help-0

[torpid narwhal]

and multiplication (a, b) + (c, d) = (a * c - b * d, a * d + b * c)

the additive identity is (0, 0)

the multiplicative identity is (1, 0)

tried doing (a * c - b * d, a * d + b * c) = (1, 0) and finding (c, d) in terms of (a, b)

is that the correct idea

[alpine sable]

Ok that’s fine

So what you’re trying to find is the amount of books this person has to sell

We call that x

We can then write the costs of printing the novel as fixed costs + variable costs * x

And the profits as profit per book * x

@compact mural do you follow

[alpine sable]

Occupied

oh sorry

Lol ok

Well if she wants help she can come get help

I see

no

#chill

#old-network

Do it in the physics server

They love nsfw over on discord.com/physics trust me

Please do not

[vale wigeon]

<@&268886789983436800> feels like something may be afoot here.

or to put it another way

we got a little situation

[sly mantle]

[vale wigeon]

cue the copswings

[sly mantle]

@compact mural no nsfw content is allowed here at all

[alpine sable]

Math is not safe for many workplaces

[sly mantle]

sigh

[alpine sable]

Trolling goes in #chill

[sly mantle]

b&

[bitter sage]

can anyone help with this?

[tight locust]

$W = Fd\cos(\theta)$

[ocean seal]

EndTimes

[tight locust]

or equivalently

$W = F_xd_x + F_yd_y$

[ocean seal]

EndTimes

[tight locust]

which is the same thing as saying

$W = \overrightarrow{F} \cdot \overrightarrow{d}$

[ocean seal]

EndTimes

[tight locust]

,w 508cos(30)

[ocean seal]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[split sapphire]

Hello

[tight locust]

greetings.

do you have a question

[bitter sage]

i use dot product?

[tight locust]

yuh

[bitter sage]

ok

so w = 346?

[tight locust]

it says round to the nearest tenth

so 346.4

[bitter sage]

sorry

thanks for the help!

[tight locust]

joules

[alpine sable]

(0.042 * 75000) ^2 e^[- 0.042 * 75000]/2 I keep ariving at a negative number when solving the equation. That should not be possible. What am I doing wrong?

[gray isle]

what are you using to calculate that expression and what exactly are you entering

[alpine sable]

just osx calc

and following BRODMAS

[livid iron]

Can someone help me transform the function for 8

[gray isle]

what exactly are you entering

[alpine sable]

hold on

something just came up. Thanks for answering. I will be back

[alpine sable]

to solve this problem would you do (180-124)+(180-6x)+2x=180

[tight locust]

yup

[alpine sable]

thanks

[west glen]

anyone know how to do 7c

i got $121320 for a and $58820 for b

[oak chasm]

OK, so the interest rate is the interest over the principal.

Like if the principal is $1 and you pay $0.05 in interest, then the interest rate is 5%.

0.05/1.

[west glen]

i think flat interest is different

i did 58820/62500 *100% tho but its wrong

the answer is supposed to be 18.8%

[oak chasm]

Right, so what did you get for that?

[west glen]

94.12%

94.112%*

[oak chasm]

OK, that's the interest rate over five years.

What's the interest rate per year?

[west glen]

ohh

thats insane

ok cheers man

got it

[oak chasm]

You too.

[analog nymph]

https://artofproblemsolving.com/wiki/index.php/2021_AMC_12A_Problems/Problem_23

i examined one path

but this probability is wrong

for some reasons

[analog nymph]

x means a corner is reached

[prime badge]

your first center-edge is different from your second cernter-edge hop

[analog nymph]

you mean i only drew one jump for the first center-edge? i assumed the other 3 jumps hav this same probability of reaching a corner

[prime badge]

reasonable, but since you;re getting wrong answer, could be wrong

i agree, like imagine this tree is quadrupled, that's same probability anyway

[analog nymph]

how would you approach this question

my tree apparently gives the probability 14/37

:((

[prime badge]

((2/8) * 0.5 + 0.5) * 0.25 + 8/16 * 0.25 + 0.5

it gives 25/32

your tree i mean

[analog nymph]

oh bruh i counted the nodes. not probability

[analog nymph]

wait why did u multiply by 0.25

[analog nymph]

sry probability is my weakness. could u pls explain the "x 0.25" and "((2/8)*0.5+0.5)" parts?

[prime badge]

uh i don't know

sorry

[analog nymph]

[analog nymph]

can someone else pls help me to read this?

[analog nymph]

nvm i understand now

[limber willow]

Hi im reviewing old exam quetions for a course on bio informatics and struggle with a question about a prove for markov chains, would someone be able to help me?

I want to prove that the sum of all probabilities of sequences of length L is equal to one

[alpine sable]

yes

same.

what's the question?

i mean what's the objective?

to find x?

that's not an eqn.

-5x + 8 is not even equation

you can't solve x with an expression, are you sure it isn't -5x+8= something else?

so sorry we can't help you

[fair vine]

@limber willow by def sum of transition probabilities from one step to another in markov chain is 1 and then its just induction n-> n+1 so it stays 1 regardless of length, cant say how to write it formally though since its been a while likewise

[alpine sable]

we tried our best

no problem

and you've come to the wrong place if you are just looking for answers.

it's like you ask me how to find the answer to 3x+1

still, recheck your expression, are you sure it isn't -5x+8 equal to something else?

can you please post a pic of the problem?

so sorry we can't help you with that

forgive us

yes, please do. that is what i was asking the whole time

thank you.

there we go.

that's an equation

and it has an equal.

that's what i was asking the whole time.

you said here there was no equal

anyways.

is this your very first time to equations?

do you then have any ideas on what our first step should be?

[untold marten]

can someone help me?

pls

[alpine sable]

i'm asking for a first step, not what our goal is

[untold marten]

i cant find the way to solve that

[alpine sable]

wait, what is this?

is it equal to 0?

can you please post the entire, precise and explicit equation?

you aren't helping me to allow me to help you at all.

even al3dium can't help

that's not an equation.

even the x is unknown

as well as ?

on the right hand side

[limber willow]

okay thank you

[alpine sable]

that's impossible

oh

that's a whole new task.

okay then.

no problem

stay safe

don't forget to wash your hands

and have a nice day

thank you

you too

@winter osprey please, for the record, read #❓how-to-get-help , you want to post your problem with all details and not excluding anything out. this all missunderstanding could've been saved if you posted the problem as a whole and not giving us pieces of info as if we are asked to guess what your problem was.

oh, uh.

[oak chasm]

@broken tidevor#0001 To help you on homework and tests, without an equal sign in it, you can't solve, only simplify or factor or something like that.

[gilded smelt]

Can someone help please

[untold marten]

can someone help plssss

[placid zinc]

The factoring of h(t) is wrong. Remember to check for common factors

[alpine sable]

this makes sense?

[placid zinc]

How do you know that s ≤ a for all a ∈ A?

[cinder shard]

This question makes no sense

What is p? Wdym "less than b packs of 250-page bundles"?

did they not buy b packs of 250-page bundles of paper?

if not, then what is p supposed to represent?

[stiff lance]

Hi

[cinder shard]

hi

[stiff lance]

I don't speak English, but I need help:, (

[cinder shard]

oh go into a different question channel

I'm only HS math

[stiff lance]

could you tell me some?

my question is about relationships

[cinder shard]

#help-4 seems open

[stiff lance]

I don't know if it's written like this

[vague coral]

what is p here ?

[cinder shard]

That's what I'M asking

[stiff lance]

Ty

[vague coral]

weird exercise

[cinder shard]

[alpine sable]

because B is bounded above by all elements of A, and so s <= a for all a in A

[cinder shard]

How is it not A?

t to get there (Morning trip), x to get back (Back trip)

nvm

stupid english

[oak chasm]

@cinder shard It's x on top, which is the slower going home trip, right?

If it's slower, it takes longer.

The x is the time it takes.

So, if the larger number is on top, the fraction should be higher than 1.

Does that make sense?

[cinder shard]

ya I saw it thx

[placid zinc]

@alpine sable
There's a gap there. Remember that s is not necessarily a member of B

[alpine sable]

Elvis and Noah want to remove the piano from the living room. Elvis pushed from behind with a force of 400 N, and Noah pulled from the front with a rope of 150 N. The mass of the piano is 225 kg, and the friction between the floor and the piano is 100 N. Get the acceleration

Someone solve this

[oak chasm]

@alpine sable We don't give answers, but we can help you with it.

So, what's the total force on the piano?

[alpine sable]

550 total pull 100 friction 225 mass , acceleration

How to get acceleration

[oak chasm]

OK, now newtons are kg meters per second squared.

So, kg is on top.

[alpine sable]

Ok

[oak chasm]

So you need your kg on bottom.

Then the kgs cancel.

[alpine sable]

Ok

[oak chasm]

Leaving you with meters per second squared.

So, 1/225 times 450 m/s².

Does that make sense?

[alpine sable]

Kind of

Wait

Yes

Ohhhhhhhh

[rugged grove]

hi is AB a+b or is it for example a=2 and b=3 so 23

[ocean seal]

Chai T. Rex

[oak chasm]

@alpine sable ^

[alpine sable]

Ty

[oak chasm]

You're welcome.

@rugged grove It depends on the problem.

Usually it's A times B.

[rugged grove]

oh alr

[oak chasm]

But it can mean digit A followed by digit B in a few problems.

[rugged grove]

so in my case a is 3 and b is 122

[oak chasm]

Oh, in that case, it's probably 366.

[rugged grove]

i need to find out what AB is

[alpine sable]

Wait that’s the final answer, right?

[oak chasm]

ab = 3 · 122 = 366.

[rugged grove]

alr so 366 ty

[oak chasm]

@alpine sable Well, reduce the fraction.

[alpine sable]

Ik

But that’s all I have to do

?

[oak chasm]

But 2 m/s² is it.

[alpine sable]

Ok

[alpine sable]

Ik

Chai T. Rex

What grade are you in

[oak chasm]

Oh, I'm done with school.

[alpine sable]

Are you in UNI?

Or are you done everything

[proven blade]

how do you find the probability for this question

[oak chasm]

Oh, done with all school.

@proven blade OK, do you know the formula for P(A u B)?

[proven blade]

not really

im not sure

maybe

[oak chasm]

Well, draw a Venn diagram.

[proven blade]

wait how do you apply the formula

[oak chasm]

Well, we'll show how to get the formula.

Then it'll be easier to apply.

[proven blade]

ok hold up

done

[oak chasm]

OK, now shade in the whole circle of A.

[proven blade]

which one is A

[oak chasm]

Label them.

A and B.

[proven blade]

ah ok

labellds

[oak chasm]

OK, so shade in the whole circle of A.

[proven blade]

including 4?

the shared one

[oak chasm]

4?

Yes.

The whole thing.

[alpine sable]

Sets

[proven blade]

done

[oak chasm]

Then shade in the whole circle of B, even the parts shaded already.

[proven blade]

done

[alpine sable]

A union B

[oak chasm]

Now, you shaded everything once and the shared part twice, right?

[proven blade]

ge

yee

[oak chasm]

OK, so if we want to count the things inside both A and B, we need to count the things in A and the things in B.

Now that will double count the things in the shared part.

So we'll get a number that's too high.

Does that make sense so far?

[proven blade]

ye

[oak chasm]

OK, so we subtract the shared part once.

Now all parts are counted only once.

[proven blade]

24

i got 24

[oak chasm]

P(A u B) = P(A) + P(B) - P(A n B).

See how I got the formula?

[proven blade]

oh ok

thanks

wait so how do you find the probility

probability

[oak chasm]

So, the hair is 8, the eyes are 12, and the shared part is 4.

So, 8 + 12 - 4, right?

[proven blade]

ye

[oak chasm]

So, what's that?

[proven blade]

16

[oak chasm]

And how many students in total are there?

[proven blade]

30

[oak chasm]

Matches/total

16/30

That's your probability.

Reduce that fraction.

And that's your answer.

[proven blade]

ohh

that's true

tanks so much

[oak chasm]

You're welcome.

[raven bolt]

Can someone help me find the angle please

[alpine sable]

If Edward has a mass of 110kg, and his girlfriend was carrying him toward his house with her rope with 300N of force and the friction is 130N then what's the acceleration?

[glass lichen]

do you have a diagram?

[alpine sable]

No

I have to use f = ma

[raven bolt]

Bruh 🤣

[alpine sable]

What

Is it wrong

[raven bolt]

I got ignored

[alpine sable]

;-;

Oh

[raven bolt]

It’s fine

[alpine sable]

300N total pull, 130N friction, 110kg mass

Acceleration is

1/300 times....

Uhhh

I’m brain dead

[glass lichen]

1. the channel is still in use by drake as was pointed out
2. you still havent answered my question

[alpine sable]

What

[glass lichen]

nvm drake moved

anyway... do you have a diagram?

[alpine sable]

No

[glass lichen]

ok so what's the direction of the pull force?

[alpine sable]

huh

[glass lichen]

forces have direction and magnitude, you've only said magnitudes

[plush kiln]

mosh can you help me after you have assistated alex

assisted

[alpine sable]

The direction wasn’t specified

So I’m not sure

[glass lichen]

Ok... then i'll assume it's anti-parallel to friction

[alpine sable]

Ok

[glass lichen]

so the pull force is $300N\hat{x}$ and the friction is $-130N\hat{x}$

[ocean seal]

Mosh

[alpine sable]

1/110 times pull over friction

They are both kg

They cancel

[glass lichen]

???

[alpine sable]

That’s what the dinasour said

[glass lichen]

there's no pull over friction

[alpine sable]

Chai

[glass lichen]

so...

[alpine sable]

f = ma

[glass lichen]

you cant divide by vectors

[alpine sable]

What

[glass lichen]

so...

it makes no sense to say vector/vector

anyway $\sum F=ma \implies 300N\hat{x}+(-130N\hat{x})=110a\hat{x}$

[ocean seal]

Mosh

[glass lichen]

since everything is in the x direction you can just consider this as scalar equations and get $300-130=110a$

[ocean seal]

Mosh

[alpine sable]

1/110kg times 170/s^2???????

what is happening

Oh wait let me read what you said

[glass lichen]

I have no clue what you are even saying

[alpine sable]

Ohhh

[alpine sable]

Ask the di salir guy

[glass lichen]

but yes, a=170/110 ms^(-2)

[alpine sable]

Dinasour

Chai T. Rex

So it’s 110a?

[glass lichen]

170=110a

[alpine sable]

A=170/110

[glass lichen]

yes

$a=\frac{17}{11}m\cdot s^{-2}$

[alpine sable]

1.5454545454

[ocean seal]

Mosh

[alpine sable]

Hello! Can’t get where is underlined in blue. I didn’t know that it was possible to do this way. Can someone explain it to me?

?

[glass lichen]

???

where tf did that come from

[alpine sable]

What

17/11m times s^-2

[glass lichen]

yeah... no

[ionic jewel]

,w sec(x) = sec(2x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[glass lichen]

17/11 is as simple as you can make it, also missing the meter units for acceleration

[ionic jewel]

lmao mosh he don't understand at all

[alpine sable]

Wait

[glass lichen]

[a] = [m/s^2] not [1/s^2]

[alpine sable]

I’m 13 leave me alone

[ionic jewel]

m for million dude smh

[alpine sable]

.

Tell me the answer and I’ll work backwards or something

[glass lichen]

17/11

[ionic jewel]

it's not true

[alpine sable]

Ohhhhhh

[glass lichen]

meters/second^2

[alpine sable]

Ohhhhhhhh

What’s the formula

[glass lichen]

?

for what?

[alpine sable]

Uh

Like for example

[glass lichen]

Newton's laws?

[alpine sable]

This one uses f=ma

[glass lichen]

$\sum \vec{F}=m\vec{a}$

[ocean seal]

Mosh

[alpine sable]

Oh ok

Thx

[glass lichen]

the sum of forces = ma

[alpine sable]

Yes

Ty

[alpine sable]

Oh, it’s not? See where the arrow is pointing to? That’s where my question comes from.

Oh, I think I get it now

I misunderstood

Thx!

Someone solve this

[jovial breach]

are you trolling

[hearty canyon]

hello, could somebody please explain how to solve this?

simplifying the equation on the top btw

[jovial breach]

make the fractions above into one fraction

by making the denominators the same

[hearty canyon]

so x+2/2(x+2)

[jovial breach]

yes

[hearty canyon]

I understand that part, but I don't get the same answer once I multiply by reciprocal of x

wouldn't it be x+2/2x+4 * 1/x ?

[jovial breach]

what do u not understand here

[hearty canyon]

I can get to that part, so I understand what you did in the picutre

but when you simplify the expression you have on the bottom, I don't get the same answer as when I put it in a simplifier calculator

I get -x / 2x^2 +4x

[hearty canyon]

thank you for writing it out btw, that helps a lot

[jovial breach]

its exactly the same thing

divide by x both num and denom

its not zero

in your case its :

[hearty canyon]

ok, I understand now

thank you so much!

[hearty canyon]

I really appreciate the illustrations

[jovial breach]

youre welcome

[rough hemlock]

in completing the square in quadratic equations, where does b in the left side of the equation go in the third step? how does it get simplified?

[ancient saddle]

Hello, do you mean what happens with -6?

[alpine sable]

Anyone?

[rough hemlock]

yes

[ancient saddle]

$x^2-6x+(-3)^2=x^2-2(3)x+3^2=(x-3)^2$

[ocean seal]

leonardogtf

[rough hemlock]

hmm, can you elaborate? it hasnt made sense to me yet

[ancient saddle]

ok, so we know that

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

[rough hemlock]

mmhm

[ocean seal]

leonardogtf

[rough hemlock]

are you continuing or is that it? i still don't get it, it just dissapears without doing anything

wait

oh

[jovial breach]

Need help?

[rough hemlock]

yeah uh thanks

[jovial breach]

completing the square means making the expression you want appear , one that suits what you already have in front of you

in our case its x^2

i see thats ok

then its -6x

now that must be our 2ax

to complete this : (x-a)^2

x^2 - 2ax + a^2

so 2 times something is 6, that something is 3 which is a

then youre missing a 3^2

just add it to both sides to make it appear

and youre good to go

got it ?

[rough hemlock]

mmmm alright i think i got it thanks

[jovial breach]

sure?

[rough hemlock]

yea

[jovial breach]

good

[alpine sable]

Idk what to do

When i do the triangles on geo gebra

help

[remote heron]

what do you get when you distribute

[alpine sable]

owh wait

[remote heron]

thats what the problem is asking you to do?

im assuming

is there more instruction?

there is some other factoring stuff you could do as well

[alpine sable]

it needs to be

wait2

[remote heron]

its not really clear what you are supposed to do though

sure

im on a bicycle so ill be in and out too

[alpine sable]

eh sorry, i already asked my friend. sorry for disturbing u

the language barrier, i don't really understand english very well

once again, sorry 🙏

[heavy mural]

if i have c/(x+2)(x+6) sum from 0 to infinity

how do i simplify it?

[slow frigate]

Hey guys, am I going nuts here

I cannot for the life of me figure out how to isolate the T in this equation

e^t - 2t^2 = 0

Is there any way I can find the roots to this without a graphing calculator?

[placid zinc]

No there isn't.

Could maybe break out Lambert-W functions but you'll still depend on calculators

[slow frigate]

Awesome thank you

It’s been driving me insane haha

[short turtle]

hi is this channel occupied?

[slow frigate]

Nope go for it

[short turtle]

can i get help with this?

it says i need to first subtract 2xy from both side

[tight locust]

(x-y)^2 = x^2 - 2xy + y^2
(x-y)^2 + 2xy = 52xy
(x-y)^2 = 50xy

i think that should be enough

then you should apply the rules of logs

[short turtle]

Ooooh i get it now

Thanks

[tight locust]

so then you get sqrt(50xy) = 5sqrt(2xy).
so then log((x-y)/5) = log(sqrt(2xy)) = 1/2 log(2xy) = 1/2 (log2x + logy) = 1/2 (logx + log2y) = 1/2(log2 + logx + logy)

[short turtle]

Ok got it thx

[alpine sable]

Why is 25^(1/2) = 5?

like conceptually

[glass lichen]

cause sqrt(25)=5

[alpine sable]

why is the square root of 25 the answer

why is n^1/2 = sqrt(n)?

I am trying to conceptually, intuitively, understand it

all I'm finding online is just assertions that the rule is that its the square root of n

[glass lichen]

ok well suppose $n^{0.5}=L$ then by exponent rules I know $n=L^2$

[ocean seal]

Mosh

[glass lichen]

by raising both sides to the power of 2

[alpine sable]

again this is just relying on other rules

"Because of this other rule, I'm going to trust that the result must be this"

It's not an intuitive/visual explanation

You can explain n^2 intuitively

"It's n times itself, n times"

[tight locust]

only for integers

[alpine sable]

but what is n times itself half of n times??

How do you visualize that

[tight locust]

basically you are saying that you want to find u such that u*u = n

[glass lichen]

you dont

it's called abstraction/generalization

the concept of n^m for positive integers m relies on the fact exponentiation is repeated multiplication

[tight locust]

you just clear the denominators of the power then the intuition still holds

of course this still only extends the concept of exponentiation to the rationals

how do you think of 2^(sqrt2) for instance

[minor anchor]

n^(1/2) is the same thing as sqrt(n). n^(1/3) would be the cube root of n, n^(2/3) would be the cube root of n^2, etc

[rain mason]

can someone help here? idk what i’m doing wrong

[alpine sable]

If exponentiation is repeated multiplication, then what does that look like when the exponent is a fraction

You're not multipling it by half of itself are you?

[glass lichen]

It doesn't exist IF you define exponentiation as repeated multiplication

It's an abstraction

n^(1/2) and sqrt(n) both have the property of squaring them and getting n

So they're equal

[buoyant edge]

@rain mason Absolute value for the log since x^2 + 5x + 4 is not always positive.

[limber thorn]

how do you find if it is continuous?

[minor anchor]

a function is continuous if every x value has a single corresponding y value

[alpine sable]

What are we defining exponentation as if not repeated multiplication?

[minor anchor]

it would be not continuous if the y value came out to be like 0 x inf, 1/0, etc

[oak chasm]

That's the definition of a total function, not a continuous function.

[minor anchor]

what I'm saying is like there are no undefined values

[oak chasm]

That doesn't make it continuous.

[minor anchor]

like for 1/x, 0 isn't defined so the function isn't continuous

[oak chasm]

You could give each input a single random output and it wouldn't be continuous.

@rocky dragon Sorry, channel is busy.

[limber thorn]

so for 41 its when there is a fraction and the denom=0 its not continuous?

[minor anchor]

yeah (at least by my understanding)

[limber thorn]

so 42 is continuous

because it is still defined?

[minor anchor]

no, where x^2+5=0 it isn't defined

[limber thorn]

oh i see cause cant have sqrt of neg

[quartz stone]

@minor anchor continuity doesn't just mean that all real numbers are in the domains of the function, as Chai T. Rex said

[cold valley]

If you remember your asymptote rules, there is a VA at x=+-√5 if im not mistaken, so it would not be continous

[quartz stone]

It means that the limit of the function at every point is the value of the point

[oak chasm]

@limber thorn You're supposed to justify your answer based on the properties of continuity, right?

[limber thorn]

yes

[oak chasm]

In the first one, you have a polynomial - 1/x.

Now, 1 and x are polynomials as well, and they're continuous when the polynomial in the denominator isn't zero.

[oak chasm]

So, the justification would be that 2x² + 5x is a polynomial, so it's continuous.

1 is continuous.

x is continuous.

Because they're polynomials.

By the rational property, 1/x is continuous when x ≠ 0.

Let's use this:

By the difference property, 2x² + 5x is continuous everywhere and 1/x is continuous everywhere except x = 0.

So, 2x² + 5x + 1/x is continuous everywhere except x = 0.

So, that problem is done.

For the second problem, x + 1 is a polynomial.

So it's continuous.

2x is a polynomial, so it's continuous.

x² + 5 is a polynomial, so it's continuous.

2x/(x² + 5) is therefore continuous when x² + 5 ≠ 0, which doesn't happen, so it's continuous everywhere.

So, x + 1 is continuous everywhere and 2x/(x^2 + 5) is continuous everywhere, so by the sum property, x + 1 + 2x/(x² + 5) is continuous everywhere.

[limber thorn]

that makes sense, thank you. I also was shakey on the definition of polynomial. does that just mean 2 or more terms?

[oak chasm]

No, it's terms that are variables to powers multiplied together with coefficients.

And one of the terms can be a constant term.

So, 2x² + 5x + 5 is a polynomial.

The terms are variables to powers multiplied together with coefficients and an optional constant term.

5 is also a polynomial.

As is 3xy.

[narrow garden]

Alr so I had a kinda stupid question, idk what you think about it

may I ask?

[oak chasm]

@narrow garden Sorry, channel is busy.

[narrow garden]

oh alr

[oak chasm]

#help-9 looks open if you hurry.

[narrow garden]

oh oki

[limber thorn]

so what would make 1+x a polynomial?

[oak chasm]

It has a constant term, 1.

The other term is variables to powers multiplied by a coefficient.

The power is 1, the coefficient is 1.

1x¹.

[limber thorn]

thanks for your help got it:)

[oak chasm]

You're welcome.

[alpine sable]

"What is the probability that a random rearrangement of the letters in the word 'MATHEMATICS' will begin with the letters 'MATH'?"

now the difficult thing about this problem is that my book is instructing me to "Think about it"

with the added comment:

"Rather than counting the total number of rearrangements and then counting which ones start with 'MATH', instead try to come up with a more thoughtful solution"

however I don't really know what this theoretical thoughtful solution would look like

[reef pebble]

Is this channel busy

[winter linden]

Ayo ayo very quick question, 1÷ -5 = 5

[reef pebble]

?

1 ÷ -5 = -4

Oh wwait

Thats not an addition problem

xD

[alpine sable]

it isn't

1÷ -5 is -0.2

[winter linden]

No no when i take -5 on top

Not divide

[alpine sable]

wdym

[reef pebble]

help

[alpine sable]

alright

basically

100 = 72+43 - (number of people who can speak both)

so 15 people speak both

[reef pebble]

[alpine sable]

72-15 = 57 people speak English only

28 people speak Cebuano only

[alpine sable]

Are you familiar with what brute force means?

[alpine sable]

yea

[reef pebble]

What is this

[alpine sable]

although i think the book wants me to find a more efficient solution

[reef pebble]

Like,why is there 8 and 13

[alpine sable]

I think its asking you not to do brute force

yeah that's the conclusion i got too

The example it gave you, where you count up all the arrangements, then count the ones that start to math, would be brute force

[reef pebble]

Where did 8 and 13 come from

[alpine sable]

It's instead wanting you to come up with an algorithmic representation

[alpine sable]

oh

it's because

8 + 14 = 22

and 14 + 13 = 27

[reef pebble]

Thanks

[reef pebble]

Am i the only programmer whos bad at math lmao

[misty pumice]

im in no rush to solve this

and you dont have too but does anyone get this?

[pulsar cloud]

what do you not get

thats the definition of a deriviative

[misty pumice]

nvm man thanks I got it

appreciate your help

[pulsar cloud]

I know thats not superhelpful answer

but honestly what part do you not understand

cause you arent really like trying to solve a problem here

[small cypress]

How do u do a n b?

[sage bronze]

for a

$$f(x) = 3x^{2}$$
$$ f(x+h) = 3 (x+h)^{2}$$
$$ \frac {3 (x+h)^{2} - 3x^{2}}{h}$$

[ocean seal]

HELLOBELLO

[sage bronze]

expand $3 (x+h)^{2}$

[ocean seal]

HELLOBELLO

[sage bronze]

and then subract $3x^2$, factorise and divide by h you should have your answer

[ocean seal]

HELLOBELLO

[sage bronze]

@small cypress

similarly with the b

[small cypress]

ahhh I see thanks

what does the h shuft mean

[brazen cradle]

Pls help

[sage bronze]

wdym

[small cypress]

this

[sage bronze]

as h approaches 0

[reef pebble]

pls help me

@alpine sable

[burnt warren]

#help-3 plz

Look

[reef dust]

Use principal of inclusion and exclusion

[vale wigeon]

de morgan's law is something completely different, arya...

it has nothing to do with incl-excl

[reef dust]

Yea I got the name wrong...

[celest void]

Why does this proof work?

isn't limit of x -> x_0 of

$\frac{x-x_0}{x-x_0}$

[ocean seal]

Serena!

[celest void]

equivalent to multiplying by 0/0

[vale wigeon]

no, because you do not care what happens at the point x=x_0

only around it

[reef dust]

We are approaching xo as closely as possible
But not actually reaching it

[celest void]

Wait so then lim x goes to x_0 (x-x_0) wouldn't be 0 then but a very small number?

[reef dust]

Yea

[celest void]

But they consider it 0?

[vale wigeon]

no, the limit would be zero

$x - x_0$ doesn't approach 'some nondescript small number', it approaches zero.

[ocean seal]

Ann

[celest void]

Ohhh

I see thank you!

[alpine sable]

Is anyone good with Microsoft word here?

[alpine sable]

word?-

bruh wdym good at word word is ez to use

[narrow elm]

Anywy care to integrate a for me?
I’m substitute t for sin(x) but can’t seem to get it

[ancient saddle]

Hello, remember

$\sin 2x=2\sin x \cos x$

[ocean seal]

leonardogtf

[minor anchor]

does that carry for any other constant? Like does sin(20x) = 20sin(x)cos(x)?

[ancient saddle]

No, it's just for the sin of 2x

[thin urchin]

i have 20 problems like this due in an hour, what should I google to solve these kind of problems?

[alpine sable]

can we tell by only seeing the eqn if it is a parabola or pair of straight lines?

<@&286206848099549185>

[cold valley]

Wdym by that

[ocean seal]

Beluga

[alpine sable]

can you tell which one is parabola and which is pair of lines

[cold valley]

What do you mean by pair of lines

[alpine sable]

this is a pair of lines

once check this out

[vale wigeon]

y = ax^2 + bx + c is a parabola oriented in such a way that its axis of symmetry is vertical

which is not beluga's case

what the actual fuck

[cold valley]

Ah I didn't see the equation posted

My bad

[vale wigeon]

impostors the lot of you

[alpine sable]

i'm the one with DND enabled

[vale wigeon]

you can change the display color of each equation if you click the settings icon on the left

[alpine sable]

it's a question
on paper there would be no graph

[vale wigeon]

anyway

okay

let's take a look

x^2 + y^2 - 2xy - 4x + 4y - 4 = (x-y)^2 - 4(x-y) - 4

[alpine sable]

i didn't get it
wdym to say by this?

[vale wigeon]

i'm saying that this equation describes a pair of lines

whose individual equations would be x-y = r1 and x-y = r2, where r1 and r2 are the roots of t^2 - 4t - 4

[alpine sable]

ohk

got it

thanks @vale wigeon

[karmic finch]

can someone help?
(c) the smallest integer k such that 5145×k is a perfect square,

(d) the smallest positive integer y such that 378×y is a cube number.

[vale wigeon]

have you made any progress so far on either of those?

("none" is a valid answer)

[karmic finch]

ok

A rectangular tray of brownie measures 480 mm by 200 mm by 80 mm. It is to be cut into small

cubes of identical size such that there is no wastage or leftovers. Find

(i) the largest possible length of the side of each cube,

(ii) the volume of the largest cube,

(iii) the total number of cubes obtained.

i suck at maths

[vale wigeon]

@karmic finch why are you posting a new problem?

i was trying to see what you needed help with in regards to the two problems you posted first.

[karmic finch]

oh

[vale wigeon]

i asked you: have you made any progress so far?

[karmic finch]

nope

[vale wigeon]

okay

could've said so right away

[karmic finch]

yeah mb

[vale wigeon]

so, let's look at part c, shall we?

we want the smallest positive integer k such that 5145k is a perfect square.

do you know what a perfect square is?

[karmic finch]

yea

[vale wigeon]

good

so now, here's an idea: factorize 5145 into primes.

[karmic finch]

prime factorization?

[vale wigeon]

yes, that's what i'm asking you to do.

[karmic finch]

3 x 5 x 7^3

[vale wigeon]

would rather you used * instead of x...

,w factor 5145

[ocean seal]

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Requested by Ann#0413

[vale wigeon]

alright

now for a perfect square we would need all the exponents on the primes to be even

do you understand why that's the case?

[karmic finch]

not really

[vale wigeon]

if you have the prime factorization of n and you raise it to the second power to get that of n^2, all the exponents on each prime get doubled

[karmic finch]

ohh that makes sense

[vale wigeon]

so in our case we will need to multiply 5145 by another 3, and another 5, and another 7 to bump the exponents up to even numbers

thus

,w 3 * 5 * 7

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Ann#0413

[vale wigeon]

i meant to ,calc rather than ,w but you get my point

[karmic finch]

yea

[vale wigeon]

same idea applies to the other problem with the perfect cubes

except now you want the prime exponents to be multiples of three

[karmic finch]

thanks alot dude

[vale wigeon]

not a dude but yw

[hasty crow]

,calc 3*0

[ocean seal]

Result:

0

[carmine lion]

how do you solve an equation like this: x-e^x=0
is this a "non-standard" equation?

[junior blade]

For that one in particular, the lambert W function is literally designed for it

But

[carmine lion]

oh wait

fuck

i just realised

i literally proved

[junior blade]

There's no form in terms of "elementary" functions (what does that even mean?)

[carmine lion]

the function is below the x-axis

for all real x

what am i asking

😭

[junior blade]

Oh

True

I dont remember what the lambert w function is the inverse of then

[carmine lion]

lmao

[delicate tinsel]

How does the solution arrive at epsilon = 1/2?

[vale wigeon]

they do not

you can use epsilon = 1/3 instead if you want

[delicate tinsel]

hmm so epsilon can be any number?

[vale wigeon]

no, not any number

but for the purposes of this argument, any number between 0 and 1 will work

[delicate tinsel]

so just pick a number between the range of f(x)?

ok i get it now. it's due to the precise definition of limits.

[vale wigeon]

you're trying to see patterns where there are none

[delicate tinsel]

Is my understanding wrong then?

From my understanding, since the range of f(x) is bounded by (0,1), the value of epsilon has to be within the range of f(x)? like it can be any number greater than 0 but less than 1?

[jagged imp]

eps>0 is a requirement for the epsilon delta definition. eps<1 comes from the need for eps<|f(x)-f(x_0)|=1

[delicate tinsel]

oh okay, seems like my understanding is wrong.

[ivory otter]

supposed to prove the identity

not sure from where to go

tried using double angle identity

didnt work

[lyric cedar]

LCM?

[ivory otter]

tried

[lyric cedar]

How far? Where did you get stuck?

[ivory otter]

maybe i didnt

gonna try

[hidden mesa]

@ivory otter iam sending you the solution

[ivory otter]

no please

[lyric cedar]

Maybe simplify it to cotx = cot2x + cosec2x and square to see if LHS equals RHS

[ivory otter]

not solutions :d

no i cant use cot and stuff like that

[vale wigeon]

"can't use cot"?

[ivory otter]

i mean i can rewrite it actually

to 1/cos

[vale wigeon]

as in your teacher will commit abuse to you if you do that?

[ivory otter]

isnt that cot?

[vale wigeon]

cot is 1/tan.

anyway

[ivory otter]

As in he will say "i didnt say you can use this, we dont have this currently"

[vale wigeon]

$LHS = \frac{\tan(2x)-\tan(x)}{\tan(x)\tan(2x)}$

[ocean seal]

Ann

[hidden mesa]

@ivory otter your solution

[grizzled saffron]

Can anyone help with a circuit diagram analysis.. I'm not sure if this comes under math?

[hidden mesa]

no in physics

[grizzled saffron]

Oh okay thanks, do u by any chance know a phy help group?

[jagged imp]

#old-network

although its not specifically a help group, they do have help channels

same deal as this server

[surreal sun]

Hi, I have (x^n)^(n-k) and by that I mean x^n that we derivate n-k times
How can I transform this to have a * x^k ? I'm looking for a

[vale wigeon]

if you differentiated it k more times after that, you would have d^n/dx^n (x^n), which is equal to n!

but differentiating x^k, k times, would produce an extra factor of k!

[surreal sun]

ohhhhhhh i think i understand ! it's n!/k! ?

[vale wigeon]

yes

[surreal sun]

thanks!

[manic pasture]

may I ask a question?

our teacher had us watch a lesson video I couldn't understand one part

our lesson is about geometric series and I don't understand how she got the answer

I understand up until the substitution in step 2

[vale wigeon]

it sounds like someone mixed up "six" and "twenty"

and also massively messed up the arithmetic

[manic pasture]

yeah yeah so I tried solving it with 20 as the nth term but still got a different answer

[vale wigeon]

the answer they write is bullshit lol

,w 6 * (2^20 - 1)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[manic pasture]

do you also think it's wrong?

[vale wigeon]

is this what you're getting?

[manic pasture]

ooh I got the same answer

[vale wigeon]

6,291,450

[manic pasture]

yeah yeah

[vale wigeon]

yeah this is correct

the video's bad

[manic pasture]

oh ok ok thanks!

[manic pasture]

but isnt the 20th term 3,145,728?

[tulip pier]

Is this correct and is the working ok?

[vale wigeon]

the 20th term itself is... let's see

,calc 6 * 2^19

[ocean seal]

Result:

3.145728e+6

[vale wigeon]

yeah, it is

but you were asked for the sum of the first 20 terms

[manic pasture]

oohh ok thanks ann!

[reef dust]

First find the equation relating velocity and time
Then integrate it to get relation between displacement and time
Thus u can find the graph

[fringe robin]

what integral log(1+2mcos x+m^2)

[reef dust]

Is m a constant?

[fringe robin]

yes

[ionic jewel]

,w integral of log(1+2mx*cos(x)+m^2)

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by 兔子#6562

[fringe robin]

,w integral of log(1+2m*cos(x)+m^2)

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by BTS MONSTER#4444

[alpine sable]

pls helppppp

[placid zinc]

Which are you on? What is your thoughts on the problem?

[tulip pier]

the question is worth 2 mark though

and your given the starting point of the displacement graph

[reef dust]

The steps might seem lengthy but they are not
Btw ur graph will be parabolic and not a straight line

[ebon finch]

sry by mistake 😅

Does there exist a cubic function whose tangent at one of its points is also the tangent of another one of its points?

[vale wigeon]

no

for a polynomial to be able to have a tangent like that, you would need its degree to be at least four

[fringe robin]

The area of the region bounded by the lines x = 1, x = 2, and the curves x(y – e^x) = sin x and 2xy = 2sin x +x^3 is?

Main concern is how do i know how to draw such graphs

otherwise its ez

Nvm got it

[tulip pier]

so then the velocity graph is y = -4x+ 8 and the displacement graph is -2x^2+8x and the do y(2) to find end point right?

[reef dust]

Did u get the constant right ?
Cause I have not tried it yet

[tulip pier]

it passes the y axis at 8

[tulip pier]

but that doesnt make sense from those equation as the question gives when t=0 the displacement is equal to 4 meters

[reef dust]

There's a condition at t=0, x=4

[tulip pier]

nvm i am stupid soz

[reef dust]

Yea cause u omitted the constant of integration and directly put it 0

[tulip pier]

forgot the constant and the constant is 4

[reef dust]

👍

[tulip pier]

thx alot

[reef dust]

Wlcm

[tulip pier]

yeah i thought that was too long for a 2 mark question with so little working out space

[reef dust]

Never mind the marks
Mind the process with which we get the answers

[tulip pier]

Can you help with this one too I am so confused

[alpine sable]

,rccw

[reef dust]

The difference between max and min of the function is given to be 1.4

I think it should be easy frm here

[tulip pier]

idk how to set the working out though

like i understand at the minimum the sine graph gives -1 and maximum gives 1

[reef dust]

max of sin=1

So max of y=....

[tulip pier]

and when you get the maximum equation - minimum equation it gives 3 + k - (3-k)

[reef dust]

Exactly

[tulip pier]

k=0.7?

and to sketch the graph it is using tranformation?

[reef dust]

Yea

[tulip pier]

thx alot man

[reef dust]

Wlcm

[ebon finch]

oh okay... thank you... but how would u prove that tho?

[vale wigeon]

let $f$ be your polynomial function and suppose we have a line $y = mx + b$ which is tangent to $y = f(x)$ at $x = c_1$ and $x = c_2$

[ocean seal]

Ann

[vale wigeon]

what i say is that the polynomial $g(x) = f(x) - mx - b$ must have $c_1$ and $c_2$ as \textbf{double} roots

[ocean seal]

Ann

[ebon finch]

ohhhh

[vale wigeon]

this means $g(x)$ must have $(x-c_1)^2(x-c_2)^2$ as factors, and hence $\deg(g) \geq 4$

[ocean seal]

Ann

[ebon finch]

okayy... got it... thank youu

[exotic mortar]

how do I do this

[vague coral]

binomial formula maybe

[exotic mortar]

How tho

itll be very long

[vale wigeon]

what i would do first is massage this a bit

you don't need the whole expansion

$\paren{x^3 - \frac{3}{x}}^8 (3x^2 - 2)^2 = x^{-8} (x^4 - 3)^8 (3x^2 - 2)^2$

[ocean seal]

Ann

[vale wigeon]

this is what i would do first and foremost

do you understand what i've done here so far

[exotic mortar]

Yep

[vale wigeon]

we need the x^12 term in (x^4 - 3)^8(3x^2 - 2)^2

[exotic mortar]

I lost you here

is it x^-8 +*x^12

which gives you x^4

[vale wigeon]

once we get the x^12 term in (x^4 - 3)^8 (3x^2 - 2)^2, it'll become x^4 when multiplied by the x^-8 i pulled out

yes

[exotic mortar]

ok Im with you

[vale wigeon]

we can expand (3x^2 - 2)^2 into (9x^4 - 12x^2 + 4)

[exotic mortar]

yep

[vale wigeon]

so now take another look

(x^4 - 3)^8 (9x^4 - 12x^2 + 4)

how can we get an x^12 term from this?

we can either get an x^8 term from the first parenthesis to multiply with 9x^4
or an x^12 term from the first parenthesis to multiply with 4

no other way

[exotic mortar]

can we split the first parenthesis in (x^4-3)^3 * (x^4-3)^5

[vale wigeon]

that would be pointless

[exotic mortar]

kk

ty

[cloud kiln]

Domain and range of f(x) = (x^2 - 3x - 4)/(x+1)

I cant calculate the range

I got domain = (-inf, -1) U (-1,inf)

[vale wigeon]

take (x^2 - 3x - 4)/(x+1) = k and find the set of all k for which this equation has a solution

it reduces to a quadratic so you can use the discriminant trick