help-23

[unique bison]

why do you think this is true

[lean otter]

subtract f(n) and divide n²-1

[humble oracle]

By simple algebraic manipulation?

[unique bison]

oh crap

i read it as (n-1)^2

[humble oracle]

Oh, lol

f(2) = 2023/3
f(3) = 2023/6
f(4) = 2023/10
I found a few values by substitution but I can’t see a pattern

[unique bison]

notice that

[lean otter]

but interesting, if we plug in n-1 to the top equation, we get something similar

[unique bison]

$(n+1)^2f(n+1) - n^2f(n) = f(n+1)$

[flat frigate]

giannis_money

[unique bison]

do you see how

[humble oracle]

Yeah

[unique bison]

$(n^2+2n)f(n+1) - n^2f(n) = 0$

[flat frigate]

giannis_money

[unique bison]

$(n+2)f(n+1) - nf(n) = 0$

[flat frigate]

giannis_money

[thick sparrow]

1, 3, 6, 10, …
This sequence should be no strangers to you if you ever mess with the topic of sequence before 🙂

[unique bison]

can you do the rest?

[humble oracle]

Triangular numbers

[humble oracle]

I think so

[thick sparrow]

Yes. Use this observation to guess for a general formula for f(n), then you can prove it by induction 🙂

[unique bison]

indeed. that's another approach

[humble oracle]

Oh wow, I like this

[humble oracle]

Actually, I don’t know what to do next

[unique bison]

$f(n+1) = \frac{n}{n+2}f(n)$

[flat frigate]

giannis_money

[unique bison]

$f(n) = \frac{n-1}{n+1}f(n-1)$

[humble oracle]

Oh yeah

[flat frigate]

giannis_money

[unique bison]

$f(n) = \left(\frac{n-1}{n+1}\right) \cdot \left(\frac{n-2}{n}\right) \dotsm \left(\frac{1}{3}\right)f(1)$

[flat frigate]

giannis_money

[unique bison]

$=2023\frac{(n-1)!}{(n+1)!/2}$

$=\frac{4046}{n(n+1)}$

[humble oracle]

Yeah I think I understood

[toxic stratus]

are we missing a factor of 2

[thick sparrow]

Thats a clever reduction

[unique bison]

yes, just realised

[humble oracle]

2(2023)/n(n+1)

[toxic stratus]

the denom deosnt have 2

[flat frigate]

giannis_money

giannis_money

[humble oracle]

2f(1)/n(n+1) 😄

Thanks!

[humble oracle]

I’ll try doing this one myself

[toxic stratus]

lol

<@&268886789983436800>?

[thin wraith]

Thanks

[toxic stratus]

amazing

[humble oracle]

What happened?

[toxic stratus]

https://tenor.com/8rWB.gif

[lean otter]

what happened

[edgy cloud]

Someone showed up and started spamming. They were banned, and the spam messages deleted.

[lean otter]

oh, thanks for the quick moderation

[toxic stratus]

i think this explains it well enough

[lean otter]

yes

[humble oracle]

Oh, lol

Why do these always happen when I’m afk for a few seconds

[safe radish]

@humble oracle Has your question been resolved?

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[humble oracle]

Thanks guys

[safe radish]

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[ionic rivet]

Hello! I'm confused about this problem. I'm pretty sure it's correct but my teacher is telling me it isn't.

[safe radish]

@ionic rivet Has your question been resolved?

[buoyant shadow]

there are parentheses missing

you didn't use spaces as was asked but also didn't use ()

[ionic rivet]

Usually she doesn't say anything about that but ill add them and see what she says

[safe radish]

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[ionic rivet]

But it is correct other than that, right?

.reopen

[safe radish]

✅

[ionic rivet]

.close

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[slow fern]

I need to compute the det(A)

[slow fern]

I considered the matrix to be of form,

1 a bc
1 b ca
1 c ab

[quasi bison]

good idea

[slow fern]

The determinant of this form is something big

I couldn't simplify things more

[quasi bison]

is it? hold on

this feels like it should be something nice

[slow fern]

I get,
ab²-ac²-ba²+ca²+bc²-cb²

[quasi bison]

= a(b^2 - c^2) + (a^2 + bc)(c-b)

= a(-c-b)(c-b) + (a^2 + bc)(c-b)

= (a^2 - ab - ac + bc)(c-b)

= (a-b)(a-c)(c-b)

up to sign or something

,w determinant {{1,a,bc},{1,b,ca},{1,c,ab}}

[flat frigate]

Results provided by WolframAlpha

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

Requested by Ann#0413

[quasi bison]

ok yeah i was right

it's (a-b)(b-c)(c-a)

[slow fern]

$a(b+c)(b-c)+b(c+a)(c-a)+c(a+b)(a-b)$ $$\thonk$$

[flat frigate]

QuantumBee

[toxic stratus]

you have a thonk command?

absolutely amazing

[slow fern]

I tried simplifying the determinant myself

@quasi bison

How do I proceed further?

[quasi bison]

trash that

and do what i did instead

[slow fern]

I understand your steps

But, why didn't I think doing the same way?

Anyways

Thanks

.close

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[lean otter]

AB+AC=A×1(CB)
Is this right?

[buoyant shadow]

no, where does C go

it disappeared

[foggy salmon]

that is true magic

[lean otter]

Oops, a typo

How about now?

[toxic stratus]

that is not correct

[lean otter]

Why? Didn't you say that we always have 1× (or -1×), but just don't write it every time?

[ashen creek]

Jus expand the answer u get and compare it with the original equation

[lean otter]

What's the difference then?

Considering that it's the same formula

[ashen creek]

First of all the formula u sent at the beginning shud be ...AB + AC = A * (B+C)

Right?

Instead of AB + AC = A* ( BC)

[lean otter]

Yes

[lean otter]

Instead of AB + AC = A×1(BC)*

[ashen creek]

Yes

[toxic stratus]

oh no you took the one with the wrong colour

[ashen creek]

wdym?

[toxic stratus]

i messed up the colours

and i changed it halfway through

but now the colours between the two equations are mismatched making it really confusing

[ashen creek]

Ah

In this equation the ( n+3)! get cancelled on both sides right?

[lean otter]

Right

[ashen creek]

SO u wudnt need to use the formula which u hve sent

Right?

lets take another example

here

a simpler one

3x+ 4x

= x(4+3) = 7x

[ashen creek]

Using this

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

Yes, but can i still technically do it?

If i want to for some reason

[ashen creek]

Yup

AB +AC = A* (B+C)

[lean otter]

AB +AC = A*1(B+C)

Like this, right?

[ashen creek]

Yesss

The one isnt require

[lean otter]

And if i really want, i can
1AB +1AC = 1A*1(B+C)

[ashen creek]

💀

Yes

Yes u can

U can also do (1 * 2 * 3* 4* 5)/(1 * 2 * 3 * 4 * 5 ) AB + (1* 2 * 3* 4* 5)/(1 * 2 * 3 * 4 5 )AC = (1 * 2 * 3 4* 5)/(1 * 2 * 3 * 4 *5 )A(B+C)

IF u realy want to

[lean otter]

How does this work?

[ashen creek]

lol

[lean otter]

5!/5!AB

XD

[ashen creek]

directly cancel out each other

[lean otter]

Ah

[ashen creek]

im trolling u lol

[lean otter]

It's one

[ashen creek]

🤣

Yes yes it is

[lean otter]

Yeah

[ashen creek]

✌️

[lean otter]

I can basically build entire equations like that

[ashen creek]

Yes

[lean otter]

Thanks

.close

[ashen creek]

✌️

[safe radish]

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[lean otter]

knowing that both B and C belong on the same line gives you a huge hint: the relation between the X and Y coordinates is the same for both points

and you can figure the Y coordonate of the B point, because of the base*height/2 formula for area - you already know the length of the base, and also the area

so you can figure the height out

and since the base is the x axis itself, it means that the value of the height is the Y coordinate of B

and then u can also find out the X coordinate

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[rose locust]

For the second part of a is it 1008 ways?

I did 64 choose 2 divided by 2

<@&286206848099549185>

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[clear tangle]

Is there a equivalent to sigma but with subtraction that works the same way, not adding, but subtracting stuff?

[cedar rover]

You can use -(sigma[...]) or (sigma[- ...]), but pay extra care to the first term

[clear tangle]

Yeah but what do you mean by pay extra care?

[cedar rover]

if you want to do 1 - 2 - 3, it's 1 + sigma(from i = 2; to 3)[-i]

There are a lot of ways to write this, just remember that the sigma part is everything that is being subtracted

[clear tangle]

Oh. right

thanks

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[cedar rover]

[clear tangle]

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[lean otter]

if a = 1 and I need to find lim x->a+ f(x)

Since its just a line with no missing point, is there just no limit?

<@&286206848099549185>

[proud belfry]

,r

.r

ok

anyway

[lean otter]

what is this

[proud belfry]

i'm trying to rotate the thing

so it's normal

anyway

the limit as it approaces 1

[proud belfry]

from larger values

[proud belfry]

perfect

$\lim _{x\to 1}\left(f\left(x\right)\right)$

[flat frigate]

hired

[proud belfry]

this is what you want to find right

[lean otter]

yes

I just dont get how there is a limit when there is no point on the end or missing area

[proud belfry]

what

this is just simple

just see what f(x) is at 1

since it's defined at 1

[lean otter]

but there are no restrictions in the equation at this point on the line so what is the point in a limit

it doesnt make sense to me

[proud belfry]

there is none

but the limit still exists

it's just f(1)

[lean otter]

oh

now it makes sense

this should be one of the easier questions then

Thank you @proud belfry

[proud belfry]

$if:\lim _{x\to a}\left(f\left(x\right)\right),=f\left(a\right):for:all:a,:f:is:continuous$

[flat frigate]

hired

[lean otter]

makes sense now

tysm

[proud belfry]

np

[lean otter]

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[gloomy scaffold]

,rotate

[gloomy scaffold]

O is the the midpoint of AB and N is the midpoint of AC. AD:AB=2:5 and AF:AC=2:5 . Area of ABC is 50 cm2, what's the difference between ADPF and PON's area?

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@gloomy scaffold Has your question been resolved?

[safe radish]

@gloomy scaffold Has your question been resolved?

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[green gust]

I am just checking if this is correct. Some sites say that it is 3 and I don’t understand how it is 3 😅

[pure agate]

$-4 - 8 = -12$

[flat frigate]

Kookiemon

[green gust]

oh! thank you.

[pure agate]

yw

[green gust]

.close

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[oak briar]

Help

[oak briar]

Is this right

[split terrace]

not quite, you had the right approach but you miscalculate square root of 16 wrong

[oak briar]

I did

[split terrace]

otherwise its great

[oak briar]

What did I do wrong

[split terrace]

8*8 is not 16 it's 64 ^^'

[oak briar]

Oh

[split terrace]

so there should be another number instead of 8

[oak briar]

But

Tutorial video I watched

[split terrace]

yes they did the same way as you did but 8*8 is not the solutions since it's 64.

[oak briar]

4*4

[split terrace]

jupp

[oak briar]

Oh ok

[split terrace]

and you a small other mistake

most likely a one of those that happen when you go too fast but the bottom 6 you wrote in your fraction (underneath 16) should be 9

[oak briar]

Oh

I did not notice

That

[split terrace]

yeah happens everyone 🙂

[oak briar]

Thank you

[split terrace]

np mate hope you got the grips on it now

[oak briar]

Mhm

Thank you

Bye

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[autumn jackal]

why is this a * (b x c) < 0 ?

let me refine my question, sorry*

Why is it that, if a * (b x c) < 0, then its in the opposite direction?

what about the converse? if a (b x c) > 0, is it in the same direction?

my confusion mainly stems from this: a * (b x c) = |a| |b x c| cos(theta)

err actually i guess that makes sense lol

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[exotic belfry]

√(4+h) -2 (√(4+h)+ 2

[exotic belfry]

How do you conjugate (√(4+h) -2 )/h

[tall fern]

First you need sqrt everything in the parentheses to get ((2+ √h)-2)/h, then you need to multiply the whole thing to cancel the h at the end to get 2h+ h-2h then combine like terms to get 1h I think

[exotic belfry]

Want to get ride of the radical

[flat frigate]

Azthony

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@exotic belfry Has your question been resolved?

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[wild brook]

can anybody help me on the measures of dispersion or variation??

[safe radish]

@wild brook Has your question been resolved?

[wild brook]

<@&286206848099549185>

[thick sparrow]

Please ask a specific question on what you are struggling on, or else no one can know how they can help 🙂

[wild brook]

measures of dispersion

mean deviation

standard deviation

skewness

[thick sparrow]

That points to textbook topics but not specific problems. Please check again how you can use the help channel properly. 🙂

[wild brook]

can you tell me from where i can learn the basics of these topics

i have applied/business statistics and maths

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@wild brook Has your question been resolved?

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[stark flame]

I know I was just here but I dont know what this abstract algebra problem is asking of me. It wants me to see if the given operation is communacative, associative, has an identity or an inverse. The problem is that the operation given is described as x*y= max{x,y}=the larger of the two #s x and y. How do I go about doing this??

[solar hazel]

commutative?

[stark flame]

oh hey layla 😅

[solar hazel]

the operation is commutative if max{x,y} = max{y,x} for any elements in whatever set this is in

hi!

[stark flame]

its in R again lol

[solar hazel]

is this true?

as in, does max{x,y} = max{y,x} in general?

[stark flame]

i have no idea, probably not tho

[solar hazel]

why not?

[stark flame]

because then the cordinates would be switched around

[solar hazel]

hmm maybe look at an example?

what's max{5,10}?
what's max{10,5}?

[stark flame]

10

so i guess in this sense, it doesnt matter the order of x and y, the number itself matters

[solar hazel]

yep, the order doesn't matter

[stark flame]

then what about associativity? how would that work?

i dont think it would be associative

since the value is what matters

[solar hazel]

why don't you think so?

[stark flame]

because if you have max {5,10} and then max 5{10,z} it would be different right?

[solar hazel]

what would be different exactly?

[stark flame]

the maz

*max

[solar hazel]

still can't tell what you mean

[stark flame]

tbh, i cant either

[solar hazel]

what does associativity mean?

[stark flame]

(ab)c=a(bc)

[solar hazel]

sure

so that would mean
max{max{a,b},c} = max{a,max{b,c}} for all real numbers a, b, and c

[stark flame]

yes, i think

[solar hazel]

yea, they are equal

both are equal to max{a,b,c}

[stark flame]

alright great then!

how would a max have an identity then?

I thought about the inverse, i thought it could be the min if the same numbers, but im unsure

[solar hazel]

well we'd need an identity first before we can have inverses

[stark flame]

yeah, thats what i was thinking

[solar hazel]

so the identity e, if there is one, must satisfy max{e,x} = x for all real numbers x

any problems there?

[stark flame]

well it would have to be any number less than x, right?

or just 0?

[solar hazel]

exactly!

well less than or equal to

almost exactly

[stark flame]

I thought that you could only have one identity value

[solar hazel]

that's right

[stark flame]

it doesnt have to be one constant value?

[solar hazel]

it has to be one constant value

[stark flame]

then how can this one have any number less than or equal to x?

[solar hazel]

it can't

so there is no identity

[stark flame]

o

💀

well then

good

then there is no inverse-

[solar hazel]

yep, saves some work haha

[stark flame]

ill probably be back later... 💀

thanks again m8 ❤️

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[solar hazel]

np!

[safe radish]

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[wanton roost]

what is mutually exclusive?

[wanton roost]

.close

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[pulsar flare]

Hey I am having with some trig integrals, is there anyway someone would be able to hop in a call or something to help walk me through some of my issues.

[pulsar flare]

Im stuck on the problem. ∫csc^2(3-2x)dx

[safe radish]

@pulsar flare Has your question been resolved?

[lean otter]

@pulsar flare do you not recall any trig function which derivative gives csc²(x) or something similar?

[safe radish]

@pulsar flare Has your question been resolved?

[pulsar flare]

yes I believe that the antiderivative of csc^2(x) is cot(x)

however, im failing to see what method i can use from there

because u-sub won't work, nor will integration by parts

oh my gosh I just realized

sorry my brain totally failed on that one

[lean otter]

no worries

[pulsar flare]

any chance while you are here you would be able to push me in the right direction for cot^3(x)

im assuming its maybe a similar process using the derivative of cot

and pulling out a cot to get cot^2(x)(cot(x)) and using trig identities

however i get a little bit lost after the substitution

[lean otter]

yes so

[lean otter]

that's good

then you can use cot²(x)=csc²(x)-1 and get (csc²(x)-1)cot(x)=csc²(x)cot(x)-cot(x).

so that you have 2 more feasable integrals

@pulsar flare would you be able to continue from here?

[pulsar flare]

yes i can defintely take it from there

thanks alot for your help

my brain was just getting caught up in some silly places haha!

.close

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[finite vigil]

Can I get help with these two

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@finite vigil Has your question been resolved?

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@finite vigil Has your question been resolved?

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[lean otter]

What is the next step ?

[balmy sky]

open the brackets

and solve the like terms

[lean otter]

oh

ok

.close

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[signal mauve]

Let T: V-> V be linear

[signal mauve]

prove ker T is subspace of ker T^2

heres my proof:

If for an x in ker t^2

and y in V

then x = T(T(y));

x= T(w); w = T(y)

therefore since T(w) is in kerT

then x is in ker(T)

therefore its a subspace

[blazing sable]

that seems correct

[signal mauve]

.close

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[maiden barn]

Can someone explain me

[maiden barn]

When solving limits

And let's say we have lim (when x -> sqrt(2))

And then let's say I have somewhere in the limit

2 / x

And I need to find the limit of that

Do I put in sqrt(2) as some form of final value

Or what?

[coarse heron]

is this characteristic equation correct

i really dont think it is

hang on it is

oops

.close

[maiden barn]

You can't close the channel xd

It's claimed by me xd

Just ask in another one ig

[coarse heron]

ah sorry, dw i figured it out anyway

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@maiden barn Has your question been resolved?

[gloomy scaffold]

In this equation, e=am+bn+cp+dq you know the value of m,n,p,q and e. How can you find the value of a,b,c and d? Is there any formula for it?

[safe radish]

@maiden barn Has your question been resolved?

[maiden barn]

Idk how come this channel is open but okay xd

.close

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[lean otter]

Kindly explain me step 3 and step 4:

[lean otter]

Another question is if in step 3 we are computing area/

Then how step 4 is giving us volume? 😀

[nova creek]

Step 3 is taking each of those tiny rectangles on the xy plane, taking its area (Δx Δy), multiplying it by the height of the function (f(x_i*, y_i*)), then adding them up

Step 4 is saying that we're taking an infinite number of these rectangles by making infinite divisions along the x axis and infinite divisions along the y axis

Step 3 is computing volume. You're summing the product of a height (the function), the length, and the width (Δx and Δy)

[lean otter]

Gotcha

Thank you 🙂 @nova creek

.close

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[wild wedge]

please help

[bold ferry]

can you type that expression?

it's very blurry

[wild wedge]

the area of rectangular field is (15x2 + x - 2) m2 what are the possible leght and width of the field (i cant type small numbers)

[bold ferry]

factor the quadratic (15x^2 + x - 2)

and you'll have 2 expressions which are the length and width

[wild wedge]

mhm

i dont know how too

[bold ferry]

hmm

https://youtu.be/kKE4t7R_KWc

this video should help you

[wild wedge]

i watch this later i gotta go school bye

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[dull pulsar]

Derivative help pls I feel like I’m doing this wrong

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@dull pulsar Has your question been resolved?

[safe radish]

@dull pulsar Has your question been resolved?

[sharp island]

@dull pulsar

Hi

Can I ask how your log_2 becomes just log in the second line of your working

[dull pulsar]

it doesnt i was being lazy

[sharp island]

I would try using the property of logarithms

,,\log_a(b)=\frac{\log_c(a)}{\log_c(b)}

[flat frigate]

Social Capital Gainer

[sharp island]

And chose c to be something convenient to this situation given that we are differentiating

@dull pulsar

[dull pulsar]

ok ill try

But I need help w this

I need help w this too

Do I make t^6+1 the u? For u sub

[safe radish]

@dull pulsar Has your question been resolved?

[mortal relic]

i suppose u could

theyll get cancelled out so it makes life easier for u

[dull pulsar]

so I skipped the problem and came back to it jus now

Idk if I did this right but I got to the correct answer

[stray socket]

I would just set w = ln(u) so dw = du/u but yeah

Otherwise you're fine

[dull pulsar]

thx

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@dull pulsar Has your question been resolved?

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[little sorrel]

i have no idea how to do these questiosn

[safe radish]

@little sorrel Has your question been resolved?

[little sorrel]

<@&286206848099549185>

[little sorrel]

<@&286206848099549185>

guys guys guys

its about to reach the one hour mark

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[ruby phoenix]

how can you know that

if x € ]0 ; pi/2[

then x < tan x

[quasi bison]

a geometric proof is possible

[ruby phoenix]

is it complicated

you know what i dont wanna know everything

.close

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[worldly remnant]

Trying to find a video explaining how to solve these types of questions

what would they be called?

Searched up dividing fractions algebraically and didn’t get what I was looking for

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@worldly remnant Has your question been resolved?

[worldly remnant]

That's so helpful

thanks

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[chrome parcel]

how do i solve the following thing

[chrome parcel]

(1/3) ^-1

[lean otter]

do you know what does negative exponent mean?

[chrome parcel]

well yes basically

if its

like

2 ^-2

then

1/2^2

[lean otter]

ok good

now can you apply that?

[chrome parcel]

soooo

mb i put

one sec

1/1/3^1?

[lean otter]

yes

simplify?

[chrome parcel]

uhhhh

cancel out 1's?

[lean otter]

what is 3^1

[chrome parcel]

3

[lean otter]

so now we have

[chrome parcel]

so just three

[lean otter]

1/1/3

[chrome parcel]

holy jesus

[lean otter]

yes

[chrome parcel]

wait

wait

holyp

holup

[lean otter]

^-1 always invert the fraction

[chrome parcel]

[lean otter]

^-2 invert and square

[chrome parcel]

one second

[lean otter]

^-3 invert and cube

etc

[chrome parcel]

this is 9th grade math dont kill me yet plz

[lean otter]

its nothing big really

[chrome parcel]

yeah for you 💀

[lean otter]

let me output it here

[chrome parcel]

fine

[lean otter]

$a^{-x}=\frac{1}{a^x}$

[flat frigate]

Tenkaishi

[chrome parcel]

right

[lean otter]

$a^{-1}=\frac{1}{a^1}$

[chrome parcel]

yeah that makes sense

[flat frigate]

Tenkaishi

[chrome parcel]

so does that

yes ik i just did that

one sec lemme finish my assingment

so

(3/7)^-1

[lean otter]

invert

[chrome parcel]

sooooo

1/3/7?

[lean otter]

yes

simplify

[chrome parcel]

1/3/7^1

so then

[lean otter]

simplify

[chrome parcel]

wait how do i do that here

[stray socket]

You know how to divide fractions?

[chrome parcel]

no not in this case

[stray socket]

What is $1 \div \frac{3}{7}$

[lean otter]

division is equivalent to multiplying with the number's inverse

[flat frigate]

Umbraleviathan

[stray socket]

That's all you're doing

[lean otter]

$\frac{1}{\frac{a}{b}}=\frac{b}{a}$

[chrome parcel]

idk?

[flat frigate]

Tenkaishi

[lean otter]

$a \div \frac{b}{c} = a \times \frac{c}{b}$

[flat frigate]

trololol !

[stray socket]

^

[chrome parcel]

o god

OOOOH

OOOOOOOOOOOOOOH

NOW i get it

its

wait

its

[stray socket]

This is stuff you should've known beforehand

[chrome parcel]

the

uhhhhhh

[stray socket]

Reciprocal

Yes

[chrome parcel]

right

yes

thats the one

ight lemme write it in holup

[stray socket]

I mean

You can just flip the fraction around from the get go

[chrome parcel]

the answer is 7/3

[stray socket]

$\left(\frac{a}{b}\right)^{-1} = \frac{b}{a}$

[flat frigate]

Umbraleviathan

[stray socket]

Yeah

[chrome parcel]

or 2 1/3

[stray socket]

Keep it as improper

Don't use mixed

Mixed is useless

[chrome parcel]

yes thats what my teacher told me

so

last one:

(5/2)^-1 =

2/5?

[stray socket]

Yeah

[chrome parcel]

i feel the power of the lord

rising me up to heaven

[stray socket]

It do be like that

[chrome parcel]

ima send a pic rn

to the chat

for ya'll to check

[lofty escarp]

next einstein i see

[chrome parcel]

ah yes

[chrome parcel]

what are you yoda

[chrome parcel]

what do you think

[stray socket]

Just =

=> means "implies"

[chrome parcel]

ok

[lofty escarp]

seems correct except for that

[chrome parcel]

where

except for what

[lofty escarp]

the imply sign

[chrome parcel]

right

no

thats my way of writing =

dont judge me lmfao

[lofty escarp]

well it's not wrong really

[chrome parcel]

but yes i get the point

ima do that next time

ight ima hop on apex rn

see ya

[stray socket]

I mean yeah but they're pretty much equal

[chrome parcel]

bye guys

[stray socket]

Close the channel

@chrome parcel

[lofty escarp]

oops he left

[stray socket]

Don't worry

.close

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[jolly minnow]

im trying to find this inverse laplace using convolution

but here i end up with a convolution that gives me an integral with stepfunction and idk how ot integrate it

<@&286206848099549185>

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@jolly minnow Has your question been resolved?

[safe radish]

@jolly minnow Has your question been resolved?

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[full citrus]

how can i calculate that?

[full citrus]

i know that it just represent the sum from 0 to n of the pair p of n choose p

[idle parrot]

What it really asks you is ${}^n C_0+ {}^n C_2+ {}^n C_4…+ {}^n C_n$

[flat frigate]

Deep.(cat gang)

[idle parrot]

You can use binomial theorem to find that

[full citrus]

i don't see how

and why do you use the C notation?

[safe radish]

@full citrus Has your question been resolved?

[safe radish]

@full citrus Has your question been resolved?

[full citrus]

<@&286206848099549185>

[lean otter]

what happens if you apply the binomial theorem on (1+1)^n + (1-1)^n?

[safe radish]

@full citrus Has your question been resolved?

[alpine goblet]

https://media.discordapp.net/attachments/903481102591750184/1018338066009706626/20220911_071857930.jpg

How to prove this

[nova creek]

#❓how-to-get-help

[safe radish]

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[lean otter]

wait i got everything before but now I am stuck again @idle sage

cause x and y are both negative

and they need to both be positive

[toxic stratus]

what do you mean both x and y are negative

[lean otter]

yes what is happening

[toxic stratus]

actually what does the question ask for you to do

graph?

[lean otter]

I know how to graph but

I don't know the rewriting part

I understand a) and b)

but I'm stuck on c) and d) now

[toxic stratus]

[lean otter]

yeah I don't get that

[toxic stratus]

what don't you get

[lean otter]

adding y to both sides

can u like show what u mean

text

[cursive raven]

add y to LHS

add y to RHS

[lean otter]

um

[cursive raven]

so the equation remains equal

to keep the equality

[lean otter]

uh

[cursive raven]

just add y to both sides

[lean otter]

oh

[cursive raven]

see yellow term

he add that

[lean otter]

ok but then what

[lean otter]

so i added both sides

[cursive raven]

LHS theres -y and y

[lean otter]

ok so

[cursive raven]

they cancel out

[lean otter]

ohHHH

so

[cursive raven]

thats why we added them

[lean otter]

what

girll

ok cancel out part i got it

[toxic stratus]

this is just the LHS

on the RHS you still have just y

[lean otter]

ok so how exactly do i make the x positive now

[toxic stratus]

you dont need to

[lean otter]

i

i dont?

[toxic stratus]

the equation should now look like

[toxic stratus]

or if you reverse it

[lean otter]

so theres no m bassically

[cursive raven]

there is

[lean otter]

oh

nvm

got it

[lean otter]

yes thank u

so

since ur here

can u help me with c) too :')

D)

HELP

what do i do with 2 y's

im gonna cry

[cursive raven]

divide by 2

wait

theres 5

so dont do that

[toxic stratus]

do you know how to make y the subject

like

in general

[lean otter]

welll i used to remember?? maybe idk

summer passed

i forgot all of this

i like know but now I forgot so I need to be reminded

[toxic stratus]

you want to isolate y by itself

[lean otter]

yes yes

[toxic stratus]

so here

we have a bunch of stuff with y on the left

we need y by itself

[lean otter]

mhm

[toxic stratus]

so we'll move it all to the right

[lean otter]

right

[toxic stratus]

does this make sense

[lean otter]

yeah i understand

[toxic stratus]

okay

so then we only want 1 y

not 2

so we divide by 2

[lean otter]

so then divide all by 2?

oh

[toxic stratus]

yes

[lean otter]

okokok

ya I remmeber this

[cursive raven]

All u have to do is subtract the terms other than y and its coefficent

[lean otter]

yes

but thats not the final answer right

or..

[toxic stratus]

well now you can split the fraction

[lean otter]

SO

y = -2.5x - 2

is that the final answer

[cursive raven]

-1

[lean otter]

oh

HELP

yes obivously

[cursive raven]

its throughoutly divided

yea

[lean otter]

its 3 am and i am crying because of some baby math

ok thank u guys

i understand finally

thank u

dont delete any messages pls cause im gonna read it again like to write notes

<333

.close

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[hearty thistle]

How would I solve this question without substituting?

[hearty thistle]

nvm got it

7=2/5x=times x

x=35/2

.close

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[brazen parrot]

help

[brazen parrot]

why is it a? can someone explain

[safe radish]

@brazen parrot Has your question been resolved?

[worthy mango]

consider the shape of each dataset:
for the girls the biggest groups are at the top and at the bottom, but for the boys the biggest groups are in the middle

[brazen parrot]

is it because the boys scores are more clustered together? meaning it has a lower iqr

is iqr the same as standard deviation?

[worthy mango]

yeah you can think of it like that

no those are distinct concepts

[brazen parrot]

oh they seem similar

[worthy mango]

they are somewhat

[brazen parrot]

ohh thank you so much

understand this topic way more now

[worthy mango]

np

[safe radish]

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[safe radish]

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[safe radish]

@pure ferry Has your question been resolved?

[crimson field]

Set a_n = 1/n^2.

[pure ferry]

if i set a_n/n^2, its j one case right?

[rich haven]

Hey, can someone please help me regardings maths aptitude

[crimson field]

It's a counter example. 🙂

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[pure ferry]

.reopen

[safe radish]

✅

[pure ferry]

but isnt it convergent (p series)

[crimson field]

Yes. I made a mistake. 😢

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[cloud rock]

Help?

[stray socket]

Change each unit to centimeter

So 200 m is how many centimeters

[cloud rock]

20000

[stray socket]

And then how many centimeters if 4 mm

[cloud rock]

0.4

cm

[stray socket]

So what's the volume of the wire with length 20000 cm and diameter 0.4 cm

Just give me the answer in terms of π

[cloud rock]

Idk😅

[stray socket]

Do you know your formula for the volume of a cylinder

[cloud rock]

πr²h

[stray socket]

Yeah

So you have your diameter and length (height)

[cloud rock]

Soooo, V=π(20000)(0.4)?

[stray socket]

Be careful

If 0.4 is your diameter, what is your radius

[cloud rock]

0.2

[stray socket]

What is 0.2 squared

[cloud rock]

0.04

[stray socket]

So it's gonna be π(20000)(0.04)

Which is 800π cm^3

Now if 1 cm^3 = 10.5 g Ag, then how many g Ag do you have if you have 800π cm^3

[cloud rock]

8400g?

[stray socket]

8400π g, yeah

So now what is 8400π g to kg @cloud rock

[cloud rock]

8.4π kg?

[stray socket]

Ye

[safe radish]

@cloud rock Has your question been resolved?

[cloud rock]

So the final answer is what?

@stray socket ?

[stray socket]

This

[cloud rock]

Ohhh okay tq

.close

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[north perch]

If we let f=e^(2x^3) and g=e^(7x), then the statement below is false. So, is it correct to say the statement is false in general for all functions?

[safe radish]

Please don't occupy multiple help channels.

[north perch]

And the follow up question to that is this.

Which I have can assume refers to the previous f but what would g then be?

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[north perch]

How would the graph of this look?

[north perch]

<@&286206848099549185>

<@&286206848099549185> Would appreciate some help.

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[lean otter]

Anyone here

[velvet monolith]

,rotate

[lean otter]

Can u ?

[velvet monolith]

yes

there are two possibilities

[lean otter]

Yes

[velvet monolith]

one is that the graph is always above the y axis

[lean otter]

Yupp

[velvet monolith]

in order for the quadratic equation to not have a real root (in other words not to touch the y axis) is that the discriminant (D) is less than zero

or better written $b^2-4ac<0$

[flat frigate]

kjmkty

[velvet monolith]

that is the general rule

[lean otter]

i took it greater than equal to zero

as is assumed that graph will either touch the axis and d = 0 and has to real roots d>0

[velvet monolith]

aha

[lean otter]

see i made 4 cases
(a+2) > 0
D >= 0
-b/4a < 5
f(5) >0

[velvet monolith]

okay the first condition must be met in every cas

e

so i would rather call it a condition

[lean otter]

coefficient of x is not + ve for all cases

[velvet monolith]

wdym

i dont understand what you just wrote

[lean otter]

which part

[velvet monolith]

this message

i didnt understand a thing in that message

[lean otter]

ok so the given function will have a parabola opening always upside i.e f(x) > 0 and

Parabola opens upward when coefficient of x2 is positive

i.e

a+2 > 0

right