help-13

[dire geode]

Use Google instead

[slender ginkgo]

The number bigger the bloody avogrado’s constant

[fallen needle]

.close

[cedar kiln]

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[mortal yarrow]

is the derivative operator linear?

[mental trail]

yes

d/dx (af + bg) = a df/dx + b dg/dx

[lone dune]

by the way for short and quick questions like this asking google is probably faster and more efficient than asking here

[cedar kiln]

@mortal yarrow Has your question been resolved?

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[fallen needle]

is the power set of aleph null bigger then aleph null

[dusky panther]

yes, it's the real numbers

[fallen needle]

k .close

.close

[cedar kiln]

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[cedar kiln]

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[chilly wyvern]

can i have help

[vital herald]

You're on your own for this one

[past sable]

😭

get the nerdiest guy here

[past sable]

guys i need help

[vital herald]

From chatgpt

[past sable]

solve the collatz conjuncture

[vital herald]

theoretically its 1

[rapid mauve]

!occupied

[cedar kiln]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[indigo lagoon]

nooo, don't use gpt

[mint inlet]

pretty sure this is notational nonsense

like why are you integrating alpha from 0 to infty but then you're summing from 0 to alpha-1

that makes no sense

[vital herald]

Im in 10th grade highly doubt I can do allat

[mint inlet]

chatgpt (sent above) is right that since the numerator and denominator only differ in this circled part, you can probably phrase it as the expected value of the circled part over some probability distribution parameterized by alpha and beta

also the circled part is a partial taylor series so it should approach 1 as alpha goes to infinity

but i still think the expression as whole is nothing more than notational nonsense as written

[cedar kiln]

@chilly wyvern Has your question been resolved?

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[meager dock]

hey so i was doing $-1/4+5/4-2+21$

[wraith dagger]

Tan

[meager dock]

i wanted to simplify

so i multiplied everything by 4

to get -1+5-8+84

=80

but apparantly

its wrong

[void sand]

you can't just multiply everything by 4

that's changing the expression

and thus the final answer

[meager dock]

its supposed to be 20

[void sand]

indeed

try focusing on simplify the first two terms first

-1/4 + 5/4

[meager dock]

well it says f(x)=2x^3+5x^2+4x+21

find the remainder when

2x+1

[meager dock]

4/4=1

but like

what if its a harder fraction

[void sand]

I'm confused as to what your original problem is

[meager dock]

like -5/80 + 2/79

[rapid mauve]

i feel like this warrants an

!xy

[cedar kiln]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[void sand]

you can always take a common denominator where suitable anyways

but this doesn't seem to be your concern?

[meager dock]

The expression 2x^3+ax^2+bx+21 has a factor of x+3 and leaves a remainder of 65 when divided by x-2.
a) Find the values of a and b
b)Find the value of the remainder when the expression is divided by 2x+1

[meager dock]

for a) i used remainder theorem to get two equations which i simultaneously solved to get

a=5

and

b=4

then for b)

i put it

like

2x^3+5x^2+4x+21

f(-1/2)=2(-1/2)^3+5(-1/2)^2+4(-1/2)+21

to get the remainder

this got me to

-1/4 +5/4-2+21

which i wanted to simplify

[meager dock]

thus this is what i got

[void sand]

okay, this looks good to me

[void sand]

what's wrong with just evaluating this expression as is?

[meager dock]

i hate fractions

and i tend to mess up

so its easier for me to convert it into integers

and then solve it

but as you said

[void sand]

you can't do that all the time, unfortunately

[meager dock]

i cant do it since it is not an equation

[void sand]

there's no such thing as "converting a fraction to an integer" - that's just changing the number involved

[meager dock]

wait!

it IS an equation

[void sand]

the best you can do is force all the terms to have a common denominator so that the numerator and denominators are integers you can add separately

[meager dock]

f(-1/2)=-1/4+5/4-2+21

multiply f(1/2) by 4 too!

[void sand]

sure, you can do that

[meager dock]

wait that would change it ;/

[dapper jolt]

im so sorry for interrupting but after this may someone help me with my math rpoblem? thanks !

[void sand]

it won't

[void sand]

you can open your own help channel c:

see #❓how-to-get-help

[meager dock]

how

it would be

[void sand]

4f(-1/2) = 80

[meager dock]

f(-1/8)=80

[void sand]

so divide both sides by 4 to get f(-1/2)

[void sand]

no

the constant doesn't go into the function

[meager dock]

but we want -1/2

[void sand]

you are getting f(-1/2)

the input of f is -1/2!

you're just multiplying the entire result by 4

[meager dock]

-1/2 factorial?

[void sand]

which you can later divide to get rid of

[rapid mauve]

just wanna put this here

[void sand]

no, just an exclaimation mark :p

[meager dock]

our f(-1/2)=80

4(f-1/2)=

[void sand]

no, 4f(-1/2) = 80

[meager dock]

4x80

[void sand]

not f(-1/2)

[meager dock]

ohhhhhhh

[void sand]

so f(-1/2) = 20

after you divide both sides of the equation by 4 :p

[meager dock]

thanks :D

.close

[cedar kiln]

Channel closed

Closed by @meager dock

Use .reopen if this was a mistake.

[meager dock]

.reopen

[cedar kiln]

✅

[meager dock]

sorry

just got another question

The function f(x)=ax^3+4x^2+bx-2, where a and b are constants, is such that 2x-1 is a factor. Given that the remainder when f(x) is divided by x-2 is twice the remainder when f(x) is divided by x+1.find the value of a and b.

Seia please help me

and higher!

[mint inlet]

you can do the same thing as the other problem

[tropic oxide]

is it just those 2 ppl you want help from and nobody else

[meager dock]

no

anyone

[mint inlet]

i know the phrasing of the problem seems more intimidating, since it says "this value is twice this other" instead of giving you the exact values

but try using the same method

[meager dock]

but i can understand what Seia says because she uses simple terms

and otheer ppl use complex

which i dont get

[dusk goblet]

seia literally said nothing

[meager dock]

so f(2)=r
and f(-1)=2r?

[mint inlet]

yeah

[dusk goblet]

i cant imagine being a woman on discord

🤣

[meager dock]

what

[mint inlet]

ok so

r is kind of annoying here

because it's this extra variable to worry about

that's not really related to the problem

so what you can do here is combine these

in a way that allows you to forget about r

do you see how?

[meager dock]

im still finding out f(-1) and f(2) and f(-1/2)

[mint inlet]

yeah, that's is your way of writing the remainders in terms of the polynomial

[mint inlet]

but specifically for these 2 equations you got here

can you see how to directly relate f(-1) and f(2), without involving this extra variable r?

[meager dock]

no

[rapid mauve]

hint: substitute

[meager dock]

i got all the equations

f(-1/2)=-a-4b=8
f(2)=8a+2b+14=2R
f(-1)=-a-b+2=R

simultaneous equation?

[tropic oxide]

always has been

[meager dock]

8a+2b+24=2R
-2a-2b+4=2R
6a+28=3R

[rapid mauve]

thought we were out to eliminate r

[tropic oxide]

i think it would have been easier to write f(2) = 2*f(-1) to begin with

[meager dock]

what difference would that have made?

oh it wouldve been easier

[meager dock]

how do i eliminate R now

[mint inlet]

let's go back to here first

as seia suggested, do you see a nice way to use substitution to combine the 2nd and 3rd equations?

[meager dock]

f(-1)=-a-b+2
2(f-1)=8a+2b+14

?

[meager dock]

put f(2) into f(-1)?

[mint inlet]

let me rewrite what you have here without the f's:
-a-4b=8
8a+2b+14=2R
-a-b+2=R

does this make sense?

[meager dock]

yes

[mint inlet]

ok

we want to get rid of R

[meager dock]

-R and 2R from RHS of both equations

?

no cuz that would add it to the lhs

[knotty ruin]

what does reopen do?

[rapid mauve]

reopens a closed help channel, but please don't barge into an occupied help channel to ask this

[knotty ruin]

sorry

[mint inlet]

do you want to try this path instead? i feel like you're getting confused with the Rs

[meager dock]

f(-1)=2(f(-1)?

[rapid mauve]

almost there!

but uh you substituted f(-1) instead

[meager dock]

do i replace the f(-1) with the actual equation

-a-b+2=-2a-2b+4

[rapid mauve]

no

[meager dock]

oh f(-1)=2f(2)

[rapid mauve]

oh i think i swapped the f(2) and f(-1)

reverse the f(-1) and f(2), my bad

i just reread your question

[meager dock]

f(2)=2f(-1)

[rapid mauve]

there we go

no more r's

you can now continue with fly's guide

[meager dock]

8a+2b+14=-a-b+2?

[tropic oxide]

hold up

who is twice whom?

[rapid mauve]

i addressed it

my mistake

[meager dock]

7a+3b=-12
-a-4b=8??

[rapid mauve]

nuked the image to prevent misunderstanding

[meager dock]

is this correct

[rapid mauve]

where did that come from

[meager dock]

this

shifted like terms to the lhs

[meager dock]

to get the first equation

and the second one is

f(-1/2)

.close

[cedar kiln]

Channel closed

Closed by @meager dock

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[cedar kiln]

Available help channel!

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

help i hate this chapter

[spark mist]

could you provide an translation

[supple rose]

its there

[spark mist]

dawg im stupid asl

alr sorry

[supple rose]

its okay vro

[spark mist]

vro 🥀

[gritty saddle]

just statistics

[spark mist]

for a you can think it as

first you can choose 8 person

then you can choose 7 person

you will get 8 * 7 * 6 * 5 * 4 * 3

do you understand why we only stop until 3 ?

[supple rose]

um why?

[spark mist]

since we can only have 6 person

simplex example

You have 2 friends you want to pick 1 to be your teamates how many way can you pick

[supple rose]

2?

[spark mist]

nice

thats right

imagine if you have 3 friend and you want to pick 1 to be your teammate ?

[supple rose]

um

wait

man idk

is it 3! ?

[spark mist]

yes

[supple rose]

oh so the answer is 6

[tranquil oracle]

Is that 3 factorial

[spark mist]

i though 3 ! as form of interjection

no it is not 3!

just 3

[tranquil oracle]

Its just 3 choices

If you want, give the friends names

Alice, Bob, Carl

3 possibilities: You+Alice, You+Bob, You+Carl

[supple rose]

so..

i got 3 ways to pick one as my teammate

[spark mist]

if you want to choose 2 from alice bob carl

you can see this as

first you have 3 choice

lets assume you pick bob

then you are left with with alice and carl

you now have 2 choice

either alice or carl

so algebraicly the way to pick 2 person from 3 person is 3 * 2

do you understand this

[supple rose]

mhm

let see i got 3 slots

in the first slot i can choose one of the three friends

[spark mist]

yep

[supple rose]

so in the second slot i can only choose one of them twos bcuz i already chose one

[spark mist]

your intuition is very good here

[supple rose]

ah i see

[spark mist]

now lets apply to 8 person

in the first slot you have 8 choice

the second slot you have 7 choice (why)?

why for every slot we go it decrease by 1

[supple rose]

bcuz theyre are different choices?

in 2 slots cant be the same person

[spark mist]

not quite right

[spark mist]

this is right

we need to rephrase it

because you already pick 1

you already choose someone in the first slot

since then we cant have that person again

[supple rose]

mhm

i get that

like 1st slot, 8 choices

2nd slot, 7 choices

and so on

[spark mist]

yeah

but remember you can only have 6 slot

since you want to pick 6 person

[supple rose]

so number of choices = 8, number of available slots = 6 ?

[spark mist]

yeah

can you count it now

[supple rose]

1st slot, 8 choices
2nd slot, 7 choices
…
6th slot, 3 choices

[spark mist]

sooo

[supple rose]

8!/2!

is that right?

[spark mist]

👍

[supple rose]

woww

so it should be 20160 ways

[spark mist]

yeah

alr we are done for part a

lets do part b

[supple rose]

yes

[spark mist]

b just mean

pick at minimum 5 girl

for 6 person team

do you understand if i say

pick 5 girl and 1 boy

pick 6 girl

[supple rose]

no

why you add them?

[spark mist]

you know what

we could not add them

since the question is ask for minimum 5 girls

we can just pick 5 grils

and just pick 1 from the rest of the team which is 12 person (17-5)

so use the same logic for the last question

but for the sixth slot we have 12 choice

[supple rose]

um wait

the question says at least 5 girls

[spark mist]

so the last person can be boys or girls right ?

[supple rose]

so in a team could be 5 girls 1 boy or 6 girls

[spark mist]

exactly

thatt's what i mean by add them

[supple rose]

mhmm

i see

but idk how to do it

[spark mist]

bro you can solve it ?

you can solve it

[supple rose]

let me try..

im sorry if it takes too long

[spark mist]

yo its okay

as long as you understand

[supple rose]

mhm

[spark mist]

if you need hint

remember you can choose 5 girls first then add 1 boy

then choose 6 girls

add the result

and that is the answer

[supple rose]

can i use 5 slots for 9 different girls and then add 1 slots for 8 different boys?

and add 6 slots for 9 girls

[spark mist]

yep

that is the right intuition

[supple rose]

so 9!/4! + 8!/7! + 9!/3! ?

[spark mist]

yes

[supple rose]

the answer is 75608

[spark mist]

yeah

[supple rose]

lets gooooo

thank you smm🙏🙏

[spark mist]

no problem

[cedar kiln]

@supple rose Has your question been resolved?

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[wary pond]

ive been stuck here for some time

[wary pond]

can i have a hint on where to start

[ancient cliff]

complete the square

[cedar kiln]

@wary pond Has your question been resolved?

Channel closed

Closed by @wary pond

Use .reopen if this was a mistake.

[wary pond]

completely forgot aobut it!,

[cedar kiln]

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[small parrot]

Yo

[small parrot]

Guys high school is starting

How do I get perfectly good grades

Cause I Wana move at 16

And I'm 14

And my mom won't let me go if I don't have good grades

[tropic oxide]

this looks like a question for #study-discussion if it's worth discussing at all

[small parrot]

😑

Kk

Th

Ty

[ancient cliff]

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[dusty wren]

If you are done with this channel, please mark your problem as solved by typing .close

[livid marlin]

.close

[faint plinth]

https://tenor.com/view/cat-cats-cat-meme-meme-meme-cat-gif-14470917232397934693

[cedar kiln]

@small parrot Has your question been resolved?

[cedar kiln]

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[meager dock]

Find the values of p and of q such that $15x^3+26x^2-11x-6$ is a factor of 15x^4+px^3-37x^2+qx+6

[wraith dagger]

Tan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tropic oxide]

15 minute rule etc...

progress?

[meager dock]

oh sorry

[meager dock]

none

[tropic oxide]

ok here is a trick

[meager dock]

i cant figure out what to do

[tropic oxide]

you know that this quartic must be equal to the product of the cubic and a linear

or to put it in less vague terms

15x^4+px^3-37x^2+qx+6 = (15x^3+26x^2-11x-6) * (LINEAR)

do you understand why? y/n

don't try to do anything from here yet

only tell me whether you understand this one step

[meager dock]

yes

[tropic oxide]

right

here's the neat thing...

you can work out the linear factor just by looking at the leading & constant terms

[meager dock]

i dont need to do trial and error?

[tropic oxide]

no trial and error needed.

[meager dock]

how

15 3 26 -11 and 6

[tropic oxide]

look at the leading terms

15x^4 will arise as the product of 15x^3 with the leading term in the linear

[meager dock]

the coefficients of x?

[tropic oxide]

no, the leading term. the term with the highest power of x

[meager dock]

15x^3 into x is 15x^4

so the first constant of our linear is x?

[meager dock]

oh the degree

[tropic oxide]

that's not what the word "degree" means.

[tropic oxide]

yes, so the linear factor is (x + ???)

[meager dock]

1?

[tropic oxide]

i said no trial and error.

[meager dock]

cuz the coefficient is not changing

[tropic oxide]

now we instead look at the constant terms

[meager dock]

15 into 1 =15

[tropic oxide]

6 will arise as the product of -6 with the linear factor's constant term

[meager dock]

oh

[tropic oxide]

though yes you can write 1x instead of x if you really want

[meager dock]

i meant it as the second constant of the linear

[tropic oxide]

then no it's not 1

-6 * (what) = 6?

[meager dock]

-1

[tropic oxide]

right

so we have just reconstructed the linear factor

as x-1

15x^4+px^3-37x^2+qx+6 = (15x^3+26x^2-11x-6) * (x-1)

now it is easy, yes?

[meager dock]

yes

i can divide 15x^3+26x^2-11x-6 by x-1

[tropic oxide]

no

no!!!!!

why divide!

why divide?!?!

[meager dock]

to get quadratic

[tropic oxide]

no!!!!

no!!! you're overthinking it!!!

15x^4+px^3-37x^2+qx+6 = (15x^3+26x^2-11x-6) × (x-1)

not division

multiplication

literally just work out the multiplication on the rhs

no need for any division at all

do you hear me @meager dock

[meager dock]

yes

the final answer i got is

15x^4+11x^3-37x^2+5x+6

[tropic oxide]

let's verify it...

,w expand (15x^3+26x^2-11x-6) * (x-1)

[meager dock]

,w simplify (15x^3+26x^2-11x-6)(x-1)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by ann_dec

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by tan211111

[tropic oxide]

yup looks good

[meager dock]

im just doubtful about this

[meager dock]

^

[tropic oxide]

what's causing you doubt

[meager dock]

for the first linear constant you look at the coefficients of x with the highest degree and for the second constant you look at the constants?

its worded terribly but i think you get my point?

[tropic oxide]

well you're right the wording is terrible

[meager dock]

if it was a x^5 then i would have to find a quadratic

i would get the first term by looking at the x^5 and x^4

but what about the second?

[tropic oxide]

well ok here is how you can make it a bit more formal

instead of trying to remember and then misremember what comes from what, you just write down the unknown linear factor the honest way ie as ax+b

and then expand the honest way

only you can still note that you care only about the two extreme terms (highest power and lowest power)

[meager dock]

yes i get that now

but what if it were not a quartic

[meager dock]

and it was 15x^5

+middle terms=15x^4 + middle terms

how would you find the middle term of the quadratic

so now we care about the 15x^5+11x^4+middle terms+6=15x^4+11x^3+middle terms-6

[tropic oxide]

well then the unknown quadratic is ax^2+bx+c so you need 3 conditions to get 3 coefficients back

so you may want to start caring about one of those middle terms

maybe the second-highest power or the second-lowest power

i will not generalize further

[meager dock]

i see

thank you

.close

[cedar kiln]

Channel closed

Closed by @meager dock

Use .reopen if this was a mistake.

[granite rose]

Bonjour Ann
Help me with that LA question in the other channel lol

[wicked mantle]

Reopen it

[granite rose]

Which one

I already asked 2 helpers and nobody responded

.reopen

[wicked mantle]

Nvm, claim a new channel

[flint cape]

And LEAVE IT OPEN, it's fruitless closing it literal minutes afterwards

[tropic oxide]

that's quite an entitled ask

[granite rose]

Sorry

[cedar kiln]

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[dusty wren]

@wanton tinsel you can post your question here

[wanton tinsel]

oh

[dusty wren]

ok, so can you find the lengths AB,BC,CD,DA

[wanton tinsel]

yeah

distance formula ig

[wicked mantle]

[wanton tinsel]

??

[dusty wren]

find them then

[wanton tinsel]

kinda confusing

[dusty wren]

y

[wanton tinsel]

ok lemme

[wicked mantle]

Have you done?

[cedar kiln]

@dusty wren Has your question been resolved?

[wanton tinsel]

i did it

but

[wicked mantle]

YESSSS!!! Can u show me ur work?

[wanton tinsel]

i have doubt on a other que

[wanton tinsel]

uhh my camera is not that good

[wicked mantle]

Oh, go ahead 🙂

[wicked mantle]

Just screenshot

[wanton tinsel]

(0,-3 ) (0,3) are vertices of equlateral triangle find the third point

[indigo lagoon]

is this another question?

[wanton tinsel]

yeah

[modern estuary]

There are two possible locations for the third point

[wanton tinsel]

+,- ?

[modern estuary]

Just imagine an equilateral triangle with one side (0,-3) (0,3)

[wanton tinsel]

yeah im

[indigo lagoon]

@wanton tinsel with this sketch, can you tell me how many possible points will be?

To satisify the requirement

[wanton tinsel]

equlateral triagle = 3 points

[indigo lagoon]

no, I mean how many possible positions can the third point be

[wanton tinsel]

2 wihc is +y and -y

idk if right cuz that might be the only posityon on the cartesian plane

[indigo lagoon]

Good job

any idea about how to find them?

[wanton tinsel]

yeah

lemme send smg wait

[indigo lagoon]

what else have you found?

[wanton tinsel]

AB = BC = CA

36= some equations

36=0

🙁

[indigo lagoon]

what is this 💀

alr, I'll give you some hints before fully reveal the solution

[wanton tinsel]

okay

[indigo lagoon]

Hint No.1

[wanton tinsel]

when did it become right angle triangle 🥀🙏🏻

[indigo lagoon]

Nooo, A(0,3) and B(0,-3) are two of the points of the triangle

we simply draw a line that is perpenduliar to AB

[wanton tinsel]

okay

[indigo lagoon]

3 minutes and I'll give u the next hint

[wanton tinsel]

pythagoras ?

gtg 🙁

[indigo lagoon]

yes

[flint cape]

Not quite

I can tell your intuition's right - that the two possible points are either side of this line

And that they're on an axis

[wanton tinsel]

yeah

[flint cape]

But if they're left or right of the line - which coordinate changes?

The x or the y?

[wanton tinsel]

☠️

both

-y +x

then ??

[indigo lagoon]

Let's take it slow

[wanton tinsel]

i gotta go bathroom 🙁

[indigo lagoon]

can you point out the two possible points in this sketch?

just draw it

[indigo lagoon]

alr

[wanton tinsel]

imma hold for a while 💀

[indigo lagoon]

Will you be back later?

[wanton tinsel]

-y -x ?

sorry

[flint cape]

Which coordinate moves left and right?

[wanton tinsel]

idk... 🥀

[flint cape]

Well shit.

[indigo lagoon]

it's ok, forget it for now

go to the restroom first

[wanton tinsel]

gonna ask my friend

[indigo lagoon]

noooo

If you find it frustrating, I can guide you in vc

you're almost there

[wanton tinsel]

dm

[indigo lagoon]

DM my main acc

@wicked mantle

[cedar kiln]

@dusty wren Has your question been resolved?

[dusty wren]

uhh

ig

[cedar kiln]

Channel closed

Closed by @dusty wren

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[wicked bane]

option 1 incorrect: leading zero
option 2: first row has leading zeros and no constants incorrect
option 3 : incorrect coeffiecents on third row
option 4: second and third row have incorrect coffecients
option 5 no constants
option 6 no constants
no options are correct
4

[surreal cave]

[wicked bane]

.close

[cedar kiln]

Channel closed

Closed by @wicked bane

Use .reopen if this was a mistake.

[wicked bane]

part a)
2t−36≥0⟹t≥18,−3t+63≥0⟹t≤21
G=18
H=21
part b)
C(t)=550(2t−36)+650(−3t+63)+1350t
t(18,21)
x1 = (2(18)-36) = 0
x2=-3(18)+63=9

x3=18

C(18) =550(2(18)−36)+650(−3(18)+63)+1350(18) = 30150

4

.reopen

[cedar kiln]

✅

[wicked bane]

@surreal cave

<@&286206848099549185>

.close

[cedar kiln]

Channel closed

Closed by @wicked bane

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[dull plover]

i wanna know

how is this even valid

how do we rewrite (ap + bq) ^x as (ap)^x + (bq)^x

[abstract breach]

what is N

[dull plover]

N = p * q

[abstract breach]

are p, q primes?

[dull plover]

and both p and q are primes

yea

[abstract breach]

have you tried expanding (ap+bq)^x

[dull plover]

wdym

[abstract breach]

mb I forgot how to say it in english

[dull plover]

i can expand it but what difference would it make

[abstract breach]

try it

[dull plover]

e1e2 are too large

😭

[abstract breach]

do you know the sigma notation for sums

[dull plover]

yea

we can expand it with the binomial theorem

but i still don't understand where ur going with this

[abstract breach]

and newton binomial formula?

[dull plover]

the first term would be (ap)^e1e2, and the rest would be the sum from 1 to e1e2 (ap)^e1e2-k * (bp)^k

[abstract breach]

yes

now look at the terms inside the sum

[dull plover]

what about them

[abstract breach]

what is their value mod N

[dull plover]

[0, N-1]

[abstract breach]

you can calculate their exact value

recall that N = pq

[dull plover]

we got the left side and right side

left side is (ap)^e1e2-k

p ^ anything is going to be 0 mod N

because N divides p

[abstract breach]

not quite

[dull plover]

mmmmmmm

[abstract breach]

p divides N, not the opposite

[dull plover]

yeah that's what i meant

[abstract breach]

but then it's not 0 mod N: you have to look at the right side as well

[dull plover]

thing is

thats true for p ^ anything mod N

but we got a constant being multiplied with p

so the value of the left side is going to be just the constant alone

and im guessing same thing with the right side

so a * b mod N

i think?

wait no

[abstract breach]

no, p^anything is not 0 mod N (for example p^1 = p is not 0)

[dull plover]

(ap)^e1e2-k * (bp)^k

a^e1e2-k * p^e1e2-k * b^k * q^k

a^e1e2-k * b^k

[dull plover]

oh yeah

well N is pq

so to be able to know the value i need to group the p and q together

[abstract breach]

exactly

[dull plover]

but idk

they're both raised to different exponents

[abstract breach]

the thing is: if e1e2-k >= 1 and k >= 1, you have pq in your product

thus N divides

[dull plover]

yeah but do i not also have a and b

imagine if Y = q

how can we say aq^x % Y divides

if it was q^x % Y i'd get it

[abstract breach]

q divides aq^x

[dull plover]

oh wai

t

uyeah

yeah yeah that makes perfect sense

so that sum entirely gives 0 under mod

and we're left with the first term of the expansion

(ap)^e1e2

wait so

im assuming

(bq)e1e2

is the last term of the expansion

correct?

this way we cut the all the lone terms from the expansion

so everything else left returns 0 mod N

yeah i think that's the case

[abstract breach]

yes

[dull plover]

thank you so much !!

have a wonderful day

!close

ooop

.close

[cedar kiln]

Channel closed

Closed by @dull plover

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mellow thistle]

suppose to be 1.496x10^7

[honest field]

check the units

[mellow thistle]

1496000?????

[mellow thistle]

14960000000????

I thought a million has 7 variables not 11

I don't understand

[honest field]

by the time you finish counting all the 0s climate change will destroy us all

[mellow thistle]

It's a million

I'm not stupid

A million has 7 variables

[dusty wren]

variables?

[mellow thistle]

For your case, numbers

Or digits

Or numeral

or integer

[tropic oxide]

one million is 10^6.

[mellow thistle]

1,000,000 = x10^7

[tropic oxide]

keep in mind also that you're converting from km to m, which picks up 3 more orders of magnitude,
and then finally 149.6 = 1.496 * 10^2

[rapid mauve]

,w 1 million in scientific notation

[wraith dagger]

Results provided by WolframAlpha

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

Requested by stseia

[mellow thistle]

oh

[rapid mauve]

,w 149.6 million in scientific notation

[wraith dagger]

Results provided by WolframAlpha

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

Requested by stseia

[rapid mauve]

,w 149.6 million km in scientific notation

[wraith dagger]

Results provided by WolframAlpha

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

Requested by stseia

[tropic oxide]

149.6 million km, in meters, becomes:

1.496 * 10^2 * 10^6 * 10^3 m

[rapid mauve]

,w 149.6 million km in scientific notation in meters

[wraith dagger]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by stseia

[rapid mauve]

wth

[mellow thistle]

I just thought of the rules of scientific figures like "Non-zero digits are always significant."

[tropic oxide]

this is not about significant figures at all

[mellow thistle]

so I thought you count 1 in 1,000,000 as x10^7

[tropic oxide]

• 1.496 * 10^2 is 149.6
• 10^6 is million
• 10^3 is a kilometer in meters

therefore,

149.6 million km, in meters, becomes:

1.496 * 10^2 * 10^6 * 10^3 m

do you understand

[mellow thistle]

Ohhhh

So 149.6 million is 1496000000000???

[rapid mauve]

,w 1496000000000 in scientific notation

[wraith dagger]

Results provided by WolframAlpha

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

Requested by stseia

[tropic oxide]

you cannot talk about only the number

[mellow thistle]

But you do not count the non zero digits

[tropic oxide]

the units are important too

forget about digits

literally forget about digits

[mellow thistle]

This is ridiculous

[tropic oxide]

this is not about sigfigs and never was about sigfigs

[mellow thistle]

1,000,000 is x10^6 making it a million

but when it's 1496000000 it's not a million

This is already confusing

How can I differenciate

And why are they not the same

Why is it not valid?

[tropic oxide]

1 million = 1,000,000
2 million = 2,000,000
2.5 million = 2,500,000
25 million = 25,000,000

[mellow thistle]

149,600,000?

[tropic oxide]

that's the number 149.6 million written out longhand yes

[mellow thistle]

149.6 x10^9

[dusty wren]

No

Those are 6 places, not 9

[low edge]

this is like the argument sketch by monty python

[prisma pike]

149,600,000=149.6x10^6

[mellow thistle]

So significant figure do not count the non zero digits?

[tropic oxide]

i think you're confused about the concept of significant figures and we're not able to relieve this confusion

[mellow thistle]

I cannot help myself

I don't know how to not be confused

I can't understand

[prisma pike]

What is one million long form

[mellow thistle]

Idfk if this is normal or I am having a mental disability

1,000,000

[prisma pike]

What is 10^1

[mellow thistle]

1?

[prisma pike]

No

[mellow thistle]

10

[prisma pike]

Yes

When you take a^x you are multiplying a by itself x times

So 10^1=10, 10^2=10x10, 10^3=10x10x10

And so on

So what is 10^2

[mellow thistle]

100

[prisma pike]

10^3

[mellow thistle]

1000

[prisma pike]

10^6

[mellow thistle]

1000000

[prisma pike]

So 1 million= 10^6

I did it gang let's go

Sorry I mean you did it gang

Let's gooo🔥

[mellow thistle]

I think I need to see a hospital because I feel like I'm not normal not understanding it at the beginning

[prisma pike]

I think you just forgot what an exponent is tbh

[low edge]

now all you have to do is say that 149.6 million is 149.6 times one million. ergo, 149.6×10^6

[low edge]

if you understood it now you're fine

[mellow thistle]

I blame this guy how in the world he got 1.496 x 10^11

[flint cape]

Because you're not done yet

[flint cape]

@mellow thistle Do you agree so far with this, first off?

[mellow thistle]

yes

[flint cape]

OKay

Scientific notation - are you familiar with this?

[mellow thistle]

im only familiar with scientific figures

[flint cape]

(i.e. writing numbers like 3.4 x 10^5 for 340 000)

[flint cape]

1. that's "significant figures"
2. not the same thing

[flint cape]

Hence me giving this clarification

Are you aware of what this is ^?

[mellow thistle]

^ is power of

[flint cape]

...

[mellow thistle]

what?

[flint cape]

I mean - do you understand this message that I'm responding to?

[mellow thistle]

yeah

[flint cape]

...Are you sure you do?

[mellow thistle]

yes

[flint cape]

Okay

[mellow thistle]

oops

I thought you might repeat the question

[flint cape]

So far we've got that this distance is 149.6 x 10^6 kilometres, right?

[mellow thistle]

yes

[flint cape]

Right - is that number, 149.6 x 10^6, in scientific notation yet?

[operative word being "yet" here]

[mellow thistle]

yes

no

yes?

[flint cape]

Love the immediate backpedal

[mellow thistle]

no??

no.

[flint cape]

No, it isn't - but do you understand why?

[mellow thistle]

no

I just answered

[flint cape]

Okay

Yh that's why I didn't just wanna say "right, it isn't"

[low edge]

Are you familiar with S.I.? (system internationale)

[flint cape]

When we write a number in scientific notation, so like m times 10^[power],, we tend to further restrict m to be between 1 and 10

(including 1, not including 10)

[rapid mauve]

(exclusive of 10)

oh oops

[flint cape]

I'm stealing your thunder

[mellow thistle]

can we just get to the point

[flint cape]

Point is here

So - the problem part is this 149.6

With me so far on that?

[mellow thistle]

149,600,00 is 149.6 x 10^6 km turn to meters it's 1.496 million which I do not know how

1,496,000

[flint cape]

This is why I didn't get to the point yet - because you're jumping off the cliff before I've given you the harness

[prisma pike]

kg?

[flint cape]

Do you understand that this number, as it is, is a problem?

[mellow thistle]

what's the problem with it?

[flint cape]

Because of this

[low edge]

our m is 149.6, which is bigger than 10

[mellow thistle]

we just figure out 149,600,00 is 149.6 x 10^6 km, I don't see the problem with it

[flint cape]

We're TRYING to get this into scientific notation

[prisma pike]

Nah but 149.6>10

[flint cape]

BUT 149.6 > 10 - this isn't DONE yet

[mellow thistle]

It is already in scientific notation like how low do you want the number to go?

[flint cape]

ffs....

[prisma pike]

Can I just show the process

[flint cape]

Did you read this.

[prisma pike]

And we can deal with the consequences later

[flint cape]

ykw sure

[mellow thistle]

I did

[flint cape]

Right - so you get that the thing we're multiplying by 10 to whatever power, has to be less than 10?

[prisma pike]

149.6x10^6=(149.6x10^-2)x10^2x10^6
=1.496x10^8

[mellow thistle]

ykw im using a calculator ffs we are not going anywhere

[prisma pike]

But this is in km

[prisma pike]

The answer gives it in metres for some reason

[rapid mauve]

SI unit for distance is metres

[flint cape]

[because most physics calculations require it in metres]

[prisma pike]

So in metres this would be
1.496x10^8x10^3=1.496x10^11

[low edge]

scientific notation means converting your units to fit the international system. When we are talking about distance, and you have kilometers, you want to convert them to meters.

[prisma pike]

I guess that is the some reason isn't it

[prisma pike]

Because the k in km stands for kilo which is a prefix for 10^3

[mellow thistle]

I don't get it

[prisma pike]

Please reference which part you don't get

[mellow thistle]

I don't know how to explain what part am I confused

[prisma pike]

Didn't you want to get to the point man

I thought you were ready to deal with the consequences

[mellow thistle]

ykw nvm

[prisma pike]

Just tell which part the explanation starts to like

Not make sense

Where do you stop following

[low edge]

Point is; 1. you dont want to have kilometers in your answer, you want meters.
2. you gotta convert the 149.6 to 1.496×10^2.

[mellow thistle]

just nvm

[flint cape]

FOK

[mellow thistle]

thanks everyone

[low edge]

look, take a break, study some basics that cover this stuff, and you can come back with more insight

[flint cape]

$$
\begin{aligned*}
149.6 \text{ million km } & = 149.6 \times 10^{6} \text{ km}//
&= 1.496 \times 10^{2} \times 10^{6} \text{ km}//
&= 1.496 \times 10^{2+6} \text{ km}//
&= 1.496 \times 10^{8} \text{ km}//
&= 1.496 \times 10^{8} \times \10^{3} \text{ m}//
&= 1.496 \times 10^{8+3} \text{ m}//
&= 1.496 \times 10^{11} \text{ m}
\end{aligned*}
$$

[wraith dagger]

Waes (Wires)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[flint cape]

okay tf

[prisma pike]

Chill with the LaTex please

[mellow thistle]

I did research and still don't get it

[flint cape]

$$
\begin{aligned*}
149.6 \text{ million km } & = 149.6 \times 10^{6} \text{ km} \
&= 1.496 \times 10^{2} \times 10^{6} \text{ km} \
&= 1.496 \times 10^{2+6} \text{ km} \
&= 1.496 \times 10^{8} \text{ km} \
&= 1.496 \times 10^{8} \times \10^{3} \text{ m}\
&= 1.496 \times 10^{8+3} \text{ m} \
&= 1.496 \times 10^{11} \text{ m}
\end{aligned*}
$$

[wraith dagger]

Waes (Wires)

$$
\begin{aligned*}
149.6 \text{ million km } & = 149.6 \times 10^{6} \text{ km} \\
&= 1.496 \times 10^{2} \times 10^{6} \text{ km} \\
&= 1.496 \times 10^{2+6} \text{ km} \\
&= 1.496 \times 10^{8} \text{ km} \\
&= 1.496 \times 10^{8} \times \10^{3} \text{ m}\ \
&= 1.496 \times 10^{8+3} \text{ m} \\
&= 1.496 \times 10^{11} \text{ m}
\end{aligned*}
$$
```Compilation error:```! LaTeX Error: Environment aligned* undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.50 \begin{aligned*}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.```

[mellow thistle]

I think I'll just fail this grade

I have no point I don't understand it

[coral jewel]

no

[flint cape]

oh

[prisma pike]

Ask your teacher about it

[wraith dagger]

Waes (Wires)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tropic oxide]

lose the $$ there

and i believe it's align*

[flint cape]

There we go

[mellow thistle]

My school is a self study. so we come back at exams only

[flint cape]

ik I always screw that up

[prisma pike]

This is actually a Monty python sketch

[low edge]

Do not give up, please. Just take it easy, and be more chill when you dont understand something, you can always learn it

[prisma pike]

Zamn

[low edge]

I SAID THAT

[prisma pike]

I'm agreeing

[mellow thistle]

idk what am I going to do

I'm literally crying

[rapid mauve]

i'm inclined to try to break it down

[mellow thistle]

I don't understand a single thing and atp im guessing the answer and might even cheat in the exams

[rapid mauve]

but uh

[flint cape]

@mellow thistle Can you understand this? If not, point to the line that isn't clear

[mellow thistle]

I said thank you

[low edge]

heyheyhey, take a walk outside, watch the clouds make all these squiggly shapes and stuff, observe other people living about their lives, and try to live yours too, without being totally hung up by some stupid physics

[mellow thistle]

I'll just write a small index card and cheat my way out

ykw whatever I feel like I can still do this

[low edge]

okayyyyy I like the attitude

[honest field]

meeting the principal any% speedrun

[low edge]

do you have a specific question?

[mellow thistle]

Let's just start from the start

So 149.6 million is 149,600,000 making is 149.6 x 10^6

[flint cape]

yes

[low edge]

Yes

[mellow thistle]

km to m is 1.496 m is 1,496,000

[rapid mauve]

if i were you, i probably wouldn't convert km to m until the original number is in scientific notation first

[mellow thistle]

okay this is where I stop

I do not know what to do next

[low edge]

There are two steps

[low edge]

one is converting your number to scientific notation

the other is to convert your units into meters

[rapid mauve]

the highlighted part is currently "illegal" in terms of scientific notation

[mellow thistle]

I do not understand

[low edge]

which part?

[mellow thistle]

everything you said and everything Seia said

[low edge]

alright, it's okay

[rapid mauve]

do you agree that this is the general form of a number in scientific notation

[mellow thistle]

yes

[rapid mauve]

focus now on m

there is a restriction on the values allowed for m

why this restriction, you might ask

because let's take an example

there is nothing mathematically wrong with this, except that this is NOT in scientific notation yet

because we have a "spare" power of 10 here

we could rewrite the red number as a number in between 1 and 10 by dividing it by 10

but the number must remain the same size

so if the m has "sacrificed" a power of 10

the actual power of 10s part must increase by 1 power to compensate

so the bottom number and the top number are the same size and are the same number

but only the bottom number is in scientific notation

[rapid mauve]

similarly

[rapid mauve]

THERE we go

now this number is in proper scientific notation

but this number is in kilometres

we need this number to be in metres

how many metres are in a kilometre?

[rapid mauve]

and here it is in colored form

entirely correct

and that's it

[mellow thistle]

YES

[rapid mauve]

so

no fancy exclusions of terms under square roots from now on?

but well done

[mellow thistle]

How did he convert days to seconds

[rapid mauve]

how many hours are in a day, then how many minutes are in an hour, and finally how many seconds are in a minute?

[mellow thistle]

hrs = 24 ; mins = 60 ; seconds = 60

[rapid mauve]

so just do 365 x 24 x 60 x 60

[mellow thistle]

why

[rapid mauve]

60 seconds in a minute, 60 minutes in an hour, 24 hours in a day for 365 days

[mellow thistle]

I don't get it

[rapid mauve]

start small then. how many seconds are in an hour?

[mellow thistle]

3600?

[rapid mauve]

how did you get this?

[mellow thistle]

60 x 60

[rapid mauve]

and why is this valid?

what's the logic?

it's correct, btw

[mellow thistle]

because 60 seconds is a min and 60 mins is in an hour so if I have to go back from hrs to seconds I have to times the seconds and mins

I hope it makes sense

[rapid mauve]

it makes perfect sense.

now let's go up a tier

how many seconds are in one day?

[mellow thistle]

86400

[rapid mauve]

logic?

[mellow thistle]

same but with hours

[rapid mauve]

good

[mellow thistle]

so 60 x 60 x 24

[rapid mauve]

so now you have the number of seconds in one day

what do you need to do to this number to get the number of seconds in 365 days?

[mellow thistle]

3153600