula with the data you have.

[versed talon]

Okay. 4 red balls each 2 dollars. so, 8, 27, 24 respectively for red,blue and yellow.
Then 59/19 - 3.1?

[raven valve]

yes....that's it.

[undone geyser]

Doing calc rn and i think ik the answer

I think

Cuz we didn't specifically study this topix

[versed talon]

So the answer is 3?
My bad, I was thinking a lot that the answer should come as a whole number since there is no decimal option given there when I found that 59 is not divisible by 19

[undone geyser]

I think u should use this formula:
$\integ pi f(x)^2

$\help

$help

.help

[muted raft]

$\int_{a}^{b} f(x)^2$

[undone geyser]

Not really fam with how thos works

[ocean seal]

zslya

[undone geyser]

Yeah that

But add a pi

[muted raft]

copy paste it and modify a and b

pi is $\pi$

[ocean seal]

zslya

[undone geyser]

$\int_{a}^{b} $\pi$ f(x)^2$

[ocean seal]

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

[undone geyser]

Yupppp

[muted raft]

close enough

[undone geyser]

But i don't think u can use this formula in this situation

Cause the area is not between the curve and the x axis

It's between 2 curves

I might be wrong

[alpine sable]

i can't do this i have some doubt as i wans't in class answer pls?

[alpine sable]

start by calculating how much meters the elevator has to descent

huh?

wanting to help withuot being fluent in english is frustrating 🥲

hey

helper

can i ask a question

[muted raft]

,w graph y=sqrt(x), y=3 from x=0 to x=9

[ocean seal]

Results provided by WolframAlpha

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

Requested by zslya#7821

[muted raft]

hm

[muted raft]

what are you integrating with respect to?

[alpine sable]

hey

i need some help

[alpine sable]

can give just ans

is the channel free

[alpine sable]

nah

[alpine sable]

help pls

[undone geyser]

In this situation the areabetwee the two curves would be $\int{0}^{9}

Why is this so hard wth

[alpine sable]

plsssssssssss

[pliant estuary]

what have you tried so far

[raven valve]

sub 2 in there and check the decimal expansion

[muted raft]

You need $ in the beginning and at the end

[alpine sable]

i need the ans rn as assign ment due is after 10 mins

[raven valve]

if it ends or repeats, then it's rational...if not irrational

[raven valve]

50 mins

[alpine sable]

i have simplified a few of them but i am unable to simplify option d

[raven valve]

that's what irrational means

not being able to simplify it

ir rational

[alpine sable]

that means option d is irrational?

can you explain pls

[dawn thicket]

Guys , if i have
x² -4>0
How to get x ?
X>2 ....

[mossy stream]

So we find the volume of this shape by adding and infinite number of circles that are infinity thin. so first we want to find the area of our circles. Well to find that we need $\pi r^2$ $\pi$ is constant so we only need to find r. r is just the x value of our blue function so solve for x to get $x=y^2$ Then multiply by dy to get $V = \pi \int_{a}^{b}y^4dy$ We can determine our bounds are 0 and 3 so set a and b equal to the appropriate bound. Then integrate and solve. Your answer should be about $50 \pi un^3$

[raven valve]

you cannot divide with zero

[alpine sable]

like in depth as i cant understand bcoz option 2 numerator is 0 and stuff

[raven valve]

0 divided by anything is zero

but you can't divide with zero

[alpine sable]

does that mean b and c are 0

[raven valve]

0/something = 0
something/0 = error

[alpine sable]

ohhh

[raven valve]

yes and you already know 0 is a rational number

[alpine sable]

ok

[muted raft]

,w pi * int 0 to 3 y^4 dy

[ocean seal]

Results provided by WolframAlpha

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

Requested by zslya#7821

[mossy stream]

oops forgot to multiply by pi

[ocean seal]

Raymon

[alpine sable]

does that mean that d is irrational and explanation is that denominator is 0 so it is not divisible? @raven valve

[raven valve]

yes

[alpine sable]

ok thanks

[mossy stream]

<@&286206848099549185>

[upbeat maple]

what is the u?

@mossy stream

[mossy stream]

u? can you clarify

[upbeat maple]

you said the answer should be approx 50pi un^3

[undone geyser]

Unit

[upbeat maple]

ahhh tyty

[undone geyser]

Feeling like q math nerd rn lol

[mossy stream]

oh yeah we arent given the unit of the axis so i just left un^3

[upbeat maple]

im just confused af now tho

bc someone else said 9 pi

i got 243/5pi

and ur saying 50pi

[undone geyser]

Close enough

[upbeat maple]

oh true actually

[mossy stream]

i rounded

youre correct tho

[upbeat maple]

yh im not sure how that person got 9 pi

thanks for the help !

[undone geyser]

Y'all are cool

Shame i started texting on this server late

Academic year ends in 3 weeks

[mossy stream]

so just remember since you are taking volume its cubic units. that number means something.

[upbeat maple]

takes one to know one

[upbeat maple]

yh ive lost too many silly marks to units before in math tests

[undone geyser]

Tytyty

[undone geyser]

The answer is 4 . 4 what ? Apples ? Oranges ?

Such a silly thing tbh

[alpine sable]

hi

who can help?

[dreamy wharf]

[upbeat maple]

lmao

[upbeat maple]

what do you need help with?

[upbeat maple]

you can just post ur question and ask for help directly

[upbeat maple]

^^

[alpine sable]

oh

[dreamy wharf]

[upbeat maple]

lol

[smoky barn]

can someone explain how to do

12(a+3)^2 - 8(a+3)=

[thorny panther]

Expand the (a+3)^2

Then multiply 12 to the expanded numbers

[smoky barn]

ohh

okay lemme try

[hazy cairn]

Why is this true

[rotund steeple]

what did you try?

@hazy cairn

[hazy cairn]

I just managed to try something and I think it works

[rotund steeple]

nice

[hazy cairn]

Q[X] -> Q homomorphism with the homomorphism being evaluation at 0

[rotund steeple]

yep exactly

[hazy cairn]

nice xD

Wait I have another ring related question

this was on a midterm review sheet and I have no idea

I've proved that if r is irreducible then <r> is maximal, but not sure how to do it the other way around

[rotund steeple]

well the intuition is similar

[hazy cairn]

hm

how would I start it off?

[rotund steeple]

hmm try exploring the intuition behind the prev statement

[hazy cairn]

ok

Am I on yhe right lines to start off by contradiction or is there an easier way

[rotund steeple]

sure, thats how id go about it

[hazy cairn]

atm im assuminh <t> is maximal but r is reducible

nice, thanks!

[wispy urchin]

Does this look like a combination or a permutation to you? I think there’s something wrong with the problems I’m using.

[edgy breach]

How do I go about doing this question? I don’t even know where to start lol

This isn’t an exam by the way it’s practice questions taken from the edexcel website

[obsidian crane]

Take the integral simple

Put 'a' for x in the answer and similarly 1 for x , subtract both resultants.

(For part 1)

[edgy breach]

Ah ok it wants it in terms of a then

Ty

What about part 2?

[wet fulcrum]

yes it is

[edgy breach]

It says find the value though, suggesting it doesn’t want it in terms of a

[dawn agate]

That is the value, since a is constant

[edgy breach]

I see, I did this, would this not be correct? @dawn agate @obsidian crane

Oh shit the first one isn’t for sure

I took 8 out rather than sqrt8

[obsidian crane]

On the second part it's just 0 instead of 1

[edgy breach]

Really? Coz for the ∫ between a and 1, u would do it for a, then subtract the value of the ∫ when x=1 (which is 1), so surely for the ∫ between a and 0 since you’re subtracting 0 rather than 1 u would add 1

Either way, do u guys know how to do part b? @dawn agate @obsidian crane

[dawn agate]

I imagine you have to solve for a in part 1 and it will be in some radical

[wet fulcrum]

<@&286206848099549185>

[alpine sable]

is it free?

i just wanted to ask to rate my poem...

.

When I was home alone,
When storm clouds rumble in the sky,
My feet’s got numb,
And my nerves freeze like ice;

I couldn’t even amble,
I heard some noise of ramble.
Someone was coming near my room,
And my room was filled with gloom.

It was like hell ,which hurts from inside;
Trying to push these demons aside.
I needed something better,
To not feel all this terror.

I wept a lot,
My father woke me up.
Oh it was a dream;
And I was Afraid without meaning.

[wet fulcrum]

f *math server

[alpine sable]

xd

[ocean anvil]

Hahahahahaha xD

[wet fulcrum]

i figure the mods wont like it but why the hell not

[slow mirage]

erm, anyone using this channel for question?

[quasi pulsar]

i keep getting random numbers when i try to solve for x

same thing if i reverse it and solve for y

[late tundra]

try adding eq3 and eq4

[wet fulcrum]

no the equations are right

[wet fulcrum]

add 3 and 4

i assure you you will get it

[quasi pulsar]

okay i’ll try

[wet fulcrum]

if stuck send a ss

[quasi pulsar]

@wet fulcrum managed to get this

[wet fulcrum]

yea thats it

i got the same

[quasi pulsar]

thanks! just been a long time since i’ve solved simultaneous equations

[wet fulcrum]

🙂

send other doubts too

its good revision for me

[quasi pulsar]

sure thing thank you 🙏 haha

[stark wadi]

any help

[rich basin]

Whoever wrote that incoherent mess?

[stark wadi]

The creators of the question?

do you have any idea on how to work it out

[oak chasm]

@stark wadi They say it's a linear function, so it's d(t) = mt + b

So, what's the distance at time 0?

[stark wadi]

0

[oak chasm]

Nope, time 0 is at 3:00.

[stark wadi]

never mind i misread that

[oak chasm]

At 3:00, how much of the race had been completed?

[stark wadi]

t=0 is 3pm correct

1/2

[oak chasm]

Right.

[stark wadi]

2.5k

[oak chasm]

Right, so at time 0, 2.5 kilometers.

[stark wadi]

yes

[ocean seal]

Chai T. Rex

[oak chasm]

So, how fast are they running?

[stark wadi]

Aliyah at 0.25 per min

[ocean seal]

Chai T. Rex

[oak chasm]

See how that works?

[stark wadi]

Yes

is this the equation for Aliyah?

[oak chasm]

You multiply t times 0.25 to get the extra distance.

What does the question ask for?

Diego or Aliyah?

[stark wadi]

Write an equation that defines the linear function d. Explain how you determined the equation for the function.

[oak chasm]

Sure, but before that.

When it's describing d.

[stark wadi]

for Aliyah

alright

[rigid scarab]

Hey I know this is math, but I need some help with history right quick lol. can anyone help?

[oak chasm]

@rigid scarab Sorry, most channels are math only.

Maybe #chill, though I'm not sure if it's OK there.

[stark wadi]

@oak chasm may I ask what mt is?

[oak chasm]

@stark wadi m is the slope, t is the input variable.

It's the slope-intercept form.

[stark wadi]

👍

[oak chasm]

y = mx + b

Here, d(t) = mt + b

[stark wadi]

@oak chasm would you know how to even approach this?

[oak chasm]

@stark wadi Sure, what's t at 3 PM?

[stark wadi]

t=0

[oak chasm]

OK, so we got Aliyah's formula, right?

[stark wadi]

yes

[oak chasm]

Fill in 0 for t.

What do you get?

[stark wadi]

0

wait

t = 1.59

[oak chasm]

Why do you think t = 1.59 at 3 PM?

Oh, I see.

You mean the distance is 1.59.

[stark wadi]

perhaps

if you filled t with 0

in the equation

[oak chasm]

Yes, whose equation is that?

[stark wadi]

Diego

[oak chasm]

OK, so that's Diego's distance.

What's Aliyah's using Aliyah's formula?

[stark wadi]

why did you choose to input 0 in T?

[stark wadi]

2.5km

[oak chasm]

Because the problem asks for stuff at 3 PM, right?

[stark wadi]

ok

got it

[oak chasm]

OK, so Diego got to 1.59 km and Aliyah got to 2.5 km at 3 PM.

Does that make sense?

[stark wadi]

Yes

got it

[oak chasm]

One nice thing about Diego is that eventually they go faster than the speed of light.

It just takes some time.

[stark wadi]

so who would finish the race first

@oak chasm

as Aliyah runs at a constant pace of 0.25 per minute

[oak chasm]

Well, what's the distance of the race?

[stark wadi]

5KM

[oak chasm]

OK, so d(t) = 5

[stark wadi]

yes

[oak chasm]

So, Aliyah's formula is d(t) = 0.25t + 2.5.

So, 0.25t + 2.5 = 5

[stark wadi]

yeah

[oak chasm]

So, solve for t.

[stark wadi]

it would take her another 10 minutes

with the constant pace

[oak chasm]

Right.

OK, so Diego's formula is d(t) = 1.59 + 0.2t + 0.01t^2.

[stark wadi]

yes

[oak chasm]

So, 1.59 + 0.2t + 0.01t^2 = 5

[stark wadi]

yes

[oak chasm]

So solve for Diego's t.

[stark wadi]

give me a sec

I believe its 11 but

the 0.01 t is confusing me

[oak chasm]

Well, it's a quadratic.

So, you can use the quadratic formula or complete the square.

[stark wadi]

yes alr

[ocean seal]

Chai T. Rex

[stark wadi]

11 and -31?

[oak chasm]

Right, and they didn't finish the race before 3PM, so it must be the 11.

[stark wadi]

👍

[solar hazel]

guys, urgent question

After I have the eigenvalues

How do I find the eigenvectors?

[woeful pulsar]

find the nullspace of xI-A

[solar hazel]

So

I can't do the part

Ax = 0

this one

[woeful pulsar]

tho I'm not sure why your question is that urgent lol

[solar hazel]

sorry, I have to turn in something

[woeful pulsar]

sounds sus

[solar hazel]

it's okay, I finally understood it

found an article that explained it better ig lol

[upbeat locust]

got a great question! Parametrize the triangle with points in (11.

(0,1), (2,0) (0,0) in that order

[woeful pulsar]

parameterise the triangle's interior?

[upbeat locust]

yes!

[woeful pulsar]

2 parameters I suppose?

[upbeat locust]

3, so between all points! its the rand!

[woeful pulsar]

wait why 3?

is it bary

[upbeat locust]

bary?

sry, im swedish, i have no clue hahaha

[woeful pulsar]

was thinking barycentric coordinates

[upbeat locust]

omg, no

[woeful pulsar]

but I'm not sure why 3 parameters

[upbeat locust]

NEVER heard of it

like the exterior lines

from (0,1) to (2,0) to (0,0) and then (0,0) to (0,1)

[woeful pulsar]

why do you need 3 parameters

[upbeat locust]

no wait! JUST two hahaha

x and y

sorry! misunderstood you completely

[woeful pulsar]

oof

yeah from there it's pretty straightforwards, just use x and y and get your inequalities

isn't it?

[upbeat locust]

well i have no idea how hahahaha

my german speaking teacher didnt quite explained how to do it hehe

[alpine sable]

I dont understand what to sub in

[woeful pulsar]

what conditions do you need to verify to check if (x, y) is inside?

[upbeat locust]

we are supposed to draw the lines with a curve!

[woeful pulsar]

wait what?

[upbeat locust]

are you with me? 🙂

[woeful pulsar]

no I don't get it

[upbeat locust]

hahaha yepp

not me either

hahahaha

[woeful pulsar]

can you show more?

the less details you have the less anyone can possibly reconstruct

[upbeat locust]

This is the answer, but i have 0 clue about how i get there

[upbeat locust]

so we are supposed to parametrize the curve between the points! and idk how...

[woeful pulsar]

oh

[woeful pulsar]

so not the interior

the boundary

no wonder

[upbeat locust]

YEAH!

hahahaahahahah

omg

maths in english is kinda hard sometimes

[woeful pulsar]

yeah you said "interior" earlier

[upbeat locust]

ik...

[woeful pulsar]

is it clear now tho?

[upbeat locust]

nope

[woeful pulsar]

how do you parametrise (0, 1) to (2, 0) using t from 0 to 1?

[upbeat locust]

not at all haha, i got the answer but idk how i should get there

thats the thing i dont get hahahaah

[woeful pulsar]

give t from 0 to 1 to one side
give t from 1 to 2 to another side
t from 2 to 3 to the last side

from there the parametrisation is quite similar to (start)*(1-t)+(end)*t

[upbeat locust]

AHHHHH

i think i kinda got it now

[upbeat locust]

thnx man

[tired geyser]

True

exactly

[dusty jacinth]

how would I solve this for v?

[woeful pulsar]

solve it for v^2 then take the square root

[lone folio]

Can anyone help me with these questions? Just learning logs right now and I'm not sure if what I'm doing is correct

[glass lichen]

which question?

[polar whale]

What have you done ?