help-23

[marsh walrus]

so just assuming that you believe it for a second, does this part make sense?

[hazy nebula]

gimme a sec reading

[marsh walrus]

okay

may help to review the beginning of the proof since its been a min now

[hazy nebula]

oh

this part make sense

[marsh walrus]

so yea

if you buy the algebra

this is how itd end

this shows you can just take the given information and the proposed formula, and get any term

so the algebra comes from just like

usually in these proofs where you need to connect screwy algebra, youll off to the side or in the margins or something, just assume what you want to be true

so wed write out $u_{n+1} = \frac{3(n+1)-2}{(n+1+1)^2} = \frac{3n+1}{(n+2)^2}$

[flat frigate]

jan Niku

[marsh walrus]

then youd eye this formula for a second

and notice you need to introduce a u_n somewhere on the rightest side of that equation

and youd hope that the algebra works out to give you the thing on the top

so you just do it

$u_{n+1} = u_n + \frac{3n+1}{(n+2)^2} - u_n$

[flat frigate]

jan Niku

[marsh walrus]

add it, subtract it, so still argebraically valid

even though we cant use any of this work directly in the proof since we just assumed the conclusion right off the bat

now, it sort of seems like, eyeing this, that itll work out

you should end up with (n+2)^2 (n+1)^2 in the bottom when you turn this into a single fraction

so all you need to do is check that the numerator works out

id encourage you to try this scratch step on your own since uhh

well to convince yourself

id start from here, and sub in the second u_n for the provided formula in part b

see if you can get to this

if you can, then your scratch work, in reverse order, gives you all the steps you need for your proof

since you began with what you want to show, if you do it backwards, youll end with showing what you want to show 😄

[hazy nebula]

i can get to this

[marsh walrus]

[hazy nebula]

damm

[marsh walrus]

fun problem

[hazy nebula]

not fun

sad moment

[marsh walrus]

hahaha

[lean otter]

XD

[marsh walrus]

well

itll get easier then

how u feel about the rest ba

[hazy nebula]

i will try

[marsh walrus]

[hazy nebula]

the rest

np

[marsh walrus]

feel free to ping

ill be floating around

[hazy nebula]

but thank you so much

!!

[marsh walrus]

np

[lean otter]

We (as me and @hazy nebula ) has 2 weeks before examination 😂 hopefully it will get easier by then 🤔

[marsh walrus]

putting in the work is all you can do ig 💪

[hazy nebula]

okok tysm @marsh walrus i will get going!

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[lean otter]

I have my answer but I just want to check to see if I got it correct. I got** 2/9-(2√15/9)i**

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[ancient escarp]

that'd be when your revenue equals your total expenses

[lean otter]

https://en.wikipedia.org/wiki/Break-even_(economics)

[ancient escarp]

yeah i'd ignore that wikipedia link if i were you

[lean otter]

why

[ancient escarp]

it has absolutely zero relevant information

[lean otter]

you can always read the references and further reading below

also did you read the construction section

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[severe meadow]

village with 500 people, men to women 4 : 1. 90% of men are right handed and 75% of women are left handed. Are there more women with left hand or men with right hand

[severe meadow]

um

[ancient escarp]

you don't even need to do any math for this

just logic

[severe meadow]

Yesh

Thats why i need help

[ancient escarp]

with what exactly

[severe meadow]

Working

Out

[lean otter]

isnt logic part of math

???

[severe meadow]

I need to whow my working out

Show

[ancient escarp]

the answer is obvious

there are not only 4 times more men, but a higher percentage of men are right handed

[severe meadow]

Ik that

I meant like

I need to know how

The workings

[ancient escarp]

well start by using the ratio to determine how many men and women there are in the village

[lean otter]

75 percent of women are left handed

[ancient escarp]

you know there is a total of 500 and there is a 4:1 ratio

[severe meadow]

Is the first step to add ratios

Then sivided them

Divide

[ancient escarp]

huh

[severe meadow]

Tell me the process

Pls

[ancient escarp]

.

[severe meadow]

I want to know how to workvout these questiom

[ancient escarp]

.

[severe meadow]

Im lost bro

[ancient escarp]

do you not know how to get a quantity based on ratios?

[severe meadow]

No im new to ratios

[ancient escarp]

if there is a ratio of men to women that is 4:1, that means there are 4 times as many men as there are women

[lean otter]

i know what would help

https://en.wikipedia.org/wiki/Ratio

[ancient escarp]

for the love of god stop sending wikipedia links

[severe meadow]

Oh ye

So the first thing i do is to add the rwtios

[ancient escarp]

yes

[ancient escarp]

ah that's what you meant up here

i thought you were talking about two different ratios

my bad

[severe meadow]

Oh

[ancient escarp]

yes, add the ratios and divide the total quantity by the sum of the ratios

[severe meadow]

500/5?

[ancient escarp]

yep

which is?

[severe meadow]

100

[ancient escarp]

right

so now you refer back to your 4:1 ratio

and multiply the new number you got, 100, by each ratio

and that will give you the total number of men and women, respectively

[severe meadow]

So 400:100

[ancient escarp]

it doesn't need to be expressed in a ratio anymore, but yes

[severe meadow]

M:w

[ancient escarp]

there are 400 men and 100 women

[severe meadow]

OMG TY

[ancient escarp]

👍

[severe meadow]

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[lean otter]

how many numbers under 500 are divisible by neither 2, 3, or 5?

[brave wagon]

are we talking prime factors?

[lean otter]

wdym

[tall sphinx]

Simple python function if you are up for that

[lean otter]

oh aight

[brave wagon]

the first thing is to delete all numbers ending in 2, 4, 5, 6, 8, and 0

[lean otter]

il do java

[brave wagon]

then delete all remaining numbers that have a digital root of 3, 6, or 9

[tall sphinx]

Np I prefer java but python is so quick

Anyhow. If I understand correctly you want all numbers not divisible by 2/3/5?

[lean otter]

yeah

under 500

[tall sphinx]

Yep that is easy

int i =500

Im on phone btw

Actually lets fo a for loop

[lean otter]

okay

[tall sphinx]

Eeh you know how it goes, just do if(i%2!=0){ add to array}

Im not gonna type the rest

I’d probably use a while loop as you can just change i in your config file

But you can do whatever

Gl and have fun

[lean otter]

yeah

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[crisp wharf]

is the center 4, -4?

My solving is wrong coz the end of the diameter 3,1 is too close to the center for the radius to be 8

[thin bridge]

,rotate

[thin bridge]

is the center 4, -4?
no

[crisp wharf]

Then wot do i do

[thin bridge]

do something like completing the square to get the equation of the circle in standard/ centre-radius form

[crisp wharf]

Yeah this is what i did

[thin bridge]

the centre (2,-2) written on the page is correct
but the radius is wrong in multiple ways (but you don't really need that)

[delicate bobcat]

If you complete the square you should get (x-2)^2

You add 4 to complete but the factored form has a 2 for those

[lone flame]

Dude

Take a look at your steps once again

[crisp wharf]

ok ill do it again

[lone flame]

Line 3
What's 2+4+4?

[crisp wharf]

10

bruh

[thin bridge]

2 + 4 + 4 isn't 8
and the equation of a circle in standard form (with centre (h,k) and radius r) is NOT
(x-h)^2 + (y-k)^2 = r

[crisp wharf]

i forgot about the 2

[lone flame]

It's r^2

Radius is sqrt(10)

[crisp wharf]

ohh

ic

so i just square at the end?

how do i put the square

[lone flame]

,calc 10^0.5

[flat frigate]

Result:

3.1622776601684

[crisp wharf]

wait i square root? ok

[lone flame]

What do you mean?

[thin bridge]

r^2 = 10
solve for r>0

[crisp wharf]

like when im writing my solution at which part of the solution do i square root

[thin bridge]

technically you don't actually need the radius

[crisp wharf]

yeah just find the point to the opposite side

but the teacher might make a fuss so ill just complete it

[thin bridge]

and if you can achieve that without getting r, don't bother getting r

[lone flame]

Here @crisp wharf

$$(x-a)^2+(y-b)^2=r^2$$
$$\text{center is (a, b) and radius is r}$$

[flat frigate]

bakasta

[crisp wharf]

oh thanks

[delicate bobcat]

It would be more trouble to somehow use the length of the radius

[lone flame]

On the right hand side you've 10

[delicate bobcat]

Use midpoint formula

To find the other end

[lone flame]

Here check this text

[crisp wharf]

aight

[delicate bobcat]

(The center is the midpoint of the 2 ends of the diameter)

[crisp wharf]

yeah

[lone flame]

His method is quite easy and less tedious

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[true lance]

Hello, I need more help with a problem I was initially working on. I really don't know what I should be doing here. I did the first few steps, turning the roots into exponents, but I don't know how to approach an expression being divided by another one.

[steel stag]

first write out all the things being multiplied or divided

it's x^3 * (x+6)^1/2 / (x^2+2x+1)^1/7

(idk if that's a cube root on top or x^3)

logarithm turns those into pluses and minuses

[ancient escarp]

looks like x^3

[steel stag]

so it becomes
x^3 PLUS (x+6)^1/2 MINUS (x^2+2x+1)^1/7

[true lance]

ahh I see

[true lance]

so would the problem be ended with x^3+(x+6)^1/2 - (x^2+2x+1)^1/7?

[steel stag]

the exponents get brought to the front too

[ancient escarp]

you might wanna refresh log rules

[steel stag]

so 3lnx + 1/2ln(x+6) - 1/7ln(x^2+2x+1)

you can factor that last bit some more too

[true lance]

yeah I got behind in this class and never really got to fully learn them but didn't know where to start

[ancient escarp]

you can google "log rules" and go to images

[lean smelt]

khan academy on logarithms

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[lean otter]

hi

[lost cove]

It's a nice tactic my dude

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[kindred bridge]

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[ivory viper]

can someone check this for me if i do this right?

[ivory viper]

.clsoe

.close

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[lean otter]

I just want to verify that my years 1 & 2 are good

The material for the class was PV (Present Value) of Annuities

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@lean otter Has your question been resolved?

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

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@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

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@lean otter Has your question been resolved?

[silent forum]

That's a rather unclear table you have there, @lean otter

[lean otter]

Hello

I spent the last 4 hours revising it

Want to look it over? It is fairly simple now.

[silent forum]

Show us the math for some specific values you want to check and i could go through it

[lean otter]

I'll give you my handwritten calcs first

You read the scenario?

[silent forum]

Yes

[silent forum]

Ok, which calcs u are most doubtful about

İ wont go through it all :)(

[lean otter]

I am fairly certain about them now, but maybe one?

*but maybe check one or two?

[silent forum]

Aight

[lean otter]

here is my excel sheet, disregard everything below row 40

[silent forum]

Math looks quite sound

İs this a uni course?

[lean otter]

hahahaha no

Well its a small college, but its intro to finance

I remember seeing this in high school

[silent forum]

Yeah well the many random calculations are not particularly appealing :))

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[silent forum]

But as long as you understand the math behind i wiuldnt worry too much about some typos

[lean otter]

so is that a stat case study?

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[silent forum]

Pretty much

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[runic tulip]

A 16m long rope is used to form the three sides of a rectangle, one of whose ribs rests along a wall, as shown in the figure below.

a. Find x and y so that the rope limits the part with the largest surface.

b. Another rope is used to limit a surface of 50m ^ 2 in the same conditions as the first. What is the shortest length he can have?

[runic tulip]

I found a) with the values x = 4 m and y being 8 m

but, Im struggling to find b)

I did: Area = x * y
50 = x * y
50/x = y. Then used this on the perimeter formula:
P = 2x + y
P = 2x + 50/x

I found the derivative of this equation, and got the values x = 5m and y = 10m

with the total length of the rope 20m

but, when I checked the answers, the total length should have been 15m

Im not sure what I've missed

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@runic tulip Has your question been resolved?

[runic tulip]

at a), I could change the original formula of the perimeter of the rectangle from P = 2x + 2y to 2x + y, but Im not sure if I should leave the Area = x * y the same in b)

<@&286206848099549185>

[thin bridge]

the bounded region is still a rectangle

so you'd still use the same formula for the area

[runic tulip]

But why am I getting a different answer?

https://media.discordapp.net/attachments/784351642945454094/915273631783870575/IMG_20211130_171011.jpg?width=960&height=540

here are my calculations

[thin bridge]

your work is fine

[runic tulip]

Do you think the author made some error?

[thin bridge]

probably

[runic tulip]

Alright, thanks

.close

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[pliant talon]

Currently I need to transpose L in fR = 1/2π√LC to make L the subject in this equation

[pliant talon]

however each time I do that it doesn't work out exactly (I rearranged it to be L = (1/2π)/√C)^2)/fR)

(and it doesn't work)

currently the values for this would be
fR = 460kHz
C = 12

and if I redo the equation with it I don't get 460kHz back

(even if I convert it in any way, shape or form)

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@pliant talon Has your question been resolved?

[pliant talon]

<@&286206848099549185>

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@pliant talon Has your question been resolved?

[pliant talon]

ITS BEEN NEARLY AN HOUR

;W;

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@pliant talon Has your question been resolved?

[pliant talon]

:(

[crystal agate]

If I may, I think the eqn you are looking for is L = (((2pi)*fR)^2)/C

It is sqrt(L*C) in the original equation correct?

[pliant talon]

yep

lemme just do the math

[crystal agate]

Did it work?

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[zenith stirrup]

can u help me with this (8m^3n)^3

[zenith stirrup]

<@&286206848099549185>

.....

<@&286206848099549185>

<@&286206848099549185> i have been waiting

😦

nvm

.close

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[strange compass]

I feel there is a very simple explanation but I must ask.
The red line is the graph of g(x).
What does it mean, then, and why, when it lets h(x) = ..... g(t)dt? Why is it represented in terms of t?

[ancient escarp]

fundamental theory of calculus

[strange compass]

Ok, but that just causes me to ask again: why is that represented with t?

[ancient escarp]

the uhh fundamental theory of calculus

g(x)=h’(x)

[lament ginkgo]

Because you can’t use x both inside the integral and as an integration extreme

It’s confusing, so they use this notation instead

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[ancient escarp]

what's confusing you?

[burnt oriole]

i may sound dumb but i have absolutely no idea what to do

[ancient escarp]

do you know how to isolate a variable?

[next gulch]

^^

[ancient escarp]

if i gave you 4x=7, can you isolate x?

[next gulch]

The subject refers to what you are solving for

[next gulch]

This is solving for y

You need to solve for x

You csn Google what a subject is if you are lost still

@ancient escarp sorry i think you were here first

[ancient escarp]

all good

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[burnt oriole]

.close

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[old willow]

Can someone please explain the rules of using parentheses here

Let h = “John is healthy,” w = “John is wealthy,” and s = “John is wise.”
a.    John is healthy and wealthy but not wise. (h ∧ w) ∧ ¬s
b.    John is not wealthy but he is healthy and wise. ¬w ∧ h ∧ s
c.    John is neither healthy, wealthy, nor wise. ¬h ∧ ¬w ∧ ¬s
d.    John is neither wealthy nor wise, but he is healthy. (¬w ∧ ¬s) ∧h
e.    John is wealthy, but he is not both healthy and wise. ¬w ∧ (¬h ∧ ¬s)

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@old willow Has your question been resolved?

[old willow]

anyone expert with Propositional Logic?

[pastel nymph]

no

[old willow]

😵‍💫

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@old willow Has your question been resolved?

[steel stag]

none of these parentheses matter

A and B and C is the same no matter where the parentheses go

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@old willow Has your question been resolved?

[old willow]

you mean I can just remove these parentheses and the answer is still right? what I know is parentheses are used to override and I agree with u that I don't see any changes if I remove them but our teacher added them and I got confused

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[slim reef]

Hi, knowing q = 11, it is possible to compute α from a(2)=3 and a(4)=4? Thanks

[safe radish]

@slim reef Has your question been resolved?

[slim reef]

<@&286206848099549185>

[crisp latch]

yes ig
bcos 2 equation and 2 variable

[slim reef]

well do you consider the fact that it's in a polynomial field?

it's a question of abstract algebra

[crisp latch]

a(2) and a(4) gives eqn in alpha and beta so can't we solve it ?
idk abt abstract algebra sorry

[slim reef]

we can't necessarily solve since it's not in Z but Zq
no problems ^^

[quasi bison]

why can't we

let's at least try and see what happens

@slim reef

Z_11 is a field, so you can solve systems of linear equations over it just fine

using the exact same motions you go through when solving a system of equations in the real numbers

the only difference is when you have to divide by something

[slim reef]

Hi Ann

[slim reef]

Yeah I understand, thanks

I'm trying to solve

[safe radish]

@slim reef Has your question been resolved?

[slim reef]

oki so:

a(2)= α2^5 + β2^3 + (2α+β)
-> 3 = 10α + 8β + 2α + β = 12α + 9β = 1α + 9β (1)
a(4)= α4^5 + β4^3 + (2α+β)
-> 4 = α + 9β + 2α + β = 3α + 10β (2)
(1), (2) -> -9+4 = -3α + 3α -27β + 10β = -3α + 3α -5β + 10β
-> -5 = 5β -> β = -1

now for α:

3 = α + 9β -> α = 3-9β = 3+9 = 12 = 1

is this correct?

(still considering the process in Z11)

@quasi bison sorry for the ping 😅

[quasi bison]

your answer matches mine

[slim reef]

thanks a lot! 😄

there was a second part to the question: in Z13, if only one equation a(i) = n, n ∈ Z13 and i ∈ {1,...,7} is known, then any α ∈ Z13 is possible

do you think it's true?

[quasi bison]

well you have two unknowns and only one equation so yeah you have insufficient info as is

[slim reef]

oki thanks!

is there any formal way to prove it?

[slim reef]

or just saying it in this way is sufficient

[quasi bison]

are we dealing with the polynomial a(x) = alpha x^5 + beta x^3 + (2alpha+beta) still

[slim reef]

yes

[quasi bison]

i would check whether x^5 + 2 has a root in Z_13

which idk off the top of my head if it does

[slim reef]

thanks

[quasi bison]

if i is one of its roots we might get some bullshit happening

though maybe not

[slim reef]

what would happen if it's one of its roots?

[quasi bison]

the equation would end up involving beta only

[slim reef]

ah I see

do we need to check whether x^3 +1 has a root in Z13 as well?

same analogy

[quasi bison]

dunno but it probably wouldn't hurt

[slim reef]

oki thanks

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[amber vine]

is BC the side adjacent or the side opposite or the hypotenuse in this right triangle?

tg means tan (tangent)

[amber vine]

<@&286206848099549185>

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[wheat sky]

can anyone identify what this is called?

[wheat sky]

or have some good material to study from

[flat spoke]

It looks like a truth table.

If p, then q. That sort of thing.

[wheat sky]

m i think thats exactly it hold up

[flat spoke]

Holding with bated breath.

[wheat sky]

sksksks

yea homie this is what i was looking for

sorry i couldnt figure out the name

tyty

.close

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[timid goblet]

Hey

I got pinged

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[rigid arch]

.help

[safe radish]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[rigid arch]

Does anyone know what this means? It’s for a scatter plot

[long copper]

I think it refers to any problems with the scatter plot which will make it inaccurate, for example some scatter plots may not be valid for certain scenarios or after they pass certain values they become invalid. When someone buys a car a scatter plot may suggest that the price of the car doesnt fall below a certain value when in reality after 100 years the car will be worthless. That would be an example of a limitation.

[rigid arch]

oh ok

.close

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[undone osprey]

I have a question, is the integral of f(x)dx from 0 to 9 equal to the integral of f(u)du from 0 to 9 given that u=x^2. Why is that?

I mean i know u and x are merely variables but i also don't understand how they can be equal in function yet u=x^2

[queen parcel]

is the integral of f(x)dx from 0 to 9 equal to the integral of f(u)du from 0 to 9 given that u=x^2.

It is not. Making this u-sub will change the bounds and add a 1/2x in the u-integral

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@undone osprey Has your question been resolved?

[undone osprey]

@queen parcel this is after the sub. The original intregal is xf(X) from 0 to 3. After substituting, you are left with 1/2 * the integral of fu du from 0 to 9

Given also that the integral from 0 to 9 of fx dx is 4

Would the answer end up as 4

<@&286206848099549185>

I am thinking it has to do with it being continuous

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[obsidian quest]

uhm hi

[obsidian quest]

.close

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[strange compass]

I am wondering how time is correlated with probability. Let me explain:

There is a game, and each round of the game you have 20% chance to win. Each round takes 10 seconds. How long, then, is the expected amount of time it takes to win the game?

[strange compass]

<@&286206848099549185> please help! ^

[rancid peak]

Well in my opinion, since you have a 1 in 5 chance to win the game, it would take on average 5 games to win, so I'd say that the expected amounted of time would be 50 seconds

@strange compass

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@strange compass Has your question been resolved?

[strange compass]

I'm not sure if it can be boiled down to so simple a conclusion. What 50 seconds represents in my opinion is "You ought to need 5 trials at most to win this game". Like worst case scenario. That's not accounting for the possibility of winning on the 1st, 2nd, 3rd or 4th trial.

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[rustic brook]

I wrote these formulas because I’m supposed to memorize these but can anyone tell me which formula is which? It’s kind of confusing

[thin bridge]

sum of first n terms in an arithmetic series
sum of first n terms in a geometric series
infinite sum of a convergent geometric series (one with |r| < 1)

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[rustic brook]

Thank you!

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[late garnet]

how to solve this

[late garnet]

<@&286206848099549185>

[quasi bison]

@late garnet do you still need help with this?

[late garnet]

yes

[quasi bison]

is it the presence of a nested fraction that is scaring you?

[late garnet]

idk how to solve problems like these

[quasi bison]

...

okay so like

you've posted a second problem here

what's up with that

which one do you want help with

the one with x or the one with t

[late garnet]

the t one

[quasi bison]

okay

have you solved linear equations before?

maybe ones where the numbers are whole rather than fractions

[late garnet]

no..

i mean yes

maybe

is it those stuff like a * b = c

[quasi bison]

if i gave you the equation 5x = 16 would you be able to solve it?

[late garnet]

hmm wait

1200

?

[quasi bison]

?!

[late garnet]

idk

[quasi bison]

you're saying the solution to 5x = 16 is x = 1200??

[late garnet]

nono

[quasi bison]

or did you just blurt out a number at random

[late garnet]

idk how to do

do u divide here?

[quasi bison]

you divide both sides by 5 to get x = 16/5, yes.

maybe relearn how to solve one-step linear equations

[late garnet]

ohh i get it now

thx

but

what if this is the problem?

@quasi bison

[quasi bison]

judging from what i've seen, this problem is too complicated for you to handle at the moment

since you struggle even when the numbers are just integers, let alone fractions

you need to practice solving equations with integer coefficients first, then come back to this

[late garnet]

.-.

[quasi bison]

there is no way around this

[late garnet]

k

-1/8 the answer right? :D

[quasi bison]

yes, the answer in this case does happen to be t = -1/8...

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[ancient escarp]

what don't you understand

yeah

do you know the slope formula?

rise/run doesn't ring a bell?

then you may want to review your notes or something

if you're learning about slope, i'm sure you were

$\frac{y_2-y_1}{x_2-x_1}$

maybe this?

[flat frigate]

a disappointing son

[ancient escarp]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line

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[left temple]

if I'm told to find the extrema values on a region described by f(x,y) and a inequality, why do I also have to find the critical values of f(x,y) in addition to completing lagrange multipliers?

[left temple]

shouldn't using delta f(x,y) = lamda delta g(x,y) find all the critical points in this region?

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[maiden mural]

please help me with this

[maiden mural]

<@&286206848099549185>

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@maiden mural Has your question been resolved?

[maiden mural]

<@&286206848099549185>

<@&286206848099549185>

[lost patrol]

@maiden mural

I'm not sure

Because I havent studied this level yet

But Im sure this must be the answer

It takes a lot of time to type, so sorry for the delay

[safe radish]

@maiden mural Has your question been resolved?

[maiden mural]

@lost patrol can you tell me like from where did u get this answer ... its clearly printed , so i am guessing you didn't "solve" it technically but also u must have not googled , because i didn't find anything like this on google. can you come in dms and tell me some of these things whenever ur free?

[lost patrol]

Its not printed

I typed it out

Haha

Thats why it took a lot of time

[maiden mural]

what !!! how?

[maiden mural]

how did u type so beautifully?

thats amazing bro

[lost patrol]

You can come into DMs and I can explain the answer

[maiden mural]

i am impressed with ur typing XD

[maiden mural]

okay

[lost patrol]

The answer is actually by integration

But I used an easier way maybe

[maiden mural]

but i haven't been taught integration yet

[lost patrol]

No calculus

Well the answer doesnt have any

[maiden mural]

its from Derivatives chapter i guess

[maiden mural]

well this is a question of calculus imo

[lost patrol]

Yeah

I didnt use calculus

Just used logic and created equations

[maiden mural]

yep i saw that. that was very smart. no calculus and still get the answer using logic

[lost patrol]

Well yeh kinda

[maiden mural]

okay. i am clear with the problem

thanks

[lost patrol]

Welcome!

[maiden mural]

btw do u have ur dms open? lets talk in dms

[lost patrol]

Yeah

They are open

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[lean otter]

ok so

i did thefirst differenc

7, 11, 15

and thats 4

4/2 = 2

so 2n^2

wrote square numbers

wait

ohh

i see where i went wrmg

[delicate oar]

are you all good with it?

@lean otter

[lean otter]

Well i got +2,+3,+4,+5

so what would that be

@delicate oar

[delicate oar]

Ok so usually what you do to find the next part is to find the 0th term

So work backwards. To go from 37 to 22 you take away 15, and for the next term you take away 11, then 7. It is going down in 4s so the 0th term would be the first term takeaway 3.

Do you understand that?

[lean otter]

hmmm

not really

[delicate oar]

ok so do you know what i mean by the 0th term

[lean otter]

yes

[delicate oar]

okey dokey so we want to find that so we are going to work backwards

how do you go from 37 to 22 (4th to 3rd term)

[lean otter]

-5

wait

22

-15

[delicate oar]

haha

[lean otter]

😅

[delicate oar]

yes that's right

Ok so the same to go from the 3rd term to the 2nd term (22 to 11)?

[lean otter]

-11

[delicate oar]

and 2nd to 1st?

[lean otter]

-7

[delicate oar]

ok so do you see that's a pattern of -4 each time

[lean otter]

yes

[delicate oar]

ok so to go from the 1st term to the 0th term do you understand what we have to do?

[lean otter]

-4

not sure

[delicate oar]

i apologise sorry i'm not the best at explaining things

[lean otter]

nope you are explaining well

I just forgot this topic my bad

[delicate oar]

so we are taking away 4 less than the previous time each term

[lean otter]

-7-4

[delicate oar]

(-15, -11, -7)

so you'd take away 4 less than -7 which is -3

sorry i don't think i really explained that very well

[lean otter]

ok makes sense

[delicate oar]

so you'd do 4-3 which is 1

so you have 1 as the 0th term and that 1 can go into your answer

so currently we have 2n^2 + 1

[lean otter]

ohh

i have a question

[delicate oar]

go for it

[lean otter]

you see

this

can i just go back 1

from +2

[delicate oar]

yup

[lean otter]

ohh ok

will it work everytime?

[delicate oar]

Will what work? Finding the 0th term?

[lean otter]

ye

[delicate oar]

yeah it should do

but do you see now that we have +1 +2 +3 +4

[lean otter]

yes

[delicate oar]

can you also see that it is n?

[lean otter]

nth term?

[delicate oar]

yes

[lean otter]

oh

yeah

[delicate oar]

so you're also adding n to it each time

[lean otter]

yes

[delicate oar]

and i believe that's the answer

2n^2 + n + 1

[lean otter]

yeah

it is

thanks

wait i have a question

[delicate oar]

go for it :)

[lean otter]

i got mixed up when u said adding n

so like what is adding n

[delicate oar]

ok so 4 is the first term yes?

[lean otter]

yes

[delicate oar]

it basically stands for the term it is so for the first term n = 1

for the 5th term n = 5

for the 900th term n = 900

[lean otter]

okay

[delicate oar]

so that's why if you work out the differences to get to the number when you have 2n^2 + 1 it is +1 +2 +3 +4 +5

because you need to add n

which is 1 in the first term, 2 in the second term, 3 in the third term etc

[lean otter]

yes

ohhh

so 1n

?

[delicate oar]

what are you asking sorry?

[lean otter]

idk im a bit confused with the +n still

the videos I watched they didnt explain this part too

[delicate oar]

i'm not too sure how to explain it. i just see it as a pattern (+1 +2 +3 +4 +5) so it has to be n. do the videos explain how to do quadratic sequences in a way you understand?

if so you should probably just listen to it

[lean otter]

my teacher taught me i just needed to look over

but i dont remember the n thing

and they dont show nsadly

[delicate oar]

Yeah i think it's because you just kind of have to see it. Does the video go through the question we just did?

[lean otter]

thee end doesnt go up 1 like us

oh

2 to 3

i see nopw

ok thank you very much @delicate oar

[delicate oar]

my pleasure. hope i helped somewhat haha

[lean otter]

you did

I have an exam on tuesday

so im tryna revise all topics

[delicate oar]

ohh wowee best of luck to you

[lean otter]

and complete the revision hw

[delicate oar]

yeah you got this

[lean otter]

thank you

im very worried

cuz this will determine sets

any tips?

[delicate oar]

You're doing all you can to be honest. You're revising hard which is all you can ask for

I'm sure you'll do fine

Most people won't revise I can assure you that

[lean otter]

yeah

it is my fault to be honest

my classmates understand the teacher

but I cannot

so i end up doing it myself

[delicate oar]

Ahh ok. I mean obviously asking the teacher to help might be useful but i get that can be a bit embarassing sometimes

[lean otter]

sometimes I try but I still dont understand

[delicate oar]

In that case you're doing all that you can do by doing revision tasks and asking on here as well

You got this

[lean otter]

i try to do like 3 hrs

a day

but im quite slow being honest

ive only completed surds.

and theres so many topics

[delicate oar]

As long as you take the time to understand what you are doing that's fine

[lean otter]

okay

im a bit confused on factorisation with x

[delicate oar]

better to go slow and understand than go fast and not understand

ah right ok do you have an example question?

[lean otter]

leme try find

well the problem is i completed them with a friend

[delicate oar]

ahh right ok

do you mean questions like this?

[lean otter]

yes

would that be

x(x-7----

idk how to do the rest

the 12 throws me

off

[delicate oar]

ok so hang on a min lemme pull up paint

[lean otter]

alright

[delicate oar]

Usually you set it out like this. Having the x^2 in the top left and the number term in the bottom right

[worthy hemlock]

https://www.youtube.com/watch?v=mXvt9OumKH8&ab_channel=TheOrganicChemistryTutor

[delicate oar]

That'd probably help

haha

[lean otter]

ok thank you both

[lean otter]

interesting method

[delicate oar]

Then I usually just right out the possible combinations to get the 12

[lean otter]

my friend told me to find common thing but it confusd me

[worthy hemlock]

I think you're talking about factoring using GCF

[lean otter]

like for the number out of brackets

[lean otter]

whats GCF

[delicate oar]

yeah dldh06 probably knows

sorry i'm not great at explaining

[worthy hemlock]

Greatest common factor

[lean otter]

oh

ye

i find it confusing to me tho

[worthy hemlock]

Like 2x^2 + 4x + 8, where all the terms, the GCF is 2

So you can rewrite as 2(x^2 + 2x + 4)

[lean otter]

alright

questions with x and indicies confuse me

[worthy hemlock]

That video should help out with that concept too

[delicate oar]

Would you say it's probably best for Zalgoh to watch the video

It's probably not worth me trying to struggle to explain it haha

I've never really helped people out with maths before

[lean otter]

well you have today

[delicate oar]

i've tried my best haha

[lean otter]

do i watch first part?

[lean otter]

thanks

[worthy hemlock]

Yes

[delicate oar]

@worthy hemlock Thanks for helping out haha

[lean otter]

yeah thanks

ill do the factorisation when im done with the hw

oh yeah

this

I learnt about it but I forgot now

[delicate oar]

i'm probably not best suited to help out with this question

do you mind closing this help channel out and then opening another one so a different helper can help i'm not the best on that topic either haha

[lean otter]

okay ty verymuch

!close

[delicate oar]

.close

@lean otter you have to do .close

[lean otter]

.close

[safe radish]

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[odd fog]

need help w this

[safe radish]

@odd fog Has your question been resolved?

[safe radish]

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[nova sigil]

Hi, what is the best way to tackle the following integral

[nova sigil]

I'm not even sure what the first step I should take to solve it is?

[smoky gull]

the first thing that occured to me was substitution, but the more i think about it the ore i have no idea what to do with it, heh

[nova sigil]

haha

Ok, I separated the top and bottom as separate square roots

[pulsar condor]

probably IBP?

[grave coral]

4t=u ?

1/4 . integral sqrt(1/u + 4) .du

[pulsar condor]

integral.

[grave coral]

yes.

sorry

eng is not my native lang

[nova sigil]

=tex[\int_{0}^{1}\frac{\sqrt{1+16t}}{2\sqrt{t}}]

How do you post tex here?

=tex \int_{0}^{1}\frac{\sqrt{1+16t}}{2\sqrt{t}}

[inland ivy]

Wrap it in $ $

[nova sigil]

$\int_{0}^{1}\frac{\sqrt{1+16t}}{2\sqrt{t}}$

[flat frigate]

chromechris

[nova sigil]

Thank you!

[inland ivy]

Np

[nova sigil]

Am I able to do integration by parts and use the denominator and nominator as either a "u" and "dv"?

I am trying to tackle an arc length of parametric curves problem:

first I found the dx/dt and dy/dt

$\frac{dx}{dt}=\frac{1}{2\sqrt{t}}$

[flat frigate]

chromechris

[nova sigil]

$\frac{dy}{dt}=2$

[flat frigate]

chromechris

[nova sigil]

then I just plugged it into the arclength formula for parametric equations

$\int_{0}^{1}\sqrt{(\frac{1}{2\sqrt{t}})^2+(2)^2)}$

[flat frigate]

chromechris

[nova sigil]

Which resulted in:

$\int_{0}^{1}\sqrt{\frac{1}{4t}+4}$

[flat frigate]

chromechris

[nova sigil]

Which then I simplified to:

$\int_{0}^{1}\frac{\sqrt{1+16t}}{2\sqrt{t}}$

[flat frigate]

chromechris

[nova sigil]

So now I don't know if there is a way that I could have simplified this simpler before, or how to proceed from this point

[safe radish]

@nova sigil Has your question been resolved?

[safe radish]

@nova sigil Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[safe radish]

@sacred forum Has your question been resolved?

[flint ledge]

$\sum_{n=2}^{\infty}a_n = (\sum_{n=1}^{\infty}a_n) - a_1$

[flat frigate]

quantum

[flint ledge]

@sacred forum

[sacred forum]

Oh thank you

How does that work though?

[flint ledge]

the first one goes a1+a2+a3+a4…

the second one goes a2+a3+a4…

the difference is a1

[sacred forum]

Oooh thats what n=2 is?

[flint ledge]

yes, the first term is a2

the first term when it starts at 1 is a1

so you have to subtract a1

[sacred forum]

From the total

[flint ledge]

write down the first few terms of $\sum_{n=1}^{\infty}a_n and \sum_{n=2}^{\infty}a_n$ if you’re confused

[flat frigate]

quantum

[sacred forum]

Is there anyway we can jump in a quick call if possible?

[flint ledge]

no

i’m in a car and i don’t vc anyways

[sacred forum]

Oh okay thank you. I still appreciate it lol you solved this from a car

Thats great

[flint ledge]

remember to .close if you’re done

[sacred forum]

Yes just 1 question what was the answer if asum n is that equation?

[flint ledge]

i can’t tell you the answer

just multiply it by a constant if needed

you did A so you can do B with this information

[sacred forum]

Do I just plug in the numbers?

Okay thank you!

Sorry how do I close out?

[flint ledge]

do .close

[sacred forum]

.close

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[sacred forum]

Sorry I had help but im still confused

I multipled it out

Was i suppose to include 9 when multiplying?

[flint ledge]

find what $-9a_1+6b_n$ is and subtract that from the answer you got from A

[flat frigate]

quantum

[sacred forum]

Ah okay thank you

.close

[safe radish]

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[silk chasm]

I need some urdent help

Urgent*

I get everything up to sin2x=-1/4

What i dont get is how they got from there to the 2x values

[flint ledge]

you don’t understand that you need to use inverse sine?

[silk chasm]

Sin-1 of (-1/4)

Does not give that

[flint ledge]

remember the limits on x

[safe radish]

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[silk chasm]

It gives -14

[silk chasm]

Oh

[flint ledge]

,w arcsin(-1/4)

[silk chasm]

Limits are 0<x<pi

[flat frigate]

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[silk chasm]

Oh

Do i do cast on that?

[flint ledge]

sin(x) = sin(pi-x)

,w sin(3)/sin(pi-3)

[flat frigate]

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[flint ledge]

,w pi-arcsin(-1/4)

[flat frigate]

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Requested by quantum#6320

[flint ledge]

@silk chasm

[silk chasm]

Ohh

So because pi is the limit

You just add that answer to it

Wait that doesnt make sense

PH

OH

Limit changes

[flint ledge]

sin(x) = sin(pi-x)

[safe radish]

@silk chasm Has your question been resolved?

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[stoic pilot]

why is $0 * 0^{-1} \neq1$? I know it's undefined by why do we make an exception to this identity for 0?

[flat frigate]

THEBIGTHREE

[pulsar condor]

cause 0^(-1) is undefined

[stoic pilot]

well yeah but we ignore undefined things all the time, what actually doesn't make sense about it

[pulsar condor]

0^(-1) is undefined

that's what doesnt make sense about it

[pulsar condor]

no... we dont

[stoic pilot]

can't you say 0^-1 = 1/0
and 1/0 = 1/0
1/0 = 0^-1
1 = 0^-1 * 0

[stoic pilot]

k maybe not all the time but sometimes

[pulsar condor]

1/0 isnt a thing

it's undefined

[stoic pilot]

why don't we just use a nonreal number to represent it instead?

[pulsar condor]

cause it has no definition

[grave coral]

We cant, because there is no number to represent

[pulsar condor]

It fails to simply work, if you're referring to something similar to i, which does in fact work and obey algebra

[safe radish]

@stoic pilot Has your question been resolved?

[wet vigil]

The distributive property a(b+c)=ab+ac follows from the definition of multiplication as repeated addition and with it we can show the following:
0a=(0+0)a=2*0a<=>0a=0 which goes against the definition of a multiplicative inverse aa^-1=1

[safe radish]

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[grim sandal]

How do I factorize (x+1)(x-2)(x+3)(x-4)-56?

[merry zenith]

expand

[safe radish]

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