help-38

[dense zephyr]

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[gritty echo]

hi

[gritty echo]

I need help in solving this

<@&286206848099549185>

[split chasm]

where be are you stuck

[gritty echo]

I am just not sure what to do in that topic

I don't know how to start

oh

can you get your own channel #❓how-to-get-help

[split chasm]

consider the relation between the central angle and the measure of be an arc

[brisk ledge]

probably have to use the arc formula to work it out?

[split chasm]

and apply basic angle sums

[vivid sage]

what

how

[gritty echo]

it's fine

thank you @brisk ledge @split chasm I now got an idea

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[real bay]

If (2,4) is a point on f(X)=X^3-2X^2+2X then what is (f^-1)'(4)

[real bay]

im lost on how to implement this into a point

[split chasm]

look up derivative of the inverse function

[real bay]

ok

[split chasm]

(do not try to explicitly get the inverse function)

[real bay]

just making sure that when im getting the inverse that's just when it becomes the original equation as a fraction with 1 on the top?

so the inverse of it would be 1/(X^3-2X^2+2X) and i just need to get the derivative of that

[austere cedar]

No haha. That's the reciprocal, not the functional inverse.

[real bay]

oh

[austere cedar]

An inverse of x² is √x
An inverse of sin(x) is arcsin(x)
An inverse of e^x is ln(x)
ect

The functional inverse of a function is the "undo" of that function

You will never get the inverse of your function. However, you don't need it.

[real bay]

just making sure i understand this the inverse of X^3 is 3rootX

[austere cedar]

Yes, the inverse of x³ is ³√x

[real bay]

ok

[austere cedar]

Note that inverse isn't something that splits over +

[real bay]

also if i dont need the inverse what do i need to do with it

[austere cedar]

Well, you just need the derivative of the inverse at some point x = 4

Which is not the same as actually needing the inverse

There's a theorem that does this well

[real bay]

so the inverse would be something like ³√x - √2x + 2x

?

(f^−1)'(a)=1/(f'(f^−1(a)))

is this the theorem?

i found it in my notes around this question

ok so would the derivative be -(1/(√2√x))+(1( ³√3x)) + 2?

[austere cedar]

No it wouldn't. Like I said, can't just split the inverse over +

[austere cedar]

That is the theorem. Basically, if you know the slope of the normal curve at a point, then you know the slope of the inverse curve at that point.

[real bay]

oooh that makes a lot more sense

@austere cedar thanks for the help that was the thing that wasnt clicking but i got the answer on the answer key.

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[zenith scaffold]

Do you have an idea of what x^3 -1 looks like in the plane?

Then start by taking a look at with desmos or smth

Then go to the 3D case and convince yourself that since y doesn't appear in the formula for z, you're essentially just going to see x^3-1 being Ctrl c Ctrl v'd as you "walk along" the y-axis

Might want to use geogebra as you suggested

Helps with intuition down the line

Draw what's in between the two y planes you placed

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[viscid quest]

guys what do you call these things

[viscid quest]

also this thing looks incomplete, where can i find complete symbols

[obsidian tree]

They relate to logic. \
$\implies$ for implication. \ $\iff$ for equivalence

$\lnot$ is another symbol for logical not

[solid kiln]

ShatteredSunlight

ShatteredSunlight

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[gritty cloud]

how do i formalize this matrix, using $a_{n,k}$ with $(n,k) \in \mathbb{N}^2$

[solid kiln]

lewis

[scarlet escarp]

"upper triangular with main diagonal values of 1 and $a_{i,j} = -(\frac{1}{2})^{i-j}, j>i$"

[solid kiln]

maximo

[scarlet escarp]

that's my best attempt

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[ocean mural]

Do you mean i>j

Or j-i perhaps

[scarlet escarp]

a_i,j is the ith row and jth column

[ocean mural]

If j>i for eg j=2 and i=1
We get -(1/2)^(1-2) = -(1/2)^(-1) = -2

[scarlet escarp]

ah right, then either j-i like you said or just (2)^i-j

[ocean mural]

Yeah

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[gritty cloud]

sorry, i wasnt here, i don't really get how that would work out

[scarlet escarp]

what do you mean by formalize

[gritty cloud]

so its 2^i-j

[gritty cloud]

like can i represent the matrix with just one formula?

like e.g. a_n,k

=

something

[scarlet escarp]

i couldn't

what i sent is about as close as i can get it

[gritty cloud]

oh

i mean it's okay to have like different cases

[scarlet escarp]

then take the cases of i > j, i = j, and j > i

[gritty cloud]

for i = j, set 1?

right?

[scarlet escarp]

yes

a_i,j where i > j, a_i,j = 0

[gritty cloud]

for j > i, it's 0

oh wait

[scarlet escarp]

i'm assuming i is the row

[gritty cloud]

other wait arround

yeah

i > j = 0

and for j > i

it's what you said, i suppose?

[scarlet escarp]

and finally j > i -> a_i,j = -2^(i-j)

that's assuming you divide by 2 every time

it could be -1/(2(j-i))

[gritty cloud]

yeah, i see

hold on

okay, got it

thank you, tho ^^

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[icy ether]

hi

[icy ether]

ik the answer, im just checking it is right

is it 3 pi

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[hushed dock]

hi im not sure how they got the answer on this one, this is discrete math and the topic is Big-O notation

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[hushed dock]

im just taking the room at this point

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[hybrid coral]

Hey, im trying to solve this pyhtogoras. Would hugely appreciate if someone knows how to solve it.

[alpine jetty]

ADC is similar to a different triangle than the one in your claim. ADC is a right angle and BAC is a right angle. What about the angle ACD?

Is it in two triangles (then apply AA)

[hybrid coral]

Thank you

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[random fox]

i need help, do i use the true method for all those question?

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[feral hornet]

could someone explain why he has squared the entire question?

[trim lichen]

wym

[sacred dew]

it's already squared

he just rewrote it

[feral hornet]

in the original question only the denominator is squared

[sacred dew]

1^2=1

[trim lichen]

1/x^2 and (1/x)^2 are the same

[feral hornet]

yep i get that, i am guessing he has just done it to make the working out a little easier?

you could only do this for an expression where the numerator is a square right?

[honest rock]

yes

[sacred dew]

i mean you can get root

still works

[honest rock]

bit more complex but yeah

[feral hornet]

mhm, I want more questions like this to practice are they on khan academy or youtube or something similar?

[sacred dew]

probably, though i have no idea the goal of your original problem

[feral hornet]

its okay, thanks

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[fresh sphinx]

Pretty simple question but is this quadrilateral a parallelogram? Don’t assume anything (no right angles and such.) I’m just confused because if the congruent signs were on different segments then it would be a parallelogram. Sorry for the crude drawing

[lethal musk]

no.

[fresh sphinx]

Thanks!

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[wraith hinge]

i dont understand how i would substitute

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[wraith hinge]

I need help with this question

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[viscid ridge]

Can someone help me understand why #1 is an invalid argument and #2 is a valid argument

[viscid ridge]

I just applied the rules

But I don't really understand why

it makes no sense to me

conclusion

[gentle zenith]

$\therefore$

[solid kiln]

Mosh

[viscid ridge]

Like, if you say 'all of unrelated y' it's invalid, but if you say some of unrelated y, it is valid

not really technical

I don't understand the reason

logically speaking

no

I mean, as a conclusion, still not really

no, not really

So you just assume that x = y?

I think I get the reason now, because you only know some x are a, you can't really say that all y are a. But if all x were A, you could say All y are A, right?

I don't necessarily get the last part, but I think I get the reason more now

[viscid ridge]

Is this true btw?

But how do you know it's not sushi, I guess you can just assume anything right?>

As long as you have nothing to prove you wrong

Alright, moral of the story, if your premises suck, you can assume anything 😅

Well, if you wanted to not have this happen, you'd have to specify than x can't be y right?

I don't think I'll get it properly

not gna lie

It makes a bit more sense now

but sheesh

Seems valid to me

I mean it makes more sense now

Yeah, it makes a lot more sense. It's very, very, abstract.

Thanks!

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[oak wren]

hello

[oak wren]

i just have a quick question:

okok

would i be right since

integral would be the main function

so it has to be an increase

and it would not be first five years

but years 5 to 10

so the only answers right can be 1 or C

A or C*

im unsure if its rate of growth gotten from this intergal of a derivative or the increse/decrease

yes, thats what i was thinking

ok

the c right?

yup

ok, thanks

well just say that was 30 seconds haha

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[toxic swift]

I would like to know how I would find the period for this function?

[toxic swift]

The full graph isn't shown so I don't know what it could be

nevermind I found out

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[toxic swift]

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✅

[toxic swift]

how would you find the d value? (Phase shift)

[tawdry sinew]

Uhhhh is x theta?

[toxic swift]

yes

[tawdry sinew]

This is a normal sin graph

as you can observe, the origin is when x=0,y=0, and the slope is positive

[toxic swift]

yes

[tawdry sinew]

So we can shift a function $f$ to the right $d$ units by doing $f(x-d)$

[solid kiln]

KurtDee

[tawdry sinew]

So yeah, what are the coordinates of the shifted center

[toxic swift]

(4,0)

[tawdry sinew]

I think it's more (4,2.5)?

but yeah that's the idea

it's 4 shifted right

[toxic swift]

oh wait yea

myb

ok but

why is it not 1?

[tawdry sinew]

What's special about 1

[toxic swift]

idk its just the first point

[tawdry sinew]

So sin(x) isn't centered about the minimum

I'm not really sure how to explain it except by saying "that's not what it is"

[toxic swift]

oh ok

its fine

ty

[tawdry sinew]

Like if you shift it left only one

it's just like

not enough

that's not where sin(x) is centered

[toxic swift]

oh ok

ty

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[arctic wolf]

Given point A and B on circle $$x^2+y^2-6x-2y+k=0$$ where tangent lines on point A and B cross at point C(8, 1). If the area of a quadrilateral that goes through point A, B, C and the center point of the circle is 12 square units, what are the possible values of k?

[solid kiln]

Hyperlix

[arctic wolf]

since A and B are both tangent to the circle, that means r = PA = PB (P = Center Point)

and since we know the center point of the circle, we can find the radius which is equal to $$\sqrt{10-k}$$

[solid kiln]

Hyperlix

[arctic wolf]

and PC = 5 since the center point is (3, 1) and C(8, 1)

since PA = PB = r where A and B are tangent to the circle, that means triangle PAC or PBC is a right angle triangle

so we can use the Pythagorean theorem here, $$(PA)^2+(AC)^2=(PC)^2$$

[solid kiln]

Hyperlix

[arctic wolf]

since we have the values of both AP and PC $$AC = \sqrt{15-k}$$

[solid kiln]

Hyperlix

[arctic wolf]

and since we know the area of the quadrilateral is 12 square units, we can make that equal to $$2\cdot\frac{1}{2}\cdot(PA)(AC)$$

[solid kiln]

Hyperlix

[arctic wolf]

since triangle PAC is a right angle triangle and there are both of them, that makes the quadrilateral a kite

but here, when you plug in the numbers, we have no real solutions, why is that?

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[arctic wolf]

<@&286206848099549185>

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[arctic wolf]

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[untold cave]

hey, i want to check my answers on this to see if i really understand it

[untold cave]

these were my solutions

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[untold cave]

<@&286206848099549185>

[ionic lance]

this is what i got idk if its correct

[untold cave]

probability cant be bigger than 1 right ?

besides your P(A1) = 0.10 and you write 0.70 in the last step

[ionic lance]

bruh

i messed up the A

[untold cave]

looks good other than that ?

[ionic lance]

ye ok ur right

i just started with prob lol

[untold cave]

yeah i did the same first

so i started to wonder if i was doing it correctly

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[eager skiff]

The number of people inside a city doubles every minute. After 5 minutes half of the population dies. After 6 minutes we have 160 people. How many people do we have at the start?

[unkempt fox]

Write x as population at start

f(x) happens every minute and its f(x) = 2x

g(x) happens every 5 mins and its g(x) = 1/2x

Now write an equation

The functions are probably useless

[eager skiff]

But just by logic, at 5 minutes didn't we have half the population of what we have at 6 minutes?

[eager skiff]

wait i don't understand, do i have to make for example, y=2x z=1/2x

[unkempt fox]

Indeed

Just multiply x by 2 and divide by 2

x * 2 * 2 * 2.... /2 / 2 / 2 = 160

[eager skiff]

I see thank you once again 🙂

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[summer dirge]

hello

[summer dirge]

I would like to start by proving that if the curves have exactly one common tangent, then they must touch each other

I believe that we have to use long algebraic expression derived in the part just before

One idea that I had was by considering the discriminant

But in order to show that they touch each other, I believe $b_1=b_2$ and $c_1=c_2$

[solid kiln]

azeem321

[summer dirge]

In order for this to happen, I think we need an expression of the form $(b_1-b_2)^2 + (c_1-c_2)^2=0$

[solid kiln]

azeem321

[summer dirge]

However, there are no squared c1,c2 terms in the discriminant hence we won't arrive at after expanding it out. So I am stuck

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[summer dirge]

did i make any algebra slips

this is the discriminant

[wraith hinge]

asking someone to check that algebra is crime

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@summer dirge Has your question been resolved?

[summer dirge]

nvm algebra mistake great..

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[cerulean hemlock]

Hi! I have a physics question, I hope it's not a problem.
We have a body in motion that must reach another motionless one. The body moves at acceleration a = 1 / d², d is the distance between the two bodies. Is it possible to find the time it takes for the moving body to reach the other?
It's a question that was asked to me by a friend of mine and I cannot find an answer with my knowledge (just got to integrals)

[austere cedar]

This is a differential equation:
d²x/dt² = -1/x²

We are looking for some function x that when subbed in, gives a true result

[cerulean hemlock]

Oh, I don't know how to solve those D:

[austere cedar]

Even worse, I don't believe this has a closed form

,w solve d^2x/dt^2 = -1/(x^2)

[solid kiln]

Results provided by WolframAlpha

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

Requested by Kaynex#7520

[austere cedar]

Nvm I lied that's very solvable

[cerulean hemlock]

f, seems way too advanced for me

[austere cedar]

Me too lol

[cerulean hemlock]

btw I remember you @austere cedar , you recommended me to learn abstract algebra or calculus

[austere cedar]

Yeah! I remember.

[cerulean hemlock]

I couldn't find any good books in my language for abstract algebra, so I went with calculus, doing great ^^

Well, thanks a lot anyways

Cya!

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[fierce latch]

help me please

[fierce latch]

been thinking for like an hr

[lapis bolt]

what have you tried?

[fierce latch]

oh wait figured it out

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[wraith hinge]

I get the integral as ln t from 1 to x. Plugging that in I get ln x-ln1. Ln 1 is zero so I know that lnx should be the ultimate answer.

The first log property is ln(p/q)=lnp-lnq
We can cleanup L with this as

Ln(x/1)=lnx-ln1=ln x

The second log property is ln(pq)
The third is ln m^p=p ln m.

How do I apply the product and power rules for this?

[wraith hinge]

ln(x×1) = lnx+ln1 = lnx
ln(x¹) = 1ln(x) = lnx
Is this good ?

[wraith hinge]

Isn't L=lnx-ln1?

I can see the power rule with the 1 working. How does that make a sum though?

Sorry if that's a dumb question.

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@wraith hinge Has your question been resolved?

[wraith hinge]

Almost. I just want to know how that becomes a sum for the product rule. Or if it's just showing that it works with ln x as a function.

[covert prairie]

are u sure u are allowed to integrate directly?

[wraith hinge]

As far as I know.

How would I show it otherwise?

[covert prairie]

i assume they want u to prove it without knowing the fact that the integral is ln(x)

[covert prairie]

u can

consider L(ab)

split the integral at t=a

and substitute t as 'ua' in the 2nd integral u get

u should notice what's happening then

[wraith hinge]

I see. Thank you. Will try working it out that way as well.

[covert prairie]

yeah

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[vernal beacon]

hi

[vernal beacon]

14.5% bigger right?

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[eager skiff]

What am i doing wrong?

[split chasm]

wheres xy = 5 coming from

[eager skiff]

wait you are right its x+y=5

now in the second equation i am left with 0=20

what am i missing now.. 😦

I get 0=20 because, x=5-y ---> (5-y)^2-y^2=5

Waiiiit

i'm stupid

Understood the problem, thank you Ramonov 🙂

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[lunar atlas]

how would i measure the surface area of a random object?

[lunar atlas]

a water bottle for example

not the normal cylinder ones

one which is thinner in the middle

so there's absolutely no way we can divide it in recognizable parts

[deep bridge]

multi variable calculus technically

[tepid hamlet]

Surface integral if you have a way to describe the surface as some equation

[deep bridge]

but surface area is weird because ur trying to measure a 2d space in a 3d world

[lunar atlas]

yes

[deep bridge]

so on curves it can be argued that surface area is infinite

[lunar atlas]

okay

but all i was trying to see was how well stefan's law applies

i put my water bottle in the refrigerator for cooling and study its rate

and compare it with stefan's

but the first problem i faced was surface area

[tepid hamlet]

Yeah measuring the surface area of complex objects isn’t really a trivial problem

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@lunar atlas Has your question been resolved?

[lunar atlas]

my basic motto is to see how well stefan's law and/or newton's law of cooling works

i can do that by simply changing to a simpler container

but after that i also want to predict the temperature curve of my bottle inside the fridge

you know, like a side project of some kind

anyways

thank you for bothering

i'll ask later if i still face difficulties

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[hidden grove]

Hey, hope you're doing well. I need help on this question. It's just revision so I have worked solutions but I do not understand them either would massively appreciate if someone could help me understand 🙏

[dapper bloom]

i can explain the solution if you send it as well if you want me to help you with how your professor solves some things

@hidden grove

[hidden grove]

Ah yeah sure

[dapper bloom]

voice chat is preferred if you dont mind, it helps me explain better

[hidden grove]

Uh yeah i sadly cant respond back in vc if thats ok?

actually

maybe i can

[dapper bloom]

well if you can hear me

its fine

[hidden grove]

Give me a few if thats ok?

[dapper bloom]

and we can talk here

yeah sure just ping me

[hidden grove]

Alrighty thanks

@dapper bloom okay im back

[dapper bloom]

join somewhere and ill come

[hidden grove]

alright

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[ionic atlas]

{ \left( { x }^{ 2 } +x \right) }^{ 3 } = { x }^{ 3 } \left( x+1 \right) ^ { 3 }

[steel osprey]

epic fail

[ionic atlas]

Is this correct? xD

[steel osprey]

idk

[acoustic ravine]

Yes

It is

[ionic atlas]

Ah ok thanks

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[acoustic ravine]

Loooool

[ionic atlas]

Haha

[steel osprey]

W

[acoustic ravine]

Any% WR

[steel osprey]

What

ok wait

[ionic atlas]

Are you writing a book, aol?

[steel osprey]

$(x+y)^3=x^3+3x^2y+3xy^2+y^3$

[solid kiln]

aol

[steel osprey]

No im on mobile

[acoustic ravine]

Bro just factor x

[steel osprey]

just need the formul

Fo

[acoustic ravine]

Bruhhhhhh

[steel osprey]

Nah nevermind im not writing that on mobile

[acoustic ravine]

Bro

Factor

X

[steel osprey]

Oh

Sorry didnt see

[acoustic ravine]

Lol

[acoustic ravine]

^

[ionic atlas]

Why is this still in the occupies category?

*occupied

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[floral cradle]

can someone help me on 8 (c)

the mean is 2 per page

does the mean change if the question ask for two pages?

[wraith hinge]

is this the poisson distribution ?

[floral cradle]

yep poisson distribution

[wraith hinge]

So c is the probability that there are 4 mistakes in two pages, that's either (1 mistake in one page AND 3 mistakes in another) or (2 mistakes in each page) or ( 4 in one page and no mistake in another)

maybe this is how we should do it

[floral cradle]

damn

[wraith hinge]

these events seem independent I think

so the probability of their union

is the sum of the probabilities of each event

[floral cradle]

I have the answer given by my teacher

how do I start

[wraith hinge]

Ah, so are we right then

[wraith hinge]

calculate the probability of each of these events

you calculate them using the same definition you used in a and b

of poisson distribution

[floral cradle]

I see

but there should have either greater than and lower than symbol right?

[wraith hinge]

not necessarily we know how to calculate $\mathbb{P}(X=k)$ when X is a poisson process

[solid kiln]

AimaneSN

[floral cradle]

ohh

so let say the first event 1 mistake in one page and 3 mistake in another

so I should calculate P(X=1), after that I sum with P(X=3)

right?

[wraith hinge]

No because here you don't have a union of probability (OR), you have an intersection (AND), and since these events are assumed independent $\mathbb{P}(X=1, X=3)=\mathbb{P}(X=1) \cdot \mathbb{P}(X=3)$

[solid kiln]

AimaneSN

[floral cradle]

O

multiply it?

[wraith hinge]

yes, but you sum in the end

after you calculate the probability of each possibility

because (A or B) is union

[floral cradle]

ah I see

aight thank you @wraith hinge for the help!

[wraith hinge]

U welcome!

[floral cradle]

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[clever wharf]

Does anyone know how to prove this by induction?

[trim lichen]

$\sum_{r=1}^n S_{\gamma}^r = \frac{S}{4} (5^n - 1)$?

[solid kiln]

Ann

[trim lichen]

is this what that says?

[clever wharf]

5^r not S^r

And 5/4 instead of s/4

[trim lichen]

and what about that subscript on the 5?

[clever wharf]

Oh just a scribble

[trim lichen]

right, so in that case isn't this just a geometric progression

[regal atlas]

hi

[clever wharf]

Yeah the first 3 terms are 5,30,155 i think

[trim lichen]

i mean that surely you can just copy-paste the argument for the geometric series formula if youve seen that before

or you could do what you do for any proof-by-induction for summation and look at the difference between adjacent terms of the sequence as given by the summation and as given by the formula, and verify they're the same

i.e. to prove $\sum_{k=1}^n a_k = f(n)$ you prove $$a_1=f(1)\quad\mbox{(base)}$$ and $$f(n)-f(n-1)=a_n\quad\mbox{(inductive)}$$

[solid kiln]

Ann

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[eager skiff]

why is xy=k a hyperbola? Shouldnt xy values have an exponential of 2 and one of them be negative?

[deep bridge]

same graph

but top is multiplied by y on both sides

[eager skiff]

I dont understand how we go from this $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=k$

to what you wrote

[solid kiln]

Lyuka

[deep bridge]

you can do the reverse by just dividing by y

[eager skiff]

Okay, i understand (from you formula) that we have x=-2*1/y

wait

okay, i understand that if we do what you wrote, we end up with a negativa y

but they dont have 2 as exponential

[deep bridge]

wait did you mean parabola or hyperbola

[eager skiff]

hyperbola

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@eager skiff Has your question been resolved?

[eager skiff]

<@&286206848099549185>

[zinc ginkgo]

have you rotated conics before?

[eager skiff]

No, never

[zinc ginkgo]

then you won't understand the answer to this

[eager skiff]

I see, thank you for the input tho

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[limpid scarab]

#calculus I need Help with this hw probrem with integration indefinite integrals. Essentially adding the last 2 integrals and I already got both the antiderivatives. I got my answer wrong.

[limpid scarab]

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[tall badge]

Hi

[tall badge]

I have a question from my computing class

The On-Safari project involves the re-development of an existing website. The park is concerned that the overall project should complete on time, so they have imposed a £50,000 penalty clause for late delivery of the On-Safari project. Pemberley Solutions, the consultancy who have been employed to develop On-Safari, estimate that the likelihood of the website re-development overrunning as 10%. They can reduce the likelihood of this occurring to 2.5% by employing a freelance web developer to work on the more technically demanding parts of the website redevelopment, at a total cost of £10,000.

Calculate the risk reduction leverage for the risk reduction action of employing the freelance web developer to work on the website redevelopment for the On-Safari project.

[mighty cosmos]

https://cdn.discordapp.com/attachments/756558609806000139/972367307160563732/Fish_yodel.mp4

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[uncut latch]

i can get those two

shouldn't alpha = theta?

am confused

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[uncut latch]

i misunderstood q like a fool

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[wraith hinge]

.open

[mighty dune]

let xyz zxy yzx be three digits numbers that form an arithmetic progression

[mighty dune]

got no idea how to solve or where to start

[upbeat lynx]

x, y and z are the digits right?

[mighty dune]

yep

so xyz,zxy,yzx is an arithmetic progression

[lunar atlas]

write xyz=100x+10y+z

might help

[mighty dune]

why tho

im bad at math so...

oh alr i got it

i mean i got why its written like that

[random citrus]

it's a form which we're more accustomed to work with

for example it would be difficult to say something about xyz + zyx

[mighty dune]

so the progression has to be done in this form

for each number

+d and 2d for the last

[random citrus]

sure

make some equations

[mighty dune]

what equations forex

for example

[random citrus]

2nd number - 1st number = 3rd number - 2nd number = d

[mighty dune]

alr let me try

should i do 2nd number -(1st number)

or are ( not needed

nope im stuck

[mighty dune]

with this

[gaunt echo]

@mighty dune arithmetic progressions go like a, a+d, a+2d

[mighty dune]

ik

[gaunt echo]

What are u stuck on tho

[mighty dune]

.

[gaunt echo]

Converting that to the problem?

[mighty dune]

i guess

[gaunt echo]

xyz = 100x + 10y + z
zxy = 100z + 10x + y
yzx = 100y + 10z + x

So

[mighty dune]

ooh

do i solve that

alr wait

[gaunt echo]

No no

Look

[mighty dune]

ok

[gaunt echo]

zxy - xyz = yzx - zxy = d

[gaunt echo]

Substitute these into the above equation

then hopefully you can find d

[mighty dune]

how

[gaunt echo]

Like

[mighty dune]

i said im bad lol

[gaunt echo]

No it’s fine

Look

zxy - xyz = yzx - zxy = d
(100z + 10x + y) - (100x + 10y + z) = (100y + 10z + x) - (100z + 10x + y) = d

[mighty dune]

i did this

[gaunt echo]

Now simplify it and see what you get

[mighty dune]

alr wait

[gaunt echo]

(Do you understand what I did there)

[mighty dune]

yep

D=189z -79x-108y

can u check pleaase

and how does this help

[gaunt echo]

I got

[mighty dune]

..

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[pine hound]

can someone help me solve this

[compact ore]

Learn how to screenshot first L bozo

[granite thunder]

Have u started anything?

[pine hound]

no we learned it today and i’m still confused

[granite thunder]

So start with the first sentence

Plug in f(x) where y is

Vice versa

So u have

Y = 9x^2

Right?

[pine hound]

yes

[granite thunder]

Now solve for x

[pine hound]

do i divide both sides by 9

[granite thunder]

Yes

[pine hound]

i got

y/9 = x^2

[granite thunder]

Yes

Now u need to get rid to the square

[pine hound]

so we put it in square root

?

[granite thunder]

Yes

So what is it simplified?

[pine hound]

x = y/9

[granite thunder]

Root y/3

Does that make sense ?

U need to square root the y and the 9

[pine hound]

ohh yes

[granite thunder]

Now reread the second part

And follow through

[pine hound]

wait so i square root y and 9 as the fraction or separately?

[granite thunder]

It would look like root y over 3

[pine hound]

ohhh

[granite thunder]

You can take the square root separately like root y and root 9, but u keep it as a fraction.

[pine hound]

ok i get it now

[pine hound]

so would this be the answer

[granite thunder]

Well u need to solve for x

Knowing that y is 2

[pine hound]

so then basically it’s square root 2/3

[granite thunder]

Yes

Equals x

For the first box

And second one

For the first box u actually might just keep it with the y

The instructions are unclear

[pine hound]

i’m pretty sure for the first box you just have to solve for x without plugging in 2 and for the second box u plug in 2 for y

[granite thunder]

That would make sense

[pine hound]

yeah

so what would i put for both of the boxes

[granite thunder]

What u said?

The expression u made with y for the first one

And the one with 2 on the other

[pine hound]

ohh okay tysm

[granite thunder]

No problem

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[quaint pendant]

i dont even know where to start

[lapis cairn]

first what would sin be

[quaint pendant]

opposite over hypotenuse?

idk

[lapis cairn]

in terms of cos

[quaint pendant]

i dont know honestly

[lapis cairn]

what is sin^2 + cos^2 @quaint pendant

[quaint pendant]

im sorry i still dont know

[lapis cairn]

ok what is a^2 + b^2 in a right triangle

a^2 + b^2 = ?

[quaint pendant]

hypotenuse to the power of 2

[lapis cairn]

yes

a^2 + b^2 = c^2

[quaint pendant]

right

[lapis cairn]

so if a is opposite, b is adjacent, and c is hypotenuse

opposite^2 + adjacent^2 = hypotenuse^2

if you divide by hypotenuse^2 you get (opposite/hypotenuse)^2 + (adjacent/hypotenuse)^2 = 1

now what is opposite/hypotenuse

[quaint pendant]

sine

[lapis cairn]

yes

and adjacent/hypotenuse = cosine

[quaint pendant]

so i solve for cosine first and then get sine?

[lapis cairn]

so sin^2 + cos^2 = 1

now what is cos^2 given cos in the problem

[quaint pendant]

?

squared

[lapis cairn]

yes

square it

[quaint pendant]

hold up

-11/36

[lapis cairn]

no

square is not negative

so 11/36

sin^2 + 11/36 = 1

sin^2 = 25/36

[quaint pendant]

ok

[lapis cairn]

sin = +/- 5/6

now how do we know if sin is positive or negative

[quaint pendant]

wait

if you passed the +11/36

why does it turn 25/36

[lapis cairn]

subtract 11/36

[quaint pendant]

shouldnt it subtract

[lapis cairn]

both sides

1 - 11/36 = 25/36

[quaint pendant]

right my bad

my god

[lapis cairn]

so sin = ± 5/6

how do we know if sin is positive or negative

[quaint pendant]

unit circle?

[lapis cairn]

yes

and what is the interval

pi <= theta <= 3pi/2

which is quadrant 3

y is negative so sin is negative

sin = -5/6

@quaint pendant use these values of sin and cos to determine the rest trivially

[quaint pendant]

alright, i think i got it.

Tysm

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[solar sun]

hello, so I got some doubts
we had this in a exam and my answer here was y = (12x+7)/5 and x = 39, but my teacher said it was wrong...
Is it?

[solar sun]

I entered that in wolframalpha and it matches

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[solar sun]

<@&286206848099549185>

[split chasm]

it's x**+**2
not -

[solar sun]

oh, silly me, thank you!

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[teal juniper]

How do I prove that if a number divides a number, it also divides the negative of that number?

[median fossil]

assume a divides b

we know that a divides 0

so a divides b-b

and since a divides b, it must divide -b

[shell barn]

-b = b - 2b

Thats what I think you're trying to get at

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[teal juniper]

how do I move an absolute value sign from one side to the other

So I'm trying to go from

|x| = y-1

to x = something

[shell barn]

The inverse of the absolute value function is +-

[teal juniper]

so x = +-(y-1)?

[shell barn]

Yes

Two possibilities

Either + or -

[teal juniper]

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[narrow hornet]

Your answer will have two parts for x<0 y= -x-1 and for x>0 y=x-1

Or you could say for x<0 x=y+1 and x>0 x= -(y+1)

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[fresh tangle]

im having trouble isolating an algebraic term in a really funky equation

[strange quartz]

Post it

[fresh tangle]

you can ignore the paragraph at the top

but i need to find Jw by itself cause this is part of a larger coding assignment that this is just the tip of the iceburg for

my first thought was to take the natural log of both sides to try and get to the Jw's that are powers

but im left with this

so i suspect that isnt what i'm meant to do

i've never seen an equation quite like this and i could find any answers by googling stuff like "equation of water flux in membrane"

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[covert prairie]

u could differentiate this twice wrt Jw

u'll get something but u might end up losing some constants

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[umbral dirge]

If you for example have the equation: -x=ln5-ln7+3

[umbral dirge]

To find x can you just change all the minus and plus symbols?

so x goes plus, ln5 goes minus

etc

so it will be x=ln7-ln5-3

[vivid scarab]

Yes, that's the result after multiplying both sides by -1

[umbral dirge]

true

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[lapis bolt]

If I had a random number generator that generated a real number between 0 and 1, and I generated 2 numbers would the probability that they are equal be 0? since there are infinitely many real numbers between 0 and 1

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[shrewd ridge]

in real software they are finite

[trim lichen]

yes

[shrewd ridge]

also i've seen something like, you can't have uniform distribution like that in the first place

i'm confused on that

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[jovial pulsar]

In an ideal-case scenario, yes. Each point on the interval [0, 1] appears with a probability of 0... but that doesn't mean it can never appear.

Measure Theory Be Trippy.

[lapis bolt]

i see thanks

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[stiff locust]

is the range right?

Oh I see.. nevermind

that makes sense since it's ordered least to greatest

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[west whale]

To see if the function is continuous check the limit at x=0

Then check is there are gaps in the function

if the limit exists and that there are no gaps the function is continuous

[rigid gull]

Yes. but the last 2 lines aren't correct

[wind saffron]

Why?

[rigid gull]

Because $\lim_{x\to 0} (x^2 - x) \neq -x$

[solid kiln]

Si Arya

[wind saffron]

Why?

[rigid gull]

It should be 0² - 0 for the left hand side. And for the right hand side, its √0

[wind saffron]

Aah

Then the function is continuous because the lateral limits are equal

[rigid gull]

Almost. Make sure that
$$f(0) = \lim_{x\to 0} f(x)$$
Which is easy

[solid kiln]

Si Arya

[wind saffron]

Eeh

[rigid gull]

And it proves that there is no gap at x = 0

Just take the derivative of f(x) for x ≤ 0 and x > 0 individually and take the limit of f'(x) as x goes to 0, i guess

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[little condor]

how do i do a)

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[foggy summit]

Ignore the 1000

[deep bridge]

how many possibilities are there for the first digit

that work

[foggy summit]

How do you mean?

[deep bridge]

what digits would fulfill the requirement for "the first digit is odd"

[deep bridge]

^

[foggy summit]

Sorry but I don’t understand you

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[modest tapir]

Find the eqn of the elipse whose foci at (4,6) and (-6,6) one vertex at (5,6)

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[modest tapir]

Pls help guys

<@&286206848099549185>

Help

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[zealous remnant]

I need help solving Logarithmic Equations

[upbeat lynx]

which one?

[wraith hinge]

you need to know the basic laws of logarithm

[upbeat lynx]

$$log(ab) = log(a) + log(b)$$
$$log(\frac{a}{b}) = log(a) - log(b)$$
$$log(a^b) = blog(a)$$

[delicate jasper]

true

[solid kiln]

Doggo

[wraith hinge]

these are the basic laws yeah^

[upbeat lynx]

those are all you need from what I can see

you also need to know how to write radicals as exponents + basic exponent rules

[zealous remnant]

Oh okay

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[wraith hinge]

yo

[glossy gale]

How do I find the reference point for problem #1?

[wraith hinge]

light work

[wraith hinge]

stick it up ur bum

and charge ur phone

[glossy gale]

Lol

Are you a troll?

Anyways

I tried doing 1/a which got me 2

Then add that to c which is -4

Then the y value is -3

So (-2, -3)

Is this correct?

[glossy gale]

@hasty heron is this a troll?

[wraith hinge]

im sorry

[glossy gale]

It's fine

Can you help though?

Or are you gonna just make random comments

[hasty heron]

muted

[zinc ginkgo]

what does this mean? are you trying to plug in -2 to the eqn for y?

[zinc ginkgo]

what is c?

you should probably just show the entire question

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[glossy gale]

I'm trying to find the reference point using this formula

My teacher gave us it

And in the form $y = \log_b(a(x - c)) + d$