help-38

[quartz yoke]

well

you answered your own question

didnt ya

i didnt have to do anything you figured it out yourself

ehhhh

some gentle nudges

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[turbid anchor]

There exists integers a and b such that 2a + 7b = 1. I know this is true because if a=4 and b=-1 then it makes it true, but for a proof, I think I need something more "mathy" if that makes sense

[turbid anchor]

Like I don't feel like it's very proof-like to say something like "given that 4 is an integer and -1 is an integer, let a=4 and b=-1..."

[inland orbit]

If the goal is to show that something exists, providing an example is perfectly valid 🤷

[magic skiff]

are you saying there exists a set of integers or there is infinite integers

[turbid anchor]

I guess a set. Idrk what you mean tho, my textbook's problem is what I already typed out

[magic skiff]

there is also 11 -3

fits

[wraith hinge]

u just need an example to prove an existential statement

[turbid anchor]

Sounds good

Thank you!!

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[daring karma]

could someone please help me understand this prove

[daring karma]

im a bit confused on how the factoring works on the second to last line

[digital bison]

they add and subtract $y^{2n+1}x^2$ and then factor the $x^2$ out of $x^{2n+1}x^2+y^{2x+1}x^2$

[solid kiln]

Zybikron

[daring karma]

yes, but how did they know to do that?

actually never mind, I understand. The next thing im confused about is the last line of the proof

It seems like (x^2n+1 +y^2n+1) just gets replaced with P2n(x,y) and then (x+y) gets tossed in front it?

am i misunderstanding it?

[digital bison]

yes

that's the assumption in line 2

[daring karma]

ohhhh completely forgot about that lol

okay thank you!

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[twilit ridge]

is this correct?

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@twilit ridge Has your question been resolved?

[twilit ridge]

<@&286206848099549185>

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[fallen ledge]

Can someone explain to me what happend here

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[solid kiln]

donut

donut

[left oriole]

the only place where there could be a problem is as x->0.. you could just use the approximation sin(x) ≈ x for small x

[solid kiln]

donut

[left oriole]

sin(x)^2 <= x^2

no, both will work here

sin(x)^2 <= x^2 is true for all x, and is sharper since x^2 <= |x| for small x, so it may be more useful in more some contexts

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[sturdy haven]

I need to model a probability distribution of time series data over T timesteps with an i.i.d that has an equivalent standard deviation and expectation. For example, if the expectation of rolling a six sided die is E(X) = 3.5, Std(X) = 1.707 and I roll it 10 times, what is the mean and standard deviation of an equivalent uniform distribution?

[trim jolt]

@sturdy haven Has your question been resolved?

[knotty locust]

<@&268886789983436800>

this ^ is in basically all the help channels

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@sturdy haven Has your question been resolved?

[cursive musk]

uniform distribution means all values are equallly likely

mean is the same

[sturdy haven]

Would this carry over to a normal/Gaussian distribution? Because I wanted to use the uniform distribution as a sort of toy example and then generalize, but I wasn’t sure how to start

[cursive musk]

what

i dont understand why you would want to change the distribution

[sturdy haven]

To put it more concretely, I have a bunch of daily wind measurements that I have modeled with a normal distribution and the goal is to model some normally distributed random variable Y which is the wind speed after 10 days. I had no idea where to start so I was trying to start basic with a uniform distribution and then see if I could generalize it to a normal distribution

[cursive musk]

wwdym which is the wind speed after 10 days

you already have a normal distribution

i dont understand what is different from the normal distribution you are trying to make

[sturdy haven]

The mean of my distribution is 5.6 m/s. If I wanted to figure out what the probability is of the wind speed being 6 or higher tomorrow I could approximate it using an integral or numerically. But if I wanted to find the probability of the wind speed being 6 m/s 10 days from now, I thought I would have to use a different distribution?

That the value 10 days from now is a different normally distributed random variable

[cursive musk]

its the same chance

your normal dist is indepdent of time

its just a bunch of speeds

[sturdy haven]

Oh, that wasn’t my understanding of how that worked, I figured that there was some sort of underlying conditional probability that I needed to account for

Thanks!

[cursive musk]

no problem!

@sturdy havenalthough what you could do

is plot on a graph instead

then you can model speed vs time

and estimate at time t = 10

and compare how far that is from the expected

idk how you would calculate the chance but im guessing theres a way

[sturdy haven]

So plot the data chronological vs as a histogram?

[cursive musk]

not histogram

like a literal graph

y = mx +b

use a function

[sturdy haven]

Yeah so chronologically

Like starting with my first point which was a year ago until today

Unless you meant something different?

[cursive musk]

thats what I mean

i would use desmos

[sturdy haven]

I have all the data stored in a bunch of python data structures and can plot them using a python module

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[delicate dock]

can someone please explain what the steps were?

[dull thorn]

like how to solve this system of equation with matrix

[delicate dock]

nevermind im sorry

.close

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[wraith hinge]

what??

i didnt delete it

Its because of the blacklist pain

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[wraith hinge]

The scores of a standardized I Q test are normally distributed with a mean score of 100 and a standard deviation of 15.

A random sample of 55 people is selected from this population. What is the probability that the mean I Q score of the sample is greater than 105?

[wraith hinge]

okay finally, the bot kept deleting it

but anyways, this should be fairly simple but i want to make sure

our standard deviation would be approximately 2.02, we can standardize the sample mean by:
[
Z = \f{\bar{X}-\mu}{\ds \f{\sigma}{\s n}}
]

i end up getting 0.00005

[wraith hinge]

this should be right, right?

.close

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[wintry ingot]

i need help i dont get this question

[wraith hinge]

what do u think it is

well actually just solve the equation and you’ll get an answer choice that way

[wintry ingot]

i know that but i dont know how to solve it

[wraith hinge]

$5m - 20 = 45$

[solid kiln]

hibyehibye

[wraith hinge]

whats the first step ?

[wintry ingot]

get M by it self?

[wraith hinge]

yea so what should we do to both sides

(first)

[wintry ingot]

divide 5 by 5 and 20 by 5 ?

[wraith hinge]

urm u could

but thats a bit more difficult some times

maybe just add 20 first?

[wintry ingot]

so add 20 to 5 and 20? and 45

[wraith hinge]

add 20 to both sides

what do you get?

[wintry ingot]

when you say both sides what numbers?

[wraith hinge]

both sides of the equation

[wintry ingot]

so add 20 to the 5m and 45?

[wraith hinge]

so add 20 to the left, add 20 to the right

what do you get ?

[wintry ingot]

oh so leave the middle by it self and add 20 to 5 m and to 45

[wraith hinge]

what do you think you get

?

[wintry ingot]

i get that i have to add 20 to 5m and 45 to make the equation 25m-20=65

[wraith hinge]

no

$5m - 20 + 20 = 45 + 20$

[solid kiln]

hibyehibye

[wraith hinge]

what does this equal

[wintry ingot]

5M=65

[wraith hinge]

yes

now how do you get m

[wintry ingot]

uhh

5 x M=65

[wraith hinge]

$5m = 65$

[solid kiln]

hibyehibye

[wraith hinge]

how do you m alone ?

[wintry ingot]

65-5

M=60

?

[wraith hinge]

no

you have 5 x m

how do you get m

[wintry ingot]

5x 13?

M divided by 5

?

[wraith hinge]

yes divide both sides by 5

$\frac{5m}{5} = \frac{65}{5}$

[solid kiln]

hibyehibye

[wraith hinge]

$m = 13$

[solid kiln]

hibyehibye

[wintry ingot]

ohhhhhhhhh ok

thank you

.close

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[compact trellis]

How would I find the solution to x, y and z?

[wraith hinge]

are all these equations given?

pick like top 2 and solve simultaneously

then x=z

[wraith hinge]

change like 21z to 21x so its just two unknowns and 2 equations

[compact trellis]

Ok

I haven’t learned about systems of equations in a long time

This is actually new to me

[wraith hinge]

a line on the left of what ?

[compact trellis]

If I can’t solve using this method, I can use another don’t worry

[wraith hinge]

like a piecewise function (?) idk what u mean

[wraith hinge]

show ur steps so far

[compact trellis]

No bueno

If I retook algebra 1, I may know

[wraith hinge]

ok so u have $17x + 4y = 21x$

[solid kiln]

hibyehibye

[wraith hinge]

and $19x + 6y = 23x$

[solid kiln]

hibyehibye

[wraith hinge]

so $-4x + 4y = 0$ and $-4x + 6y = 0$

[solid kiln]

hibyehibye

[wraith hinge]

wait

does this even have a solution ?

[wraith hinge]

did u make this question up or is from a hw problem ?

[compact trellis]

Chemistry

[wraith hinge]

there is no solution to that set of equations

[wraith hinge]

wdym

is the last line 3x + 3y = 52 or 5z?

if its 5z there is a solution

[compact trellis]

5z

[wraith hinge]

okay

so $-4x + 4y = 0$ and $-4x + 6y = 0$

[solid kiln]

hibyehibye

[wraith hinge]

therefore

$-4x + 4y = -4x + 6y = 0$

[solid kiln]

hibyehibye

[wraith hinge]

solve for y

[compact trellis]

I’m getting 0 for some reason

[wraith hinge]

thats correct

so what did u get for y and z

[compact trellis]

x and z?

I think I know the solution

Currently solving

Yeah they’re all 0

Thanks for the help

.close

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[fervent grotto]

The function g(x) is a reflection of the function f(x) = -2(x - 3)^2 - 9 over the line y = x + 2. What is g(x)?

[fervent grotto]

how do you do this

[long basin]

Replace x with y and f(x) with x+2

Solve for y

[blissful viper]

any 1 wanna play roblox

[fervent grotto]

bruh

[fervent grotto]

wait what

can u explain

[long basin]

x + 2 = -2(y -3)^2 - 9

Isolate y

[fervent grotto]

wait so you plug in the equation for the line instead of y

and then u put y instead of x?

[fervent grotto]

and then when u solve that is the new equation?

[long basin]

Should be

If I didn't do a dummy moment

Lemme check

Yeah it works

Although

Although f(x) is not invertible ...

Unless you restrict its domain

[vivid elk]

cause it touches y=x+2 at some point right

and that would be very weird to invert

[long basin]

No

That's not the reason

[vivid elk]

is the reason it being infinite

[long basin]

Assuming the range of f(x) is also its codomain, then f(x) is surjective only

The range of f(x) will become the domain of g(x)

But if f(x) is a parabola where two inputs can have the same output, then g(x) will have an input with two outputs

And that's not a function

As long as no horizontal line passes through f(x) more than once, then the function is invertible

And that accounts for every infinite horizontal line on the XY plane

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[fossil grail]

!help

[fossil grail]

Is the answer to B | 694 cars

[sharp tundra]

yes

[night zodiac]

Yes and no

[fossil grail]

How does that work

[night zodiac]

How did you get 694?

What was the work for that?

[fossil grail]

(125/360) x 2000

[night zodiac]

And you get 694.44444, correct?

[fossil grail]

Yea

[night zodiac]

Yes it's correct because you rounded down, but because it's cars, you should round up to the nearest whole number instead

Because that's 40% of a car, technically, you can't dismiss 40%

[fossil grail]

Which is 694

[night zodiac]

you should round up to the nearest whole number instead

[fossil grail]

is that 695

[night zodiac]

Yes

[fossil grail]

It's 694.4 though

anything below 5 is rounded down

[night zodiac]

but because it's cars, you should round up to the nearest whole number instead

[fossil grail]

confusing,

[night zodiac]

Think about like this, what if it was 694.4 people?

Would you just remove that 0.4 of a person?

That person still counts, so you round up to make it a whole person

[fossil grail]

0.4 of a person is basically a person with half of their body

ill have to see what the teacher says

[night zodiac]

But it would still count, like you just can't get rid of them, so rounding up makes more sense in that scenario

[fossil grail]

It does make sense

[night zodiac]

Like 40% of a car is like the body of a car and tires, it still a car, so it can't really be ignored, so you round up to include that

[fossil grail]

I se

[night zodiac]

In my opinion, logically, you should round up

But ask your teacher

[fossil grail]

I got x = 23/3

But that doesn't make sense here

[night zodiac]

Show work

[fossil grail]

3x + 5 = 28
3x = 23
x = 23/3

My bad

Acknowledged it just now

2(3x + 5) = 28

[night zodiac]

Yes

That's better

[fossil grail]

6x + 10 = 28
6x = 18
x = 3

Alrighty, thanks

!close

.close

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[zealous sun]

The answer I'm getting at the end here is wrong. Apparently g'(x) is 3e^x-4 instead of what I have. Why is that?

[rugged latch]

Is the problem find f’ for $f(x) = -(4x \cdot 3e^x + 4)^3$?

[solid kiln]

Stephen

[zealous sun]

Yes

[rugged latch]

Well for g’ u have to use product rule

[zealous sun]

Ohhh that would make sense

[rugged latch]

Wait is it 4x * 3e^x or 4x - 3e^x

[zealous sun]

Minus

[rugged latch]

Bruh lol u said it was multiplication here

Anyways

[zealous sun]

Oh I didn't even catch that, my b

[rugged latch]

U good

Lemme look at it again

Ok hmm f’(x) looks right, the reason they got 3e^x -4 is because they factored in the -1

From the -3

They made it 3(4x -3e^x +4)^2 * (3e^x - 4)

[zealous sun]

Oooooh

[rugged latch]

Instead of -3 at the start

[zealous sun]

So it's not that I'm incorrect, it's just that the answer that I was checking against did it differently

[rugged latch]

Yep

[zealous sun]

That would explain my confusion lol, thanks for the assistance

[rugged latch]

No problem

[zealous sun]

.close

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[zealous sun]

If trying to find f'(x) when f(x) = 9cos(x), is it safe to ignore the 9 or do I have to do product rule?

[quartz yoke]

well you can technically ignore the 9

see why

let g(x) = 9, h(x) = cos(x)

then f(x) = g(x) h(x)

[zealous sun]

g'(x) would just be 1 anyways then, leaving just h'(x)

So the answer would be yes and no then, I understand. Thanks

[quartz yoke]

yep yep

[zealous sun]

.close

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[quartz yoke]

g'(x) won't be 1

,w differentiate 9

[solid kiln]

Results provided by WolframAlpha

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Requested by DerpZ#9141

[quartz yoke]

see

it's 0

@zealous sun

[kindred pier]

g'(x) would be 0, not 1

[zealous sun]

Ah

[quartz yoke]

I did not use wolframalpha because I forgot

[zealous sun]

I forgot as well lol don't worry

Same outcome though, f'(x) would still be -sin(x)

[quartz yoke]

*9

[zealous sun]

So we don't ignore the 9

[quartz yoke]

you don't ignore it

[zealous sun]

-9sin(x) then

[quartz yoke]

you just don't have to

tediously do the product rule

yep

[zealous sun]

Just leave it be, gotcha, thanks

.close

[quartz yoke]

yeah it's already coosed

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[proper vessel]

what are these equations for?

[split chasm]

waves passing through different mediums,
refraction

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[proper vessel]

@split chasm thank u very much

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[crisp minnow]

How I can solve it??

[main sigil]

sin=opposite/hypotenuse

do you know that?

[crisp minnow]

More or less, I’m still trying to learn this topic

[crisp minnow]

So In this case sin= x / 20??

[main sigil]

exactly!

And you also know that sin(alpha)=3/4

so 3/4=x/20

[crisp minnow]

so x = 15?

Thanks very much

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[daring karma]

i dont understand this at all

[daring karma]

my first question, why is it assumed that Q implies R is a formally proved tautology?

my second question: how is it known that the whole statement (Q implies R) ...... (P implies R) is a tautology?

[sullen flicker]

it is condition

if (P -> Q) is an FPT and (Q -> R) is an FPT then ...

[daring karma]

Oh so in reality, Q implies R may not be a tautology?

in the proof, it's just saying if Q implies R is a tautology, and then proceeding from there, right?

[sullen flicker]

it has to be FTP because it is condition of the theorem

[daring karma]

oh i see

but then, how is the whole statement a tautology?

[daring karma]

like how is this a tautology?

[sullen flicker]

sorry dont know, i am not much into tautology things

[daring karma]

that's okay. Thank you anyways for your help!

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[hybrid hollow]

so, i'm confused on what the second and third statements are saying 😭 is |b| referring to the modulus of b? (modulus as in distance between complex number and origin)? but then if so what does (mod 4) mean?

[digital bison]

|b| is the modulus, yes. or absolute value.
3(mod 4) means that b is a 3 + 4k for some k. In other words, 3 more than a multiple of 4

[hybrid hollow]

wait so it's saying that the modulus of b must be... equal to 3 + 4k? for bi to be a gaussian prime
is k restricted to just natural numbers?

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[hybrid hollow]

<@&286206848099549185>

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[wraith hinge]

hello, I'm starting calculus and would like some tips/resources to practice from

[wraith hinge]

can any1 help me?

[main sigil]

khan academy

https://www.khanacademy.org/math/ap-calculus-ab

[wraith hinge]

how did u memorize the rules?

there r so many

[main sigil]

I didnt

I can derive them

[wraith hinge]

what is ur favorite rule?

[main sigil]

chain probably

most simple and easiest to derive

[wraith hinge]

that is the hardest

I think u have to multiply by u(x) somewhere

[tender yacht]

keep the list in front of you and practise 50 question within 1-3 days

pretty sure ull b okay after that

[wraith hinge]

50 hard questions or easy questions and from where?

[wraith hinge]

I have to keep it in my memory for 1 year and 3 months

do u think I can remember for that long?

[sour token]

I just had list of rules open while doing problems, after doing sufficient number of them

you'll get used to them and remember them automatically

[tender yacht]

doesnt matter, as long as they have some trigonometry, quotient and chain rule applications

[wraith hinge]

oh yeah, we get a formula sheet with the derivative rules

should I still memorize?

[tender yacht]

I assure u if u do those 50 questions

u wdnt need to memorize

[wraith hinge]

do u know hyperbolic functions

like cosh

and sinh

[tender yacht]

those r very easy to derive

[wraith hinge]

can u differentiate these or no?

[tender yacht]

of course

[wraith hinge]

is e^x the only thing that stays the same through differentiation?

[tender yacht]

yes

or the constant 0

[wraith hinge]

how do u know which rules to use first if there is a problem where u should use multiple rules?

[main sigil]

exercising

especially when you integrate, the rules are often not quite obvious

[wraith hinge]

😭

there is no pemdas for rules in calculus?

[tender yacht]

integration is a completely different story 😭

but differentiation, just practise

[main sigil]

In derivatives its quite easy tho you see product-apply product rule

[main sigil]

true

[wraith hinge]

I only know the power rule for derivatives and integrals

the power rule in integrals is disgusting. cant imagine the rest

[tender yacht]

maybe focus on being thorough with differentiation first?

[wraith hinge]

so product rule first always?

[wraith hinge]

integrals seem more useful in the real world imo

[tender yacht]

its usually the chain rule but really, depends on the question

[main sigil]

When there is product of something, you can either simplify it to some polynomial or apply product rule

[wraith hinge]

do u guys know partial fraction decomposition?

[tender yacht]

yep but starting both at the same time doesnt seem very efficient

[wraith hinge]

apparently we use it in calculus

[wraith hinge]

do u guys use it normally in integrals or derivatives?

[tender yacht]

yep

integrals

[main sigil]

in derivatives its loss of time ig

[wraith hinge]

ok thanks guys

should i learn maclaurin series after derivatives?

or after derivates and integrals?

[main sigil]

its quite usefull

and interesting topic

are you learning it by yourself or in school?

[wraith hinge]

i need it for my school test

[tender yacht]

its there in khan academy's calculus bc series

[main sigil]

yep

[tender yacht]

not sure if its there in ab

[main sigil]

also multivar calc

[wraith hinge]

but i want to learn on my own because my teacher is crap

[tender yacht]

so u cd follow the same order

[wraith hinge]

my friend did ap calc ab

I think I'll ask him to help me

ok bye guys

thnx

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[wraith hinge]

can someone help me

[wraith hinge]

i need some sort of help

i've tried so many different things and nothing's worked

sorry my working is very messy

is it ok if i can try explain?

thanks

basically

i drew out a right angled triangle

with sides

6 8 10

where

6 is the height

8 is the base

and 10 is hypotenuse

i then tried to work out d

which i got

by realising that the ratio of the sides

of the two triangles formed inside the big triangle

was equal to b/h

here is the triangle for reference

in my case

[frozen plover]

I think you should use trig

Instead of distances

[wraith hinge]

i see

in what way?

[frozen plover]

Well let's say that bottom angle is A

Bottom left

[wraith hinge]

yes

[frozen plover]

So we know sin A = h/l

[wraith hinge]

ye

[frozen plover]

those two triangles should be similar right, the two smaller right angled ones

[wraith hinge]

yup

[frozen plover]

Can you identify the location of that point on the line

Like the ratio of the distances that the point that's d distance away from the wall and floor cuts l into

[wraith hinge]

well

see in my exmaple

with the 6 8 10 triangle

it was splt into the ratio 1:0.75

so the lengths were 30/7 & 40/7

[frozen plover]

But it's not necessary for it to be a 6:8:10 triangle

[wraith hinge]

ur right

the ratio is 1:either b/h or h/b

depending on which part of l u choose

and whether h is greater than b or not

[frozen plover]

Alright I think I got it

So you know sin A is h/l

[wraith hinge]

ye

[frozen plover]

The bottom left angle on the smaller upper right triangle is also A

For this one tan A = (h - d)/d

[wraith hinge]

agreed

[frozen plover]

Now you just need to eliminate the trig ratios

sin A = h/l

So $\tan A = \frac{h}{\sqrt{l^2 - h^2}}$

[solid kiln]

NEONPerseus

[frozen plover]

$\frac{h}{\sqrt{l^2 - h^2}} = \frac{h}{d} - 1$

[solid kiln]

NEONPerseus

[wraith hinge]

wait sorry

surely

root(l^2 - h^2) would be b?

no?

[frozen plover]

b?

[wraith hinge]

base

of the triangle

[frozen plover]

It's the base of a triangle

Not this one in particular

[wraith hinge]

right

i see

[frozen plover]

That's the value of tan A for sin A being h/l

I hope you got that

[wraith hinge]

tana would be opposite over adjacent

[frozen plover]

Yes

[wraith hinge]

so

the oppoite is h

is the adjacnet d?

[frozen plover]

Draw a triangle where sin A is h/l and use the Pythagorean theorem to get the adjacent

[wraith hinge]

ohhh

ye ok

that makes sense thanks

[frozen plover]

np

[wraith hinge]

so whats the step after this?

[frozen plover]

Well what are you asked for

h in terms of l and d right?

[wraith hinge]

yes

[frozen plover]

Well now just move stuff around so that you get h = something

[wraith hinge]

how would u do that in this particular case

because h is stuck in the denominator

in a square root

so that would affect the other h terms in the equation

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[latent prawn]

I need help with this, not the actual question, but the part about the tip. So would we say that vi in N instead of i in V?

would it be like working with an array, where you have elements on the array up to index N?

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[latent prawn]

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[wraith hinge]

hi guys

[wraith hinge]

i dont really understand why the proof for the FTC part II is so long

why cant we just say this:

if f(x) is a function continuous on [a,b]

Let $F(x) = \int_a^{x} f(x) dx$

$\implies F(b) - F(a) = \int_a^{b} f(x) dx - \int_a^{a} f(x) dx$

$\implies F(b) - F(a) = \int_a^{b} f(x) dx$

i dont understand why we cant just do this

why does the proof involve setting g(x) as also an antiderivative and finding that F(x) = g(x) + C and all that crap

[solid kiln]

いろさん

いろさん

いろさん

[wraith hinge]

like why can we not just do this

[zinc ginkgo]

None of what you did shows the conclusion of FTC2

https://activecalculus.org/single/sec-5-2-FTC2.html

[wraith hinge]

isnt the conclusion of ftc2 just the last thing

[zinc ginkgo]

No

Read the link

[wraith hinge]

oh ok i understand

its cuz i defined F(x) here to be something exact

whereas the actual thing says that any antiderivative can be evaluated like this

thats why you have to use g(x)

omg

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[languid pier]

Its the same problem but (x+1) is (x+5) so i converted it and its wrong

[long basin]

Are you allowed to use a calculator or

Or wait nvm

It wants exact length

[languid pier]

ya

[long basin]

Well you can't just replace (x+5) with (x+1) everywhere

Try to see what they're doing to get the antiderivative

[languid pier]

:O

its just that 181 constant tho

turns into 37

[long basin]

,w expand (48(x+1)^2)/2

Eh oh wait

Maybe it's not liking the (0+37)

[languid pier]

still wrong

[long basin]

Try to simplify as much as you can

Lemme check up on something

[languid pier]

ive simplified it as much as possible, i think something may be wrong

[long basin]

,w Integrate[Sqrt[36x + 37], {x,0,3}]

[solid kiln]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[languid pier]

o

[long basin]

Yeah it's with the 3/2 apparently

Uh show me your steps

For your work

[languid pier]

i has no steps

[long basin]

Moment

[languid pier]

these were my steps

cool thats right

[long basin]

,w 2/3 ((108+37)^(3/2) - (37)^(3/2))

[solid kiln]

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Requested by Umbraleviathan#3607

[languid pier]

ah

well, tysm

ill prolly be back soon

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[wraith hinge]

(2ab^2) x (-3ab)

[wraith hinge]

i cant understand this

any1 can help

[subtle prairie]

what here that you are struggling ?

$(2ab^2)(-3ab)$

[solid kiln]

Dubleyou

[subtle prairie]

Do you want to multiply them?

[wraith hinge]

i have to transfer it into regular form of single member

sorry its in different language

its in georgian

and i cant translate it right

[subtle prairie]

i'm not sure by this

Do you have the answer this you?

[wraith hinge]

like i have to make it into single thing

[subtle prairie]

right

so basically you have to multiply them together

[broken cave]

Yes

Use laws of exponents

[wraith hinge]

ok

[broken cave]

Yupp

[wraith hinge]

i still dont get it what do i do

please help

[subtle prairie]

Well, basically you can treat each variables as some specific numbers

and think it as simply multiplying some bunch of numbers

as multiplication is commutative,

$-6ab^2*ab$

[solid kiln]

Dubleyou

[subtle prairie]

if you know laws of exponents, add the exponents for each of like terms

or reason out this way, in first product b is multiplied 2 times, in second one, it's 1 times

so combined b is multiplied 3 times

similarly for a

$-6a^2b^3$

[solid kiln]

Dubleyou

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[mint burrow]

We know by the definition of return times that $E_x [T_y] = E_x [ H_y]$ where $T_y$ is the first return to $y$ and $x \neq y$. However, how can I generally calculate $E_x[T_x]$? I'm thinking along lines of the definition of expectation where $E_x[T_x] = \sum_{n=1}^{\infty} n \cdot P_x(T_x = n)$

[solid kiln]

gusrytl

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[mint burrow]

<@&286206848099549185>

[zinc ginkgo]

You just apply the definition

Each problem is different

[mint burrow]

The definition?

[mint burrow]

I guess you could use the asymp. freq. theorem but I guess I'm wondering in which we don't have a stationary distribution available to us

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[zinc ginkgo]

the definition of expectation you wrote

[zinc ginkgo]

what are you talking about?

show an actual problem

[mint burrow]

For example, we want to find $E_0 T_0$ on a MC with $p(0, 1) = 1$ and $m \geq 1, p(m, m+1) = \frac{m}{m+1}$ and $p(m, 0) = \frac{1}{m+1}$

[solid kiln]

gusrytl

[zinc ginkgo]

finite transition matrix?

[mint burrow]

infinite

[zinc ginkgo]

Z+?

[mint burrow]

Yes

[zinc ginkgo]

is this just a random walk?

with some drift

[mint burrow]

For this example, since the MC is irreducible I have that $P_0 (T_0 < \infty) = 1$ but don't really understand how to appraoch $E_0 T_0$

[solid kiln]

gusrytl

[mint burrow]

yes

[zinc ginkgo]

you have the probabilities. calculate the series

[mint burrow]

So just the probabilities of going from 0 -> m multiplied by the probability of going back from m to 0

[zinc ginkgo]

depending on the algebra, yours might be more easily evaluated if you used this identity

but i haven't worked out the details for your specific MC

https://web.ma.utexas.edu/users/gordanz/notes/advanced_random_walks_color.pdf

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[bitter bison]

say its root x^2 - 1/4 do we use -1/2 or 1/2 for acoshu

[burnt mulch]

It wouldn't really matter (since the negative will become a positive after squaring), though ig I would pick the option that yields the differential being positive for convenience.

[bitter bison]

alright

.close

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[violet nest]

the -infinity confuses me

we will be multiplying by t^-3 right?

[burnt mulch]

Yeah, divide the numerator and denominator by $t^3$.

[solid kiln]

Civil Service Pigeon

[wise cipher]

I think this one is just 0 isn't it?

Cause the degree of numerator is less than the diameter even if it is -infinity

[burnt mulch]

Yeah, it's 0

[violet nest]

0 was right

would this be multiplying by x^2?

[burnt mulch]

I'd do ||difference of squares||

alternatively, divide by ||sqrt(x)||

[violet nest]

i dont understand

[burnt mulch]

Why do you think you would multiply by $x^2$?

[solid kiln]

Civil Service Pigeon

[violet nest]

because previous problems have done the same

multiplying by x^#

[burnt mulch]

try not to think of it algorithmically - you don't even have polynomials here

that being said, the logic is very same - you do divide/multiply by something.

[violet nest]

dont we get rid of sqrt x by multiplying x^2?

[burnt mulch]

try it out and see what it gives you

[violet nest]

1

[burnt mulch]

🤔

send your working

[violet nest]

oh its x^2 sqrt x

idk why it didnt get rid or sqrt

[burnt mulch]

think simple

[violet nest]

multiply by sqrtx ?

to get x

[burnt mulch]

you're right about working with sqrt x

[violet nest]

not sure

what ur getting at

[burnt mulch]

well if you want to cancel sqrt x with sqrt x, what do you do?

[violet nest]

(sqrt x)(sqrt x) give me x

[burnt mulch]

what operation

[violet nest]

multiply?

something

[burnt mulch]

||divide||

[violet nest]

gives me 1

[burnt mulch]

exactly.

divide numerator and denominator by $\sqrt{x}$

[solid kiln]

Civil Service Pigeon

[violet nest]

top will have -1?

[burnt mulch]

yes, $-\frac{\sqrt{x}}{\sqrt{x}}=-1$.

[solid kiln]

Civil Service Pigeon

[violet nest]

the answer was not 8

[burnt mulch]

how did you get 8?

[violet nest]

81 -1 over 9+1 is 80/10

[burnt mulch]

What do you get after dividing the numerator and denominator of $\frac{81-\sqrt{x}}{9+\sqrt{x}}$ by $\sqrt{x}$?

[solid kiln]

Civil Service Pigeon

[violet nest]

do i divide by the 81 and 9 too?

sqrt

[burnt mulch]

yes lol

otherwise you don't preserve equality

[violet nest]

i get 2

but thats wrong

[burnt mulch]

ok

send all of your work

[burnt mulch]

Dividing $81$ by $\sqrt{x}$ does not mean take the square root of $81$, same logic for $9$.

[solid kiln]

Civil Service Pigeon

[violet nest]

so its 81/sqrtx ?

[burnt mulch]

✅

[violet nest]

o

i got -1

am i just dividing u^2 for this one

[burnt mulch]

expand it

[violet nest]

so (u^2 +7)(u^2 +7) is on bottom

and the multiply by u^-2 for everything?

[burnt mulch]

there's two factors, each with a leading term with u^2 tho

[violet nest]

not sure what you mean

[burnt mulch]

just expand everything out into standard form and you'll see my point

[violet nest]

top becomes 8u^4 + 7u^2 - 1

bottom goes back to (u^2 + 7)^2

[burnt mulch]

expand out the bottom now lol

[violet nest]

i got u^4 + 14u^2 + 49

[burnt mulch]

and now it's just like all your other exercises

I'll leave it to you to finish

[burnt mulch]

my idea here was that when you multiply out the leading terms, there's a u^4 on the top and bottom

[violet nest]

.close

[trim jolt]

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[ashen yacht]

ello

[ashen yacht]

i need a tiny teeny lil bit of help understanding something

which is

x^(3)*y^(2)+x^(2)*y^(3)

how and why does it end up with x2y2(x+y)

[main drift]

Factor an x^2y^2 out

[ashen yacht]

out?

wym?

[main drift]

Like 2x+2y=2(x+y)

[ashen yacht]

hmmm

still dont goti t

[main drift]

Do you understand this?

[ashen yacht]

yes

[main drift]

Do the same with the original expression but factor an x^2y^2

Notice that both terms have an x^2y^2, so you can factor it out

[ashen yacht]

damn it

what does factor out mean

[main drift]

Factoring out a 2 in 2x+2y is 2(x+y)

[ashen yacht]

and how do you factor an x^2y^2

OHHHHHHHHHHHHHHHHHHHHHHHHH

[main drift]

Can you factor an x^2 from x^4+3x^2

[ashen yacht]

uhhh

no how do you do that

[main drift]

x^2(x^2+3). Basically I’m dividing an x^2 from all terms and multiplying them back

[ashen yacht]

ohhhh

so that's how you factor

so basically like factoring an x^3 from x^6+12x^3

is x^3(x^2+12)

[main drift]

No

[ashen yacht]

but i divided

[main drift]

What’s x^6/x^3

[ashen yacht]

2

[main drift]

What

[ashen yacht]

oh no

it's x^3

[main drift]

Yes

[ashen yacht]

what was wrong in my expression

[silent canyon]

What's x^6/x^3?

[main drift]

This is x^5+12x^3

[ashen yacht]

oh right cause we add the powers rather than multiply

[main drift]

Yes

[silent canyon]

It's odd that you know the exponent rules but not factorization

Strange gap

[ashen yacht]

trust me my brain in mathematics is like letting a kid with a keyboard mess up with the system32 files

like a hard drive that has been overwritten

[silent canyon]

Math is pain sometimes

[ashen yacht]

For me it's chronic pain

wanting to love something and can't understand it is literally paralysis

[ashen yacht]

Thank you good gentlemen

[silent canyon]

What if we ladies

[ashen yacht]

mmmm

idk how to talk to women

[trim jolt]

@ashen yacht Has your question been resolved?

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[ashen yacht]

@main drift i will come back

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[wraith hinge]

Wouldn’t the first one be 9x + 18

[main drift]

The large square or the largest square

[wraith hinge]

Large

[main drift]

It would be (x+9)^2-x^2 if I’m understanding correctly

[delicate jasper]

Have no idea what they mean with adjoining rectangles

[wraith hinge]

I clicked on “practice another” and it was the same question with different numbers and it was 8x + 16

So I was confused

[main drift]

This is (x+4)^2-x^2

Basically, find the area of the whole square and subtract the little one

[magic nacelle]

can u help me

[frail nova]

#❓how-to-get-help

[delicate jasper]

Isn't it 9*(9+2x)

[magic nacelle]

What is the quotient of 5/4?

[wraith hinge]

It was wrong

[frail nova]

Is (a) asking for the largest square

[wraith hinge]

Large

Square

“Find the area of the two adjoining rectangles and large square in the figure”

[main drift]

The largest square is still large

[frail nova]

ABED?

[main drift]

18x+81 is correct?

[delicate jasper]

Aren't they asking for the area of ABED+BCEF+DGEH

[main drift]

Yea it should be right

[delicate jasper]

.

[wraith hinge]

It’s my last attempt

I won’t be able to do it again if I get it wrong

[delicate jasper]

Do they except factorizations

Accept*

[wraith hinge]

No

[delicate jasper]

18x+81 then

[wraith hinge]

But I feel like it should’ve been 9x+18

[main drift]

Why

[wraith hinge]

Because it gave me the same exact question

And I put 8x+16

[main drift]

Use math to support your reasoning

[wraith hinge]

And it was right for that one

[frail nova]

$ADBE=9^2=81$
$BECF=9x$
$DGHE=9x$

[solid kiln]

jay.

[main drift]

Yea this is (x+4)^2-x^2. Just replace 4 with 9

[wraith hinge]

^

[frail nova]

Send us that question

[wraith hinge]

^

[main drift]

Exactly

[frail nova]

How did you get to the answer?

[wraith hinge]

What

Wdym

[delicate jasper]

Lol our reasoning is correct

[wraith hinge]

I added 4+4 and got 8 then added 8 and 8 and got 16

So I put 8x+16

[delicate jasper]

What

[frail nova]

Math ain't mathing

[wraith hinge]

man idk

[delicate jasper]

It's basically the area of the two rectangles + area of large square

What do u think is the area of one rectangle?

[trim jolt]

@wraith hinge Has your question been resolved?

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[quiet pollen]

can someone help explain how to solve this problem?

im kinda j stuck on getting the common deniminator

[night zodiac]

Did you factor the denominators?

[quiet pollen]

wdym

like 4(x-2)

[night zodiac]

Yeah

[quiet pollen]

(x-2)(x+2)?

but what do I do from there?

[night zodiac]

Use that to find your common denominator

[quiet pollen]

Yea im not sure how I would go about doing that

I got that far but im not sure what ur supposed to do once u have those numbers

[night zodiac]

One method, to finding a common denominator is, just multiply all the denominators together

[quiet pollen]

ok i got 4(x-2)^2(x+2)

for the denominatore

Oh

ok io got it

thabnks ds;dj06

.close

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[thorn shale]

what would i do on this?

i know the anti derivative of u^(8) and of tan(u)

but they’re being multiplied together

did i do my u substitution wrong?

[knotty locust]

Use the identity that sec^2(x)=tan^2(x)+1

to reduce the power of sec^4(x) to sec^2(x)

then substitute u=tan(x), and du will be? and that should work out nice for you

[thorn shale]

are my other steps correct?

it would be a second u sub?

[knotty locust]

no , I mean restarting the problem from the beginning

[thorn shale]

i’m kind of stuck

i got this down

[knotty locust]

,, \int{\tan{x}^{8}\sec{x}^{4}}

[solid kiln]

AustinU

[knotty locust]

that looks good so far

what you have on your paper

[thorn shale]

maybe i’m thinking ahead but

if i u sub tan

actually wait

u^(9) + u^(10)? @knotty locust