help-36

[worldly spruce]

$\frac{5 \times \sqrt{3} - 5 \times \sqrt{5}}{-2} = \frac{(-1) \times (5\sqrt{3} - 5\sqrt{3})}{(-1) \times (-2)}$

[soft zealot]

USS-Enterprise

[worldly spruce]

There we go

Okay

So

Left is what we had

[tawdry horizon]

Like that

[worldly spruce]

And then I multiply with -1 on top and bottom

[worldly spruce]

,rccw

[worldly spruce]

Yes

And then just

$\frac{(-1) \times (5\sqrt{3} - 5\sqrt{3})}{(-1) \times (-2)} = \frac{-5\sqrt{3} + 5\sqrt{3}}{2}$

[soft zealot]

USS-Enterprise

[worldly spruce]

Exactly what you did

Then we can factor out 5 from the numerator

[tawdry horizon]

waiiiit

[worldly spruce]

$\frac{-5\sqrt{3} + 5\sqrt{3}}{2} = \frac{5 \times (-\sqrt{3} + \sqrt{3})}{2}$

[soft zealot]

USS-Enterprise

[tawdry horizon]

how u get sqrt 3

isnt it sqrt5 sqrt 3

[worldly spruce]

Damnit

Yeah

Just me being dumb

I am sorry

[tawdry horizon]

$\frac{-5\sqrt{3} + 5\sqrt{5}}{2}

its alr

[worldly spruce]

All the second roots are 5 yes

$\frac{-5\sqrt{3} + 5\sqrt{5}}{2} = \frac{5 \times (-\sqrt{3} + \sqrt{5})}{2}$

[soft zealot]

USS-Enterprise

[worldly spruce]

Like this

Didnt even notice

And then you can just take 5/2 out

[tawdry horizon]

its ok, thank you for helping

[worldly spruce]

And rearrange the roots because of associativity

And end up with

[tawdry horizon]

holdom lemme write this dwon

[worldly spruce]

$\frac{5}{2} \times (\sqrt{5} - \sqrt{3})$

[soft zealot]

USS-Enterprise

[worldly spruce]

Yeah I am sorry

I know how hard can it be to follow along

If I am making stupid mistakes like these

[tawdry horizon]

its fine, its my first time doing further maths so im sorry for the pace im going lol

[worldly spruce]

$\frac{5 \times \sqrt{3} - 5 \times \sqrt{5}}{-2} = \frac{(-1) \times (5\sqrt{3} - 5\sqrt{5})}{(-1) \times (-2)} = \frac{-5\sqrt{3} + 5\sqrt{5}}{2} = \frac{5 \times (-\sqrt{3} + \sqrt{5})}{2} = \frac{5}{2} \times (-\sqrt{3} + \sqrt{5}) = \frac{5}{2} \times (\sqrt{5} - \sqrt{3})$

[tawdry horizon]

ohhhhhhhhhhhhhh i seeeeeeee

noooo wayyyyy

that hits so much different now

[tawdry horizon]

,rccw

woops

[soft zealot]

USS-Enterprise

[worldly spruce]

There we go

This is everything

[worldly spruce]

,rccw

[worldly spruce]

Ah

[tawdry horizon]

lemme send the pic again

[worldly spruce]

the bot

[tawdry horizon]

,rccw#

[tawdry horizon]

THATS RUBBER EXCESS NOT DAndruff

lol

[worldly spruce]

Yes, exactly

[tawdry horizon]

but ye is this correct now

okay alr

dayum u have really come in clutch

can i add u?

[worldly spruce]

Sure, but don't take it personally if I ever remove you. Every now and then I go and remove a lot of people 😅

[tawdry horizon]

ita alr

tyyyyy

[worldly spruce]

No problem 🙂

[tawdry horizon]

btw what education level arre u in alevel?

or uni

or an american grade level

[worldly spruce]

I am in Europe

High school

[tawdry horizon]

ooo how tf

im nearly done w it and u can do all this

dayum if ur in the uk ur set for life icl

[worldly spruce]

😂

We did this in first year

[tawdry horizon]

daaang

is that like 16 or 18 must be

becasue we only just sarted this shi

[worldly spruce]

First year is 15-16

[tawdry horizon]

ohhhhh ok that makes sense

[worldly spruce]

Yeah

I am in 4th now

[tawdry horizon]

bc im in year 11 rn

[worldly spruce]

(last)

[tawdry horizon]

finally huh

[worldly spruce]

We have 9 years of elementary then usually 4 years of high school

Then again usually 4 years of university

[tawdry horizon]

we sort of do that, except highschool for us is a levels

well thank you anyways, i need to go, god bless you 🙂

[worldly spruce]

I see

No problem

Have fun

[tawdry horizon]

ty

u too

.close

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[autumn canyon]

I just need help with the first question

[vital crag]

why not the rest of your test

[autumn canyon]

It’s my hw

I’m taking the class online and I just need guidance

I think if I know how to do it the rest will be easy

[vital crag]

factor the denominator

[autumn canyon]

(x-6)(x+1)

[final saddle]

@autumn canyon Has your question been resolved?

[autumn canyon]

<@&286206848099549185> pls

[vital crag]

did you plug your factorization into the denominator?

[autumn canyon]

Wdym

Like 3-x/(x-6)(x+1)

Idk where to go from there

[vital crag]

what happens to each (3-x), (x-6) and (x+1) as x goes closer to 1

use uhhhh

,tex .limit rules

[soft zealot]

[autumn canyon]

Idk??

It gets super close to 1 but never reaches it?? Like 1.00001 or 0.9999

[vital crag]

that's the x value yes

what about 3-x

what does 3-x approach

and the other two factors

[autumn canyon]

3.00001 or 2.9999 and 6.00001 and 5.9999

Right

[vital crag]

no

3-1.01 = ?

3 - 0.99 = ?

you should review and the rest will be easy

http://tutorial-math.wip.lamar.edu/Classes/CalcI/LimitsProperties.aspx

[autumn canyon]

How do I know if it exists or not

[autumn canyon]

Yeah I’ve been looking at PowerPoints and videos all day it’s not helping

Like I need step by step help

[vital crag]

it's there on the page

3 - x is a polynomial

so the limit as x goes to a = 1 of 3-x is just the polynomial at a=1

[autumn canyon]

What is that supposed to mean

Do I not plug in any numbers

[vital crag]

you do

that's what this symbol means

p(x) is a polynomial in x

in this case p(x) = 3-x

find p(1)

maybe watching a video would help you better than reading

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-2/v/introduction-to-limits-hd

[autumn canyon]

Atp can you just solve it step by step and I’ll just see what you did

I’ve spent like an hour on this question 😭

[vital crag]

it's right there

if p(x) = 3-x, do you know what p(1) is?

[autumn canyon]

2

[vital crag]

yes

[vital crag]

why did you think it was 3.0001 or 2.9999

[autumn canyon]

Bc you worded it like that

So the answer is 2?

[vital crag]

i worded it exactly the same

3 - x "approach" means limit as x goes to a value a, what does 3 - x equal

in this case a = 1

[autumn canyon]

Sorry this is all new to me

[vital crag]

that's why you should read

[autumn canyon]

I’ve been reading

[vital crag]

or watch videos

[autumn canyon]

And watching videos

I literally don’t understand

So the limit of f(x) as x approaches 1 is 2?

[vital crag]

for f(x) = 3- x yes

[autumn canyon]

So what do I do with the denominator

[vital crag]

the same thing

instead of 3-x, it's something else

[autumn canyon]

So rn it’s 3–x is 2

And the denominator is (1-6) = -5 and (1-1) = 0

Right

And what do I do from there

[vital crag]

dividing by zero is undefined, so watch the video about infinite limits
https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-14/v/introduction-to-infinite-limits

[autumn canyon]

Okay so if it’s undefined it doesn’t exist right

[vital crag]

depends how your teacher wants their answers

some want +infinity, -infinity, others want "does not exist"

[autumn canyon]

So is that it

Is that the answer

[vital crag]

depends on your teacher ¯_(ツ)_/¯

[autumn canyon]

Omfg that’s it?? It’s that simple

[vital crag]

this was simple for you?

okay sure

[autumn canyon]

YES

IF YOU EXPLAINED IT LIKE THAT FROM THE BEGINNING OMG

ok so what about 1c 1d and 1e

Are they all the same answers

[vital crag]

giving you the answer from the beginning wouldn't have taught you anything

[autumn canyon]

This is all new to me 😭

I know like finding basic limits

[vital crag]

if you're just looking for answers then this server isn't really the place

[autumn canyon]

Not from fictions

Functions^

[autumn canyon]

Right I’m trying to learn but it’s just the way you explained it

With the examples there were graphs

So can you also help me with 1c please

[vital crag]

why would i help you if you're just gonna complain

stop pinging me

[autumn canyon]

I’m sorry I didn’t mean to come off that way

I was just frustrated that it took an hour to complete that one question and I still have like 3 pages to go

I understand if you don’t want to help me anymore but can you find someone who can

[vital crag]

you're just wasting my time by not wanting to learn and just wanting answers

[autumn canyon]

I do want to learn??

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[mystic estuary]

the arithmetic mean of b,2b-a is b

[mystic estuary]

is part of a solution to some problem.

how can this not be a typo?

[fierce lagoon]

b+2b-a/2 = b

what is the question

[mystic estuary]

sorry

i double checked and still did it wrong

it says

Observe that the arithmetic mean of b,2a - b is b

so I swapped the variables there

[fierce lagoon]

you know what arithmetic mean is right?

[mystic estuary]

the solution is longer. I think focusing on the question distracts from this particular line I may misunderstand

so

arithmetic mean in that case would be:

0.5*b + 0.5(2a-b)

which according to my calculation is just a

[mystic estuary]

sus

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@mystic estuary Has your question been resolved?

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[plucky scaffold]

im unsure here

im thinking

x = "abcba", x' = "abc"

or x` = "abcba"

idrk

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[plucky scaffold]

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✅

@plucky scaffold Has your question been resolved?

[mystic estuary]

I mean abcba is a prefix and a suffix and is the longest

seems to work with aaaaa too

[plucky scaffold]

so x` = "abcba"

[mystic estuary]

i don't know

[plucky scaffold]

ok

[mystic estuary]

I would say it works

basically you must just give 1 example

so reread the whole thing with having a solution candidate in mind

and see if it contradicts at any point

eg ☑️

you're assuming x' is one of these we suggested

and also you can assume x = x', because it seems it's free to choose

and it's a simple choice

[plucky scaffold]

ok

[mystic estuary]

so you just try for the last paragraph

what does it mean among all substrings of x, x' is ..?

[plucky scaffold]

like combos?

[mystic estuary]

hm

it's a double statement the way i see it

x, x'

perhaps meaning among all substrings of x and among all substrigs of x' is ...

but if i'm not mistaken you can make the statement "among all substrings of a is .." easier

[plucky scaffold]

ye ill just ask

[mystic estuary]

think about it

isn't it the same as ".. is a substring of a?"

I might be wrong

"among all substrings of a is .." = ".. is a substring of a" ?

ok lets think this thrugh with an example

let a = "1234"

so substrings are "1", "2" "4", "12", "123", "1234", "23", "234", "34", and more

and something is among those

so simplification seems to work

that something is a substring

[plucky scaffold]

ye

[mystic estuary]

hm

so you can try understanding things more deeply that way

unless you learned a particular method to solve such problems, I think most people don't understand that fully when trying to solve the problem

but I'd recommend give that problem like 20 min to understand. try to grasp each such concept. (like the simplification we just did)

and if you don't have a way to get to a solution then put it aside for some time.

and look at it the next day etc

[plucky scaffold]

ok

[mystic estuary]

even if you don't solve it then. it will deepen your understanding

good luck

[plucky scaffold]

thx

[mystic estuary]

🙂

[mystic estuary]

and don't be afraid to ask later on. that's what you have teachers/professors for.

[plucky scaffold]

ye

[mystic estuary]

just asking you know what a substring is at this piont yeah?

[plucky scaffold]

ye

[mystic estuary]

if not you can likely figure out from the incomplete list of substrings I provided for "1234"

cool

👍

but I can tell you it took me some thought too

because the exercise wants you to think differently is my guess, and I'd try just practice that 😄

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[terse lake]

Is this simplified correctly?

[fossil geyser]

This step is incorrect

It looks like you just multiplied the first term in each bracket, and same with the second term

but (a+b)(a+b) is not a^2 + b^2

[terse lake]

Oh yeah. I have to FOIL right?

[fossil geyser]

Yep 👍

[terse lake]

Thanks! I'll re-check once I've done it over.

.end

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[rose hamlet]

i was thinking of differeniation the given condition

[rose hamlet]

then using that under the integral to make the derivatives cancel out

is it possible?

[vital crag]

Try it and see

[rose hamlet]

I did

i got stuck in acircular loop of by parts

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[snow quarry]

Can someone help me factorise

[mystic tapir]

factor the x out

then it will be a quadratic

[amber narwhal]

x(4x²+27x+7)

[snow quarry]

x(4x^2+27x-7)

[inland kettle]

after that only middle term splitting

good

[snow quarry]

huh

[mystic tapir]

use splitting the mid term

[snow quarry]

into what

[dull grotto]

determine the pairs of the product of a and c such that their sum is equal to b

[snow quarry]

oh

[snow quarry]

a+c = b?

it should be that?

[mystic tapir]

a is coefficent of x², b is the same of x and c is constant term

[snow quarry]

okayy

soo

[mystic tapir]

find two numbers p and q such that p+q = b and pq=ac

then write bx as px+qx

then factorise

that's it

[snow quarry]

so

a = 4 b = 27 c = -7

[mystic tapir]

yep

and also

[snow quarry]

need something that multiplies to -28 but adds to 27

oh i see

-28 and +1

[inland kettle]

yeah

[snow quarry]

whats next

[inland kettle]

good

now you can change that to

x(4x^2 + 28x - x - 7)

do you see it?

[snow quarry]

nope

u mean

-28 + x

[inland kettle]

4x^2 + 28x can be factorized

[snow quarry]

or

[inland kettle]

so can -x - 7

no i mean 28x - x

[mystic tapir]

take common factors out of the first 2 terms and the same withy last two terms

[snow quarry]

last 2 terms

havent got common factors

or am I js being dum

[mystic tapir]

what do you get from 1st two

[snow quarry]

4x(x+7)

[mystic tapir]

then take out "- " from the last two terms

[snow quarry]

huh

I dont get it

[mystic tapir]

-x-7 is the same as -(x+7)

[snow quarry]

oh u can take out the minus

i see

[shut gazelle]

Have you been taught any method on factoring polynomials?

[mystic tapir]

now there is x+7 with both 4x and -

[snow quarry]

so

it becomes

4x(x+7)-x(x+7)

?

[mystic tapir]

take the x+7 as common

[snow quarry]

what so

only 1 (x+7) ?

[mystic tapir]

use reverse distributive property

[snow quarry]

yk damn well

i dont know what is

[shut gazelle]

Have you been taught any methods on factoring before?

[snow quarry]

what do u think

[shut gazelle]

It depends, the people here could be showing you a way that they do it but something your teacher didn't show

Maybe your teacher taught a different method

[snow quarry]

I was probably taught how to but its been a long time

so

im just trying to recap it

cuz ive forgot

[snow quarry]

explain it

[shut gazelle]

There are many different ways to factor. One of the ways is the one shown above, where you facotr by grouping

[mystic tapir]

a(b+c) = ab+ac

[snow quarry]

wait

so

[shut gazelle]

There's also the AC method, where you would multiply A times C and find the factor pairs that sum to B

[snow quarry]

(4x^2+28x-x-7)

becomes 4x(x+7)

[mystic tapir]

think of a as x+7, b as 4x and c as -1

[snow quarry]

and -(x+7)

can u carry on from there

[mystic tapir]

you take x+7 commo and regroup the remaining coeffcients

4x(x+7) -(x+7) = (x+7)(4x-1)

and since we factored out an x before, it is x(x+7)(4x-1)

[shut gazelle]

If it helps, here's a video
https://www.youtube.com/watch?v=4v-EQIxqpMQ&ab_channel=TheOrganicChemistryTutor

[snow quarry]

Oh , I preciate that

Ill have a look at it after this

Thank you

[snow quarry]

oh I see

[snow quarry]

how did the 4x become 4x-1

[mystic tapir]

distributive property

pq+pr = p(q+r)

think of p as x+7, q as 4x and -1 as r

[snow quarry]

where did the -1 come from

[mystic tapir]

-(x+7)

[snow quarry]

sorry but im rly confused

[snow quarry]

so the - is a -1?

[mystic tapir]

it is the same as -1(x+7)

yep it is if it is multiplied

not added or subtracted

you don't write x as 1x

[snow quarry]

ok here me out

this is what im confused about

[mystic tapir]

it is the same with -x being -1x

[snow quarry]

the 2 things we have

are

4x(x+7) and -1(x+7)

[mystic tapir]

yep

[snow quarry]

the 4x and -1 are on the opposite sides

so how do they come together

[mystic tapir]

because they have x+7 in common

[snow quarry]

OHHHHHHHHHHH

AH

im so sorry 😭

[mystic tapir]

and that's basically it

[snow quarry]

I understand cuz both of them multiply with (x+7)

right?

[mystic tapir]

yeah

[snow quarry]

alright

tysm ranak

[mystic tapir]

yw

[snow quarry]

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[vital crag]

Use inverse function theorem

[barren crescent]

but i would have to set the function to 0

how do i solve that

[vital crag]

Why do you think you need to do this

[barren crescent]

the domain of inverse is the range of f(x)

and i would need to do that for the derivative of a inverse function

[vital crag]

You just need to check that the integrand is continuous at 0

[barren crescent]

why is that?

i thought it had to be the whole fucntion

[vital crag]

The integral of a continuous function is again continuous

[barren crescent]

and?

[vital crag]

That should answer this

[barren crescent]

i’m confused on how that answers

[vital crag]

Sorry meant to reply to this one

Did you mean when is f(x)=0

Or did you mean f(0)

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@barren crescent Has your question been resolved?

[barren crescent]

this one

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[outer granite]

hey to solve this, do i have to replace j with another variable equal to one?

[outer granite]

for example if i were to say let j = i + 5

[young verge]

Which one

[outer granite]

just for a

first problem

[young verge]

You can split them all up

[outer granite]

yea but before i do that

doesnt the value of j have to be 1

[outer granite]

what i did was let j = i+5 then i got n = 14 and and replaced i = 1

then i went 2(i+5) - 3(i+5)^2 + (i+5)^2

is this correct? can i just multpily this out and then split them up

[odd seal]

Or you could have done sum 1 to 19 - sum 1 to 5

but yours works too

[outer granite]

so im on the right track?

[odd seal]

But I would clarify with the teacher which way they want it, coz in schools, sometimes people want a certain way to answer

[odd seal]

yes

[outer granite]

this is the way our teacher taught us

[odd seal]

Then no problem. You can do it the way you are doing. You are on the right track

[outer granite]

thanks i appreciate the help 👍

.close

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[chrome cipher]

hi im just looking for some help with some review qs for my exam on thursday

[royal swan]

You can paste your questions, work etc instead of opening and closing multiple channels

[chrome cipher]

KNIEF HELP ME

pls

[rocky tusk]

wait nevermind

it said review

[chrome cipher]

yes bruh

[rocky tusk]

misread

[chrome cipher]

why u being an opp

i just need help reveiwing

[rocky tusk]

when you asked how to type it in

[chrome cipher]

wym

[rocky tusk]

it made me think it was a quiz

in your last help channel

[chrome cipher]

no

my quiz in on thursday

is

im supposed to be in algebra

[royal swan]

If you show your work then only people can review it

[chrome cipher]

oops okay nvm i got priv dm

[white sphinx]

i thought i was dyslexic when i clicked on this emoji to read its name

[chrome cipher]

.close

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[lilac zealot]

I understand that this is a geometric distribution but I'm not sure what to do next.

[lilac zealot]

Would I use this formula for the probability distribution: P(X = k) = (1 - p)^(k-1) * p

so it becomes (.8)^(4) * 0.2?

or is it a binomial distribution?

[stoic temple]

Binomial

[lilac zealot]

why?

[stoic temple]

Little trials, relatively moderate probability

[lilac zealot]

oh wait ya

so then to find the prob distribution: (5 choose 1 ) (.2)^1 (1 -.2)^4 ?

and variance is 5(.2)(.8)

that doesnt really seem right

[stoic temple]

It says at most 5

It means it could be 5,4 ,3,2or 1 trials before he gets a head

[lilac zealot]

so for prob distribution i have to sum up for 1, 2, 3, 4, 5

and same with variance

OH wait so P(X <= 5) = P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)

and then for each p, n = 5, p = .2.

[stoic temple]

He stops when he gets a head

[lilac zealot]

oh wait then wont that be super complicated cause id have to do every case for every trial?

[lilac zealot]

i can restrict the space to {0, 1} but im still lost

H + TH + TTH
like that

?

[final saddle]

@lilac zealot Has your question been resolved?

[lilac zealot]

No 😭

[stoic temple]

What I meant is that x=1, x=0 always

Only the number of tries changes

[final saddle]

@lilac zealot Has your question been resolved?

[lilac zealot]

okay hmmm

[final saddle]

@lilac zealot Has your question been resolved?

[final saddle]

@lilac zealot Has your question been resolved?

[final saddle]

@lilac zealot Has your question been resolved?

[final saddle]

@lilac zealot Has your question been resolved?

[hollow sorrel]

it's not 'really' a standard distribution

so firstly note that either they get a head in the first 5 flips

in which case Y will be 1

or they don't get a head in the first 5 flips

in which case Y is 0

(you can calculate these with a geo. dist.)

then from this point, Y is just a bernoulli r.v. so you can easily calculate variance

[final saddle]

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[deft ravine]

You're the same Bepo I helped before, aren't you? If so:

Das ist einfach eine lineare Funktion.

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@thorny folio Has your question been resolved?

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[surreal trellis]

@worldly spruce

:3

[white sphinx]

wot

what do you need help with

[surreal trellis]

q4 b, c, d

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[final saddle]

Please don't occupy multiple help channels.

[mint burrow]

hello i cant get further from here

[latent fractal]

@mint burrow it looks like you have two identical help channels

[mint burrow]

yes i was confused

so i accidentally opened two

sorry

this is my first time so

[latent fractal]

just .close one of them so that you don't end up with conversations in both

[mint burrow]

lemme close this one

.close

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[naive wedge]

i am stuck with part 2, i am a bit unsure on how to apporach the question

what can i do to check if one span is within another?

[languid yoke]

linear combinations

e.g in C, you know x is a linear combination of y and w, so this equality is true

[naive wedge]

full question

[naive wedge]

may be a dumb q, but how is x a linear combination of y and w

[languid yoke]

w is a linera combination of x and y right

so you can just rearrange

[naive wedge]

yes

but what about z?

or does Z not matter here as its not mentioned in the span

[languid yoke]

in C it doesn't matter

[naive wedge]

for option E, would it be true as

W is linear comb of x and y
z spans z

[languid yoke]

yes

[naive wedge]

for option B true bc,

w spans w
x is a linear comb of z/y

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@naive wedge Has your question been resolved?

[naive wedge]

.close

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[fierce yew]

I used 46(2.78)sin(40.9) and it didn't work

[fierce yew]

*I tried 83.73 it also didn't work

[humble swift]

Shouldn't it be cos(40.9)?

Oh wait nvm

And yea y coordinate

U have gravity too

U can't use speed=distance/time

U should be using

s=ut+1/2at²

@fierce yew

[fierce yew]

Like this?

[humble swift]

Yes

[fierce yew]

the answer didn't work

so 90.01 doesn't work , i also tried 90.01(2.78) to find distance

[humble swift]

Ok so did u find the time of ascent

No listen

The object is not going up only

It will go up and then stop and fall again

So did u find max it can go?

[fierce yew]

how do you find that?

[humble swift]

Ok so

What is the

y velocity?

@fierce yew

Velocity along y direction

[fierce yew]

46sin(40.9)

[humble swift]

Yes

What is the acceleration?

Along y

[humble swift]

Nah just leave it that way for now

[fierce yew]

wdym

[humble swift]

In terms of sin

[humble swift]

Noo listen

Oof

What is the acceleration?

It's not zero so u can't use that

[fierce yew]

its this isn't it?

velocity divided by time

[humble swift]

No

Do u know these

v=u+at

s=ut+1/2at²

v²-u²=2as

These 3?

[fierce yew]

not really

[humble swift]

Wait then

U gotta learn these

Before solving trajectories

[fierce yew]

wait are they the same as these

[humble swift]

Yes

Same

[fierce yew]

if we use the first formula then

if it doesn't specify initial and final

[humble swift]

No no

I'll walk u through

Just answer my questions

[humble swift]

U said initial velocity is this thing

For maximum, the final velocity should be zero

What is the acceleration?

[fierce yew]

it should be this

[humble swift]

Nop

"Gravity"

[fierce yew]

where would there be gravity?

for acceleration?

[humble swift]

Yes

Since it's y direction

U have gravity

[fierce yew]

found it

[humble swift]

U

Did the same thing

Again

...

[fierce yew]

its literally correct

[humble swift]

Then

Wait

Ah

I didn't see properly

U didn't put sin the first time

[fierce yew]

ahh ic

thx for ur help

wait why did u even ask for me to find acceleration anyways

[humble swift]

Ok so

[fierce yew]

its not in the formula at all

[humble swift]

There is this case

Sometimes

They give u time

Which actually

Is the time when it starts falling again after reaching max height

At that time

Ur y coordinate increases first and then decreases

So u need to check now

[humble swift]

-9.8 is the "gravity"

[fierce yew]

ohh ic

[humble swift]

Yep

[final saddle]

@fierce yew Has your question been resolved?

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[storm cloak]

so I was solving for integrating factor
and p(x)=x^2-x
so it was e^ int(x^2-x)
and I was doing it
and I was like
e^x^2e^-x
so then
(e^x)^2e^-x
e^2xe^-x
e^(2x-x)
=e^x
can I assume that there are no parenthesis around the integral (It is true that (e^x)^2 will always equal e^2x? (Why did someone tell me that it's SOMETIMES true that e^(x^2)=e^(2x), cause x^2 doesn't equal 2x, so I'd assume never...)
because if I do, I get the right answer

[storm cloak]

(Also, can someone help me get through my differential equations study guide and all the proofs/definitions for my exam in the morning, I'm not gonna sleep tonight if someone will be able to help me through the night)

[fallen vigil]

(e^x)^2 = e^(2x) not equal e^(x^2)

[storm cloak]

can you prove that it's not equal to e^(x^2)

[steel plaza]

Just take a random example

[fallen vigil]

hi bit <3

[steel plaza]

Let e be 2 and x be 3

e^(2x) = 2^(2×3) = 2^6

e^(x^2) = 2^(3^2) = 2^9

[final saddle]

@storm cloak Has your question been resolved?

[storm cloak]

so e^(x^2) will never equal e^2x

so in this example when we are finding integrating factor, it's ok to do e^(x^2-x)=e^(2x-x)=e^x

[steel plaza]

It'll be equal

When x = 2

because x² and 2x will be 2² and 2(2)

Also if x = 0

0² = 2(0)

[steel plaza]

e^(x² - x) = e^(x(x-1))

not e^x

[storm cloak]

oh yeeeah

fire

that's crazy

weird

yo

[storm cloak]

e^(x² - x) = e^x^2 * e^-x = (e^x)^2 e^-x = e^(2x) e^-x = e^(2x-x) = e^x

[final saddle]

@storm cloak Has your question been resolved?

[whole halo]

the to-the-power-of operator ^ works right-to-left
so 2^3^4 means 2^(3^4) = 2^81 = 2.418 septillion
a^b^c^d^e is read as a^(b^(c^(d^e)))

if you force the order to be left-to-right using ()s, you can simplify using an exponent law
(2^3)^4 = 2^(3*4) = 2^12 = 4096

(e^x)^2 just means (e^x)(e^x) which is e^(2x), not very interesting
on the other hand e^(x^2) is e^(x * x) which you can see isnt the same thing as e^(2x)
when someone writes e^x^2, they mean e^(x^2) because ^ goes right-to-left by default

[final saddle]

@storm cloak Has your question been resolved?

[final saddle]

@storm cloak Has your question been resolved?

[whole halo]

@storm cloak what are you stuck on

[storm cloak]

oh so

since it goes left to right

you're saying its e^(x^2)

by default

that's weird bro

[whole halo]

yea its the only way you can have ^ mean something different

otherwise you do ^ ^ ^ ^ ^ and its just ^ ( * * * * )

[storm cloak]

why not let it be e^x^2=(e^x)^2 instead of left to right always to be e^(x^2)

is that just a

forced thing

left to right

(oh it's because tis the operator huh)

[whole halo]

because then you wouldnt have a reason to ever do a^b^c

[storm cloak]

(so it NEEDS to be e^(x^2)

[whole halo]

I dont know what youre saying

[storm cloak]

I'm just saying

does e^x^2 NEED TO BE EQUAL TO e^(x^2)

cause that's mainly where I see you pointing

[storm cloak]

yeah you even said it here

[whole halo]

thats a "why"

not a "what"

the reasoning behind why an operator has to work a certain way isnt "just because"

otherwise that's a "what"

the why is that if you had a^b^c^d just mean a^(b * c * d), then you would no longer need to use more than one ^

it would just be one exponent then the rest is multiplication

if you want to force exponents to be calculated, doing them right-to-left doesnt allow exponent laws to "cheapen" the operation

so a^b^c^d means something different than just a^(b * c * d), its much larger

so e^x^2 is equal to e^(x^2) because if it was (e^x)^2, you might as well just write e^(2x)

[storm cloak]

true

lol

alr

(The question was inherently tied to a differential equations bernouli's eqn problem)

(since we had p(x)=x^2-x.....so it was like e^x^2-x, which we wanted to simplify to e^2x-x=e^x

which did get us the right answer

[whole halo]

then its written (e^x)^2 not e^x^2

[storm cloak]

I mean

it's the intergating factor

u know DE?

[whole halo]

you tell me why it worked then

at least show the original DE

[storm cloak]

x^2 dy/dx + y^2 = xy, y(1)=1

[whole halo]

@storm cloak you also got y = x / (1 + ln x) right

[final saddle]

@storm cloak Has your question been resolved?

[storm cloak]

yeah

[magic crest]

Wait a min

I've seen you somewhere

Are you from the chemistry Server

[whole halo]

I had an integrating factor of e^(int 1/x dx) instead
https://www.desmos.com/calculator/exchzk1von

[storm cloak]

????????????

I got the integration factor of e^(x^2-x)

odddddddd

[whole halo]

go show your work

[storm cloak]

wait I thiink that was fir another problem

I have the same integration factor when I checked my work for this one

one sec

It was

dy/dx + 2xy=y+4x-2

I'm 90% sure

(if it isn't then it has to be x^2 dy/dx + x(x+2)y = e^x, which it isn't so it's right. I'm 1999.99% sure)

[whole halo]

then yea the integrating factor is e^(x^2 - x)

because of the order of operations, (e^x)^2 is not the same thing as e^(x^2)

[storm cloak]

ye

[whole halo]

you can graph e^(x^2) and e^(2x) to make sure of it

then compare that with (e^x)^2 and e^(2x)

[storm cloak]

wait so is it ok to treat it as e^x^2 e^-x in this case

[whole halo]

yea thats correct

[storm cloak]

how can I explain that to a gorup of people who don't believe me

[whole halo]

you didnt really believe me at first I think

just use my explanation

[storm cloak]

no I 100% believed you

[whole halo]

oh thats not good

[storm cloak]

I was just asking so I could explain

[whole halo]

have them go on desmos.com and go graph:

then tell them that the ^ operator goes right-to-left

[storm cloak]

oh well

they were saying the integration factor is

[whole halo]

e^x?

[storm cloak]

e^ (intp(x)dx)

which it isn't

it's e^int(p(x)

[whole halo]

those are identical

[storm cloak]

parenthesis matter here cause of x^2

no?

[whole halo]

e^(int p(x) dx) = e^(int (p(x)) dx)

your extra set of parentheses doesnt do anything

by default p(x) is treated as one term

when something gets substituted, you can assume an extra set of parentheses comes in with it

[storm cloak]

wait so I can just say that e^(x^2-x)=e^x^2e^-x and remove parenthesis

or ignore them

[whole halo]

that works

not very readable but its plausible

[storm cloak]

how do I know when to not take away parenthesis/when parenthesis matter

[whole halo]

thats a question for PEMDAS/BODMAS

you see what the default order is of the thing you wrote down, then use parentheses in case something gets done out of order

try not to use extra parentheses

[void sluice]

😢

[final saddle]

@storm cloak Has your question been resolved?

[final saddle]

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[lime crest]

"Given the sequence...... find the sum of the first 2005 terms"

[lime crest]

i dont see the pattern at all

[final saddle]

@lime crest Has your question been resolved?

[lime crest]

<@&286206848099549185>

[sour kindle]

thetes a simply formula for this

[lime crest]

what is it?

[sour kindle]

n(n+1)/2

where n is the last term

[lime crest]

thats for an arithmetic sequence bro

[sour kindle]

what language is that in i can’t read it

[royal swan]

@lime crest I see a pattern but if we exclude 1,1 then only

[sour kindle]

my bad i’m dense

[royal swan]

Its not an arithmetic progression

[lime crest]

?

[royal swan]

Nah I was wrong, no pattern yet

[lime crest]

oh

[final saddle]

@lime crest Has your question been resolved?

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[vocal iris]

Can you check if the trend and direction of opening if its correct before we proceed to the vertex And others I need help with

<@&286206848099549185>

[humble swift]

!15m

[final saddle]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[gray acorn]

seems good

i think

[stoic temple]

What does it mean by "trend"

Is that only for positive values of x

[mint arrow]

it seems as if It refers to whether the function is increasing or decreasing

[stoic temple]

Okay

[vocal iris]

Sure??

[vocal iris]

Uhm i dont think so coz look at this

[stoic temple]

Have you learned derivatives

[stoic temple]

Even though

[mint arrow]

I mean that's how the op must have concluded over that

[vocal iris]

This is the first page

My answers are wrong huhu help

[vocal iris]

Noo

[stoic temple]

Still don't get trend

[mint arrow]

Wait so how did you even conclude over the nature of functions regarding whether it's decreasing or increasing

[stoic temple]

You should be given a range of x

Are you sure trend isn't like : increases then decreases

[spare hazel]

maybe that can be used

[stoic temple]

,w plot y=x^2

[soft zealot]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[stoic temple]

Decreases and then increases

For y values

[vocal iris]

Huhh

[stoic temple]

Wait are they talking about the gradient

[vocal iris]

Gradient??

What is that

[spare hazel]

calculus topic

[stoic temple]

Ratio of Change in y to change in x

[stoic temple]

Probably

[vocal iris]

Hello?

Oops

[vocal iris]

Nah this is grade 9

[stoic temple]

Okay

What did you learn in this topic

[stoic temple]

From this I might be able to find out what to do

[spare hazel]

those both are based on algebra

and I could only find these methods

[vocal iris]

Vertex graphs

Parabolas

[stoic temple]

Yes

Anything else

@vocal iris

[vocal iris]

Huhh

How do i get the minimum and maximum value

[spare hazel]

for the equations of the form F(x) = a(x-h)^2 +k

min/max value is vertex

[final saddle]

@vocal iris Has your question been resolved?

[vocal iris]

Guyss

<@&286206848099549185>

WHAT

BUT LIKEE

Did I made a mistake

[quick sorrel]

<@&286206848099549185> I need help

[final saddle]

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[fallen vigil]

can I think of correspondence theorem as, with group G, normal subgroup N,

we have a map f: G -> G/N

f restricted to subgroups containing N is an isomorphism.

additionally, subgroups are mapped to subgroups and normal subgroups are mapped to normal subgroups

[hollow sorrel]

i think you mean "subgroups containg N is a homomorphism"

[fallen vigil]

yea, but isnt there one to one correspondence as well thus an isomorphism?

[hollow sorrel]

not necessarily

[fallen vigil]

:(

[hollow sorrel]

otherwise G/N would be isomorphic to a lot of subgroups of G

[hollow sorrel]

i'm not entirely sure what you mean by subgroups are mapped onto subgroups, cus that follows from the 1st iso. thm

[fallen vigil]

oh

[hollow sorrel]

but yep, normal subgroups are mapped onto normal subgroups

[fallen vigil]

sorry, 3rd line was supposed to say subgroups containing N

does that change anything?

[hollow sorrel]

yeah i figured

i think it's kinda like this

if we have a group G, then there's an obvious hom. from G to G/N

[fallen vigil]

is it an isomorphism?

[hollow sorrel]

no

[fallen vigil]

yea

[hollow sorrel]

if we had some N <= K <= G

then you can think of the restriction of f to K as "the hom. from K to K/N"

[fallen vigil]

yes

where does the correspondence come in :(

[hollow sorrel]

the correspondence says that if i have a subgroup K

i can associate it with a subgroup of G/N

namely K/N

and that if i have a subgroup of G/N

i can associate it with a subgroup of G

(obviously this is interesting because what i actually mean by 'associate' is there is a 1-to-1 bijection)

i think maybe let's take G = Z

N = 12Z

then G/N is Z/12Z which has lots of subgroups

[fallen vigil]

yes

[hollow sorrel]

one of them is say {0, 4, 8}

this subgroup of G/N corresponds to the subgroup of G namely 4Z

cus 4Z / 12Z = {0, 4, 8}

[fallen vigil]

but it isnt an isomorphism because...?

[hollow sorrel]

well 4Z is not isomorphic to C3

[fallen vigil]

it isnt?

[hollow sorrel]

4Z = {0, 4, 8, 12, etc., -4, -8, -12, etc.}

i.e. isomorphic to Z

whereas C3 only has 3 elements

[fallen vigil]

ohh

so theres a bijection between the subgroups containing N and subgroups in G/N. this bijection maps subgroups to subgroups and normal subgroups to normal subgroups. however it isnt a homomorphism?

[hollow sorrel]

well i mean it's a bijection between sets

we don't have a group structure so it can't really 'preserve structure'

[fallen vigil]

i see

thank you!!

.close

[final saddle]

Channel closed

Closed by @fallen vigil

Use .reopen if this was a mistake.

[hollow sorrel]

nw!

i think perhaps a useful way to interpret quotient groups G/N is 'G with N killed'

[fallen vigil]

yea i was thinking of that

[hollow sorrel]

so 2 things in G are considered the same if they differ by N

[fallen vigil]

instead with N collapsed to a point

[hollow sorrel]

thinking of it like that might make the correspondence thm more intuitive

[fallen vigil]

it is time to try understand the proof

[final saddle]

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