help-33

[cobalt sentinel]

Now just do that last simplification

[karmic herald]

and that would simplify to $\frac{y}{2}$

[elfin berry]

Zyme><SOL

[cobalt sentinel]

Yep, nice

[karmic herald]

thx dude

[cobalt sentinel]

Np

[karmic herald]

.close

[marsh citrus]

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[hard stratus]

how do i do sarah needed 1/3 cups of flour to make 1 apple pie. if she made 9 apples pies how many cups of flour would sarah need

[hard stratus]

helpppppppp

<@&286206848099549185>

[marble violet]

1/3cup=1pie

how can you make the pie into 9

[hard stratus]

add them

[marble violet]

multiply both sides

[hard stratus]

wdym

[marble violet]

multiply both sides by nine

that way the one pie becomes 9

[hard stratus]

so i do 1/3 x 9 for both of them

[marble violet]

yeah so it becomes 1/3 x 9 = 9 pies

[hard stratus]

ok now what

[marble violet]

multiply 1/3 by 9

thats it

[hard stratus]

how many cups of flour would she need tho

[marble violet]

9*1/3 cups of flour

whats 9 times 1/3

[hard stratus]

its 28/3

cuz 9x3 +1 right

[marble violet]

no

[hard stratus]

9/27

[marble violet]

no

[hard stratus]

how do i do it

[marble violet]

you multiply the numerator not both

so 1x9 divided by 3

[hard stratus]

?

what does it look like

[marble violet]

whats 1 times 9

[hard stratus]

9

[marble violet]

divide that by 3

[hard stratus]

why

[marble violet]

1 pie=1/3 cups

1 times 9 pies = 1/3 times 9 cups

9 pies equals 1/3 times 9 cups

1/3 times 9 becomes 9/3

[hard stratus]

how do i do it using fractions tho

[marble violet]

whenever you multiply fractions by a whole number

like 2 times 1/2

you multiply the top

to get 2/2

or 1

[hard stratus]

so its 9 x 1/3?

[marble violet]

yes

[hard stratus]

ok so its 9x1 and its the same answer?

[marble violet]

no

its 9x1 over 3

so 9/3

[hard stratus]

oh ok

[marble violet]

what is 9/3 equal to

[hard stratus]

umm 3/3

[marble violet]

not 3/3

3

[hard stratus]

ok

i have another quesion

a soup kitchen had 6/12 gallons of soup at the start of the day. they had 2 1/10 gallons of soup left by the end of the day. how many gallons of soup did they use during the day

i subtract?

how

6 1/2*

[marble violet]

I need to do smth gimme a min

[hard stratus]

ok.

[marble violet]

alr back

what grade of math is this btw

[hard stratus]

i dont know

im in grade 8

[marble violet]

ah

[hard stratus]

yea so what do i do

[marble violet]

basically when subtracting you want a common denominator

in this case 10 is the easiest one to use

[hard stratus]

for what

[marble violet]

if you are adding/subtracting you need a common denominator

[hard stratus]

ok

[marble violet]

because you’re dealing with 6 1/2 and 2 1/10

how do you make 2 into 10

[hard stratus]

how do i get a common denominator

[marble violet]

you find a number both the denomators can multiply to

2x5=10 and 10x1=10

[hard stratus]

oh ok

[hard stratus]

wdym

[marble violet]

how can you turn 2 into 10

[hard stratus]

2x5

[marble violet]

good

you cant multiply only one side though

so multiply both sides by 5

1/2

[hard stratus]

why cant i do 2x5 and 10x1

why 5 tho

[marble violet]

thats how you figure out the common denominator

both 2 and 10 can be multiplied into 10

so the common denominator is 10

[hard stratus]

so i just copy the 5 from 2x5

[marble violet]

think of it like this

you know how 2/4 is 1/2

[hard stratus]

no

[marble violet]

im not good at explaining let me see if i can find someone

<@&286206848099549185>

[hard stratus]

ok

oh ithink ik now cuz the 2 row has a 10 in it

so what do i do next

helpers

help

it gives the denominators 10 and 50 idk what to do

[lean lily]

you need help with basic operations with fractions

or like power rules

[marble violet]

basic operations

[marble violet]

.

this is the problem

[lean lily]

ok so mixed number

turn that into a fraction

multiply your whole number by denominator then add that to your numerator

so for your example 2 * 10(your denominator) + 1 (current numerator) = new numerator

so 21/10

wait how is there negative soup

whatever

who gave them soup

[marble violet]

they started with 6 1/2 then ended with 2 1/10 how much did they use

[hard stratus]

i got 13/2 and 21/10

[lean lily]

so youd do 21/10 -

[marble violet]

its 6 1/2

[lean lily]

and make it neagtive

[marble violet]

They mistyped the first time

[lean lily]

ah

[hard stratus]

what do i do now

[lean lily]

sso then youd do 13/2 - 21/10

[hard stratus]

ok its 8/8?

[lean lily]

what youd do isss get common denominators

a way that always works is take your first denomimnator and then multiply that to both the numerator and denominaotr of the other fraction so 21 * 2/10*2

then youd do that to the otherside

so 13 * 10/2 * 10

and then you get 130/20 - 42/20

more visual example

then you do 130-42 on the top and leave it divided by 20 so youd get 88/20

or 4 and 2/5

simplifed to a mixed number

[hard stratus]

what do i times it by

[lean lily]

sorry 2/5

[marble violet]

4 2/5

[lean lily]

what are you referring to

[hard stratus]

21x2 and 10x2 and 13x2 and 2x2?

[lean lily]

no you need common denominators so you can do the subtraction

[hard stratus]

how do i find common denominators on a multiplication chart

[lean lily]

you dont you take the denominator of the other fraction and multiply it to both the numerator and denominator

numerator being number on top denominator number on bottom

[hard stratus]

idk what youre saying

21x2 and 10x2?

[lean lily]

yes

then multiply the other fraction by the denominator number on the bottom being 10

[hard stratus]

what about 13

[lean lily]

so 13 * 10/ 2 * 10

you'd multiply it by 10 because that's the other denominator

[hard stratus]

oh so its 12x10 and 2x10

jm

13*

[lean lily]

yup

[hard stratus]

ok i got 130/20 and 42/20

[lean lily]

then youd do 130 - 42 on the top and leave the denominator so youd get 130-42/20

[hard stratus]

88/20?

[lean lily]

yup

now you reduce

[hard stratus]

wdym

[lean lily]

and turn it into a mixed number if it ask for that

[hard stratus]

how do i do that tho

[lean lily]

to turn it into a mixed number youd do 88 divided by 20

so 20 goess into 88 4 times

and you get a reminder of 8

so 4 and 8/20

[hard stratus]

so how many gallons of siup did they use during the day

[lean lily]

4 and 2/5 like we said earlier

[hard stratus]

its not 4 8/20?

[lean lily]

its both

both are correct

4 (8/4)/(20/4) = 4 2/5

[hard stratus]

idk how you got 4 2/5 but ok

[lean lily]

you have to find the greatest common factor did you learn that yet

[hard stratus]

yea

[lean lily]

its the biggest number that can be multipled by another number to equal it thatss the same for both

so factors of 8 are 1 2 4 8

20 1 2 4 5 10 20

biggest number in both of those is 4 which is the gcf of that fraction

and you can divide it out like you multiplied to get your common denominator

so both the numerator and denomiator get divided by 4

i.e. 4 (8/4)/(20/4) = 4 2/5

[hard stratus]

oh ok i kinda understand

you just find the common denominators by just switching the bottom denomaintors to times them?

i have another question btw

[lean lily]

yea so if you had random numbers or variables it would be

that is the process you'd use for finding common denominators

[hard stratus]

a cake recipie called for using 6 5/9 cups of sugar before baking and another 5 4/9 cups after baking. what is the total amount of sugar needed in the recipie

its addition?

[lean lily]

yup

theyre common denominators already sso itsss a bit eaiser

write it all out but youll end up with 12

[hard stratus]

umm

idk what to do

[lean lily]

if it helps you can ignore the whole numberss for now and look it as

then add 5 and 6 after

since its already common denominators you'd add the numerators

[hard stratus]

its 9/18?

[lean lily]

no you leave the denominators alone once they are equal

or "common"

[hard stratus]

its 4/9?

9/9?

[lean lily]

yes

and how many times does 9 goes into 9

[hard stratus]

1

[lean lily]

so 9/9 =1

then you can add the whole numbers

so 1+6+5

[hard stratus]

wdym why do i have to keep the same denominators

[lean lily]

becausse they are already common denomtaors

9 and 9 are the same

2 and 10 arent the same so thats why we did the multipkying

[hard stratus]

3 and 3 are common denominators?

cuz theyre the same

oh ok

the answer is just 12?

noooo

dont go

.close

[marsh citrus]

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[marsh citrus]

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[red meadow]

You have two events A = {2} and B = {2,3}.

If A happens then B has to happen. But if A doesn't happen, B could still happen.

If B doesn't happen then A doesn't happen. But my question is what if B happens? A doesn't have to happen right? But how would this look in a Venn diagram. If 3 is the outcome of the experiment, will intersection A and B not be filled in?

[runic temple]

yes

if b happens, it could be 3

[brittle mist]

hey

is there a spanish channel?

[red meadow]

idk but this channel is for help dude

[runic temple]

no, this is an english server

[red meadow]

If 3 is the outcome of the experiment, will intersection A and B not be filled in?

or will it be filled in since the event B has occured

[runic temple]

what do you mean

what kind of experiment is this?

[red meadow]

are u familiar with a venn diagram

[runic temple]

yes

[red meadow]

yes so since A and B arent disjoint, the intersection A and B is 2

[runic temple]

i know tha

[red meadow]

is this how it will look if the outcome is 3

[runic temple]

a should be contained in b

[red meadow]

But if 3 is the outcome of the experiment then A intersection B can't be filled in right?

[runic temple]

i dont think so

[marsh citrus]

@red meadow Has your question been resolved?

[marsh citrus]

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[random gust]

im guessing I have to use log on both sides

and then bring the exponents to the front

but idk the next step

*also the goal is to find x

[glass silo]

Did you manage to get to that point at least?

[random gust]

yes thats why I said it

[glass silo]

Cool cool, can you show what you have then please

[random gust]

4x-1 (log 2) = 1-x (log 3)

[glass silo]

Think there should be some brackets around the (4x-1) and the (1-x) right?

[random gust]

yeah ik

[glass silo]

But otherwise, you know that log(2) and log(3) are constants

Solve it like you would if those log(2)’s and log(3)’s were any other constants

[random gust]

no calculator preferred

[glass silo]

Alright, say I gave you instead the equation a(4x-1)=b(1-x)

Could you solve that for x in terms of a and b?

[random gust]

then it would be (1-x) (log3/2) + 1 all over 4

equals x

?

.close

[marsh citrus]

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[merry terrace]

Question 58

This is very easy but

We can start by squaring x and y:
x² = ((√3+√2)/(√3-√2))² = (√3+√2)² / (√3-√2)²
y² = ((√3-√2)/(√3+√2))² = (√3-√2)² / (√3+√2)²

Now we can add the two equations together:
x² + y² = (√3+√2)² / (√3-√2)² + (√3-√2)² / (√3+√2)²

By simplifying the denominators, we get
x² + y² = (3+2√6+2√3) / (3-2√6) + (3-2√6-2√3) / (3+2√6)

By combining the numerators, we get
x² + y² = 6/0 which is undefined

From chat gtp

And

[merry terrace]

My work

We all got different answers

Is this question exist?

[still temple]

dont trust chat gpt

[lucid hinge]

[merry terrace]

I didn't but my answer is different too

[still temple]

,w ((sqrt3+sqrt2)/(sqrt3-sqrt2))^2+((sqrt3-sqrt2)/(sqrt3+sqrt2))^2

[elfin berry]

Results provided by WolframAlpha

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

Requested by Toby#2275

[merry terrace]

Yeah it is 98 there

[still temple]

reading

[merry terrace]

Where did I messed up

[merry terrace]

Feck I see

[still temple]

you still need denom

[merry terrace]

I wrote 36-24

But it would be 36-(24×2)

36-48

,w 36-2(36-48)

[elfin berry]

Results provided by WolframAlpha

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

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[merry terrace]

Wtf

Ah let me do the whole thing again

[still temple]

6+6=12 not 6

and -2(-12)=+24

x is not 6+2sqrt6

you need to divide by (2+3)

(I assume you rationalised to get what you got)

[merry terrace]

My god

[merry terrace]

Yes

[still temple]

all your ideas are right, just need to make sure the arithmetic is correct

[merry terrace]

Yupp that's why you shouldn't do maths at 3am

[still temple]

haha yeah

[merry terrace]

Now ok

,w 100-2(5-2√6)(5+2√6)

[elfin berry]

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Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[merry terrace]

Yeah now correct thanks@still temple

.close

[marsh citrus]

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[lost pelican]

How do I solve this?

[stoic saddle]

!status

[marsh citrus]

What step are you on?

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

[lost pelican]

2

so I got p+s=15

2.30p plus 3.20s=15(2.72)

but thats all I know. might not be correct

but i dont know what to do klnow

[stoic saddle]

okay, so i take it that p and s represent the amounts of peanuts and smarties (in kg) respectively

yes, the equations p + s = 15 and 2.30p + 3.20s = 2.72*15 are correct

you now have a system of linear equations

do you know how to solve those?

[marsh citrus]

@lost pelican Has your question been resolved?

[lost pelican]

.close

[marsh citrus]

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[civic moss]

I don't really understand compound interest

[lilac bane]

Hmm

[civic moss]

the idea of simple interest makes sense: the starting amount is S, and the rate is r per time period, then it's just Sr^t

but why would you compound "monthly"

[lilac bane]

Hmm

[lilac bane]

Are you sure that this is simple interest?

[civic moss]

whoops, wrong terminology

I just mean

if you add 10% to a bank account once every year

then it's clear it'll be S * (1.1)^t

where t is in years

but what does it mean for the 10% to be "compounded twice a year"

then it becomes S * (1.05)^2t

isn't that just 5% interest per half-year? why would you relate it to the 10% per year?

[lilac bane]

That's compounded annually

[civic moss]

right, yeah, like

I'm imagining a button "add 10%"

that you click at midnight on Jan 1

every year

lol

[civic moss]

?

[lilac bane]

Hmm

I am not sure exactly why we divide the rate by the number of divisions in between the time period

But I think that if you did (1+0.1)^1 is approximately the same if you did (1+0.05)^2

Approximate is of course not exactly the same

But I am not sure why the interest is divided like that

https://math.stackexchange.com/questions/2627519/why-do-we-divide-by-the-number-of-compounding-periods-when-calculating-compound

Perhaps this helps?

@civic moss

[marsh citrus]

@civic moss Has your question been resolved?

[civic moss]

oh thank you

yeah that helps a lot

thanks a lot

[marsh citrus]

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[languid lagoon]

Hello! First time getting help here!
So I'm not currently taking classes. This question is in relation to a personal project I'm working on. My knowledge of math goes up to calc 1 just fyi.
So this is a equation for projecting a vector onto a plane: https://www.maplesoft.com/support/help/maple/view.aspx?path=MathApps%2FProjectionOfVectorOntoPlane
I really only want help with reading this equation. I'm unfamiliar with much of the notations. What subject would this fall under math wise?

[proper zodiac]

Linear algebra. Buzzwords: dot product and norm/ magnitude

[languid lagoon]

ah okay. just to make sure I'm on the same page. In the numerator is the dot product, and in the denominator is the norm/ magnitude.

[sharp mortar]

Yes

[languid lagoon]

Okay thanks for the help. Thats all I need for now.

.close

[marsh citrus]

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[cinder sorrel]

I don't understand this proof.
I'm having a hard time understanding what exactly it's saying. What is an "opposite remainder modulo 1000" Does that mean if something has remainder 1 it's opposite would be 999? What's the proof in laymans terms?

[tight furnace]

yeah

you're right

two numbers can't have the same remainder, or their difference will be divisible by 1000

they can't have "opposite remainders", or their sum will be divisible by 1000

[marsh citrus]

@cinder sorrel Has your question been resolved?

[runic temple]

the proof is basically saying
because you can subtract two numbers, if the remainders are the same, the difference will be a multiple of 1000, so they must be different
you can pick numbers from 0 to 999 that are remainders when divided by 1000
if you pair them up based on when they sum to 1000, you have 998 numbers paired and 0 and 500
there are 499 pairs and 2 extra numbers
you cannot pick both numbers in a pair without having them sum to 100, so you can pick a maximum of 501 numbers
the 502nd will fill a pair

[marsh citrus]

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[thorny jungle]

im not understanding how they are choosing their N1 and N2 here

[marsh citrus]

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[modern vigil]

how do i know which answer to choose in this picture

[unreal oxide]

u want x <= 31/3 OR x <= 5 to be true

[crisp imp]

You could use a number line to help you out

[modern vigil]

would it be a?

[crisp imp]

How?

[modern vigil]

i have no idea thats just the choice it usually does 🥲

[crisp imp]

You'd better draw a number line, and plot those two points

[modern vigil]

it usually does the answer from the first inequality

[crisp imp]

It usually does, wdym?

[modern vigil]

the answer choice is usually the answer from the first inequality, i mean

[crisp imp]

It'd not be always so

Here, let me help you out.

By giving you a number line to work on

[modern vigil]

well i usually pick the choice that could maybe satisfy both of them but i keep getting it wrong

[modern vigil]

i really think it's b but i feel like it's gonna say that's wrong 🥲

[crisp imp]

Well

I'll help you again.

[modern vigil]

im sorry lmaoo

[crisp imp]

So now, what would be the solution?

So x should be either less than or eq to 5 OR less than or eq to 31/5

So, what could you say x is

As SilverSoldier said, you want x <= 31/3 OR x<=5 to be true

[modern vigil]

so does that mean i could pick either a or b and the answer be correct

[crisp imp]

No

I drew the number line for a purpose

[modern vigil]

im sorry

[crisp imp]

Look at the number line

What values can x have

If you see

(well screw these VCs I usually streamed such problems)

[modern vigil]

anything less than 10 1/3??

[crisp imp]

Yep anything less than that

[modern vigil]

oh okay thank you

[crisp imp]

That red line comes as a part of that blue line

So

If you say that x <= 31/3

That also means x SHOULD BE <=5

Since 5<31/3

[modern vigil]

omg

that makes so much more sense

[crisp imp]

So that makes both of them true.

Well uh, Im sorry, we both had a hard time yk, explaining and understanding, just the gap created cause of the text thingie

Congrats on gettin it

[modern vigil]

thank you very much

[unreal oxide]

okay im kinda doubting myself now, if x is between 5 and 31/3, x <= 31/3 is true

altho x <= 5 is not

[crisp imp]

Uh?

[unreal oxide]

but x<=5 OR x<=31/3 is still true ?

[crisp imp]

Well uh, it said "OR"

So like

OR represents set union

So its asking

values of x that satisfy eqn 1 or 2

So it is the union of both sets

[unreal oxide]

oh yeah yeah

[crisp imp]

Youre a student ig too haha

[unreal oxide]

yeah, so if x for any reason did not satisfy the first inequality it must satisfy the second one

[crisp imp]

Yup

[unreal oxide]

i am abt to enter university lol

[crisp imp]

Actually

Haha

Im in the last stage of senior HS too

[unreal oxide]

ive finished schooling

[crisp imp]

I see

Id have, if the edu thing didnt change in my place yk.

[unreal oxide]

oh

[crisp imp]

Haha, anyways, this is a help vc and um we cant talk this stuff here, we better go another place

[modern vigil]

okay can i close this

.close

[marsh citrus]

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[marsh citrus]

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[marble glacier]

https://gyazo.com/288ab8ee33fd3e5a2985e1d6ba5941e0

[marble glacier]

https://gyazo.com/9cebd4603de39fdb55c2620d24be9f86

i know this is a maths server

but how are these equuations the same

specfically the integral part

[unreal oxide]

this is the law of biot savart?

[unreal oxide]

and i think here u r trying to find the magnetic field at a distance a away from some point on a wire?

[marble glacier]

Yep

[unreal oxide]

what are a and y there exactly

can u send a picture maybe?

the integrals are the same coz u use the definition of the cross produt

ds x r = |ds| * |r| * sintheta * u

sintheta is probably found using a right triangle there

so u get a 1/sqrt(a^2 + y^2)

[crisp imp]

Well, the question is unclear, theres no context to whats going on, whats getting found out

And

[vast shoal]

Is this biot savart law equation?

[marble glacier]

No hes on the right track

its making sense now

[crisp imp]

What exactly are you doing with the a and y thing

[marble glacier]

https://gyazo.com/17bdaaf8586e3cf75d101deba3d0c990

like tihs?

[crisp imp]

You would've sent this earlier and Id not have said that

[marble glacier]

Yea

[unreal oxide]

right so sin theta = a/sqrt(a^2 + y^2)

[vast shoal]

I think it should have r^3 instead of r^2 then since its in vector form

[crisp imp]

Well um no, its the unit vector there

[vast shoal]

Oh right

Missed that

[unreal oxide]

so the vector r wud be the hypotenuse

and the vector ds wud be dy

[elfin berry]

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

[crisp imp]

@vast shoal

[vast shoal]

Yeah I get it, I didnt see r hat, thought it was r vector

[crisp imp]

Yup yup

[marble glacier]

thanks

yall are nerds fr

.close

[marsh citrus]

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[limpid condor]

hey!

i have these 2 question from my textbook (Nelson Advanced Functions 12)
i was wondering if anyone could make me a questions that is similar to them and uses the double angle formulas,

the sections is solving linear trigonometric equations and i am just looking for a new questions thats it, please make sure it is solveable.

[limpid condor]

anyone

<@&286206848099549185>

pinging since it has been 15 min

damn

[marsh citrus]

@limpid condor Has your question been resolved?

[marsh citrus]

@limpid condor Has your question been resolved?

[thorny slate]

so for the first one you just want to set the temprature = to 32

then re-arrange for d

gimme a sec

[marsh citrus]

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[marsh citrus]

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[wraith gull]

How would I begin this?

[tacit fjord]

If ab = 0 for some numbers a and b,

what can you say about a and b

[wraith gull]

They can’t be 0 at the same time maybe?

[tacit fjord]

a = 0, b = 0

ab = 0

No?

If theyre both 0, ab = 0 for sure.

===
To rephrase, I am asking if 2 numbers multiply to make 0, what can you say about them

[wraith gull]

Atleast one of them is 0

[tacit fjord]

correct

[tacit fjord]

apply this fact to your problem

[wraith gull]

Should I solve 3SinX - 2 = 0 and TanX - 4 = 0 separately?

[tacit fjord]

yes, at least one of those are true

[wraith gull]

Ok let me try that

Worked wonders thank you

.close

[marsh citrus]

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[lucid zenith]

the rule i learned is
first see if the angle is 0, 180 or 90, 270
if the angle is 90 or 270, you change the function to its "opposite" (sin to cos, tan to cot, sec to csc and vice versa)
if the angle is 0 or 180 then you keep the same function

to figure out the sign you use the astc acronym

a s t c - all, sin, tan, cos

in the first quadrant all trig functions are positive

in the second quadrant sin and cosec (its reciprocal) are positive

and so on

so if you have 90 - a then it would be the first quadrant but if you have 90 + a then it would be the second quadrant\

it's just a rule

all of these identities are derived from the angle sum identities these are just shortcuts

as in?

what do you mean by "positive in the first quadrant"

[lucid zenith]

did you understand this much

think about it in this way

if you have cos(270-a) then which quadrant would that angle lie in

for small values of a

yep

and

astc

so only tan and cot are positive in the third quadrant

[lucid zenith]

meaning the value of this will always be negative

now since you have 270 you have to switch the function

so this would be

-sin A

yeah

if you try this with different values using the angle sum identities you'll see where these patterns come from

yeah

but it is negative because

cos(180+a) = -cos A

yep

sin(A+180) = - sinA

it's a property

hold on

see if you understand now

sin(180+A) = - sinA, cos(180+A) = - cosA, sin(90-A) = cosA and cos(90-A) = sinA

using these four properties you can do any of these questions

the thing i was talking about before is just a shortcut

ye

[marsh citrus]

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[marsh citrus]

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[hollow nova]

i need help

[nova totem]

Just post it

[hollow nova]

okay

just those four please

[nova totem]

161 = 2x^2 + 6x - 15

What have you tried

[hollow nova]

one sec

17.6, 2.75, and 4

and it was all wrong

[nova totem]

I meant what work

Not answers

I need to see work.

[hollow nova]

okay

just carried the 15 over

did 176=64x

and then got x = 2.75

hello? ;-;

<@&286206848099549185>

[nova totem]

That ain't right

I would move the 161 over

$$2x^2 + 6x - 176$$

[elfin berry]

$e^{\text{Umbraleviathan}}$

[nova totem]

Use quadratic formula @hollow nova

[hollow nova]

and set it equal to zero?

is the answer 8?

@nova totem

[elfin berry]

Chris.

[nova totem]

Yes. Use quadratic formula

There could be 2 answers

There are 2 answers

8 is one of them

[hollow nova]

but i only have one answer box

which is X

8,-11

.close

[marsh citrus]

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[open hemlock]

Hey! Need to roughly estimate the length of a n-size bezier curve

[open hemlock]

Needs to be cheap to compute

[proper zodiac]

approximate the arc length integral by sums?

[open hemlock]

I can do that, but not sure if that's fast enough

I need a very course estimation, idc if it's off 1 or 2 units

coarse *

[proper zodiac]

you'll get better advice about speed you might want to consult the people over at the compsci server

[north sparrow]

whats 1 or 2 units in percent here

[proper zodiac]

you could calculate the length of lines that go between the control points

or whatever theyre called

idk how coarse that would be

[open hemlock]

Hmm good one

Very coarse lol

But that's fine

[proper zodiac]

yeah indeed lol

esp is t he curve is very curvy

[open hemlock]

It's used to determine the step size used later

Longer curve, smaller step size

[proper zodiac]

hm that might give you false positives then

just look up efficient ways to approximate integrals

i imagine thats very well documented

[open hemlock]

It's not about machine learning

Like, I'm following a path of motion that needs to be smoothened

[proper zodiac]

i mean that it could tell you a curve is longer than another when it really isnt

[open hemlock]

Oh that's fine

It's just used to determine step size

So a long curve has a similar precision as a short one

[proper zodiac]

honestly it sounding more and more like you should just use a random number generator

[open hemlock]

Hahaha why?

[proper zodiac]

lol just the more information you reveal the more it sounds like you dont really care how long these curves are

[charred jungle]

maybe choosing like n different points on the curve (and maybe being a little quirky and adding a random +k to wiggle those points around a bit) then calculating the sum of the "consecutive" points that you chose

for a small n, pretty fast I'd say

[proper zodiac]

yeah just put however many points you want on your curve and make lines between them and calc lengths of those

(this is just approximating the integral)

[charred jungle]

🤭

[proper zodiac]

or

guess!

[marsh citrus]

@open hemlock Has your question been resolved?

[marsh citrus]

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[wispy silo]

Help me please

[bright jay]

With what?

[runic temple]

!status

[marsh citrus]

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

[wispy silo]

this statement on 7

is ny brain not computing it

[bright jay]

It's an equilateral triangle

All the angles are the same

You only listed one of the 3

When you did the math

[wispy silo]

Oh

so its supposed to be

33x-6

[bright jay]

Not quite

[wispy silo]

oh no

18

33x-18?

[bright jay]

Yes

Like that

Then solve for x

[wispy silo]

yes so its 6

[bright jay]

Yes

@wispy silo Feel free to .close if you are done with the channel

[wispy silo]

.clsoe

.close

[marsh citrus]

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[alpine musk]

Hello

[alpine musk]

Anyone able to help me with this one?

Find the equation of a tangent line given f(4) = 3 and f' (4) = 2 at x=4

I'm having trouble figuring out how to start, never tried one of these before

[night mica]

2x-5

[alpine musk]

What

[night mica]

the derivative is 2

and 2*4-5=3

[alpine musk]

where did u get the 5 from

[night mica]

because f' (4) = 2 force you to set 2x+k with k costant

then you have only to find k... so put f(4)=3

[alpine musk]

Oh ok

[alpine musk]

So f(4) = 3 would be 3*4-5?

[night mica]

no

you know that f(4) = 3 i.e. 2*4+k=3...then solve for k

and you get k=-5

[alpine musk]

so how would I setup the tangent equation using all this info?

sorry I'm not familiar with "K" I think i use a different format

[night mica]

the equation of a line its the form of hx+b right ? (with h and k constant)

[alpine musk]

point slope form

[night mica]

ok so you know that the slope is h

[alpine musk]

yep

[night mica]

and you can find b by an equation

[alpine musk]

then we need Y and X

y-y1 = m (x - x1)

[night mica]

ok this is another method

[alpine musk]

Yeah

[night mica]

if you have f(4) = 3 and f' (4) = 2

[alpine musk]

Yep

[night mica]

the x_1=4 and y_1=3

and m=2

then you have your equation that describes the line

[alpine musk]

How is the slope 2

Show me the math for that one

[night mica]

the slope for a line its the derivative of the function which describes the line

f' (4) = 2

[alpine musk]

Oh right

Thanks @night mica

[night mica]

gg

[alpine musk]

Actually I have one more question if u can help lol

but idk if u know how to do this one

different problem

[night mica]

i know everything

[alpine musk]

ok O_O

[alpine musk]

i can change the amount of solutions as well, it could be more or less

just dont know how to solve it

this is my last question btw

that i am having trouble with @night mica

let me know how to start

[night mica]

so do you know what is slope .

[alpine musk]

yes

[night mica]

its basically the derivative in a point

so compute f' to know the derivative for every x

[alpine musk]

ok so

3x^2 + 6x + 1

[night mica]

well

[alpine musk]

3(1)^2 + 6(1) + 1

10

oh lmao

[night mica]

why you put 1 in the derivative of a function

?

[alpine musk]

i interpreted that as "every x"

how do I compute f' to know derivative for every x then?

[night mica]

yes its correct that you evaluate f' in a particular x in general ..but now you chose x=1 completely random

[alpine musk]

oh right I see what I did, used the slope of x=1

[alpine musk]

so what numbers do i use to evaluate f' then

[night mica]

you want that the slope is actually 1 ... x=1 it nonsense here

[alpine musk]

ok

[night mica]

ok so you want to know x such that f'(x)=1 right ?

[alpine musk]

right

[night mica]

in other words you have to solve this equation 3x^2 + 6x + 1=1

this is a second degree polynomial and you should be able to solve it

[alpine musk]

x is 0 and -2 in that

[night mica]

yes

[alpine musk]

so is that one coordinate point

[0,-2]

[night mica]

mh...

the x's are 0 and -2

[alpine musk]

oh

[night mica]

the y's are f(0) and f(-2)

[0,-2] are you x's and its not a point

[alpine musk]

ok

[night mica]

go in peace

[alpine musk]

what

[night mica]

sorry

[alpine musk]

oh u can't help me anymore?

rip

[night mica]

yes

the last one

[alpine musk]

wait so what are the coordinate points tho

if it's not [0,-2]

[0,0] and [-2, -2]?

sorry but im confused bruh its hard over discord

[night mica]

the point of the graph of f are of the form [x,f(x)]

[alpine musk]

X's are 0 and -2 y's are f(0) and f(-2)

what are the pairs

[alpine musk]

oh

[night mica]

you have to substitute 0 and -2 to the x

and you get two point

[alpine musk]

so [0, f(-2)] is one

so theres only one solution?

[night mica]

no...

X's are 0 and -2

[alpine musk]

oh wait then other is [-2, f(0)

[night mica]

so you have two points with x equal 0 and -2

[alpine musk]

then ys are f(0) and f(-2)

[night mica]

yes

[alpine musk]

can u format it for me

i see what ur saying but not the formatting part

[night mica]

doesn't make sense this

[alpine musk]

ya i dont undersrand how to write the final answers formatting

[night mica]

just compute this [x,f(x)]... firstly with x=0

and use () instead of [] because the text uses this notation

[alpine musk]

[0,f(-2)]

hows that wrong, 0 is X and then f(-2) is the f(x)

[night mica]

the points of the graph are the form of (x,f(x))..why you write (x_1,f(x_2)) with x_1 not equal to x_2?

for example the point of the graph x=y are (1,1), (-2,-2) and not (0,-2)

[alpine musk]

so how should I write it? i'm not understanding this part but once u show me it will ring a bell

[night mica]

you have to do it yourself because it’s simple

just compute this [x,f(x)].

if you put x=0

the first coordinate become 0, and the second..?

[alpine musk]

Ok I'm trying

[alpine musk]

0

[night mica]

f(0)=0?

[alpine musk]

yes

[night mica]

if your compute is correct yes one point is (0,0)

are you sure that f(0)=0?

[alpine musk]

ya

why wouldn't it be 0?

[night mica]

i think its 7

[alpine musk]

why

[alpine musk]

oh

[night mica]

ok one point is (0,7)

and the other is (-2,f(-2))

now you have to compute f(-2)

[alpine musk]

ohhhhh

i see what ur doing

ok

[night mica]

i m just compute (x,f(x))

[alpine musk]

i got 9

[night mica]

ok so the other point is (-2,9)

[alpine musk]

got it

[night mica]

gg

[alpine musk]

dang i see now

that scrazy how i didnt see thatbefore lol

ty @night mica have a good one man

[night mica]

yeah i know

[alpine musk]

gonna close

.close

[marsh citrus]

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[upbeat gust]

how do i prove 5 to the 18th - 25 to the 8th is divisible by 120

[runic temple]

!status

[marsh citrus]

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

[upbeat gust]

3

so now im at 1

[runic temple]

!show

[marsh citrus]

Show your work, and if possible, explain where you are stuck.

[upbeat gust]

so i changed 25 to the 8th to 5 to the 9th and so 18-9 the 9 so my answer was 5 to the 9th but that was wrong

[runic temple]

Ah

so 25=5^2 right

[upbeat gust]

yeah

[runic temple]

So we replace the 25, we get (25)^8=(5^2)^8

Do you know exponent properties?

[upbeat gust]

yeah

[runic temple]

What does (5^2)^8 become?

[upbeat gust]

200

[runic temple]

...no

[upbeat gust]

oh oops

1 sec

[runic temple]

thats ${(5^2)}^8$

[elfin berry]

GarlicBredFries

[upbeat gust]

so 25*25 8 times

[runic temple]

...also no

[upbeat gust]

bruh

OHHHH

wait no

nvm

[runic temple]

Well technically yes but not what i was looking for

${(5^2)}^8=5^x%

${(5^2)}^8=5^x$

[elfin berry]

GarlicBredFries

[runic temple]

Find x

[upbeat gust]

i think its here

[runic temple]

:I

[upbeat gust]

oh wait you mean like solve it

[runic temple]

If youre gonna be annoying ill stop helping

[upbeat gust]

nononononono im sorry mr fries

x=16???

[runic temple]

Yes

so $5^{18}-25^8=5^{18}-5^{16}$

[elfin berry]

GarlicBredFries

[upbeat gust]

yes that makes sense

[runic temple]

For reason that will become apparent immediately after, factor out 5^15

[upbeat gust]

3-1

[runic temple]

Its 5^3-5^1

[upbeat gust]

but you removed the 5s

oh wait nvm

[runic temple]

No

[upbeat gust]

hmmm

so its 5funnysymbolforexp2

right

[runic temple]

No

5^3=what number

[upbeat gust]

125

[runic temple]

And 5^1=?

[upbeat gust]

5

OHHHHHHHHHHHHHHHH

[runic temple]

125-5=

[upbeat gust]

120

tysm mr fries

[runic temple]

So thus, we know $5^{18}-25^8=5^{15}(120)$

[elfin berry]

GarlicBredFries

[upbeat gust]

yes

[runic temple]

Therefore it is divisible by 120

[upbeat gust]

yes!!!!!!!!!!!!

but how do i format it

[runic temple]

5^15

[upbeat gust]

YES!!!!!!

THANKS!!!!!!

:)))))

[runic temple]

Youre welcome

Dont forget to .close

[marsh citrus]

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[echo verge]

so i was trying to solve this, and i put them into a plane grapher thingy and i was confused as to what type of case this is, it looks as follows

[echo verge]

when i tried solving it w the online calculator it gave me this as the answer

but that point does not work

i guess they never intersect all 3

but why does the calculator give me that answer if they don't have a point of intersection

[nova totem]

,w RowReduce[{{4,1,1,2},{5,-3,2,-5},{1,-2,1,3}}]

[elfin berry]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[nova totem]

They do intersect

[echo verge]

oh well when i try to graph this point into geogebra it doesn't look like the point of intersection at all

let me jus try again

the point would be (-16/3, 5, 55/3) right?

[nova totem]

Yeah

That's through Gaussian elimination

[echo verge]

this is where the point is compared to the planes

[echo verge]

i haven't learned this

[nova totem]

Did you graph your planes correctly

[nova totem]

It's just elimination

Like if I told you to solve:

2x - 5y = 7
x + 5y = 4

[echo verge]

oh okok

[echo verge]

yeah i just checked again and they look the same

[nova totem]

Strange

That shouldn't be

[echo verge]

awe man

[nova totem]

Creeper

[marsh citrus]

@echo verge Has your question been resolved?

[echo verge]

oh i found it its because it only showed a portion of the planes so they didnt go far enough to reach that point

.close

[marsh citrus]

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[fresh maple]

.

[marsh citrus]

@fresh maple Has your question been resolved?

[marsh citrus]

@fresh maple Has your question been resolved?

[marsh citrus]

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[sharp sigil]

Is there any math patterns or equation for like cbrt(a)*a = ?

[sharp sigil]

Or is there no pattern?

[marsh citrus]

@sharp sigil Has your question been resolved?

[sharp sigil]

.close

[marsh citrus]

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[gritty heath]

I need help on this

[still temple]

the left side is the x values, and the right side is the y values when plugging in that x value right

so in the function f(x) = ax^2+bx

you can plug in the values for f(x) and x

to get an equation in terms of a and b

so you make two of those equations using different values of x

[gritty heath]

thank you so much man........you dont know how much impact ur creating by helping people on this channel. love you.

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[weary sage]

How would I prove that if 6 divides n, then 2 divides n and 3 divides n

[weary sage]

I'm super new to number theory and proofs honestly (besides high school geometry)

I know that n|m such that m=nk, but like would I basically try to spin it since 2 and 3 are factors of 6?

[still temple]

Hint : use formula dividend = divisor * quotient + remainder

Suppose let that number be 2X