precalculus

[scenic musk]

i mean rational

soz

[patent beacon]

Oh, just multiply top and bottom by x^(2/3)

Yes, as you said

[scenic musk]

okay thank you for ur time

appreciated

[viscid thistle]

How u do dis

[patent beacon]

What's f(6)?

[willow bear]

inb4 "i dont know how do u find it"

[viscid thistle]

f(6) was not give but I calculated it to be a half

*given

[willow bear]

ok, so $f(6) = \frac12$

[obsidian monolith]

Ann:

[willow bear]

what about $f(9)$?

[obsidian monolith]

Ann:

[viscid thistle]

It's negative 1/3

-1/3

[willow bear]

and $f(12)$?

[obsidian monolith]

Ann:

[viscid thistle]

-1/2

[willow bear]

you sure about that

[viscid thistle]

Uh lemme double check

Oops it's -2

No wonder my graph is looking so weird

[willow bear]

and f(15)?

[viscid thistle]

3

[patent beacon]

Lol

[viscid thistle]

I don't mind h

[willow bear]

you may notice that $f(n+12) = f(n)$

[obsidian monolith]

Ann:

[patent beacon]

Ahh clever

[viscid thistle]

Oh yeah.

[viscid thistle]

Hello

I'm having the feeling this is a weird result

Why would the number be so small?

For S_3 the result is 192500, what makes sense, the number is increasing

But for S_30 the number is really small

Why?

It's because the numbers decrease to the point they start subtracting?

Is it only 1 that is to the power of 30?

No, It's one half to the power of 30

:)

Lonely, and miss lonely...

I'm still figuring it out, I've never done series before.

Oh!

[glacial island]

inverse cos / sin /tan (arccos/arcsin,arctan) is used to find the angle degree right?

[viscid thistle]

@glacial island make your question in a question channel available! :)

I'm guessing it's cause once the 110000 on the left is being subtracted by a smaller power fraction, the number gets smaller each time. And then the number gets subtracted by 110000. But like for example if it's 110000× (1/2)^3, then the number wouldn't get that small, so once it's subtracted by 110000 it will be a small negative number, then that negative number is just doubled and it becomes positive. But if it's 110000×(1/2)^30 the number is way smaller, and a "smaller number" subtracted by the same "big number 11000" then it will make a "big negative" which is doubled and turned into a positive. Idk if I totally just answered a different question or not h-

Hold up

Oh yeah I didn't explain it 100%

You mean it's increasing by a little right?

No, your are saying exactly what I thought

When S_3 all the number from 1-3 are positive, but there's a moment in the sequence when we start having negative values, that why S_30 is just a small number

Negative values, How?

I think it just increases more slowly when the series has a bigger number, but it doesn't get negative

[viscid thistle]

There's a moment it gets negative

See?

Oh

You are right...

There's a lot of positive decimals

Right now I'm struggling to make a decision based o.n all the data I have

I need to answer this questions

Choices:
$240,000 a month
$19,912,500 a month
$220 a month

The $220 option is the one I have trouble understanding

[proud sparrow]

erm

what's the data there?

[viscid thistle]

How did I get it?

[proud sparrow]

what's the original question?

[viscid thistle]

The original question is to calculate every choice

I already did that, now I need to make decisions with this results

[proud sparrow]

I see a 220 about here https://discordapp.com/channels/268882317391429632/363224154469826562/630124886941106176

but honestly, I have no idea what the question is

[viscid thistle]

The one in the middle is my set of numbers

This is already done Element

What I need help with is understanding choice 3(?

Like, the sum of this sequence, $220, is really the monthly payment?

Cus my head can't understand the logic behind it

[proud sparrow]

ah

it's an assignment where you get one of many possible questions

I see

[viscid thistle]

I guess...

I don't understand how ( for choice #3) you could be gaining $192,000 on day 3 but on day 30 your total amount is $220

[proud sparrow]

ah

[viscid thistle]

[proud sparrow]

It's the total area for the 30 days

[viscid thistle]

Yeah

[proud sparrow]

So for 30 days, the total area is adding up the square for day 1, 2, 3 to 30

you need to add up the areas

[viscid thistle]

But why suck as small number like 220 would be de answer

What about the $192000 from up to day 3?

[proud sparrow]

you have it

you need to add the area for squares 1, 2, 3 to 30

add all the area

[viscid thistle]

It's 220

[proud sparrow]

it can't be less than the area until day 3

[spring thunder]

i'm p sure your calc is saying 220k not 220

[proud sparrow]

ah

that makes sense

there's both a dot and a comma

[viscid thistle]

:0000000

Wait no

Why the comma?

Can you guys do it with the bot?

[spring thunder]

well in EU decimal separator is a comma

but idk

[viscid thistle]

I don't think it's saying 220,000

Well

Maybe yes

[proud sparrow]

,w (110000*(1/2)^30-110000)*(-2)

[viscid thistle]

Well that's pretty confusing

[obsidian monolith]

Display results online and refine query

Requested by Element118#2437

[proud sparrow]

there

should be fine now?

[spring thunder]

i mean do you really need a calc to see this is almost 220k tho

[viscid thistle]

I need to be sure

[proud sparrow]

well, the first term is negligible

so you can throw it away

[viscid thistle]

Well thank you guys, it seems like I'm considerably blind

[pseudo sonnet]

can someone help me with the inductive step

[tall granite]

(k+1)!= (k!)(k+1)

and k+1>2

[pseudo sonnet]

does (k+1)! simplify to $(k!) + (1)!$

[obsidian monolith]

Vici:

[pseudo sonnet]

or

$(k+1)! = (k!)(k+1)!$

[obsidian monolith]

Vici:

[tall granite]

no

those are garbage equations

not true

[stuck lark]

@pseudo sonnet if it helps, expand the factorial (k+1)! a tiny bit

[pseudo sonnet]

how do i expand that

[stuck lark]

how do you expand 5!

[pseudo sonnet]

5 * 4 * 3 * 2 * 1

how does that relate to the above though

[stuck lark]

what about k! for any natural number k

[pseudo sonnet]

i dont know :#

[stuck lark]

notice the pattern for writing 5!

you start with 5 then multiply it with 5-1, which is 4

[pseudo sonnet]

so

k! = (k-1)! ?

[stuck lark]

no...

then you multiply again by 5-2 which is 3

[pseudo sonnet]

i see what you mean by the pattern

[stuck lark]

let's try expanding k!

what's the first number in the product?

[pseudo sonnet]

k! * (k-1)!

[stuck lark]

i'll go back to 5!

what's the first number in the product?

[pseudo sonnet]

20

[stuck lark]

i just want the expansion

[pseudo sonnet]

5 * 4

$k * (k-1)$

[obsidian monolith]

Vici:

[stuck lark]

the first number is 5, the second is 4, what's the third?

[pseudo sonnet]

3

K - 2

[stuck lark]

now focus only on the expansion of k!

what numbers do you have so far?

[pseudo sonnet]

$k * (k-1) * (k-2)$

[obsidian monolith]

Vici:

[stuck lark]

but remember there could be more numbers that come after k-2

[pseudo sonnet]

i know

[stuck lark]

change what you wrote so it's equivalent to k!

[pseudo sonnet]

$k! = k * (k-1) * (k-2) ... (k - n)$

[obsidian monolith]

Vici:

[pseudo sonnet]

like that

[stuck lark]

there you go

actually not quite, eventually you'll reach k-(k-2) and k-(k-1) which are just 2 and 1

$k! = k(k-1)! = k(k-1)(k-2)!$

[obsidian monolith]

RokettoJanpu:

[stuck lark]

this is probably as far as you want to go

[pseudo sonnet]

so

how does this help me with

$(k+1)!$

[obsidian monolith]

Vici:

[rare zephyr]

ain't it just (k+1)(k)(k-1)(k-2).....?

[pseudo sonnet]

ye

[pseudo sonnet]

https://i.imgur.com/ZHUwE7i.png

i understand the first and second line

but how did she get

$2^{k+2} - 1$

[obsidian monolith]

Vici:

[stuck lark]

$2 = 2^1 \\ 2 \cdot 2^{k+1}=?$

[obsidian monolith]

RokettoJanpu:

[pseudo sonnet]

OH

$2^{1} * 2^{k+1} = 2^{k+1+1}$

[obsidian monolith]

Vici:

[pseudo sonnet]

smh its so easy

but this notation

makes everything confusing

its like math induction is a new math

[proud sparrow]

induction is the same math

it's another tool

[pseudo sonnet]

ye but induction step so hard

its manipulating powers, fractions, etc to get the same equation

on both sides

nah im op now i get it all

[proud sparrow]

you think you are op

use that as motivation to learn more

and show us that you would be really op

Hypothesis: @pseudo sonnet is OP
Proof: Let's wait and see

[pseudo sonnet]

my work speaks for itself

[pseudo sonnet]

$8^{2k+3}$

[obsidian monolith]

Vici:

[pseudo sonnet]

$ = 8^{2k} * 8^{3}$

[obsidian monolith]

Vici:

[pseudo sonnet]

can the 8^2k

be simplified any further

can someone tell me where i went wrong

i did..

at the bottom

448 isnt a factor of 57

so that didnt work out

i got a decimal

which line?

all of them are wrong?

how is it wrong

[rigid sun]

you can't just move products like that

ab+cd=a+c*bd

wtf

[pseudo sonnet]

LOL.

[rigid sun]

hacker

[simple flume]

Please help. I get 2 answers and none seem to work.

[stuck lark]

show your work

[simple flume]

calculator

[rigid sun]

its asking for a function

[simple flume]

x=0, x=12

[willow bear]

do you understand what the problem asks you to do

[simple flume]

lmao wait i get it now

ok thx bye

[stoic ember]

Hello, I got my first problem to prove it by induction: $\forall n \in \mathbb N*: S_n = 2 + 4 + 6 + ... + 2n = n(n+1)$

[obsidian monolith]

Alaanor:

[stoic ember]

So, to solve it, I start by the initialisation, $S_0 = 0$ and $S_1 = 2$ so it's true and it work

[obsidian monolith]

Alaanor:

[stoic ember]

then the induction: $P(n) \implies P(n+1)$, hence $S_{n+1} = S_n + 2(n+1)$

[obsidian monolith]

Alaanor:

[stoic ember]

and then I end it by $(n+2)(n+1)$

[obsidian monolith]

Alaanor:

[stoic ember]

And in the book, it's the answer, but I'm like ? what

that's the answer ?

how does it prove anything

[heady jewel]

...

if the general formula is n(n+1)

what do you get by replacing n with n+1

[stoic ember]

the next occurence

[heady jewel]

yea

or

(n+1)(n+2)

[willow bear]

(n+1)((n+1)+1)

[stoic ember]

my brain need a moment to understand it

ahhhh

got it ! understood (Thx !)

[shrewd urchin]

PEMDAS

L-->R

[willow bear]

...

??

[stoic ember]

[viral imp]

,, y=\frac{1}{4^x-3\cdot2^x+2}

[obsidian monolith]

Umma.Gumma:

[viral imp]

I'm interested in finding the domain of this function

I'm not sure how to proceed in this case though

that 3 complicates things somehow

[tall granite]

it's defined everywhere except where denominator is zero

so solve the equation denominator=0

do find where it's not defined

that's just a quadratic equation

[viral imp]

edit: I don't understand how to get a canonic exponential equation, starting from that denominator

,, a^{f(x)}=a^{g(x)}

[obsidian monolith]

Umma.Gumma:

[blazing parrot]

why do you need that?

[viral imp]

how would I do otherwise?

[blazing parrot]

$$ 4^x = (2^x)^2 $$

[obsidian monolith]

Not Chezstick:

[viral imp]

I don't get how this should help

[blazing parrot]

for real x anyway

so you are solving $$ 4^x-3\cdot2^x+2 = 0$$ right

[obsidian monolith]

Not Chezstick:

[viral imp]

indeed

[blazing parrot]

set u = 2^x

[viral imp]

not following

[blazing parrot]

now can you rewrite the equation in terms of u?

[reef rune]

if a power function can be written as $x^\frac{-1}{4}$ would $\frac{1}{\sqrt{4}{x}$ also be considered a power function

[blazing parrot]

do you mean the square root sign to go over the x as well?

and it to be a 4th root not a square root?

[reef rune]

oh yeah

my bad

[willow bear]

$\sqrt[4]{x}$

[obsidian monolith]

Ann:

[willow bear]

did you want this

[reef rune]

yeah

[willow bear]

to answer your question: yes it would

[reef rune]

mhm

weird

I wrote it the other way around on my test and lost a point

guess I'll have to justify

[viral imp]

Ann would you give me a hint on this please

,, y=\frac{1}{4^x-3\cdot2^x+2}

[obsidian monolith]

Umma.Gumma:

[viral imp]

I'm trying to assess the domain, which I understand it has to be obtained solving the equation in the denominator

problem is, I know how to solve exponential equations only when they're in a canonical form

[uncut mulch]

a hint was already given
let u = 2^x
and rewrite the denominator in terms of u

[viral imp]

the hint did not help at all

[uncut mulch]

(and that 4^x = (2^x)^2)

did you try rewriting it?

[viral imp]

that I know, but I would appreciate a general way of approaching this problem

rather that a shortcut to solve this function in particular

[blazing parrot]

there is not a way to put this in canonical form immediately because of the +2 at the end

[viral imp]

ok this is interesting

then?

[blazing parrot]

let u be 2^x , rewrite in terms of u

[viral imp]

,, u^{2x}-3*u+2

[blazing parrot]

not exactly

your first term shouldnt be 2u

[viral imp]

wait my bad

[obsidian monolith]

Umma.Gumma:

[blazing parrot]

try again

why is there a x?

$$ 4^x = (2^x)^2 and 2^x = u $$

[obsidian monolith]

Not Chezstick:

[viral imp]

,, u^2-3*u+2

[obsidian monolith]

Umma.Gumma:

[blazing parrot]

now do you recognise this type of equation

[viral imp]

I do my question is what is the justification to proceed this way

[blazing parrot]

you are trying to get 2^x = something

in this case by solving this quadratic, you can solve the 2 exponential equations that you get from it

[viral imp]

right

therefore, given that the two root are 2 and 1

,, 2^x=2 ==> x=1 and 2^x=1 ==> x=0

[obsidian monolith]

Umma.Gumma:

[viral imp]

wil do the trick

to be precise

,, \mathbb{R} -{0, 1}

[obsidian monolith]

Umma.Gumma:

[blazing parrot]

so you now know the denominator is 0 when x = 0 or x =1

so you can write the domain of the function ie when denominator not equal to 0

[viral imp]

well thanks a lot

I'm not quite confident with this procedure, guess I'll do more of this

[blazing parrot]

good luck!

[trim fable]

How would u do this

[blazing parrot]

do what

[trim fable]

one sec

that

what i did was

v=lxwxh
1008=(30-2x)(20-2x)(x)
1008=(4x^3-50x^2=600x)
0=4x^3-50x^2=600x-1008

[undone pawn]

I mean they've done all the work lmao

you just need to solve the cubic

[trim fable]

what do i do now

what?

so im doing it right so far right?

[blazing parrot]

dont expand it

[trim fable]

oh

oops

then what do i do?

[blazing parrot]

just use the factorised form to find 0s

[trim fable]

uh

so

1008=(30-2x)(20-2x)(x)
x=1/15 and 1/10?

[blazing parrot]

you knoe the thing where if a*b = 0 then a=0 or b=0

[trim fable]

uh what?

[blazing parrot]

if a*b = 0, it follows that either a=0 or b=0

[trim fable]

question this is precalc right? coz the course is called advanced functions and i have heard its the equivalent to precalc

oh ye

coz its =0 so one of them has to be 0

[blazing parrot]

im not very sure im not from US i dont know the curriclum

yes

[trim fable]

oh

[undone pawn]

well, you could work smart and factorize 1008

I think that might just work

[trim fable]

oh

[spring thunder]

hoping the dimensions have to be integers

[undone pawn]

yeah

xD

[blazing parrot]

oops i think i did a dumb

[trim fable]

divide everything by 4!!!!?

😛

[undone pawn]

yes

[trim fable]

yesss!!!

[undone pawn]

that's a good step to begin with

[trim fable]

yes

i agree

[undone pawn]

nobody wants redundant factors

eugh

[patent beacon]

No 50 isn't divisible by 4

[trim fable]

oh

lol

true

[undone pawn]

uh 50?

[blazing parrot]

what 50

[undone pawn]

what

[trim fable]

tho the answers 3,4.92 either 3cm by 3cm or 4.92 by 4.92

[patent beacon]

Going with this
v=lxwxh
1008=(30-2x)(20-2x)(x)
1008=(4x^3-50x^2=600x)
0=4x^3-50x^2=600x-1008

[trim fable]

^answer at the back

[patent beacon]

But there's a random = in there so idunno

[undone pawn]

just divide out the common factors oof

[trim fable]

ye typo^^

[undone pawn]

why're you carrying the extra four around

[trim fable]

it was supposed to be a + sign not =

[undone pawn]

it's simplified as 252=(15-x)(10-x)(x)

[patent beacon]

Oh yeah you can divide out the 4 from there

Then that 50 is wrong

[undone pawn]

and 252= (2^2)(7)(3^2)

and we know x must be <10

[patent beacon]

Hacks

[trim fable]

and 252= (2^2)(7)(3^2)

how did u get that^^

[patent beacon]

Prime factorization is unique

[undone pawn]

prime factorization

[trim fable]

um

idk how to do that lol

[undone pawn]

you dont know how to break down a number to its prime factors?

[patent beacon]

Not the way you're supposed to do it, but a very cool way to do it

[undone pawn]

^

[trim fable]

oh

[undone pawn]

the rigorous way would be to solve the cubic

[trim fable]

ye were learning to solve cubics hehe

using guess and check with the factors

[undone pawn]

oof then what are you asking here

oh

rip

[trim fable]

asking what?

lol i usually never ask anything for advanced functions

[patent beacon]

Know how we got to
252 = (15-x)(10-x)(x)

[trim fable]

ye

u divided by 4

well no

nvm

lol

hehe

[undone pawn]

yes we did

[trim fable]

oh

[undone pawn]

like what else could we have done

[trim fable]

30.-2x-> 15-x is /2 tho

[patent beacon]

Yes, we divided two of the factors by 2, which is the same as dividing both sides by 4

[trim fable]

oh

well i always end up expanding things heheh

[patent beacon]

You don't have to do this, you can expand first

[undone pawn]

but you'll have to solve the cubic

which sucks

but I guess if it's for school, do that

[trim fable]

but like would and expand and then try to guess and check till the remainders 1008?

or should i move it to the other side and use 1008

till i get 0?

[patent beacon]

After you expand, 4 should be a common factor

[trim fable]

ok

[undone pawn]

but if you're guessing anyways, factorizing 252 method is as good as any

[trim fable]

so i was doing ir tight before..?

[undone pawn]

I guess

[trim fable]

right*

[undone pawn]

what did you even ask for

🤦

[trim fable]

no clue

LOL

[patent beacon]

,w expand (30 - 2x)(20 - 2x)(x) - 1008

[undone pawn]

wtf

[obsidian monolith]

Display results online and refine query

Requested by Kaynex#7520

[patent beacon]

Noice

[trim fable]

wow cool

OH

OMG I MADE A DUMB MISTAKE

the 50 was messing me up

with this question lol

😛

[patent beacon]

Naturally, 4 is a common factor
4x³ - 100x² + 600x - 1008 = 0
x³ - 25x² + 150x - 252 = 0

[undone pawn]

anyways for closure, continuing my method, options for x are 2,3,4,6,7,9

and second trial shows, x=3 is a winner

[trim fable]

ye

i knew how to do this i just messed up with the 50

[patent beacon]

For solving the cubic, any rational root has to be a ± factor of 252

[trim fable]

it was supposed to be 100 heheh

[patent beacon]

Which is a lot of options ew

[trim fable]

i think i forgot to multiply one of them

coz i was doing it in my head lol

ye ik

which is why i hate guessing and checking

lol

[undone pawn]

i still like my way 😂

[patent beacon]

Thankfully you know the solution should be positive, and 3 is a smol number

[undone pawn]

^

[patent beacon]

Yes Flynn yours is much faster and cleaner.

[trim fable]

yes

[undone pawn]

specifically since this setup ended up with neat numbers

in general, cubic is the more robust sol

but eh

[trim fable]

okdone

i got it

thanks!!

[undone pawn]

gg

[trim fable]

my question was

do u have to always guess and check

or is there an easier way

coz its annoying lol

lol

i have another question

@undone pawn will u help me:P

[serene heath]

Post question

[trim fable]

i did all of that my question was

[patent beacon]

Why delet?

[trim fable]

coz i thought no one cared LOL

so im like ye i should delete it ehe

😛

sorry LOL

[patent beacon]

The solution can't be 2/3

[trim fable]

ik it was a story

[patent beacon]

Via rational root theorem

[trim fable]

hehe

about a test 😛

ok i guess ill tell u noww

so the unit before this

had guess and check for cubics

and then on my test

there was a question p/q

question

and i had to skip it coz

i couldn't guess it

so then i did the rest of my test then

came back to it

and i still wasn't able to guess it

so then i randomly guessed 2/3 and i was like plzzzzz workkkkk

[undone pawn]

pls stop spam

[trim fable]

and i had 5 min left

and got 0! so then i was like yay! @patent beacon there now u know

[patent beacon]

Hai

[trim fable]

uh @undone pawn sorry but i wasn't spamming i was telling a story! and i think i just type too fast

lol

[patent beacon]

Glad you could find it, always keep the rational root theorem in mind, it's useful

[undone pawn]

type single message then

[trim fable]

ohhhhhh

true

[undone pawn]

and in #chill maybe next time

[trim fable]

lol ok

😛

[river kindle]

Guess and check is not reliable. In regsrd to your question, learn to factor and use a better method likr quadratic formula, complete the sqaure or ac method

[patent beacon]

Did you want to factor that other one? @trim fable

[trim fable]

im on part d but like how would

I find the max height?

I did this in physics last year but forgot

[patent beacon]

Where's the zeroes?

[trim fable]

at

-2 and 3

-3t(t+2)(t-3)

[patent beacon]

Okay, so we also have a zero at t = 0, as we'd expect

[trim fable]

oh wait so would the max height occur at -2+3/2

?

[patent beacon]

You can't find the max without calculus

[trim fable]

oh

so i just sketch it?

[patent beacon]

So they must not want that much accuracy

[trim fable]

oh ok

[patent beacon]

You can always put a few points in to find a general shape?

[trim fable]

well i guess it doesn't matter then

for now

since its a sketch

[river kindle]

Could you factor out one t then get the vertex from there since itll be a quadratic with a fsctor t removed?

[trim fable]

so then for e, how would I find the time it goes down at

[patent beacon]

Nop, the max of the cubic is not necessarily the max of that quadratic

[river kindle]

Yeah, that is fair when I think of it.

[trim fable]

coz it starts going down after the max height right?

which is why i wanted to find the max height so i could do part e

it does say estimate so do i just guess?

[patent beacon]

Hmm, I'm not quite sure how they expect you to estimate that

[trim fable]

like -2+3/2 ?

[patent beacon]

Sure?

[trim fable]

but the answer at the back is

1.8 hours

idk why

[patent beacon]

,w maximum of -3t^3 + 3t^2 + 18t

[obsidian monolith]

Display results online and refine query

Requested by Kaynex#7520

[patent beacon]

,w decimal expansion of 1/3 + sqrt(19)/3

[obsidian monolith]

Display results online and refine query

Requested by Kaynex#7520

[trim fable]

oh

thats 1.78

so 1.8

but what was that?

[patent beacon]

Wow wolfram not useful lel

[trim fable]

lol

but thats equal to 1.8

so i guess it is 😛

[patent beacon]

That is the exact x value of the maximum

[trim fable]

ye but i think

my teacher said local max and mins are part of

calc

right?

so i cant do this yet?

[patent beacon]

,w graph -3t^3 + 3t^2 + 18t between x = 0 and x = 3

[obsidian monolith]

Display results online and refine query

Requested by Kaynex#7520

[patent beacon]

That looks like what you'd expect

[trim fable]

ye

[patent beacon]

You really could guess 1.5 and be close

[trim fable]

but how would ik to sketch it likethat 😛

oh ok

0+3/2 and then sub it in

to find the max

right?

[patent beacon]

Ask your teacher, I'm not sure what's expected

[trim fable]

oh ok

so by doing that

[patent beacon]

And yeah, finding maximums and minimums is easy once you know some calculus

[trim fable]

i got a max of 23.625

by doing that lol

[patent beacon]

By plugging in 1.8 into the function?

[trim fable]

no

1.5

[patent beacon]

Fair

[trim fable]

ok

😛

i just have 1 more question

i feel like i cant do these the way i want coz i dont know calc yet

lol

[patent beacon]

That's not a question

[trim fable]

we had to use a graphing calc for this one

[patent beacon]

Oh I see

[trim fable]

how would i do part c?

is 0.25 V(t) so like 0.25= (equation) or like plug it into t?

[patent beacon]

Yes, you want V(t) = 0.25

Then solve for t

[trim fable]

using guess and check? ;c

aww ;c

lol

[patent beacon]

Since these numbers are ugly, you would not likely be able to do it that way

[trim fable]

i started doing the quadratic formula

lol

[patent beacon]

Oh yeah you could

Nvm

[trim fable]

ye

[patent beacon]

Oh no you couldn't

Nvm

[trim fable]

oh really?

oh

lol

coz i did

[patent beacon]

Once the -0.25 is there

[trim fable]

0.25=t(0.027t^2-0.27t+0.675)

[patent beacon]

Quadratic formula only finds the zeroes of a quadratic

That isn't helpful when the left is 0.25

[trim fable]

so then 0.27+- square root of -o.27^2-4(0.0027)(0.675) over 2(0.027

which is why i made it into a quadratic by factoring the t

oh so i cant do it?

[patent beacon]

Nope. Your first priority when solving any of these should be making one side 0

[trim fable]

so then how do u even do this question?

oh

[patent beacon]

Graphing calculator lol

[trim fable]

what

lol how

do u know what desmos is

we use desmos when we need a graphing calc

[patent beacon]

Yeah, it's a good program

[trim fable]

thats the graph so

do i just look at 0.25

[patent beacon]

And you want when that's 0.25

[trim fable]

ok

[patent beacon]

You can subtract 0.25 off, and look for the zeroes

[trim fable]

oh ok

3.33

0r 0.447

ohhh thats the answerr

makes sensee

thanks

lol i was just trying to solve this LOL

rip 😛

@patent beacon Thank you 🙂

[pseudo sonnet]

https://i.imgur.com/c3fLju3.png

for this do I use the binomial theorem to expand all the values

[trim fable]

pascals triangle?

ye

use pascals triangle

[pseudo sonnet]

wdym

[trim fable]

use pascals triangle for this

[pseudo sonnet]

like the combinations/binomial theorem

[trim fable]

uh whats that?

[pseudo sonnet]

summation

[trim fable]

?

well what i would so is

[pseudo sonnet]

https://miro.medium.com/proxy/1*PHraeWdzWdmOfl2JhRdTVg.png

[trim fable]

oh

idk what that is tbh

i was gonna say

[pseudo sonnet]

LOL

thats binomial theorem

[trim fable]

lol

😛

pascals triangle^

[pseudo sonnet]

how do i apply it to (2-3x)^10

[trim fable]

what grade are u in?

[pseudo sonnet]

im taking precalc

[trim fable]

oh so thats advanced functions?

right

coz im canadian

but i think its the same course just called different things

wait so are u in grade 12?

or 11?

[pseudo sonnet]

no im freshmen in college

[trim fable]

(2-3x)^10
1(2)^10(-3x)^0 + 10(2)^9(-3x)^1)+45(2)^8(-3x)^7 etc...

do u get what im doing?

@pseudo sonnet

ur in college?

im in grade 12 rn

so like that would work too^ i learned it last year but idk what way ur supposed to use since ur in college 😛

how old are u? @pseudo sonnet 20? or something

coz im prob younger than u lol

i have never done the thing u said but

would it be like this

i just plugged everything in does that help u? tho idk what that is but like i put it into the thing u sent

Tho idk the value of k soo

[patent beacon]

That's the 0th term, you want the third one

[trim fable]

oh

@patent beacon I was trying to help vici so ye i have no idea what that is

lololol

i just plugged the question into the format they sent lol

[patent beacon]

The third term is
10C3 × 2^(10-3) × (-3x)^3
@pseudo sonnet @trim fable

[trim fable]

lol i think they are older than me and i still tried to help lol

i was telling them to use pascals triangle 😛

[patent beacon]

You were close, just needed k = 3

[trim fable]

i dont even know what I did LOL

i never learned that ever yet

lol

[patent beacon]

And the Σ goes away, since we're talking about a single term, and not the sum of multiple terms

[trim fable]

hmm i have no clue on what ur saying

what grade is this stuff?

[patent beacon]

Yours! Just terms you may not be used to

[trim fable]

oh

ohhh

cooool

maybe im gonna learn it sooooon

😛

well this year

in this course lol

question just coz im curious

how did u know that

k was 3?

and what is that equation

anyways?

just coz idk 😛

it yet lol

[patent beacon]

For example,
(x + 1)³ = Σ nCk (x)^k (1)^(3 - k)

[trim fable]

whats nck?

[patent beacon]

But that Σ just means to increase k, and sum term

[trim fable]

oh hmm

so is this stuff like arithmetic series and geometric series?

[patent beacon]

nCk is the number on pascal's triangle down n rows, and over k

[trim fable]

coz i did that last year

ohhhh

okkk

so instead of doing the thing i was telling them to

with pascals triangle

until u reach the term they wanted to find

u use that to make things

simpler?

[patent beacon]

You were perfectly right, just needed to set k = 3, not k = 0

[trim fable]

coz they wanted to find x3

so that would be the third value in pascals triangle

wow i get this

this is cool 😛

so k is just the position in pascals triangle

from left to right

😮

woww

did i just do college level work 😮

cooooooooool 😮

lol

@patent beacon do u know computer science?

[patent beacon]

Kinda!

[trim fable]

oh wow

really

will u help me with comp sci 😛

also i looked through my textbook and didn't see any of that stuff. Maybe I missed it but is it part of advanced functions?

or calc?

@patent beacon 😛

[pseudo sonnet]

@patent beacon

i got

$-414720x^{3}$

[obsidian monolith]

Vici:

[trim fable]

whats that

[pseudo sonnet]

for the problem

[trim fable]

ohhhh

[formal iris]

does the base of a Expo function have to greater then 1

where are neg bases not allowed

[willow bear]

negative bases are not allowed if you want to allow the exponent to not be an integer but bases between 0 and 1 are fine

[formal iris]

thank you

is it because of Complex numbers?

man everyone just hates them

[willow bear]

no to both of those things

[formal iris]

why then arnt neg bases allowed

[pseudo sonnet]

i think if you have neg bases

they become fractions

[willow bear]

no

[pseudo sonnet]

so it becomes a rational funct

[willow bear]

no

no

no

no

[pseudo sonnet]

LOL

chill

[willow bear]

no.

the problem with negative bases is

you can't even define (-1)^(1/2) in the reals

bc you'd LIKE that to square to -1

but no real number does that

and this exact same issue arises for most fractions

so you can't even begin to extend this to irrational exponents, bc there's nothing to extend

[pseudo sonnet]

so you cant have the base number be a fraction

just like u cant have a base number be a negative number

for exponential functions

[willow bear]

you CAN have fractional bases just fine

were you under the impression that (7/3)^x isn't a well behaved exponential function

[pseudo sonnet]

no i was trying to make sense of what you said

[willow bear]

did i at any point even talk about the BASE being a fraction or not

[pseudo sonnet]

"and this exact same issue arises for most fractions
so you can't even begin to extend this to irrational exponents, bc there's nothing to extend"

[willow bear]

given that the 1/2 in (-1)^(1/2) is the exponent, and not the base...

[pseudo sonnet]

oh so fractions in the exponet becomes a problem

not in the base

[willow bear]

did i at any point even talk about the BASE being a fraction or not

[pseudo sonnet]

no

[willow bear]

what do you mean by "solve"

can you post the entire problem exactly as stated

[willow bear]

can you post the entire problem exactly as stated

...

wow.

ok

so that really WAS the entire problem

....................no fucking clue what they want then

[heady jewel]

Simplify?

[scenic musk]

how can we check if a number is divisble by 6 without division or modulus

[native timber]

divisible by 2 and 3

[scenic musk]

im not allowed to divide

its a software question moreso

[native timber]

are you allowed to use bitwise operators?

if so, divisibility by 2 is trivial; divisibility by 3 reduces to the divisibility of its digital root (in which you only have 4 cases you need to check: 0, 3, 6, 9)

even if you're not allowed to use bitwise operators, you can look at the last digit and see its parity without using bitwise operators

[heady jewel]

@scenic musk subtract 6 from the given number unless you reach a number <6

and check if it is 0

definition of division

[scenic musk]

i dont understand @heady jewel

if i have the number 24

which is divisble by 6

24 - 6 = 18

i dont understand what i do from here

oh

i see what u mean

[small cedar]

repeated subtraction

18-6=12

12-6=6

6-6=0

[scenic musk]

ahh tyvm

that solves it

[dark fable]

tan(a)=1/2, cos(b) = -3/5

What's (cos(a)-2sin(b))/cot(a)

[blazing parrot]

you need cos(a) and sin(b) and cot(a) to sub into the equation

what is the definition of cot(a) @dark fable

[dark fable]

It wasn't provided

I think it wants it in terms of a and b (sum and difference formulas)

[blazing parrot]

you don’t really need to do that

okay so what is cot(a) in terms of tan(a)

[dark fable]

2

[blazing parrot]

yay

okay so imagine a right triangle of which one of the angles is a

then tan a is O/A of this triangle right?

[dark fable]

what

[blazing parrot]

okay

[dark fable]

oh yes

[blazing parrot]

so you know O/A = 1/2

[dark fable]

oh but

a is in quadrant I

b is in quadrant III

[blazing parrot]

that makes things more interesting

[dark fable]

so I think it is supposed to be sum and difference formulas

[blazing parrot]

hmm

[dark fable]

so its like

sinacosb + cosasinb

or something

cosacosb - sinasinb

[blazing parrot]

but then you won’t know what sin(a+b) or cos(a+b) is

or the differences either

[dark fable]

hmm I think it's just supposed to be left in terms of a and b

[blazing parrot]

hmm it is explicitly titled sum and diff formulas

[dark fable]

yup

[blazing parrot]

okay let me think about it for a bit

okay

so you have

$$ \frac{\cos a - 2\sin b }{\cot a}$$

[dark fable]

yep

[blazing parrot]

so what is 1/cot a

[obsidian monolith]

Not Chezstick:

[blazing parrot]

oh i must go

[dark fable]

oof

can you tell me the answer then I can reverse engineer lol

[blazing parrot]

sin a - sin b

don’t actually need sum/diff

[trim fable]

hey

@patent beacon

😛

will u help me

[patent beacon]

Ya

[trim fable]

so the

question is

and someone tried to help me but complicated my code and im super confused and i wanna simplify it

there

[patent beacon]

Welp, can't say I know much about programming and programming style sry

[trim fable]

how can i do that simply.. like the parsing is confusing and i wanted to use asci

[patent beacon]

My bad for telling you to put this in the server, didn't think it would be so programming oriented

[trim fable]

lol

ok

its fine

ill remove it

[viscid thistle]

What is 1/ba^2

[proud wraith]

How do I insert a fraction in Aleks?

I tried "/" and " \ "

the manual says to use "/"

nvm. I'm just braindead

[velvet elm]

How do I enter this into a calc to get a result?

[viscid thistle]

You just plug it in?

(ln(25/4))/3

[lethal oracle]

Anyone there that can help?

[velvet elm]

I mean like a traditional calc with a log function

[lethal oracle]

53

Find all solutions to the equation in the interval 0 to 2pi

[uncut mulch]

what have you tried?

[lethal oracle]

Factoring

[uncut mulch]

what did you get?

[lethal oracle]

Well I can’t come to an answer

[uncut mulch]

show your working out

[uncut mulch]

what are the solutions to tan(x)=0?

[lethal oracle]

0, and pi

[uncut mulch]

what are the solutions to sin^2(x) - 1 =0? ||but can you use those||

[lethal oracle]

Wouldn’t it be 0 and pi also?

[grim current]

Place the 1 to the right side of the equation.

[lethal oracle]

Ya so it’s sin(x)=plus or minus sqrt of 1

[grim current]

Right. So what are the solutions to it?

[lethal oracle]

0 and pi

[uncut mulch]

what is sin(0)?

[lethal oracle]

Wait the solutions are pi/2 and 3pi/2

[grim current]

Yes.

[uncut mulch]

yes. but can you use those solutions in this question?

[lethal oracle]

Ya sorry I was getting confused

No

[uncut mulch]

so what would be your only solutions?

[lethal oracle]

The solutions to tan in this equation which are 0 and pi

[uncut mulch]

what was your justification for not being able to use x=pi/2 or 3pi/2?

[lethal oracle]

I’m going to be honest I can’t really remember the reason my teacher told me

Can you explain whyv

?

[uncut mulch]

tan(x) is undefined at pi/2 +k*pi (where k is an integer)

[lethal oracle]

Oh because my solutions need to satisfy both?

[uncut mulch]

not quite

the presence of tan(x) imposes a restriction on the values of x

[grim current]

Let's say you have tan(x) = sin(x)/cos(x). If you were to substitute x for π/2 or 3π/2, for example, you'd get undefined values, like ramonov said.

[lethal oracle]

Oh I see

[grim current]

Your solution needs to satisfy the conditions imposed by the tan(x), which can be applied to the other functions as well.

[lethal oracle]

31

I need to prove the identity by making one side equal to the other

[viscid thistle]

@lethal oracle (cos^2x+sin^2x)(cos^2x-sin^2x)

That is the LHS.

And what does cos^2x+sin^2x equal to?

[lethal oracle]

1

[viscid thistle]

So 1*(cos^2-sin^2).

Which then proves what you're looking for.

[lethal oracle]

Ya I see thanks

[viscid thistle]

👍

-_-

[lethal oracle]

I need to do the same for this one

I can do it by using the conjugate, right?

[winter isle]

woah

we are doing log functions

[viscid thistle]

Stephen this is not the time.

[winter isle]

we don't start basic trig for another month

[viscid thistle]

Good for you.

[lethal oracle]

I’m kind of confused on how to use conjugates

Like especially when

[viscid thistle]

$\frac{x+y}{x-y} \cdot \frac{x+y}{x+y}=\frac{(x+y)^2}{x^2-y^2}$

[obsidian monolith]

leviosa:

[viscid thistle]

Conjugates are usually to take out radicals from the denominator and whatnot.

But it can be used in many other ways as well.

Take the conjugate though.

That's gonna lead you to your answer.

[lethal oracle]

So just foil them out?

[viscid thistle]

Honestly I would multiply by sinx+cosx to both the numerator and denominator.