help-0

[keen sonnet]

why is this wrong

[carmine shuttle]

Why f(-10)=33?

f(-10) should be 480.

(I think you substituted into f'(x) instead of f(x))

[keen sonnet]

oh

oops

ill try that

one sec

[carmine shuttle]

ok (tag me if you want me to reply)

[keen sonnet]

kk

i got it ty

[tender dew]

also why last interval has higher minimum than previous 2?

[lone heart]

@keen sonnet Has your question been resolved?

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[keen sonnet]

all of that work is wrong lol ignore it

oops wrong reply @tender dew

[lone heart]

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[weary wyvern]

Wdym by "only complex roots"

@hot bison

Hmm

Ah

[gray isle]

that's just a fancy way of justifying that the argument is positive for all real x

[weary wyvern]

They mean roots with an imaginary part

Real roots are complex

Think about the graph of the parabola

It has no real roots

When is it positive?

[weary wyvern]

(So it never crosses the x axis)

[real gazelle]

Oof, technically if it gives you a function, it should tell you the domain, so that's kind of a bad question

[hot bison]

wait so if it is imaginary

will it then have that domain if the parabola opens up

?

[weary wyvern]

Wdym by imaginary exactly

Not real?

[hot bison]

like imaginary roots

with i in them

not real yeah

or can it have real roots

?

[weary wyvern]

So 5 is not imaginary?

[hot bison]

yeah

[weary wyvern]

Try this

[gray isle]

I'd recommend not putting too much focus on imaginary

or complex

[hot bison]

isnt it dependent on if it opens up or down?

[hot bison]

wait why?

[weary wyvern]

Yes

Does it open up or down?

[hot bison]

say it opens up

what does that mean?

if it opens up and has imaginary roots

[weary wyvern]

Having imaginary roots just means it never crosses the x axis

[gray isle]

because it's only for arguments that are quadratic functions

[weary wyvern]

Because it doesn't have real roots

X intercepts are real roots

[gray isle]

and for these types of problems it's better to focus on the basics

[hot bison]

ok

[hot bison]

thats true

so is it possible to have only imaginary roots, and a parabola that opens up while not having a domain of ?

[weary wyvern]

I'd say forgot about the domain for a sec

Can u visualise the parabola

Given what you know about it

[hot bison]

yes

yeah

[weary wyvern]

What do u know about how it looks

(Other than its shaped like a parabola)

[hot bison]

I know it opens up and extends in the left and right direction

[weary wyvern]

Yes

[hot bison]

And I could determine that it never stops

I guess i'll just do that for now and ask my teacher about that proof later

thanks for the help

.close

[lone heart]

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[alpine sable]

I think the statements are parallel but im not sure.

[weary wyvern]

You mean the lines are parallel?

[gray isle]

those matching arrows indicate that those two lines are parallel

[alpine sable]

no the equations

[gray isle]

what equations

[alpine sable]

So I would set the equations equal correct

i mean terms

sorry

[gray isle]

what terms

[alpine sable]

9

x+4

12

[gray isle]

be as clear as possible by writing the actual equation you think you should be using

[alpine sable]

2x

[gray isle]

is not an equation

[alpine sable]

i can either do

x+4=9

or

2x=12

[gray isle]

no

[tacit arch]

Also those give you different values for x

[alpine sable]

yeah ik

[gray isle]

don't just blindly set random things you equal see to each other

consider what you have, apply the appropriate theorems

[alpine sable]

yeah but i thought they were equal since the parallel lines

[alpine sable]

ok

so what therom should I use here

[gray isle]

consider similar triangles

[alpine sable]

So proportions?

9/x+4=2/12x

?

.close

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[tawdry jolt]

I put 4 in as a dummy answer to see what they said. How the frick did they get this answer for dy/dx?

[tawdry jolt]

Oh wait, they just divided

Gosh darn it

!close

.close

[lone heart]

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[native cloud]

Can anyone help me?

[wary stream]

Did you try anything?

[native cloud]

Not sure how to start

Should I be using chain rules or

[median leaf]

Wait omg, airtoastie are you taking calc 1 rn

[wary stream]

You take the derivative

[native cloud]

No

[median leaf]

What class is that

[native cloud]

AP Calculus BC

[median leaf]

Oh lmao nvm

[wary stream]

It's implicit differentiation

[native cloud]

So substitute dy/dx in y?

No chain rules required?

[wary stream]

You don't substitute

[dry ridge]

y is a function of x.

[native cloud]

Sorry Ben I sorta got lost last time

and forgot

[wary stream]

https://youtube.com/watch?v=xbviQHhU1rA

[native cloud]

How can I see two equations from there?

[native cloud]

How did 100 disappear?

[wary stream]

Because that's a constant

[native cloud]

Oh right

All y parameters become 2* (^n-1) and gets dy/dx multiplied?

[wary stream]

It's the same idea as taking the derivative of x^2

[native cloud]

.

So for this one I just do

6y * (dy/dx) + 2x - 1 = 0?

[wary stream]

Close

[trim axle]

Still need help?

[wary stream]

Last term, product rule

[trim axle]

@wary stream is correct

[native cloud]

?

Confusion

[trim axle]

Product tule

Rule#

In the last term

I’ll be

-y-x(dy/dx)

[wary stream]

My bad, I meant product rule

[trim axle]

Apply product rule between x and y

[native cloud]

Only for this one? 6y * (dy/dx)

[wary stream]

No

You apply product rule to the last term

[native cloud]

wdym?

I'm confused

[trim axle]

Ok

Do you know what’s the product rule of derivatives?

[wary stream]

Do you know product rule?

[native cloud]

Yes

[wary stream]

Because that's x * y

Where it's a product

Hence product rule

[native cloud]

x' * y + y' * x

[wary stream]

What's the derivative of x?

[native cloud]

1

[trim axle]

And what’s the derivative of y?

[native cloud]

1

[wary stream]

No

[native cloud]

uh

[trim axle]

dy/dx

[native cloud]

okay

[trim axle]

We’re solving for the implicit equation

[native cloud]

Then the equation would be

6y * (dy/dx) + 2x - 2(dy/dx) = 0

Right?

[trim axle]

No

😭

-(y+x*dy/dx)

[native cloud]

1 * y + dy/dx * x

[trim axle]

And then you simplify and solve for dy/dx

Mmm will something visual help you?

[native cloud]

Yes please

[wary stream]

I suggest watching that video

[native cloud]

But wait I think I'm messing the product rule

[native cloud]

Okay will do

[native cloud]

1 + y + x * dy/dx

[wary stream]

Because of you notice the video screenshot image, it has an example with 4xy which apply product rule

[native cloud]

I'll be back after watching

[trim axle]

Hope this helps

[native cloud]

What's this one?

Okay then starting over

[trim axle]

💀

[native cloud]

It would be

[trim axle]

That’s means implies

[wary stream]

That's an arrow

[native cloud]

Oh okay

6y * (dy/dx) + 2x - ((1 * y) + (x * dy/dx) = 0

Like this?

[trim axle]

Yeah

Now solve for dy/dx

👍🏽

[wary stream]

Pretty much get everything that's not dy/dx on one side, factor and get dy/dx alone

[native cloud]

Just algebra?

[wary stream]

The video should show that too

[trim axle]

Yes

[wary stream]

Yes

[trim axle]

Algebra is king

[native cloud]

xD

6yD + (Dx) = - 2x + y

d/dx(6y + x) = - 2x + y

[trim axle]

Mmm

Now 6y+x will do the invert of multiplication to the other side

And you are done

[native cloud]

dy/dx = (- 2x + y)/(6y + x)

:)?

[trim axle]

6y-x

You didn’t distribute the minus sign correctly

[native cloud]

Oh

(- 2x + y)/(6y - x)

So this is the answer?

[trim axle]

One of the possible ones

You can try to simplify a little bit more

[native cloud]

Why is it "one"?

[trim axle]

But if you are in high school that’s good enough

[native cloud]

Okie thanks 🙂

.close

[lone heart]

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[native cloud]

.reopen

[lone heart]

✅

[native cloud]

Sorry had another question

For this one

I do the same like the above and sub 2 in x and 4 in y, right?

[wary stream]

Yes

[native cloud]

Okay thanks ❤️

.close

[lone heart]

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[ancient agate]

how do I fill this out, I understand if I have both 1380 and the number next to it

I tried writing out euclidean theorm with unknown variables but I dont think its possible that way

[lone heart]

@ancient agate Has your question been resolved?

[ancient agate]

<@&286206848099549185>

[lone heart]

@ancient agate Has your question been resolved?

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[storm tusk]

So I've tried long division which is what my professor suggested but I don't really know how I'm supposed to move forward with that as I end up with something I don't know how to really deal with

[harsh girder]

$$2x+y=5t+1$$

[ocean seal]

秋水

[harsh girder]

$t = \frac{2x+y-1}{5}$, then you can eliminate $t$

[ocean seal]

秋水

[storm tusk]

I see...I don't know why he spent on the whole lesson on long division and not this

Thank you!

.close

[lone heart]

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[craggy steeple]

hry

[craggy steeple]

hey

for the first fraction

which side is the negative on

numerator or denominator

[median oar]

doesn't matter

it's all the same

[craggy steeple]

oh

so

it can be

-x-1/6

?

[median oar]

$-\frac{x+1}{6}=\frac{-x-1}{6}=\frac{x+1}{-6}$

[ocean seal]

Frosst

[craggy steeple]

oh

then i do x6 to both side

oh ok

thanks

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[lone heart]

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[median oar]

multiply by 12 might be better

[lone heart]

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[craggy steeple]

hey

[craggy steeple]

its me again

pls help

[median oar]

ok

[craggy steeple]

it says solve each porblem

algebraicaly

[median oar]

yeah

ok so let's say he has x dimes

how many quarters does he have?

[craggy steeple]

x+25?

pp[s

o

no

x-25

[median oar]

25?!

[craggy steeple]

omg

[median oar]

are we reading the same question

[craggy steeple]

im stupid

20 20

ims orry

[median oar]

ok

how much is a dime worth

[craggy steeple]

10 cent

[median oar]

idk i dont live in the US

and quarters are 0.25?

[craggy steeple]

uea

ya

[median oar]

ok so

if he has x dimes

and x-20 quarters

how much money is that in total

[craggy steeple]

x+x-20=5.50?

[median oar]

that's if each coin was worth 1 dollar

[craggy steeple]

oh.

0.25x+10x-20=5.50?

0.10*

[median oar]

that is so not right

x is dimes

x-20 is quarters

[craggy steeple]

oh

0.10x+0.25x-20=5.50

[median oar]

you have (x-20) quarters

[craggy steeple]

yes

[median oar]

brackets very important

[craggy steeple]

oh

0.10x+(0.25x-20)=5.50?

[median oar]

that's the same

what you're writing means that you have x dimes

x quarters

and then you're missing 20 bucks

[craggy steeple]

o

erm

im stuck

idk what to do

is the 0.1x part right

tho

[median oar]

how did you go from "x dimes is equal to 0.1x dollars"

[craggy steeple]

oh

[median oar]

apply the same logic to "(x-20) quarters is equal to...?"

[craggy steeple]

uhm

x-20 is

x-20

so

its

x dimes

-20 dollars

?

[median oar]

let's say i have 10 quarters

[craggy steeple]

right

[median oar]

how much is 10 quarters worth

[craggy steeple]

uhm

like

2.50

[median oar]

right

according to your expression

10 quarters * 0.25 - 20

i have -17.5 dollars

with 10 quarters

[craggy steeple]

oh..

so the -20 part isnt correct

[median oar]

well ok that's a bad example

say i have 40 dimes

and 40 - 20 quarters

now the dimes is worth 0.1 * 40 dollars so 4 dollars

[craggy steeple]

40 dimes

is

4 dollars

[median oar]

now if i have 20 less quarters than i have dimes

[craggy steeple]

oHH

[median oar]

how many quarters do i have

[craggy steeple]

20

quarters

[median oar]

right

and how much is 20 quarters worth

[craggy steeple]

uh

like

5

bucks

[median oar]

notice how we MINUS before we multiply by the value of the coin

when u write 0.25x - 20

you MULTIPLIED before you minus'd

[craggy steeple]

O

SO

0.25(x-20)?

[median oar]

yep

[craggy steeple]

OHHH

THANKS

SO FINAL EQUATION IS LIKE

[median oar]

so instead of 0.25x+10x-20=5.50?

what should you have

[craggy steeple]

uh

idk

u put

it into

[median oar]

remember the bracket

[craggy steeple]

parentheses

so u subtract before you multiply

[median oar]

just like this

[craggy steeple]

so 0.25x +10(x-20)

[median oar]

is equal to?

[craggy steeple]

5.50

[median oar]

right

solve for x

[craggy steeple]

OHHH

OK THANKS BRO

FR i appreciate it

.close

[lone heart]

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[median oar]

now solve for x solves for how many dimes he has

[craggy steeple]

i love this server

[median oar]

you need to also find the number of quarters

[craggy steeple]

oh

uhm

so i have another question

uh forst

frot

r u still there

.reopen

[lone heart]

✅

[median oar]

yes im still here

[craggy steeple]

ok

so if i solve for x

[median oar]

#❓how-to-get-help

[craggy steeple]

0.25x+10x-200??

sorry

[median oar]

what

[craggy steeple]

dawg

im kinda

calculator

[median oar]

#❓how-to-get-help

[craggy steeple]

this is my help question sapce

dawg

[median oar]

dont spam other people's channel

[craggy steeple]

u gotta go to the available math

frost i think hes trolling

bro said he was african americcan and didnt get full education

and he got 69 in his name

[median oar]

just ignore him

[craggy steeple]

ok

so

10(x-20)

u distribute 10 to x and 10 to negative 20

right>

soi that would be

[median oar]

each quarter is worth 10 bucks?

[craggy steeple]

oh

[median oar]

<@&268886789983436800>

[craggy steeple]

no each quarter is not 10 bucks

but

oh i messed up

shouldnt it be

0.1x+0.25(x-20)?

[median oar]

ty

[craggy steeple]

bc 0.1 is the dime

[median oar]

right

[craggy steeple]

and 0.25 is the quarter

[median oar]

right

[craggy steeple]

so u distrivute 0.25 with x

and - 20

[median oar]

yep

[craggy steeple]

ohh

so x-5?

oops

-.25x-5

0.25x-5

[median oar]

yep

[craggy steeple]

so

0.1x+0.25x-5

so 0.35x-5=5.50?

[median oar]

yep

[craggy steeple]

iggg'

so

0.35x=0.50?

[median oar]

5.5 + 5 = 0.5?

[craggy steeple]

oops

oops

yea

6

no

10.5

0.35x=10.5

[median oar]

what is x

[craggy steeple]

dimes

[median oar]

yeah but what is the value

[craggy steeple]

0.10

[median oar]

no that's the value of dimes

what is the value of x

x is the number of dimes

[craggy steeple]

idk

erm

my lights just turned off

and i think im having power outage

uhh

i cant see the problem anymore

im just going to

yk

like

sleep

.close

[lone heart]

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[craggy steeple]

thanks for helping me tho

but im rlly stupid

so

[lone heart]

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[nimble fiber]

Is this a valid proof to show that the sum of two logs is the product

[nimble fiber]

this rule^

[echo raptor]

yes

[nimble fiber]

ok ty

[echo raptor]

np

[nimble fiber]

.close

[lone heart]

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[magic monolith]

Hello! Could anyone help explain to me why this is correct? I don't fully understand the question

[tight locust]

Z5 is the set of integers mod 5

Look at n^2

[magic monolith]

yep

do you just start with calculating n^2 + 2n^3 for n=0,1,2,3,4 ?

[tight locust]

n^2(1+2n)

[vale wigeon]

the calculations seem not to be so bad.

[magic monolith]

yep, so i got 0, 3, 20, 63, 144 but im not sure what the requirements are

that they cannot be in Z5

[vale wigeon]

you were supposed to calculate their remainders mod 5 lol

[magic monolith]

ahh mb! thanks

then it would be 0, 3, 0, 3, 4 ?

i still don't see anything that sets n=1 and n=2 apart from the rest

[lone heart]

@magic monolith Has your question been resolved?

[lone heart]

@magic monolith Has your question been resolved?

[tight locust]

what numbers in Z5 aren't in this list

[magic monolith]

AH got uu 🙂

thank you so much!!! 💗 have a good day

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[alpine sable]

Why there are two different formulas for vector projection?

[alpine sable]

How to know which formula is suitable?

<@&286206848099549185>

[tight locust]

Basically there are two different projections going on here

The scalar projection and the vector projection

Take the scalar projection and multiply it by the unit vector in the direction of b

And you get the vector projection

Typically the projection means the vector projection though

@alpine sable

[alpine sable]

I see.

Thank you @tight locust 🙂

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[lone heart]

@mortal river Has your question been resolved?

[harsh girder]

the two triangles are similar

so $\angle F = \angle C$, $\frac{DF}{FE} = \frac{AC}{CB}$

[ocean seal]

秋水

[mortal river]

so x/26=x/19?

[harsh girder]

why AC is x?

$AC = \sqrt{27^2+19^2}$

[ocean seal]

秋水

[mortal river]

oh yeah

so ac is 33?

[harsh girder]

,w sqrt(27^2+19^2)

[ocean seal]

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Requested by 秋水#5244

[mortal river]

yh

which leaves DF=45,157

[harsh girder]

,w sqrt(27^2+19^2)*26/19

[ocean seal]

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[mortal river]

should it not be .. 26/19=x/33?

x=DF

or am i thinking of something else?

[harsh girder]

yes, you are correct, more accurate is 33.015148...

[mortal river]

what?

[harsh girder]

I mean this

[mortal river]

but should it not be this?

[harsh girder]

yes

I just mean AC = 33.01548......, if you use 33, it's okay

[mortal river]

oh alright

[mortal river]

so this is the same thing, just a different way to calculate?

[harsh girder]

you mean how to get AC?

[mortal river]

no sorry i mean this one

[harsh girder]

it's the solution of the equation

[mortal river]

i did the solution like this 26/19=x/33

[harsh girder]

yes, the solution is x =33*26/19

same as in the picture

[mortal river]

nvm

im just overcomplicating things

thanks for the help 秋水

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[old valley]

hi i've been stuck on this for a while :)

idk how to do it

[vale wigeon]

got a diagram?

[carmine shuttle]

@old valley

[wary stream]

No one was asking you to draw it for them. Ann was asking the OP if they had a diagram to see if they understood what the problem was asking

[carmine shuttle]

OK, diagram deleted

(I have finished drawing before Ann asking for it 😅 )

[vale wigeon]

@old valley still there?

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@old valley Has your question been resolved?

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[dim epoch]

ok so i got the question: a bikeshop has 56 bikes for 99 people. how many of them are tandems and how many normal bikes. i have 0 clue where to start without just guessing

[mortal trellis]

let n be the number of normal bikes and t be the number of tandems

can you set up an equation involving these two variables?

[dim epoch]

idk ofc n+t=56

been a long time since ive done any math whatsoever

[mortal trellis]

good that's one

now a different one using the amount of people?

[dim epoch]

yeah thats where i have no clue

n+2t=99?

[mortal trellis]

if you have 5 normal bikes and 6 tandems, how many people can use those

[dim epoch]

17

[mortal trellis]

yes

so that gives n+2t=99 like you said

now you have two equations in two variables

what happens if you subtract the first equation from the second equation

so subtract n+t=56 from n+2t=99

[dim epoch]

is that just t=43?

[mortal trellis]

yup

[dim epoch]

omg thanks so much :9

i get it now :))

[lone heart]

@dim epoch Has your question been resolved?

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[alpine sable]

Plzz anyone can help me to solve it

[native granite]

Do you know the definition of intercept ?

Of a line

[alpine sable]

Y=mx+b

[alpine sable]

I have applied it but wouldn't get any given answer

[sacred fiber]

what do you think the 'm' and 'b' mean in that equation ?

[alpine sable]

Ys

I think so

But I'm not sure

[sacred fiber]

did you learn what the m stands for ?

[alpine sable]

Ys

Slope of line

[sacred fiber]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/a/slope-review

[alpine sable]

I k

[alpine sable]

I'm just stuck in this question

[sacred fiber]

That article has a section "Slope from two points", which is exactly the kind of question you need to anwser

[alpine sable]

Slope is already given in question statement

[native granite]

Yep, so intercept is the only thing we miss here

[alpine sable]

Yeh

[native granite]

In fact, one possible definition of intercept is : the value at x=0

[sacred fiber]

there are two slopes in the anwers a positive an negative, which is the correct one ?

[alpine sable]

No idea

That's y I get confused and miss it

[sacred fiber]

if you would draw these two points with a line through them, would the line rise (increase) or fall (decrease) ?

[wary stream]

Well, the given slope, is it positive or negative?

[alpine sable]

No Idea😶

[wary stream]

What's the value of the given slope?

[alpine sable]

5/4

[wary stream]

Is that number positive or negative?

[alpine sable]

Obviously positive

[wary stream]

So then is the slope positive or negative?

[alpine sable]

Positive

[wary stream]

And in the equation y = mx + b, where m is the slope and b is the y intercept, what is the y intercept?

[alpine sable]

That's was the question which I was asking about 15 mints😐

[wary stream]

The y intercept is where it crosses the y axis, if it crosses the y axis, what is the value of x?

[alpine sable]

Can you provide me it's proper solution?? if possible

[wary stream]

I already know the answer. I'm trying to teach you

What is the x coordinate if it crosses the y axis?

[alpine sable]

don't know

[wary stream]

Do you know what the xy coordinate plane is?

[alpine sable]

Ys

[wary stream]

So if it's a y intercept, it crosses the y axis, the vertical line, in the xy coordinate plane

What is the value of x along that vertical line?

[alpine sable]

0??

[wary stream]

Yes

So the y intercept has an x coordinate of 0

You are given some coordinates, use the above stated info, and tell me what the y intercept is

[alpine sable]

A??

[wary stream]

What do you mean A?

[alpine sable]

Option a

[wary stream]

I'm asking you to identify the value of the y intercept

[alpine sable]

In question statement

Y-y'=m(x-x')

[wary stream]

You are given some coordinates, as stated the y intercept has an x coordinate of 0, what given coordinate pair has a 0 for x?

[alpine sable]

(0,-5)

[wary stream]

So the y intercept is?

[alpine sable]

Y-5=5/4x
y=5/4x + 5

[wary stream]

No

Stop deviating from my original question

[wary stream]

This is the coordinates of the y intercept, what is the value of the y intercept?

[alpine sable]

?

[wary stream]

What is the value of the y intercept?

It means what it means

State the value of the y intercept

[alpine sable]

Idk

[wary stream]

The y coordinate

Here is my suggestion
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:intro-to-slope-intercept-form/v/slope-intercept-form

[sacred fiber]

y intercept, is the value for y where it crosses the y-axis (x = 0)

[wary stream]

Since you already declared that the slope is positive, you need to determine what the y intercept is and apply it to y = mx + b

Someone else can help you now. I'm busy now

[sacred fiber]

I think it would really help if you to grab a pen and paper, draw those two points and a line through them. It's so much easier to understand when you can see what the question actual means

[alpine sable]

Okay

Thank you so much

.close

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[carmine shuttle]

You have basically asked for similar questions for many times...Could you explain how do you evaluate for Q1 and Q2?

and let me spot the error. Thanks.

[lone heart]

@acoustic plover Has your question been resolved?

[turbid sigil]

@acoustic plover 1) is 6^5, do you understand why?

[old valley]

Shit my bad I went to eat dinner

[vale wigeon]

we will have to continue this in a new help channel or #geometry-and-trigonometry

[carmine shuttle]

@acoustic plover Don't worry. Let's take step by step.

First of all, how many outcomes are possible for 1 dice?

Yes, how about 2 dice?

Yes, 6^4.

Do you know why now?

Could you explain why?

First of all, count what kinds of number in 3 dice and 1 dice can be resulted.
like
(1, 1, 1, 2), (1, 1, 1, 3), (1, 1, 1, 4), ...
basically you are choosing 2 different numbers.

For each set of combination, there can be 4! of arrangement of dice, if each dice is distinguishable.

no, it is not directly 4!.

(but I don't think that the answer is 120)

should be (36-6) x 4!

OK, I got the it...

should be (36-6) x 4 = 120
The order of dice is distinugishable.

The reason of (36-6) is to have choose 2 numbers, 1 for repeated value and 1 for non-repeated value.
The reason of 4 is that you can have 4 arrangements for same set of numbers, i.e. (y, x, x, x), (x, y, x, x), (x, x, y, x), (x, x, x, y)

You still need to choose for 2 numbers, but you would have 7 arrangements instead of 4.

[north adder]

@acoustic plover

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@acoustic plover Has your question been resolved?

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[real vessel]

Hi, I rlly need help with my math project. I am required to use 6 different graphs to form an image, one of the graphs im using is the modulus function, but i have not learnt anything about it. Can anyone kindly explain the standard formula + what each variable does?

[lime bobcat]

$|x|=\begin{cases}-x & \text{if }x<0\
x & \text{if }x\geq 0\end{cases}$

[ocean seal]

Categorist

[real vessel]

So how do i make the graph like narrower?

[crisp pine]

To make it narrower, you could increase the gradient

so |2x| for example

[real vessel]

so |x|=x?

[crisp pine]

What sorry?

y = |2x| for example

[real vessel]

according to this

[lime bobcat]

How can you say this looking at what I wrote up there?

Did I write |x|=x?

No

[real vessel]

Relax bruh i dont even know whats going on

[crisp pine]

Basically, if the thing inside ur modulus is negative, it becomes positive

so |5| = 5

|-5| = 5

|0| = 0

|2(5)| = 10

[real vessel]

Ohhh i see

[crisp pine]

|(2(-5)| = 10

[real vessel]

Is there anyway to adjust its position?

[crisp pine]

Yes, just like a normal graph

To shift it C to the left, do |x+c|

(hence to shift it to the right to |x-C|)

To shift it up by C, do |x|+C

[real vessel]

so up and down i do the same for y?

ohh

[crisp pine]

Yep 🙂

[real vessel]

Thanks!!

[crisp pine]

Np

[real vessel]

.close

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[undone iris]

im getting math error

:/

[frigid rune]

math error when doing what?

[abstract fractal]

You really don't even need to perform any math here. A knowledge of what the cross product returns and how it relates to the crossed vectors is enough

[frigid rune]

^^

[undone iris]

oh damn

so just i and j

that means x and y values only?

so its 90?

[abstract fractal]

It would be 90 regardless of the vectors

AxB produces a vector perpendicular to both A and B

[undone iris]

always?

or just in this case

[abstract fractal]

Always

[undone iris]

how?

[abstract fractal]

In some sense, that's part of the definition of cross product

[undone iris]

so dot product makes 2 vectors colinear and cross products makes 2 vectors orthogonal?

[abstract fractal]

Dot product doesn't produce a vector

[undone iris]

i mean the magnitude

[abstract fractal]

"The cross product a × b is defined as a vector c that is perpendicular to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span."

How can a scalar be collinear to vectors

[undone iris]

hmmmmm

[abstract fractal]

How can scalar numbers be collinear in general. I mean, I guess all real numbers are collinear, cuz they all lie on the number line

[undone iris]

hmmmmm

also isnt this 6W?

[abstract fractal]

Show your work

[undone iris]

$$\vec F \cdot \vec S = (3 \cdot 2) + (4 \cdot 1) + (1 \cdot 2)$$
$$\vec F \cdot \vec S = 6 + 4 + 2 = 12 =\text{work}$$
$$\text{power}=\frac{\text{work}}{\text{time}}$$
$$\text{power}=\frac{12}{2}=6W$$

[ocean seal]

Invisible

[undone iris]

yes this

?

[abstract fractal]

You're forgetting to consider that F and S aren't pointing the same way

[undone iris]

but i dont know their directions right

[abstract fractal]

You have the vectors in component form

That is the direction

[undone iris]

but dot product doesnt involve a direction right

where am i going wrong

[abstract fractal]

Of course dot product involves direction. The dot product of two vectors depends on the angle between them

[undone iris]

but doesnt it give just the magnitude

and also you can multiply 2 vectors in component form without knowing the angle

[abstract fractal]

The answer is a scalar, but the answer of that scalar depends on what direction the vectors are facing relative to each other

[undone iris]

so where did i go wrong?

[abstract fractal]

You can also find the roots of a quadratic without graphically seeing where the graph crosses y = 0. Doesn't mean the roots aren't where the graph crosses y = 0

Gimme a sec

Nope, I'm mistaken

Well, I'm not mistaken, the dot product depends on direction

But so does the work done

The work is indeed 12 J

So I don't know why the work isn't 6 W

[undone iris]

hmmmmm alr

thanks

just wanted to confirm

[abstract fractal]

The problem was I was mistemembering the formula for work as F • S * cos θ

But it's actually |F| * |S| * cos θ

Which is identical to F • S

[undone iris]

i see, no problem

.close

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[shy wasp]

If F represents the antiderivative of a function

[shy wasp]

Why is the antiderivative of f(-x), -F(-x) and not F(-x)

[dry ridge]

Chain rule?

the derivative of -x is -1.

[shy wasp]

Yes I get that, so do U have to divide by that?

I just don't understand why you have to include that, wouldn't F(-x) be enough to write as it represents the antiderivate of that function

[dry ridge]

you can also u-sub when integrating f(-x).

[abstract fractal]

The derivative of F(-x) is not f(-x), so it's not the antiderivative of f(-x)

[carmine oar]

first
the antiderivative of f(x) with respect to x is F(x)
the antiderivative of f(-x) with respect to -x is F(-x)

[shy wasp]

This is what I mean, so F(-x) represents the antiderivate with respect to -x

[carmine oar]

of f(-x)

sorry typo

yes

[shy wasp]

Ok so

[carmine oar]

now your job is to turn with respect to x into with respect to -x

[shy wasp]

If I had a function f(-x) and I wanted to find the antiderivate with respect to x

I would have to divide F(-x) by -1 because F(-x) is respect to -x

[carmine oar]

I would represent it like this

[shy wasp]

Ok a follow up question

[carmine oar]

suppose x' = -x (not to confuse us)

$$ \frac{d x'}{dx} = -1$$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[carmine oar]

$$ d x' = - dx$$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[carmine oar]

and so

$$ d(-x) = - dx$$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[carmine oar]

yeah so that's how I would do it

[shy wasp]

Ok

I get it, just got confused when F(-x) is the antiderivate with respect to -x and not just x

[carmine oar]

this takes time to digest

[shy wasp]

So for f(g(X)) the antiderivate with respect to x would be F(g(X)) divided by g'(X)

[carmine oar]

let me see

[shy wasp]

Ok

[carmine oar]

,tex $$ let u = g(x) $$\ $$ \frac{du}{dx} = g'(x)$$\ $$dx = \frac{du}{g'(x)}$$ \ $$dx = \frac{d(g(x)}{g'(x)}$$

[carmine oar]

so yes

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[shy wasp]

Alright cheers

Thanks a lot

[carmine oar]

np

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@shy wasp Has your question been resolved?

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[thick lynx]

How do you know with what to start a proof?

[thick lynx]

For example

How do you know if you should start with $a = a$ or $b = b$ or $log_a(b) = x$ or something else?

[ocean seal]

Kepe

[minor needle]

maybe give us more concept

like question

[mortal trellis]

experience and trial and error

you can't expect to always know how to start a proof

[thick lynx]

oh

[dry ridge]

remember log_a(b) = m iff a^m = b.

you can start there.

[thick lynx]

so basically if someone asks somebody to prove something and he right away does it perfectly, it's from memory?

[mortal trellis]

either from memory or from experience

or getting lucky

[thick lynx]

how would you know from experience with what to start?

similar proofs?

[mortal trellis]

you just kinda get to know how to start certain stuff

yeah similar proofs and such

[dry ridge]

also a lot of proof involves working out the definition involved.

[gray isle]

start from basic definitions

and/or axioms

[minor needle]

also realize that there is no only one way, called "perfect" way to prove something, you can have other start and also get correct solution

[thick lynx]

if I asked you to prove $log_a(b^x) = x * log_a(b)$, you probably wouldn't start with that though

[ocean seal]

Kepe

[thick lynx]

so it varies for every proof with what to start

[dry ridge]

I would start with it to see what I got then try something else if its not working.

[thick lynx]

oh, alr

so trial and error like Denascite said

[mortal trellis]

to show that log_a(b^x)= (something) you would probably start with a^(something) and see if that is the same as b^x

just from the definition of log

[thick lynx]

alr, thx

btw, is a problem that says "show that a = b" the same as "prove that a = b"?

[mortal trellis]

yeah

[thick lynx]

alr

.close

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[devout lantern]

Id like to get help is there any formula how to compute it?

[mental jungle]

What are you looking to compute exactly?

@devout lantern

[lone heart]

@devout lantern Has your question been resolved?

[devout lantern]

if there exist some formula for that that I can compute it without writing program

[mental jungle]

what is "it"

[placid zinc]

Number of possible locks in which a key can fit?

[fervent kelp]

#help-2

[devout lantern]

for example I give you K = 2 and L = 3

and compute it

with some formula or sth like that

[mental jungle]

what do you want to compute? The number of possible valid locks?

You haven't explained what you want to compute

[placid zinc]

I guess this is also "number of sequences of length K where adjacent numbers differ by at most one unit, and are capped between 1-L"

Right?

[mental jungle]

seems to be the most likely question

@devout lantern are you familiar with Catalan numbers?

wait, this is not a Catalan number problem, my bad

[placid zinc]

Kind of. I see what you were thinking Espio. I wonder if we can fix it?

[mental jungle]

I think it's too far from Catalan

you can start at any height and you dont have to end at the same height as where you started

so the whole recursive definition that gives you the Catalan numbers would not apply

[placid zinc]

Interesting problem, it might be difficult. Are you sure that a known way to do this exists @devout lantern ?

[devout lantern]

for example K = 2 and L = 3, then it should be 111, 112, 121, 122, 211, 212, 221,222 , if K = 3 and L = 2 then 11, 12, 21, 22, 23, 32, 33,

and for example if I gave you K = k and L = l if there exist any formula for this to compute it without writing program to do that

[mental jungle]

compute the number?

you want a formula that takes K and L and give you the number of valid locks?

so if I plug in K=2 and L=3 into the formula I should get 8?

[devout lantern]

yes, we want to compute number of possible keys with those parameters

[devout lantern]

Im not sure thats why Im asking here

[mental jungle]

Seems difficult

I think Catalan numbers could actually be involved

hmm

if you want to calculate the number of paths of length K that start at a height of 1 and never go below one, you could get a recursive formula using the Catalan numbers

but that's like half of one specific term in a big sum you'd want to find a closed form for

oh wait, you don't have to go up or down, you can go straight ...

I think this is a little beyond my capabilities

[devout lantern]

[lone heart]

@devout lantern Has your question been resolved?

[lone heart]

@devout lantern Has your question been resolved?

[lone heart]

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[verbal juniper]

Could someone teach me about integrals? (More specifically derivatives and derivatives of integrals)

[verbal juniper]

I know what an integral does, but not how to do it by hand

[swift shore]

That’s like a whole month of lectures lol

I would recommend Khan Academy’s ap calculus sequence

[verbal juniper]

Hm

one moment

alright

thanks!

.close

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[obtuse hatch]

https://cdn.discordapp.com/attachments/915059486484496384/992048781388414996/SPOILER_unknown.png

[obtuse hatch]

dont understand this explanation

the g(x) in the first one