help-10

[tacit sorrel]

and wait

say that the first term wasn t 1

we can t do it ?

if it just continues to go up the same way?

[sage geode]

Can't do what exactly?

[tacit sorrel]

if the first term was like idk 33

can we not calculate the sum till u90?

with the formula

if it goes by the same way

[sage geode]

If we are given or are able to evaluate the common ratio, then we definitely can calculate the sum

[tacit sorrel]

with the same formula*

[sage geode]

Simply plug in u0 = 33, n = 90 and q = whatever q is into the formula

[tacit sorrel]

?

[sage geode]

Yes

[tacit sorrel]

and does the 1 in the beginning of 1-q^n+1 changes

into like 33 or no

[sage geode]

No, the value of the first term, even if it isn't 1, doesn't change the way the sequence grows/goes up

[tacit sorrel]

okii perfect thank you u just enlightened me

and now back to the exercice if ur okay w it

here

[sage geode]

Yeah, right

Since we have derived this earlier: [ 1 + q + q^2 + \dots + q^n = \frac{1-q^{n+1}}{1-2} ] We can simply plug in $q = 2$ and $n = 63$

[warm shale]

A Lonely Bean

[sage geode]

That gets us the same thing as what the solution in your screenshot says, namely, [ 1 + 2 + 2^2 + \dots + 2^{63}= \frac{1-2^{63+1}}{1-2} ]

[warm shale]

A Lonely Bean

[tacit sorrel]

and how do they simplify it to 2^64 -1 please

[sage geode]

1 - 2 is just -1 and dividing by -1 is the same as swapping every term's sign

So 1 - 2^64 turns into -1 + 2^64

[tacit sorrel]

yes

and then its just -1+2 = 1 and done?

that easy?

[sage geode]

Yes

[tacit sorrel]

wow thank you so much for ur patience LOL as last question the formula wouldn t work the way we want if we don t consider the n+1 right ?

it would just mix our mind and give us q^n+1 of what we wanted right

automatically

if we did like q^64 it would have given me q^65 instead ?

[sage geode]

If the sum was up until q^64, then the formula would include q^65, yes

[tacit sorrel]

okii perfect thank you so much let me save the convo so i can look back to it

tysm

[sage geode]

You are welcome

I am going now so if some doubt comes up about what we've discussed just ping me and I will see the message later

Good luck

[tacit sorrel]

oki perfect thank youuu small detail i wanna know how will the first term starting at whatever number appear in the formula please ? @sage geode

[obtuse pebble]

@tacit sorrel Has your question been resolved?

[sage geode]

It will just be $u_0\cdot\frac{1 - q^{n+1}}{1-q}$

[warm shale]

A Lonely Bean

[sage geode]

Because, again, every geometric sum is basically $u_0(1 + q + \dots + q^n)$

[warm shale]

A Lonely Bean

[obtuse pebble]

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[glacial widget]

Can anyone help me with this? I dont understand how to do it.

[obtuse pebble]

@glacial widget Has your question been resolved?

[glacial widget]

<@&286206848099549185>

[wide rose]

first find the inner pentagon angles

using vertical angles

[glacial widget]

oh ok

i think i found them

[wide rose]

use them to find star's angles

and the rest is ez

[glacial widget]

ohhh okay thank u

.close

[obtuse pebble]

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[indigo pendant]

Why did they multiply row/ column of A? Why couldn’t they have multiplied the row/column for B?

[obtuse pebble]

@indigo pendant Has your question been resolved?

[obtuse pebble]

@indigo pendant Has your question been resolved?

[cedar aspen]

Whenever you multiple matrices, you take the dot product

So you multiple each element by the corresponding element and take the sun

You always multiple row by column

so the first row of matrix 1 by the first column of matrix 2

In prolem B, You go column by column before switching rows (theres only one column in matrix 2 so we switch to row 2 of matrix 1)

we continue until we have a new matrix

heres a helpful representation

We continue multiplying row by column, before switching rows when we run out of columns

We slowly can build and answer

Switching the two matrices and multiplying gives a different answer because we are multiplying a different row by a different column

[obtuse pebble]

@indigo pendant Has your question been resolved?

[obtuse pebble]

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[mild stirrup]

anyone know how to solve this?

[mild stirrup]

I got f'(x) = -2/3x^2

so f'(a) would be -1/6

and delta y = -1/6 (1/4)

[fallen pine]

I don't think that derivative is correct

[fallen pine]

yeah that's not what you wrote

[mild stirrup]

my fault

f'(a) would be -1/4

so delta y would be -1/4 * -1/4

so -1/16

[fallen pine]

yeah

[fallen pine]

wdym by delta y

Also (-1/4) * (-1/4) is 1/16 not -1/16

[mild stirrup]

it said approximate f(2.25)

so I thought it meant like like the diff of f(2.25) and f(2)

I think I just don't understand this question like what exactly does it want from me

[azure anchor]

i think its asking for a linear approximation

[mild stirrup]

what is a linear approximation '

we haven't gone over that

[azure anchor]

when you find the tangent line to f(2), you create a linear (straight line) approximation of the curve near a = 2

so once you find the equation of the tangent line, L, you find L(2.25)

[fallen pine]

^

[mild stirrup]

did I get the right tangent line ?

[azure anchor]

well you didnt write any equation

you only found the slope of the tangent

[mild stirrup]

-1/4(x)

[azure anchor]

point slope intercept form

you need x and y

y - y1 = m(x - x1)

[mild stirrup]

man

I do not know how to solve this one

[azure anchor]

f(a) = y1

a = x1

f'(a) = m

[mild stirrup]

by brother

I am not getting this one

[azure anchor]

its not as hard as you may think

[indigo pendant]

[fallen pine]

son calculus only gets harder from here 😭

[indigo pendant]

Yep

[mild stirrup]

na son I am just gonna ff the course

[indigo pendant]

save ur tears for later

bro said ff

[azure anchor]

for real though, this is still baby's first steps for calculus. i wouldn't even consider it calculus until you get to integrals. everything prior is the "buildup"

[mild stirrup]

I can do integrals sorta

that one im ok with

antiderivative +c aint that bad

[indigo pendant]

[azure anchor]

this is really all you're doing for this problem

[indigo pendant]

[azure anchor]

finding L(x) and then plugging in 2.25

[mild stirrup]

guy I am like ONE week into my first year of uni

[indigo pendant]

ME TOO

[mild stirrup]

guy

[indigo pendant]

• I’m challenger

[mild stirrup]

I don't think you understand my school was not good at teaching calculus

+I am unranked

[indigo pendant]

Why not

[mild stirrup]

I don't play leauge that often

[indigo pendant]

i had to learn english and learn math at same time sooo

[mild stirrup]

womp womp

[indigo pendant]

1/

[obtuse pebble]

@mild stirrup Has your question been resolved?

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[obtuse pebble]

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[glass night]

hello there i solved this one

[glass night]

but when i enter it online for my assignment it says that its wrong

this is what i entered

[violet sentinel]

remember when you have a^b/a^c, then it's a^{b-c}

you added tem

[glass night]

says its incorrect

[glass night]

i didn't get it

[violet sentinel]

yeah you added the exponents instead of subtracting

$\frac{a^b}{a^c} = a^{b-c}$

[warm shale]

MellowDramaLlama

[glass night]

ohhh

so i subtract

[violet sentinel]

bingo

[glass night]

omg thanks

[violet sentinel]

yep np!

best of luck to ya 🙂

[glass night]

thanks

u mind checking after im done?

[violet sentinel]

yeah sure

[violet sentinel]

nice work!

that's exactly right

[glass night]

great

great

thank u so much!

[violet sentinel]

of course!

best of luck to you

[glass night]

thanks

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[sweet sparrow]

why is 1.75 false for the first one

1.9 *

isn't it in the margin of error

why is 1.9 incorrect

[sweet sparrow]

bro this is my channel

get tf out of here

[violet sentinel]

visit #❓how-to-get-help to see instructions on how to create your own channel

[obtuse pebble]

@sweet sparrow Has your question been resolved?

[sweet sparrow]

.vlose

[nocturne minnow]

.close

[obtuse pebble]

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[thick knoll]

I don't know if I'll ever get this

I might have to switch majors xd

I'm so stupid it hurts

[alpine raven]

you need to solve the equation Ax = 0 I guess

[thick knoll]

I mean yeah

[alpine raven]

with 0 the zero matrix 3x1

[thick knoll]

what does "mapped into" even mean

[alpine raven]

A represents a linear transformation

Like a function f, for a given x, you get f(x)

[thick knoll]

I don't see any connection to that and my question

[unreal atlas]

its just fanciness for matrix multiplication

[alpine raven]

you wanted to know what "mapped into" means, so I gave an example

[unreal atlas]

Ax = b, means you multiply matrix A by vector x. You can say x gets mapped to b by some linear transformation with A, i.e x -> Ax

[thick knoll]

so the question is asking what x values result in Ax =0?

[unreal atlas]

yep

[thick knoll]

I wish they'd just said that but

okay

that's a start

so

the answer to this question

is very confusing to me

if these vectors match up columns to rows

why are there two of them

why are we adding them

and why are they named 3 and 4?

[unreal atlas]

I think the first column vector gets mapped to zero and so does the second one

v1 = [ 8 4 1 0 ]
v2 = [-6 -2 0 1]

Av1 = 0
Av2 = 0

so Av1 + Av2 = 0 + 0 = 0
A(v1 + v2) = 0

Av1 * x3 = 0
Av2 * x4 = 0

A(v1 * x3 + v2 * x4) = 0

Not sure why they named those x3 and x4 its probably in the way they found these vectors

but I forgot how to do everything numerical with linear algebra lol

[thick knoll]

after you row reduce A, it has you do this:

I understand the part where we're talking about the variables in terms of free variables

they lose me where they start turning these equations into a fucking vector

makes ABSOLUTELY NO GOD DAMN SENSE

so I don't even know what this notation means

and clearly it's trying to make sure no one knows what it means

[unreal atlas]

so the solution should be a vector right

Ax = b (x is a vector and so is b)

so when they say Ax = 0 they mean the zero vector

[thick knoll]

right

you know what confuses me

why is this

suddenly

different

than plugging in x_1 x_2 x_3

like

earlier in the class

that's how Ax=b worked

now it's this whole

different thing

when we were using a matrix as a set of linear equations, x_3 was either one value or another

how can it be 4 different values?

what the fuuuuuuuuuuuuuuck

the x vector should look like

[x_1]
[x_2]
[x_3]
[x_4]

not this

so

[unreal atlas]

So

A x = b

Where x = [x1 x2 x3 x4] and b = [b1 b2 b3 b4], since they are both vectors

However when you did the augmentation thing we noticed that when x1 = 8x3 - 6x4 and when x2 = 4x3 - 2x4 we get Ax=0

So now x = [x1 x2 x3 x4] = [8x3 - 6x4 4x3 - 2x4 x3 x4]

Which is the same as saying

[thick knoll]

OH.

[unreal atlas]

[8x3 4x3 x3 x4] - [ 6x4 2x4 0 0 ]

[thick knoll]

okay

I think

I'm starting to get it

holy fuck

that actually makes sense

[unreal atlas]

[8x3 4x3 x3 0] - [ 6x4 2x4 0 -x4 ]

if I did this right

[thick knoll]

it almost makes sense...

okay yeah I see it

[unreal atlas]

then x3 * [8 4 1 0] - ....

try not looking at the solution and getting there yourself

[thick knoll]

nah I understand it now

it is kind of a single vector

it's just

visually deceptive

because of the free variables

thanks for writing all that out

idk how

but it made it click

[unreal atlas]

exactly

it is a single vector they just made it a sum of two vectors

[thick knoll]

I just solved a similar question on the first go

makes total sense

thanks a ton @unreal atlas

.close

[obtuse pebble]

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[final epoch]

im not sure where to start

[unreal atlas]

do you know how to graph functions y = ax + b?

[final epoch]

no

is that the formula im supposed to use ?

[nocturne minnow]

No

That's just the equation of a line using a instead of m

y = mx + b

[final epoch]

so how am i supposed to graph the function f

with the f(x) given

[nocturne minnow]

Use y = mx + b, plot both equations

[shrewd jolt]

i need help guys

[nocturne minnow]

Then you limit it

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[final epoch]

so like

y=4x+3

[unreal atlas]

https://youtu.be/AOxMJRtoR2A

[final epoch]

whats the difference between an open circle and a closed circle in terms of like plotting points

[final epoch]

thankss

.close

[obtuse pebble]

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[fast knot]

This is a very stupid, quick question, but I'm having a bit of confusion regarding this stack overflow post regarding convexity using the hessian:

[fast knot]

To be specific, my question is this:

Is x just [f(x,y), f(x,y)]?

The equation in the post I think is wrong, but I just wasn't too sure exactly how they got a normal function into a vector

Unless it's just [f(x,y), f(x,y)]?

[obtuse pebble]

@fast knot Has your question been resolved?

[fast knot]

<@&286206848099549185> (It said I can use this ping after 15 minutes)

[obtuse pebble]

@fast knot Has your question been resolved?

[obtuse pebble]

@fast knot Has your question been resolved?

[tardy epoch]

No, x = (x, y). The post should have used vector or bold notation on the left side

[obtuse pebble]

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[light depot]

Hi , I need help with this question. I don't think I know how i should approach this question. Thanks!

[obtuse pebble]

@light depot Has your question been resolved?

[light depot]

<@&286206848099549185>

[fierce moth]

Hi

I need help with Indices

anybody can help i also need some help with LCM and HCF problems!

[latent walrus]

#❓how-to-get-help

[obtuse pebble]

@light depot Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[soft stratus]

Five consecutive terms of an arithmetic sequence have a sum of 40. The product of the first middle and last terms is 224. find the terms of the sequence.

[autumn adder]

What step are you on

[soft stratus]

I have no clue where to start

Or what equation to use

my tutor gave me these two equations

[autumn adder]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[autumn adder]

AH aight

Well the first thing you'd do is define an arithmetic sequence

[soft stratus]

a, a+d, a + 2d, a + 3d

a constant rate of change between terms

[autumn adder]

Yep

[soft stratus]

oh wait

so i have that = to 40

[autumn adder]

No

[soft stratus]

a, a+d, a + 2d, a + 3d = 40?

[autumn adder]

The product of the first, middle and last terms

First, what are the five terms

[soft stratus]

ohhhh

[autumn adder]

Oh sorry

Mb

Yeah

The sum

Of all the terms

@soft stratus

First, what are all the five terms

[autumn adder]

These are only four terms.

[soft stratus]

would i set it up as
(a-2d) + (a-d) + a + (a+d) + (a+2d) = 40

[autumn adder]

Your choice

[soft stratus]

5a=40
a=8

[autumn adder]

Yep, cool!

Now use the second piece of information you have

[soft stratus]

(8-2d)8(8+2d)=224

(64-4d^2)=224

4d^2=160

d^2=40

[autumn adder]

Nooo

The last term is (8**+**2d)

[soft stratus]

oh crappy myb

does

d=radical 40?

wait no

no

wait

idk

brb

help

@autumn adder

did i do this right

i redid it agin

<@&286206848099549185>

[tacit scarab]

seems fine

[autumn adder]

I could recommend taking the 8 to the other side, but nonetheless will yield the same result if done correctly

[soft stratus]

i shall multiply these gwo

[autumn adder]

Sure

When you're done ping me

[soft stratus]

ok

wtf

@autumn adder

is this the correct answer

[autumn adder]

Huh?

No

$$(8-2d)\cdot (64+16d)=224$$
$$8\cdot (64+16d) - 2d\cdot (64+16d) = 224$$

[soft stratus]

what did i do wrong.

[autumn adder]

How even will the d term cancel

[soft stratus]

okay i will do this

[autumn adder]

You wrongly multiplied apparently

Write it out

[soft stratus]

okay

@autumn adder

[autumn adder]

Why on earth do we have a SQUARE ROOT

It cancels out

Simplify the fraction bru

[soft stratus]

oh shit

IM DUMB

okay

@autumn adder thank you

[autumn adder]

You're welcome

Now find the terms by plugging in values 🙂

[soft stratus]

si

i already did

i shall close now

.close

[obtuse pebble]

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[shy night]

what is the quickest way of solving these questions without a calc?

[shy night]

just finding the critical values and doing some sort of sign diagram?

[solar trellis]

Ideally you want to eliminate the denominator on both sides

[shy night]

that would eliminate some solutions

[crisp garden]

you can compensate for it afterwards

[shy night]

yep

[solar trellis]

Consider cases for when it's positive and negative

[shy night]

u can do x^2+25<=10x first

and then consider the denoms

[crisp garden]

first we'll assume x > 1 and x <-3

that makes both the expressions positive

cancel out the denominators and solve for the solution set

[solar trellis]

No such x exists

Or instead of and

[crisp garden]

that's a different story

whether any solution exists in that range or not

I'm just saying we go step by step

then we'll assume x is between -3 and 1

flip the inequality signs because the expressions are negative

then solve

[wintry swift]

you have 3 cases. x < -3, x >1 and x between -3 and 1

[crisp garden]

correct

[shy night]

yes

[solar trellis]

Considering cases that don't exist is not a good use of time

[shy night]

so just sign diagram those cases?

[solar trellis]

The denom will be positive or negative in each case

Sp u flip the sign if needed and solve the quadratic inequality

[crisp garden]

yes

[shy night]

.close

[obtuse pebble]

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[shy night]

ok thanks

[obtuse pebble]

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[clear kraken]

is this a mistake?

[clear kraken]

I thought for Euler's totient function, we have $\varphi(pq)=(p-1)(q-1)$

[warm shale]

Kalgar

[clear kraken]

So shouldn't it be $(2-1)(2-1)\cdot (5-1)(5-1)=16?$

[warm shale]

Kalgar

[obtuse pebble]

@clear kraken Has your question been resolved?

[wide rose]

what is phi here?

[analog python]

no, it's phi(pq) = phi(p) phi(q) if p and q are coprime which is the first step

then phi(p^k) = p^k-p^(k-1) if p is prime

which is the second step

[obtuse pebble]

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[wide rose]

againg Pythogoras

[fluid gulch]

i dont get it

[royal basin]

make a diagram first.

[fluid gulch]

i did

[royal basin]

show your diagram

[fluid gulch]

ok

[wide rose]

angle XPY is 90*

[fluid gulch]

well no sh*t

[royal basin]

you can curse here, it's fine.

no need to censor yourself.

[royal basin]

brb

[fluid gulch]

aight calm

[fluid gulch]

is the answer 148 degrees and 51 minutes

[royal basin]

dunno

if you show me your calculations maybe i could verify

[fluid gulch]

the angle in the triangle is tan^-1 (950/420)

so the bearing is 360 - 145 - tan^-1 (950/420)

= 148 degrees and 51 minutes

[royal basin]

,calc 360 - 145 - atan(950/420)*180/pi

[warm shale]

Result:

148.85047390808

[royal basin]

,calc 0.85047390808 * 60

[warm shale]

Result:

51.0284344848

[royal basin]

ok yeah checks out

[fluid gulch]

aight thx

[obtuse pebble]

@fluid gulch Has your question been resolved?

[woeful talon]

hello jeppyma

familiar friend

i didn't think u would need help for trig

[obtuse pebble]

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[light oriole]

Did I do this right? Help me with finding the domain and range of multiplication of functions please.

[opaque ruin]

it's like f(g(x))
so sqrt (g(x)+2)

[light oriole]

Ah, no. I'm sorry for the dirty handwriting, but it was supposed to be written as f•g, not f○g.

[opaque ruin]

do you mean multiplying or composite functions

[light oriole]

Multiplying.

[opaque ruin]

oh
then i think youre right

[light oriole]

Really? Thank you.

Close

close

[opaque ruin]

wait
how did you get the range of y

[light oriole]

Uh, wait. I don't know how to explain.

I plugged in 0.4 in the function, and got -5.948 as the lowest result.

Can you see?

[opaque ruin]

it might be 0.41928902809
you cannot get the exact answer by that method

we have to use differentiation to find the exact value

[light oriole]

How did you get 0.419... ? Also, I don't know how to do differentiation.

[obtuse pebble]

@light oriole Has your question been resolved?

[obtuse pebble]

@light oriole Has your question been resolved?

[obtuse pebble]

@light oriole Has your question been resolved?

[obtuse pebble]

@light oriole Has your question been resolved?

[mortal lava]

Please can someone help me here with simplifying polynomials I know my answer is wrong but I’m not sure where I went wrong

,rotate

[true geyser]

correct

[light oriole]

.close

[obtuse pebble]

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[vague isle]

what operation are they doing in this passage?

i tried to decompose fraction

[alpine raven]

2n+2 = 2(n+1)

[thin star]

they divided the n+1

[vague isle]

which one

and by what

[thin star]

you can factor an n+1 on both numerator and denominator

they just cancelled them

[vague isle]

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaarghhhh

[alpine raven]

(n+1)² = (n+1)(n+1)
on the denominator you have 2n+2 = 2(n+1)

[vague isle]

didnt see that

thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Need help on this

[timid silo]

The only hint I have is that I got to use the intermediate value theorem

Im stuck at f(1/2) I don’t know how to calculate it

[tardy epoch]

Why do you need to calculate f(1/2)

[timid silo]

Because according the the ivt I have to show that g(1) x g(0) is negative

And g(x) = f(a+1/2) -2-f(a)

If I substitute I got the f(1/2) left

So I need to get ride of it

I thought about changing the interval and taking <1/2,1> since it’s in <0,1>

Do you understand me ?

So I’m stuck at calculating g(1) and g(0)

[night igloo]

This is a sneaky one

Basically you gotta show that 2 is contained in the interval bounded between f(1/2) and 4 - f(1/2)

And after that it's a straightforward application of the IVT

[timid silo]

I tried to use the corollary

[night igloo]

What corollary

[timid silo]

sorry i didn’t get it

[timid silo]

Well nvm

[night igloo]

What part don't you get

[tardy epoch]

Maybe try a different g

[timid silo]

No I got what u said but I don’t have any clue about how to show that 2 is between f(1/2) and f(1/2) -4

[night igloo]

That's the sneaky part

Suppose you have an interval (a, b)

[timid silo]

I don’t think so ?

[night igloo]

What can you say about the arithmetic mean (a + b)/2

[timid silo]

A center ?

[night igloo]

Yes

So in particular it's contained within (a, b)

Right?

[timid silo]

Yes so I will use another interval ?

[night igloo]

Yes, take a = f(1/2) and b = 4 - f(1/2) for instance

[timid silo]

okay okay

So if I take it I should show that 2 is included in that a,b

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[gilded ferry]

Hi. It’s not a question in some work book or anything, I just want to clarify what average is.

Here’s all many students that ATTENDED throughout 4 days of school. Meaning 4 days of school passed and below are numbers of each student that how many days already attended.

4
4
4
4
4
4
4
2
4
4
3

You would add all numbers and then divide with 11 (amount of numbers) and then again divide with 4?

[tight patio]

Do u know the meaning of average?

[gilded ferry]

Not really

[celest sandal]

I need help

[tight patio]

!help

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[tight patio]

Google it

And tell me

If u understand it

[gilded ferry]

Ok anyways could you tell me how would you do it

@tight patio

<@&286206848099549185>

[tight patio]

What’s the meaning

Of average

[gilded ferry]

Idk

Can u tell me

CAN U

FJRJDJKGFKKRKGKLG

@tight patio

<@&286206848099549185>

@royal basin

[tight patio]

Google it smh

Google it

And copy paste here

It’s not that hard

[royal basin]

weh?

[gilded ferry]

But I have total number of 4…

Guys…

[tight patio]

Ok

[tight patio]

What’s the total number of these jumbers

Like how many numbers are there

Like

How many observations

[gilded ferry]

11

But like the maximum days are 4

Yk what I mean

[obtuse pebble]

@gilded ferry Has your question been resolved?

[obtuse pebble]

@gilded ferry Has your question been resolved?

[obtuse pebble]

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[modern palm]

not sure what I did wrong tbh

other than the second one i missed a decimal

.close

[obtuse pebble]

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[obtuse pebble]

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[calm axle]

claim

[calm axle]

Ok so I need some help with this , the question is that I need to find the average rate of change from 0 seconds to 2 seconds and from 2 seconds to 4 seconds and describe whats happening. Time , t is seconds.

figured it out actually

.close

[obtuse pebble]

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[sick wing]

help?

[sick wing]

<@&286206848099549185>

Im doing this question

I did it quite normally

[upbeat lantern]

use the definition of divisibility

[sick wing]

im really not great at maths

i just put n=1

till like 10

and ig that should be enough

but apprenlty its not

[upbeat lantern]

all that does is show that its divisible by 1-10

[sick wing]

and everyones trying to explain it in a complex way so i feel well dumb

[sick wing]

mhm true

[upbeat lantern]

there is a very real possibility that its not divisible by 11, right? so you have to consider all cases

[sick wing]

valid

[upbeat lantern]

so to do that we need the formal definition of divisibility

[sick wing]

theres one?

[upbeat lantern]

yes

[sick wing]

should i search it up?

[upbeat lantern]

a | b (a divides b) if b =ac for some integer c. this probably doesnt make much sense tho

[mighty torrent]

gcd(x,y) ≠ 1, right?

[upbeat lantern]

so to simplify

do you agree that 5 | 15 (5 divides 15)

[sick wing]

yes

15/5

yep

[sick wing]

whats gcd

[upbeat lantern]

so by our definition if we want to prove it formally, 5 | 15 if 15 = 5x

or 5 times another integer x

and it does! 15 = 5*3

[sick wing]

so its a multiple? is what you're trying to say?

[upbeat lantern]

basically

[sick wing]

wdym by formally please?

[mighty torrent]

Greatest common divisor function

[upbeat lantern]

so like here are some examples

2 | 4 because 4 = 22
4 | 20 because 20 = 54
2 | 24 because 24 = 2*12

he said he isnt great at maths dude that answer likely makes no sense lol

[upbeat lantern]

so in math we could say

[sick wing]

thank you 😔

[upbeat lantern]

like okay if i asked you "how do we figure out the next number" you could be like "well just count"

like for any number

[sick wing]

mhm

yep sure ig

[upbeat lantern]

but a lot of times, like if we want to make a computer program

[sick wing]

its a length time taking way tho

[upbeat lantern]

that wont really help because computers dont know how to count

[sick wing]

oh so algorithms is what we need

[upbeat lantern]

thats just a really specific example tho, this becomes useful when u have more complex statement

s

yes!

[sick wing]

so thats why we work with functions and stuff

ah

[upbeat lantern]

so what we could do to make a formal definition, or a definition that are unambiguous

unambigious meaning theres no confusion for anyone

[sick wing]

uh huh

ok ok ok

[upbeat lantern]

we could say it like this

"to find the next number for any integer n, compute n+1"

okay back to ur problem

[sick wing]

gotcha

[sick wing]

that really helped with developing the mindset there

Yes back to this

[upbeat lantern]

🙂

so i think it might help to try a simpler problem

prove that 2n | 4n for any integer n

remember a | b if b = ac for some integer c

any ideas? if not thats fine

[sick wing]

mhm i wanna think about it

[sick wing]

a divided by b

if b = ac for some integer c

[upbeat lantern]

or 2n | 4n if 4n = 2n*c for some integer c

[upbeat lantern]

a divides b*

or like a goes into b evenly if b = ac for some integers a, b and c

[sick wing]

so thats you also saying

b=ac

[upbeat lantern]

yes

[sick wing]

because b divided by a

= c

[upbeat lantern]

!!!

exactly

[sick wing]

ok ok ok

[upbeat lantern]

so here if we want to prove 2n | 4n we just have to rewrite 4n as 2n times something else or 4n = 2n*c

[sick wing]

so maybe 2^n - (-1)^n = k

[upbeat lantern]

try doing this

what would c be here

[sick wing]

2?

[upbeat lantern]

yes!!!

[sick wing]

yay

[upbeat lantern]

so 2n | 4n because 4n = 2(2n)

[sick wing]

🌻

[upbeat lantern]

and 2n | 4n = 2

[sick wing]

ah

gotcha

back to the problem yes

[upbeat lantern]

so 2^n - (-1)^n | 3

[sick wing]

OH

OHHHH

OHHHH

[upbeat lantern]

yep

[sick wing]

YOU'RE A GENIUS DUDE

dang

[upbeat lantern]

https://tenor.com/view/card-no-u-wave-uno-card-gif-15455638

[sick wing]

bro gave me an insane amount of direction right there

[upbeat lantern]

but u still got it lmao

[sick wing]

but dont i have to prove thats for all positive integers?

[upbeat lantern]

nope that would be really hard

impossible

if you can prove it algebraically

[sick wing]

so whats the answer bruv 😭

were back to sqaure one

[sick wing]

ive been stuck over this since mornin or sm

[upbeat lantern]

2^n - (-1)^n

[sick wing]

ok

[upbeat lantern]

is there a way to rewrite this at all

[sick wing]

erm

its not equal to smthn

so no ig?

unless we assume

that

x^n is =y

or smthn

[upbeat lantern]

welll

whats -(-1)^n

[sick wing]

1^n

[upbeat lantern]

okay but we have 2^n+1^n now

[sick wing]

3^n

[upbeat lantern]

which is?

yes

hold on what the flip

we are try to show that 2^n-(-1)^n is divisible by 3

[lyric crane]

is this not just casework

[sick wing]

yes

but for all positive integers of n

[upbeat lantern]

but we just showed that 2^n-(-1)^n is 3^n

[lyric crane]

yeah sure

so one case is where n is odd

and the other is where n is even

[sick wing]

i solved it till n=10

[upbeat lantern]

yes

you cant just do every number tho

[sick wing]

and they were all divisable by 3

well yes

[lyric crane]

this is not true

[sick wing]

cant do till infinity

[upbeat lantern]

oh wait fuck bvm lmao

[lyric crane]

well unless you're mod 3

[upbeat lantern]

yeah ur right

okay @sick wing ignore that then lol

[sick wing]

both of you are confusing me brub

[upbeat lantern]

do you know the fornal definition of a even number

and odd nimber

[sick wing]

uh no

[upbeat lantern]

okay so an even number is a number that can be rewritten as 2k for some integer k

an odd number is a number that can be rewritten as 2k+1 for some integer k

16 is even because 16 = 8*2

17 is odd bc 17 = (8*2)+1

this statement is really hard to prove on its own, but it might be easier if we break it up into 2 parts

since every integer is either even or odd, we can prove that its true when n is odd and we can prove its true when n is even and that covers everythijg

[lyric crane]

(it's also much easier if you do this in mod 3)

[upbeat lantern]

and that will be easier

[upbeat lantern]

i doubt he knows mods

[sick wing]

whats mods

[lyric crane]

i mean this is introductory number theory

oh

nvm

[upbeat lantern]

bc he said he struggles w math and also tried to prove it with n=1 through n=10 so

[sick wing]

damn

i feel insulted in math

[upbeat lantern]

does this make sense tho

[lyric crane]

ok then this is a bit weirder

if you don't use mods

[sick wing]

kinda

[upbeat lantern]

(mood)

[sick wing]

one of my seniors said they use induction method or sm\

[sick wing]

eek

[lyric crane]

induction???

with this???

[sick wing]

yea

[lyric crane]

i mean you could

i think

but whyyyy

[sick wing]

idk

how old are you tho

[lyric crane]

im in 9th but i've taken number theory courses before so I know this material

[sick wing]

dang

[upbeat lantern]

i dont think he knows induction

[sick wing]

same

but then how do yk induction and i dont dawg

[lyric crane]

me?

[sick wing]

weird

[upbeat lantern]

ay i did the same thing when i was in 9th

[lyric crane]

nice

[upbeat lantern]

no i kbow u know it

lol

[lyric crane]

lol

well if you dont use mods this is pretty icky

[sick wing]

is there any way around this for me to understand and solve it

[upbeat lantern]

remember how i told you that every integer is either even or odd

[sick wing]

yep

[upbeat lantern]

n is even if n = 2k
n is odd if n = 2k+1

[sick wing]

ok

[upbeat lantern]

so try plugging in 2k and then prove its true if n is even by factoring it and shit

[sick wing]

but i can just take

1

2

[upbeat lantern]

then once uve done that uve proven it for half of the integers

[sick wing]

3

4

5

as odds and evens

[upbeat lantern]

i dont think wed have wnough time

to do that

because we need to ahow its true for every integer

[sick wing]

im gonna send you three other questions

check if those are right or wrong

then well come back to this

[upbeat lantern]

then we automatically half half the integers, after uve proven that try plugging in 2k+1

[sick wing]

bevause i think ill understand comparitively better

[upbeat lantern]

okay

[sick wing]

is that okay?

okay

A :

this is what i did

uh @upbeat lantern

[upbeat lantern]

looks right

[sick wing]

okay second question

i did this

how about this one

[upbeat lantern]

cos(π/4) = 1/√2

[sick wing]

what

where

@upbeat lantern wait so its wrong?

[obtuse pebble]

@sick wing Has your question been resolved?

[obtuse pebble]

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• Be polite and have a nice day!

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[burnt thunder]

can someone help me with 5a

[burnt thunder]

i just wana see it dine

done

bec im a bit confised

,rotate 270

[burnt thunder]

f(x)=x^2-4

[neon eagle]

so what is f(-x)

[burnt thunder]

i thought u put the whole thing in

😭

[neon eagle]

what do you mean “put the whole thing in”

[burnt thunder]

like

everything after f(x)

[neon eagle]

After or inside the ( )

[burnt thunder]

like

(-x^2+4)

i thought it was this

but i dont think so

[neon eagle]

noo…

[burnt thunder]

the answers say otherwise

😭😭😭

[neon eagle]

Ok look

[burnt thunder]

yes

[fair monolith]

f(2) means you plug in 2 for x

everywhere x exists

[neon eagle]

^

[fair monolith]

f(2) when f(x) = x^2 - 4

is (2)^2 - 4

as you are plugging in 2 for x

[neon eagle]

2^2-4

Yes

[burnt thunder]

yes

so i just do

-x^2-4

[neon eagle]

plug in -x for x

[burnt thunder]

?

[neon eagle]

No

[burnt thunder]

help

😭

[neon eagle]

What is (-x)^2

[burnt thunder]

x^2

[neon eagle]

Ok good

So what is f(-x)

[burnt thunder]

x^2-4

[neon eagle]

Exactly

Cool

[burnt thunder]

yes

okok

[burnt thunder]

so i dont do anything with the 4

[neon eagle]

There is no x in it

So no

[burnt thunder]

so for the next one

-f(-x)

its -f

[neon eagle]

the question asks for -f(x) Right

[burnt thunder]

oh mb

yes

its -x^2

[neon eagle]

What happened to the 4

[burnt thunder]

-4

is it -4?

[neon eagle]

no

[burnt thunder]

ohmagaud

😭😭😭🙂

[neon eagle]

x^2-4 right

[burnt thunder]

as u can see

i suck at math

😭

[burnt thunder]

yes

[neon eagle]

-f(x) just means you times everything by -1

[burnt thunder]

oh ta

ya

yesyes

[neon eagle]

So it would be…

[burnt thunder]

-f(-x)

does the -f

mean

[neon eagle]

What

[burnt thunder]

i multiply

the 4

by a negative

[neon eagle]

Yes

[burnt thunder]

help

did i make

a mistake

[neon eagle]

Everything

Idk why you keep writing -f(-x)

The question asks for -f(x)

[burnt thunder]

u said multiply

-f by everything

so i did

i multiplied the x

[neon eagle]

what

[burnt thunder]

i think the textbook did that too

lemmie see

5a

[neon eagle]

-f(x) means -1 times f(x)

[burnt thunder]

didnt they do that too

[neon eagle]

Weird