help-0

[alpine sable]

if a product is equal to 0, it means that one of the factors is 0

????????

and the zeroes are easy to calculate

sorry im so lost

dw its alr

ok so lets say that

hhhh im sorry, im shit at explaining myself lol

nO ITS FINE

IM JUST REALLY DUMBJLED

NO u arent

its okay this shit can be confusing sometimes haha

jkhdehked

ok anyways

idk how it works

so it feels like I guessed

if the product of something is 0

ye

like, 3x = 0

3 multiplyed by what gives us 0

0 right because 3 x 0 = 0

yes

so if the product of something is 0, it means that one of the factors is 0

yesh

ok thats good so, finding the points in which y=0 is real useful for analyzing graphs

because

[wicked plover]

hi

[alpine sable]

since the function involves multiplying

[alpine sable]

use another channel pls

[wicked plover]

how do i get rid of BC?

[alpine sable]

Channel in use pls

yeah

I need help

like rn lol

its not for a test

its a regents practice

ok soooo, we know the function involves multiplying

yes

[shadow furnace]

You want to get rid of BC or do you want BC?

[alpine sable]

and finding the points in which the product of something is 0 is easier than plugging different x's and sketching

because for finding that, you gotta get an x such that one of the factors becomes 0

therefore, one of the factors is 0, making everything 0

aka y=0

in this case is p easy to find the points that make one of the factors become 0

oo

wait if one of the factors is 0 wouldnt the polynomical function just be 0

yeaaa

thats what we're looking for

because finding the values of X such that the polynomical function is 0 in order to analyze a graph is easier than plugging different values for X and then sketching

waittt

huh

khan academy has videos on this

im confused

really

where

they explain this shit WAAAY better than me lol

type khan academy zeroes of a polynomial

or smthn like that

alright ty

hold up isnt this algebra 2

yea

[shadow furnace]

Lol relatable

[alpine sable]

for my school it says its algebra 1

So we're being asked to find whats the graph of a certain polynomical function.

In order to find that graph, we can look at the points in which the outcome of the function is 0 (y=0) that match our functions outputs (because this is way faster and easier than plugging different values to X and sketching em). This is a function in which we're looking for the y=0 right, and for that to happen, we can use this:

if the product of something is 0, it means that one of the factors is 0.

so, lets say that we have (x-3)(x-6) = 0
here we have two options; x = 3 or x = 6 as both of these make one of the factors 0 (therefore making the output y = 0, which is what we're looking for).

Now we look at the graphs and see which one of em have both (3, 0) and (6, 0).

[alpine sable]

TJANK YOU

np

pls if you didnt get something or something is confusing, tell me

one day id love to teach maths and for that to happen i need to improve the way i explain things lol

[alpine sable]

oo nice

I just want to major in math when im older :p

but is it clear now?

ayoo

a bit

math major pog

yes

[shadow furnace]

I think you could explain things with pictures

That would help people

[alpine sable]

yeyeye

[shadow furnace]

But that is really not possible in discord chat

[alpine sable]

wait this might clear up things a bit more

if you have to find the matching graph of a function you ain't going to graph every single point of X right? youre just going to take some points and see what graph matches with said points

its the same thing we're doing here with finding the y=0

[alpine sable]

yes

I think the problem inst ur explanation

the problem is im trying to speedrun high school algebra

ahaha

my entrance exam requries it

Algebra I Any%

so im kinda fucked

oo

ye

nah youre going to be fine

it also requires geo

and field questions go up to pre calc

so rn im in a panick

ooo

well you have until the end of the month right

yeah tofinish algebra 1

oo isee isee

and than 3 ish months till entrance exam

khan academy can help you a lot then

you know khan academy?

https://es.khanacademy.org/math/precalculus

this covers pretty much everything about precalc lol

they have a ton of videos and exercises

although matrixes and vectors belong to linear algebra more than precalc lol

they have courses on algebra i and algebra ii too

[meager jasper]

I'm 99% sure this is right but i'm a little drifted on how to find it...

I wouldn't mind an explanation

[ionic jewel]

it is not right

basically if you could draw that part of the graph without picking up your pencil its continuous

[meager jasper]

so i'm confused then

[ionic jewel]

which in this case you cant do it at 2, and you cant do it at -1 (because of the red line showing it)

[meager jasper]

Would it be none of them?

Oh -1

[ionic jewel]

dont you see how it jumps at x = 2?

[meager jasper]

Yeah

[ionic jewel]

you cant teleport your pencil

its not a continuous line

the formal defintion involves limits if you know those?

[meager jasper]

I'm in pre so a little confused

I think I know what you mean

[ionic jewel]

well i wont give you the limit definition then

but its basically if you could draw it without picking up your pencil

eg, not discontinuous

[meager jasper]

Okay so -1 and 2 would discontinous then

since those are the parts where you stop the pencil wouldnt be

Oh yeah it is -1 and 2, I see what you mean

The parts where they can't be drawn without hopping

@ionic jewel tyty

[ionic jewel]

np

[wicked plover]

@ionic jewelhi

can u help me

[ionic jewel]

what have you tried

and also dont ping me specifically

[wicked plover]

oh ok

i write it in standard form

?

[ionic jewel]

okay

well

you want to isolate a variable from one equation

then sub what its equal to into the other equation

(substitution)

[wicked plover]

what?

2(x - 4) + y = 6

3 - 2 (y - 3) = 13

this is the standard form right?

[ionic jewel]

no

thats what you were given in the problem

[wicked plover]

oh

what would be the standard form

...?

[ionic jewel]

you dont even want it in standard form

you want to isolate one of the variables in one of the equations

[smoky harness]

Find the best move for black

[wicked plover]

oh

how do i do that?

[ionic jewel]

knight promotion

[ionic jewel]

I would look up a video on substituion for solving sets of equations, I do not want to explain algebra right now

[ionic jewel]

matter of fact the knight promotion is the only move that doesnt lead to a forced loss in fewer than 3 moves

not only is it the best, its the only non-losing move

[smoky harness]

ye

[gaunt magnet]

hi

question

[ionic jewel]

hi

answer

[gaunt magnet]

Do you write this as log _2(x^3-4x^2)/{(x+4)

[ionic jewel]

what?

plaintext of that would be log_2((x^3-4x^2)/(x+4))

if thats what you meant

[ocean seal]

ShurjoA

[ionic jewel]

but yeah that probably simplifies

[gaunt magnet]

ok so this question i got the answer

how will i write this on a computer

[rigid smelt]

imagine posting the answer without the question

[ionic jewel]

oh i have no idea how your specific computer program wants the answer

[gaunt magnet]

I did post the question

[ionic jewel]

dont even know what program it is

[gaunt magnet]

log_2((x^3-4x^2)/(x+4))
im guessing this would be correct

[gaunt magnet]

btw was the answer correct for this ques

[ionic jewel]

looks right but it might be able to be simplified

,w simplify log((x^3-4x^2)/(x+4))

[ocean seal]

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[ionic jewel]

yeah yours looks good

[gaunt magnet]

for this ques i got the answer

-7781/792

[ionic jewel]

you could just use wolfram to check your answers

[shadow furnace]

Actually I don't think that's correct

[ionic jewel]

,w 6^(x+1) = 5^x

[ocean seal]

Results provided by WolframAlpha

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Requested by 兔子#6562

[shadow furnace]

I would take the ln on both sides

[ocean seal]

ShurjoA

[gaunt magnet]

dont know how to use that bot

[gaunt magnet]

🤔

[ocean seal]

ShurjoA

[gaunt magnet]

they want the answer in exxact form

[ionic jewel]

https://www.wolframalpha.com

[twin haven]

@ionic jewel can you tell what are determinants in a matrix?

and how are matrices used to solve simultaneous equations

[ionic jewel]

what is it with people pinging me

a matrix has a determinate

look it up if you want to

co-efficient matrices can be reduces to RREF quickly (by computers) to solve simultaneous linear equations

[twin haven]

like can you show me how can you solve
x+y=15
x-y=10

by matrices

[ionic jewel]

yes

,w rref {{1, 1, 15}, {1, -1, 10}}

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

x = 25/2, y = 5/2

[twin haven]

so what happened here?

[ionic jewel]

im not doing it by hand though, look up "rref matrix" to learn how to do it

[twin haven]

I know crammer's rule

[ionic jewel]

its basically efficient elimination method for solving it

[twin haven]

not sure how to use them in matrices tho

[zenith trail]

help

[ionic jewel]

i dont even know what cramers rule is

oh

its just an explicit formula for 2 and 3 equation systems

just go learn how to rref matrices @twin haven

[zenith trail]

what is answer

[ionic jewel]

find a linear algebra textbook and read the first like 2 chapters

[zenith trail]

@ionic jewel

[twin haven]

ok

[twin haven]

can you recommend a book?

[ionic jewel]

i swear if one more person pings me individually im just leaving

[ionic jewel]

dont ping specific helpers

im not answring your question

the last ones just happened to be ones i wanted to answer anyways

[sly mantle]

generally it solves nxn systems given det!=0

[ionic jewel]

"linear algebra and its applications, by david lay" is the one i used, but any of them would work

[sly mantle]

but in practice it's slow for anything over n=3

[twin haven]

cant you just fill in the values of x and check for the corresponding value?

[gaunt magnet]

can this get simplified more

[unborn nova]

can anyone help me with this

[gaunt magnet]

bruh channel taken read #❓how-to-get-help

[alpine sable]

i dont think so

[unborn nova]

sorry

[sudden plover]

lmfao

[unborn nova]

.-.

[gaunt magnet]

<@&286206848099549185>

[alpine sable]

@gaunt magnet no

[noble sinew]

You can combine the denom into one ln

[gaunt magnet]

this?

[noble sinew]

Si

[gaunt magnet]

so that would be the final answer?

[noble sinew]

Si

[sweet mica]

Conditional Probability!!

maybe conditional probability...

P(A,B,C | Defective)

That would be my guess

[noble sinew]

Law of total prob

So ||0.35 * 0.015+0.35 * 0.01+0.3 * 0.02||

[alpine sable]

hey, for some reason I think there should be a ratio

x/q = z/y

here just by noticing this equation

is this even valid or am I delusional

[vale wigeon]

x/q = z/y you mean

[alpine sable]

yes

a^z

yes

yes there is apparently @vale wigeon cause like

I mean

yeah

there is probably

cause for any to the power, there should be some prime which divides them, and its only possible when they have some common primes, which they have to because they are in a equation

and for the common primes the equations can be simplified for any number I assume, and then you get a ratio

just checking my hypothesis, although the solution is straight forward

[opal wyvern]

How do you find distance traveled from an interval and velocity function?

Scanning the internet. Finds. Nothing.

[thorn kindle]

Integral

[ionic jewel]

integral

shoot i was too slow

[alpine sable]

integral

integral

[opal wyvern]

Antiderivative of velocity function evaluted over the interval?

[ionic jewel]

yep

[opal wyvern]

The anti derivative is just 3

Wait no its not

lmao

[alpine sable]

😏

$\int_{a}^{b} v dt = $ distance traveled from t = a to t = b

[ionic jewel]

$\int_a^b v(t) , dt$ is distance traveled from t = a to t = b

bruh why am i so slow

[alpine sable]

where texit

[ionic jewel]

fine ill do it with texit

[thorn kindle]

$$integral$$

[alpine sable]

@ocean seal

[ocean seal]

AMD

bunny

[alpine sable]

$\int_{a}^{b} v dt = $ distance traveled from $t = a$ to $t = b$

[ocean seal]

omeganebula

[alpine sable]

ok finally

[opal wyvern]

My answer is still wrong lol

[alpine sable]

what's the question?

[opal wyvern]

So v(t) is 3t-8

[alpine sable]

ok nice

[opal wyvern]

[0,5]

[alpine sable]

fastest way to learn analysis for solving stuff

[alpine sable]

for t?

[opal wyvern]

For interval of velocity

[alpine sable]

that's where you're wrong

[opal wyvern]

Wait yes for t

[0,t,5]

ik thats not correct interval notation but you get the point

[ionic jewel]

,w integral from 0 to 5 of abs(3x-8)

[opal wyvern]

Thats what I got

[ionic jewel]

calculating by hand is for chumps

oh

hmm

[alpine sable]

[opal wyvern]

-2.5 is somehow wrong tho

[ionic jewel]

wait

of course

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

you want distance traveled, not displacement

theres the actual answer

[opal wyvern]

whats the fricken differenc e

[ionic jewel]

you need to absolute value

otherwise you start going backwards haflway through

[alpine sable]

bro 9th grade physics

[ionic jewel]

so the change in distance is lower than the actual distance traveled

[opal wyvern]

i dont remember what i ate last night bro

[alpine sable]

bro

[alpine sable]

same bro same

[ionic jewel]

displacement vs distance though

[alpine sable]

same bro same

[alpine sable]

fr bro

ok bro

[opal wyvern]

ong vro

[alpine sable]

is this correct?

[opal wyvern]

Onto my last mf homework assignment of Summer Calculus

[alpine sable]

all the best!! you got this bro

[hexed bloom]

anybody got any idea how to do this?

[opal wyvern]

lowkey going crazy rocking out to kelly clarkson over 60 hours of calc over the past week

[alpine sable]

as far as I remember this equation is satisfied when theta + 2*theta + 3*theta = 180?

[hexed bloom]

i gotta show working too 😅

<@&286206848099549185>

[rigid smelt]

you do know you ping helpers after a minimum of 15min of inactivity right?

[alpine sable]

wait no this is wrong sorry

[hexed bloom]

wait is that so?

[opal wyvern]

gets banned

[hexed bloom]

uff

[alpine sable]

you confused me lol @alpine sable it isnt true for pi either

[alpine sable]

sorry bro

[alpine sable]

the irony

[hexed bloom]

i had no idea that is how it's supposed to be

anyways, anyone got any idea?

[alpine sable]

tan 6 theta = 0

its literally available on toppr xD

||https://www.toppr.com/ask/question/the-number-of-solutions-of-the-equation-tan-theta-tan-2theta-tan-3theta-tan/||

@hexed bloom tan(A + B + C) = (tanA + tanB + tanC - tanA.tanB. tanC)/(1 - tanA.tanB - tanB.tanC - tanC.tanA)

[alpine sable]

[hexed bloom]

o lol i didn't see

[hexed bloom]

thanks a lot <3

[alpine sable]

is any1 good with transistors

[opal wyvern]

no im only good with trans sisters

[alpine sable]

[opal wyvern]

is that a cat playing a lute

[topaz scaffold]

lmaooo

[opal wyvern]

what a nice cat

lets throw money at him

[paper oar]

[wicked plover]

help me pls

[alpine sable]

[paper oar]

[wispy olive]

How did we come to this ratio, can someone please explain?

How did we come to
1/x = x-1/1.

Should not it be
1/x = 1/x-1 ?

[thorn kindle]

no

in fact that second equation you wrote there has no solution

1/x can never equal 1/(x-1)

unless you are working within the extended reals such that 0 has a reciprocal

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

69420
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[ionic jewel]

unfortunately you pinged the wrong person, i know this but the person i was helping does not

[ocean seal]

69420
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69420
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69420
Compile Error! Click the reaction for more information.
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[wispy olive]

Can you please explain how did we come to 1/x = x-1/1 ?

[ocean seal]

69420
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[alpine sable]

god i hated series

[thorn kindle]

red/blue = blue/orange

[wispy olive]

What?

[strong furnace]

#chill for shitposting

[dull onyx]

hello, i have the function f(x) = x^3 + 3x^2-9x + a^2- 4a
questions
a) show that the function f has a relative extrema and a relative maxima
i did this but im confused abt question b
b) find a∈R where the relative maxima will be 3 times the relative min…

like what😭 im so confused

[noble sinew]

Find a such that relative max is equal to 3 times relative min

So you should have a expression for value of max and min in terms of a so you can then solve an equation

[dull onyx]

but we find the relative extrema using the derivative right

f’(x) = 3x^2 + 6x - 9?

[noble sinew]

Yes so you have x value for min and max?

[dull onyx]

yep

[noble sinew]

Plug in original and you only have a left

Set max equal to 3x min

And solve for a

[dull onyx]

x = -3, x = 1

is that what u mean

oh

OH

yes

@noble sinew so do i plug in 1 to find the min?

i found it -5/3 umm

[noble sinew]

If relative min was 1 then yes set f(-3)=3 * f(1)

[smoky harness]

Find the best move for black

Is there a better move than e8 to d8?

U have to see it's threats too

[quaint pond]

hello can someone help me understand the solution to this problem?

the solution is this:

[dull onyx]

okay i got it

the channel is being used

[quaint pond]

sure

[dull onyx]

actually idk cuz i kinda took a while to respond but im still using it sorry!!

@noble sinew so do i just find f(1) and plug in -5/3 in every a

okay i think i did that!! thank u

[quick surge]

can anyone teach me this please

[alpine sable]

just divide the cost of one magazine by total cost

[plucky sleet]

let x be the number of sold magazines

[alpine sable]

@plucky sleet don't solve it completely

[plucky sleet]

and let 30x>4000

then you can find the number of magazines

[alpine sable]

english only (i guess)

• i believe this channel is not open rn

[quick surge]

oh ok ty

[pale oyster]

anyone got the answer?

[hallow flax]

Do you have any idea?

[alpine sable]

... #❓how-to-get-help

no help with tests or homework

[cunning obsidian]

I’m currently struggling with this q, noticed the bottom thing is just 2/(sinx-sqrt3 cosx) but idk how to prove the numerator to be sin3x >_>

[sleek elbow]

it says "mocktest" at the top, isnt that just practice?

[alpine sable]

mock test are supposed to test you, if you don't get a question save it look at it later

[cunning obsidian]

And the range of x is [pi/2, pi]

[rigid smelt]

do you know sum of angles indentity?

we need the identity for cos(x-y)

particularly

[cunning obsidian]

cos(A+-B)=cosAcosB-+sinAsinB?

[rigid smelt]

yeah sure

just apply that

before that, distribute the 3 inside (5pi/6 -x)

[sleek elbow]

well also true

[cunning obsidian]

Ohh okii

Is it possible if I use triple angle formula?

[rigid smelt]

im not sure

[cunning obsidian]

y’know, the cos3x=4cos^3x-3cosx

[rigid smelt]

it might be

but its very ugly

the main thing the question wants is that the x is isolated (argument-wise)

tbh you dont need to expand cos(3(5pi/6-x)) if you dont feel like it

because theres an identity for cos(5pi/2-3x)

[cunning obsidian]

and cos(5pi/2-3x) is just

sin3x right

[rigid smelt]

yeah if i didnt do the math in my head wrong

[cunning obsidian]

i think you didnt ^^

ty for the answers tho, i was thinking of using the triple angle formula all along because part a of the q asked me to prove it XDD

[rigid smelt]

ehh no i was wrong

its -sin(3x)

oh oops nvm me, being insecure again

[cunning obsidian]

^^

[rigid smelt]

yep

[cunning obsidian]

Thank you for your help anyways <3

[rigid smelt]

i think theres someone who knows how to answer a lot of question

iirc the name is Google

[gusty zodiac]

Find the surface for the shaded surface

anyone that could help with that?

[rigid smelt]

area between two curves is always the integral from a to b (a and b are the intersections) of f(x)-g(x) dx

where f(x)>g(x)

a more general formula can be the integral from a to b of |f(x)-g(x)|dx

[gusty zodiac]

the thing is i suck at math

is it too difficult to do for you?

[rigid smelt]

yes it is

[ruby current]

f(x) is greater than g(x) on [a,b] so it's just what waler said

[dreamy bone]

Is this one free? How can I tell?

[keen salmon]

How do I solve this

[quaint trout]

They literally tell you tho

[keen salmon]

Yeah, but I am not really getting the upper formula

[quaint trout]

What do you mean getting it?

They give it to you, so you can just use it

[keen salmon]

like how many times should I subtract n

[quaint trout]

If you want to see why it's true, multiply out the LHS

Oh

[keen salmon]

when I am putting n = 3, not getting the same answer

[quaint trout]

Use n = 3 in that equation

What do you mean?

Show what you did

Btw

[keen salmon]

like should I do n-1, n-2, n-3 until it gets equal to zero

[quaint trout]

The n you have in the given equation and the n you are substituting in with cuberoot(n+1) are not the same n

[quaint trout]

Yes

So for n = 3

The equation is

$$(x-y)(x^2 + xy + y^2) = x^3 - y^3$$

[ocean seal]

Lunasong the Supergay

[quaint trout]

x has exponent 2 and y has exponent 0 in the first term, then you decrease the exponent of x and increase the exponent of y with each term until it swapped and x has an exponent of 0 and y an exponent of 2

[keen salmon]

oh I get now, thanks

[quaint trout]

👍

@dreamy bone it is free now

[dreamy bone]

Thank you

I was just confused because I was watching a lecture about stats and this guy was tryna show the difference between stats and probability

He gave this example^^
But I don't really get it...like what does it mean when he says "and at least 65 will be cured with 9.99% chances" ?

[quaint trout]

There is a 99.99% chance that 65 or more people will be cured, and a 0.01% chance that fewer than 65 people will be cured.

[novel breach]

Hi, I was interested in the proof for this.

Does anyone know where I could find it?

[alpine sable]

(-2)^2 = 2^2
are you saying -2 = 2?

[split oriole]

Try proving by making fraction

[alpine sable]

also another counter example, $\omega^3 = 1^3$
\according to your principle, $\omega = 1$ which is simply not true

[ocean seal]

omeganebula

[alpine sable]

$a = b \implies a^n = b^n$ sure

[ocean seal]

omeganebula

[alpine sable]

but the converse doesn't hold

[novel breach]

does this work at least for most of algebra?

[quaint trout]

It's true for all positive real numbers

[alpine sable]

with n not equal to 0

[quaint trout]

Yes

ty

[novel breach]

thats cool. thank you

[quaint trout]

You can even allow a and b to be negative, but then you only get that a = b or a = -b if n is even, since an even n will absorb the sign.

[alpine sable]

why does he keep fkin deleting the messages

[quaint trout]

I mean, any example would have to have the same value for a and b

Since that's the whole point

[alpine sable]

well

[quaint trout]

It's useful for when a and b are unknown

Stop pinging me and deleting your messages, or I will block you. It seems like you're trying to annoy me on purpose.

[alpine sable]

if you're given $a^7 = b^7$ with $a, b \in \mathbb{Z}^+$ then you can deduce $a=b$ which is muchh easier to deal with

[ocean seal]

omeganebula

[alpine sable]

then why you deleting

its annoying

[quaint trout]

Because you are giving me ghost pings, I come to the channel because you ping me and then the message is gone

[alpine sable]

and doesn't give context to people who decide to read this afterward

[alpine sable]

also this

just don't fkin delete the messages

[quaint trout]

Or I will just stop engaging with you :)

Bye

[alpine sable]

byee have a good day!!

[novel breach]

i dont understand second part, "a=-b if n is even"

[smoky harness]

What's the best move for black

[alpine sable]

nice question dood

[quaint trout]

If you have a^2 = b^2, then you cannot necessarily say a = b, you can also have that a = -b. Like in the (-2)^2 = 2^2 example.@novel breach

@smoky harness #chess-go-shogi

But don't get help in the middle of a game, that's cheating

[smoky harness]

wtf

Obviously

[novel breach]

ah i see. that makes sense

@quaint trouti think these two answers match up with what you were saying right?

[quaint trout]

Yeah, basically

Because the power is even, you only know it is +- the other thing

[alpine sable]

help please, how to solve it using the 2nd method ; quadratic one (absolute value equation)

[noble sinew]

Wdym with 2nd method

[alpine sable]

smth like this ig

[alpine sable]

is this even needed?

whatever, just square both sides and the modulus sign will go away

[noble sinew]

Then just square it and solve?

[pallid sail]

u forgot about the denominator

[alpine sable]

hi guys

i am new here

what will be the value of - + multiply equals?

[quaint trout]

I don't understand the question

What are you multiplying?

[noble sinew]

Negative. Negative number times positive number gives a negative number

[quaint trout]

Ah

[alpine sable]

i mean what will be the value of - + mutiply

[alpine sable]

dont add +

just - and multiply

[hallow flax]

Do you maybe have a specific task?

I don't get the question.

[alpine sable]

yah i am adding some questions

[noble sinew]

I gave you the answer?

-3*2=-6 for example

[alpine sable]

oh ok thanks

you got it:)

[noble sinew]

-3 is negative number and 2 is a positive number

[alpine sable]

thanks

[languid moat]

help I'm a noob, can someone please break it down for me

this is the function

[gritty thunder]

f(x+h) = 2(x+h)^(2) - 3x + 1

[languid moat]

still can't understand, halp ,-_-,

[hallow flax]

The just insert (x+h) for the x in the functions equation you sent.

Then they simplify it.

Then, you get: $f(x+h)=2*(x+h)^2-3*(x+h)+1$

[ocean seal]

Sparender

[hallow flax]

Then the second part of the fraction should be clear, that's just the equation of this quadratic function, and then the simplify that. Do you get it up to that point?

[languid moat]

still trying to understand it, thanks

[hallow flax]

Do you get, how I got this: $f(x+h)=2(x+h)^2-3(x+h)+1$ ?

[ocean seal]

Sparender

[languid moat]

is this the same with 4x+2h-3?

[hallow flax]

No, it isn't. Try to simplify that expresion I sent above.

So this one: $f(x+h)=2(x+h)^2-3(x+h)+1$

[ocean seal]

Sparender

[hallow flax]

Do you know how to simplify that?

[languid moat]

yes, but I'm slow so spare me some patience

[hallow flax]

Take your time!

[languid moat]

thanks!

what should i do with -3(x+h)? will it be -3x -3h?

[hallow flax]

correct

[languid moat]

i got $f(x+h) = 2x^2 + 2h^2 - 3x - 3h + 1$

[ocean seal]

saini123

[hallow flax]

Almost!

$(x+5)^2$

[ocean seal]

Sparender

[hallow flax]

There is a mistake with that.

Its a binomial formula, do you know about them?

[languid moat]

nope, sorry I'm not good with math but interested to learn

[hallow flax]

Ok, look:

This is solved like that:

$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2$

[ocean seal]

Sparender

[hallow flax]

Thats the binomial formula we are looking at.

There are more, but this is the one we need here.

With that information, can you simplify that: $(x+5)^2$

[ocean seal]

Sparender

[languid moat]

wait

will it be $x^2 + 25$

[ocean seal]

saini123

[hallow flax]

No, to simplify that: $(x+5)(x+5)$

[ocean seal]

Sparender

[hallow flax]

You first do $x*x$

[ocean seal]

Sparender

[hallow flax]

then $x5$, then $5x$ then $5*5$

[ocean seal]

Sparender

[hallow flax]

So at the end you get: $x^2+5x+5x+25$

[ocean seal]

Sparender

[hallow flax]

that simplifys to: $x^2+10x+25$

[ocean seal]

Sparender

[hallow flax]

Thats the basic sheme.

Now try the same for $(x+h)^2$, as we need it in your question.

[ocean seal]

Sparender

[hallow flax]

This is how it was explained to me, maybe that notation helps a bit.

[languid moat]

oh the foil method

[hallow flax]

Yes, I think its that.

So now, you can try to simplify that.

[languid moat]

i think it will be

$x^2 + xh^2 + h^2$

[ocean seal]

saini123

[hallow flax]

almost.

[languid moat]

xh + xh

[hallow flax]

Its $x^2+2hx+h^2$

[ocean seal]

Sparender

[hallow flax]

Yes, that 2hx

[languid moat]

oh i knew it

there was something wrong

[hallow flax]

Good, so now, lets go back to your question:

we need:

$\frac{f(x+h)-f(x)}{h}$

[ocean seal]

Sparender

[hallow flax]

https://cdn.discordapp.com/attachments/490557019623915520/868492145466683392/unknown.png

[languid moat]

this was the part that confused me most

[hallow flax]

With this function.

Now, just insert (x+h) into every x of the function equation, that -f(x) [the normal, unmodified function] / h

So it will be as follows:

[languid moat]

oh so i will do it step by step not all of them at the same time

[hallow flax]

$\frac{(2*(x+h)^2-3*(x+h)+1)-(2x^2-3x+1)}{h}$

[ocean seal]

Sparender

[hallow flax]

Yes, thats a good idea.

[hallow flax]

That's how I would start off. Now you can go ahead, and just simplify that thing.

[languid moat]

will do but it will be slow

[hallow flax]

No worries! Take your time! Don't rush 🙂

[languid moat]

this is my first step

$2(x^2 +2xh + h^2) - 3(x+h)+1)$

[ocean seal]

saini123

[hallow flax]

$(2(x^2 +2xh + h^2) - 3(x+h)+1)$

[ocean seal]

Sparender

[hallow flax]

You forgot some brackets 🙂

[languid moat]

oh sorry

[hallow flax]

But, yes, that looks good, now simplify that!

[languid moat]

will $2*2xh be 4xh or 4xh^2$

[ocean seal]

saini123

[hallow flax]

4xh

[languid moat]

thanks

wait so should i not multiply it by 2 because it is at the outermost parenthesis?

oh actually i just confused myself

[hallow flax]

You just multiply $(x^2+2hx+h^2)$ by $2$

[languid moat]

what about the last +1 should i multiply it by -3?

[ocean seal]

Sparender

[hallow flax]

No, that you just leave

[languid moat]

ok

[hallow flax]

it stays +1

ok, so after simplifying, what did you get?

[languid moat]

nope still completing it

will i get -3xh or -3x and -3h?

[hallow flax]

-3x-3h

so -3x and -3h

[languid moat]

ok now i got it

[hallow flax]

Ok, what did you get?

[languid moat]

wait

$2x^2+4xh+2h^2-3x-3h+1$

[ocean seal]

saini123

[hallow flax]

Looks good.

So in the fraction we have:

$\frac{(2x^2+4xh+2h^2-3x-3h+1)-(2x^2-3x+1)}{h}$

[ocean seal]

Sparender

[hallow flax]

Now, you can simplify that further.

[languid moat]

oh now that i see it, i only did the left side hehehe

[hallow flax]

the right side is just the equation of this quadratic function. Now you have all of them together, and can simplify the whole thing.

[languid moat]

help how can i simplify further

[hallow flax]

simplify the top part of the fraction.

For example $2x^2-2x^2$ can be simplified

[ocean seal]

Sparender

[languid moat]

oh now i see it

[hallow flax]

and also, don't forgot, a - before parantheses means that the +/- signs swap, so:

$\frac{2x^2+4xh+2h^2-3x-3h+1-2x^2+3x-1}{h}$

And that, you can now simplify.

[languid moat]

this is what i got $4xh + 2h^2$

[ocean seal]

saini123

[hallow flax]

One second.

[ocean seal]

Sparender

[hallow flax]

How did you get that?

[rancid narwhal]

can anyone pls explain to me the following:

WHAT ARE THE USES OF:

1] Sin A = sin(180-A)
2] Cos A = -cos(180-A)
3] Tan A = -tan(180-A)

pls

<@&286206848099549185>

[hallow flax]

The channel is in use, please check another one.

And Helpers tag only after 15 minutes.

@languid moat are you still here?

[languid moat]

yup

[hallow flax]

Sorry for my terrible handwriting. Does that make any sense to you?

Thats how I simplified this part.

[languid moat]

yup

[hallow flax]

Good, so now we have:

[languid moat]

so $4xh + 2h^2 / h$

[ocean seal]

saini123

[hallow flax]

$\frac{4xh+2h^2-3h}{h}$

[hallow flax]

no, you are missing -3h

[ocean seal]

Sparender

[hallow flax]

Like this

[languid moat]

oh i saw it, sorry

[hallow flax]

Good, now, do you have an idea, how to simplify this fraction further?

[languid moat]

nope I'm really bad fractions

[hallow flax]

Do you see anything you could do in the top part of the fraction, considering the h's?

[languid moat]

expanding the 2h^2?

[hallow flax]

you can just do as follows:

$\frac{h(4x+2h-3)}{h}$

[ocean seal]

Sparender

[hallow flax]

You get it?

[languid moat]

right

[hallow flax]

I just took the h out, and now, you can simplify further.

[languid moat]

wait can you walk me further, when i said I'm really bad at fractions i mean it

[hallow flax]

What I did, is you see, there is a h in the bottom part of the fraction.

[languid moat]

what is h/h

[hallow flax]

Which means, if we can factor h out of the top part of our fraction, we can just simplify that real good.

[hallow flax]

1

And basically, I saw that we can factor h out of the top part of our fraction, so we get that:

$\frac{h(4x+2h-3)}{h}$

[ocean seal]

Sparender

[languid moat]

what about 2h/h

[hallow flax]

and that, you can simplify, by just remove both the h's, because we have the factor at the top and bottom.

[hallow flax]

2

[languid moat]

ohhh so it will be 4x + 2h - 3

[hallow flax]

Correct 🙂

And thats the final answer, also according to the solution you sent.

[languid moat]

thank you very much this is the first time someone walked me step by step this detailed

[hallow flax]

Thanks, you are welcome! If you have any further questions, just send them, I will be happy to help!

[languid moat]

ok

[tawdry saffron]

what is this function

[woeful pulsar]

well it's a function represented by a graph

[tawdry saffron]

I don't know what it is in english but what is f(x)= something something

[woeful pulsar]

ah you want an algebraic expression for this function

@tawdry saffron are you supposed to write a piecewise-defined function?>

[tawdry saffron]

well the full question is something else but yea I need the definition of the function

This is what I have so far

Dunno how to make a function out of ut

we just gotta know g'(pi/3)

[noble sinew]

This is correct

[woeful pulsar]

that looks good

[woeful pulsar]

so here you probably need to use chain rule

or you can fall back on the definition of derivative

[tawdry saffron]

what's the chain rule

[woeful pulsar]

not too hard to google

[spiral wren]

other than subtracting the area of the triangle from the area of the sector is there a general formula that can be used?

[tawdry saffron]

don't I need to do anything else with this information?

or can I just continue with that to the next step of the exercise

[woeful pulsar]

yeah, it's essentially the same probably

[woeful pulsar]

it depends how you want to follow on

because you can always use definition of derivative to differentiate g(x)

but i guess chain rule is fine too

[spiral wren]

seems I'll have to stick to the long process🥲

[tawdry saffron]

I don't know how to write down the actual function from there

can I just derive without needing the actual function

[woeful pulsar]

what have you done so far?

[tawdry saffron]

ah I got it

yea I did the chain rule and it worked smoothly from there

[alpine sable]

Can anyone direct me to a resource that may help me understand this? Struggling hard

I'm trying to do it on paper but can't figure out how to get from (x + dx) ^ -2 to that next step.

[tight locust]

1/(x+dx)^2

1/(x^2 + 2xdx + dx^2)

= 1/x^2 * 1/(1+2/x*dx+dx^2/x)

= 1/x^2 * 1/(1+dx/x)^2

which is the second line

[wild lagoon]

are there only 2 predominant frequency components for this graph (timeseries)?

[vale wigeon]

it appears so!

[tawdry saffron]

how

[gray isle]

where did you get stuck?

[tawdry saffron]

I did e+x = u

but then what is dx and the limits of the integral

[gray isle]

the problem is simple enough to do without a substitution,
but if you do, you just through the general steps of it

differentiate to get dx in terms of du

and sub the bounds in your substitution equation to get your new bounds

[tawdry saffron]

integrals are not very fresh in my memory, had it 2 years ago but now I want to study physics and am trying to get them in my head again

how can you do it without substitution

is it just ln(e+x)-1?

or -x

or something

[shell widget]

Yes its ln(e+x)

[tawdry saffron]

oh okay

[shell widget]

and then plug in the bounds

[tawdry saffron]

wow I thought it was way more complex

anyone knows a good channel on yt that explains integrals from basics to more advanced?

[shell widget]

searching particular integrals might help

[full cypress]

how is this -2? i thought you're supposed follow pemdas remove the exponent 3 first

[vale wigeon]

you should not "follow pemdas" blindly

also you aren't doing arithmetic

you're solving an equation

[full cypress]

so first im told to follow pemdas

now im not supposed to follow it blindly?

@vale wigeon

how am i supposed to follow it then?

[bleak ibex]

U first isolate the variable and then follow pedmas

[full cypress]

i do the cube root on x cubed right?

[bleak ibex]

That's the last step...

[full cypress]

so move 9 first

ight

[vale wigeon]

you're not supposed to do anything blindly tbh

it sounds like you're having trouble with algebra in general so you should like. go back to review linear equations or something

[full cypress]

i get what you mean but this just wasnt stated before

i was just told to follow pemdas

[vale wigeon]

bad teacher

like...

i see some ppl say "reverse pemdas when solving equations" but even that doesn't work all the time

[full cypress]

ahh gotchu

thanks for being a good teacher tho

[vale wigeon]

don't thank me i didn't teach you shit lol

[bleak ibex]

Reverse pedmas?

[vale wigeon]

in algebra you can do two things:
do the same operation on both sides,
or do some simplification on one side independently of the other

of course these can both manifest in different ways but that's the very very high level overview

[bleak ibex]

Ahh, understood

[vale wigeon]

this is not reverse pemdas

this is algebra as it is

[bleak ibex]

So, uhm what's reverse pedmas?😅

[vale wigeon]

reverse pemdas is like "undo addition first, then undo multiplication, then undo exponents"

which, again, very often doesn't work

[bleak ibex]

Ohh, ok, so that's what it's called

Thanks!

[sterile beacon]

hello

how can I calculate the f of interval for this problem?

[ancient creek]

So start by finding f(X) at X = -3, that will give you the lower bound (or whatever it is called) of the interval, then find f(X) at X = 0, and that will give you the upper bound of the interval...

(This is what believe you are asking but I'm not too sure :P )

[gray isle]

you misinterpreted the question

they want
|dx/dt|

[ionic jewel]

I'm fairly sure you can do this with trig anyways

distance can be found with trig, time can be found when theta = pi/2

[gray isle]

its a calculus question that involves trig

[ionic jewel]

don't think you even need the calculus though do you

[gray isle]

pretty sure you do

[ionic jewel]

the plane has a constant speed, you know distance traveled and time taken to travel that distance, and speed = distance/time

,w (3arctan(pi/6))/(pi/20)

hmm

the idea seems sound though

ramonovs is the real answer

[gray isle]

x is represented in the diagram

and t represents time

the wording of the question may be a bit vague

and as a result you're overthinking it

but do they really just want |dx/dt|

[warped phoenix]

For f(n) = 9 + 2(n - 1)

how is n greater than or equal to 1

shouldnt n be equal to or greater than 9

well the first term of the sequence is 9

what

oh mb

[ancient creek]

this is how I did it

took derivative of x with time (in seconds) ds

After calculating the derivative, i plugged in the given values

to get the answer

[gray isle]

its just the equation you get if you isolated x first

where's pi-theta coming from?

is not pi-theta

[ancient creek]

Oh shit, sorry for just blurting out the answer, try to solve it on your own; maybe use this as a reference if needed

[molten lotus]

can anyone help w this please?

this is the worked example

for 4 a) is it just 9! ?
i'm kinda confused

uh

what about 5 though

then it would be product

yeah...

it's kind of weird

[ancient creek]

Yeah, permutations are hard in the beginning to understand. I'd advice to look up some videos about permutations on Khan Academy, and also practice some question there.

[molten lotus]

thank you! I will do that

if it was the number of combinations would it just be 9?

or would that not work

(for 4a)

[viscid cove]

if you're asking for ways to choose 9 elements out of a set of 9 elements, there's only one way

so its probably one. The others are right, get yourself familiar with the concept atleast to the point where you feel comfortable asking questions

that being said, can someone please help me with BINOMIAL THEOREM&EXPANSION

pre-calc *the 0,1,2 in the first lines are subscripts btw

i understand the topics of general terms and midterms along with combinations pretty well but i have no idea how to approach these questions

also, if anyone knows what these types of questions are called in general or know how to go about them do spill your beans. I simply go blank when they show up

[light sparrow]

@viscid cove for the first one, because the RHS is C(2n,n), it makes sense to consider (1+x)^2n

because we wanna get 2n somehow

so you might notice that in fact, C(2n,n) is the coefficent of x^n in (1+x)^2n

now try writing (1+x)^2n in a different way and see if you can get the LHS

also are you allowed to assume the formula C(n,k) = n!/(n-k)!k!? Im guessing not

[viscid cove]

*yes its allowed

[light sparrow]

ah right, that makes the 2nd and 3rd parts easier then

Im not fully sure how do the 3rd one without it lol

but yeah hopefully that gives you some ideas

[viscid cove]

wait so in these questions we always assume they are the coefficients of some term? got it, its due to the absence of x

i dont know if it makes sense but can you tell me what you look out for

[light sparrow]

are you talking about the first bit

alright

sorry yeah I get what you mean

these things just sorta come with practice, but you just gotta spot that C(2n,n) is the coefficent of x^n in (1+x)^2n

often with these problems either comparing coefficnets or subbing in nice values for x are good ideas

ohh

[viscid cove]

so in the third, is the rhs nC2?

[light sparrow]

yeah

it is

well

(n+1)C2 I think

[viscid cove]

whoa yeah

still dont understand how you got that so quick

[light sparrow]

nvm sorry uhh

which bit

[viscid cove]

(n+1)c2

[light sparrow]

ah I just remember nC2 = n(n-1)/2

so (n+1)C2 must be (n+1)n/2

but yea sorry I think the only way you can do (3) is by using the n!/(n-k)!k!, im not sure any other way

[viscid cove]

do i multiply the given (1+x)^n with (1+x) for that {n+1} power?

[light sparrow]

you can try something like that

[light sparrow]

but if you're allowed to assume this, you can simplfy each term on the LHS very nicely

[viscid cove]

sorry i'm new to the server

as i was saying, when i multiply the given rhs buy (1+x) there'll simply be two groups terms. How do you continue?

[light sparrow]

so im not sure that method works

you're suggesting doing (1+x)^(n+1) = (1+x)^n (1+x) = (C0 + C1x + .... + Cnx^n)(1+x) right

and then finding the coefficent of x^2?

right so the coefficent of x^2 in the RHS will be (nC1) + (nC2)?

if you think about how the rHS expands

so that would show that (n+1)C2 = (nC1) + (nC2)

which is correct but not quite the thing we're after

so the way to do the last question is really to think about what each of the terms in the LHS is

and it should simplfy a lot

[viscid cove]

hey what if you start from the proof?

Replace C1,C0,C2,C1...yada yada

it looks like integers cancel out too

[ocean seal]

drunkzurg

[light sparrow]

its not a coicidence, thats the whole point!

(and besides, there are no coincidences in maths)

[sudden crypt]

I can try to help anyway

So do you know the limit definition of continuity?

[glacial hedge]

yes

the limit of f(x,y) = f(x,y)

and the limit is undefined

because its different when you aproach from x=0, y=0, and x=y

wait

nvm

im stoopid

so it cant be continuous regardless of what a is

[sudden crypt]

uhh dont remove the ping, that will be a ghost ping now

[glacial hedge]

uh... whoops

[sudden crypt]

its fine just keep that in mind next time

[viscid cove]

What happened in the second step? how did it condense?

binomial expansion

[tight locust]

n has been factored out

[fathom violet]

is that a typo? shouldnt it say 1+(n-1)+ ((n-1)(n-2))/2!+...

[agile coral]

does the probability of every result happening after a certain amount of tries change as the amount of possible results changes, if the amount of tries depends on the amount of results?

what i mean is, if you roll a 100 sided die 200 times, and you roll a 10 sided die 20 times, is there a difference in the probability that you will get every number at least once

or is it the same

[ionic jewel]

if you roll a 1 sided dice 2 times there's an 100% chance you get every number once

so yes, it changes

[agile coral]

so as the amount of results increases, the amount of times you would expect to have to try before you get every result increases faster?

[ionic jewel]

yeah that sounds about right

of course a one sided die is rather a problem

because even with infinite rolls of any other die you are never guaranteed 100% chance of rolling each number

idk i was never that into stats maybe i shouldn't have answered lol