help-39

[green dew]

thats it

[candid solar]

made it look more complicated than it seemed

tysm

[green dew]

stopping here was enough tho

but

yk

spice it up

[candid solar]

yea my teacher wanted to be "simplify simplify"

like till i cant simplify no more

[green dew]

oh

well u did answer the question at that point

but

u can go hams on it even more

if ur teacher likes that

[candid solar]

i think she might be good on that one

[green dew]

oki

[candid solar]

tysm again

[green dew]

ofc bud

[candid solar]

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[naive dirge]

Bbbbbbbbbb

[naive dirge]

Bbbbbbbbbb

I’m baffled, astonished, and overwhelmed by the solution on the site

He

He

Expanded that stuff

It feels like I being tasered

[versed mica]

why don’t you just take a picture of the problem

no need for a video

[naive dirge]

But I’m trying to show the solution

[versed mica]

i think we can get the solution

what did you try

[naive dirge]

Does we have to expand it

Couldn’t we see the solution of the equation in that form

[versed mica]

do*

[naive dirge]

Thank you

[versed mica]

and yes you ought to do that but first cancel the x+1

[naive dirge]

I see

[versed mica]

but make sure you remember that x≠-1

[naive dirge]

It is solved, thank you knief

You are the kindest and smartest yet most charming person I have ever seen

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[grizzled trench]

can someone explain how they know that?

[blissful cloak]

are you familiar with p/q?

[grizzled trench]

i'm aware that p is the numerator and q is the denominator if that's what you mean but otherwise no

[blissful cloak]

take all the factors of the first coefficient (p), and of the trailing coefficient (q), take all the plus-minus cases and check to see if the polynomial returns a 0 for any of these

if it does then it's gauranteed to be a factor of the polynomial you tested

in this cases our "rational roots" they're so called are -1 and 1

as it turns out if you plug 1 into the denominator polynomial

it returns 0

so we're gauranteed for x-1 to be a factor of Q(x)

[grizzled trench]

what is first coefficient and trailing coefficient supposed to mean here?

[blissful cloak]

in your denominator the leading coefficient is in front of the x^3

and the trailing is the +1

[grizzled trench]

ok i think i got it

in any rational function check the denominator polynomial's highest and lowest exponent term's coefficients and plug that number into the denominator's polynomial and if it equals 0 that number is a root

and in this case it was just 1 but if it was 5x^3 and plugging 5 equalled 0 (x-5) would be a factor

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[naive dirge]

I can’t see how he get c’(t)

<@&286206848099549185>

[midnight haven]

Umm

U want an equation for c, then differentiate c with respect to time

So c=sqrt(a^2+b^2)

A is a function of time, b is not

So c’=df/du * du/dx

u = a^2 +b^2

du/dx= 2a (mistake starts here)

Df/du=d/du sqrt(u)

=-1/sqrt(u)

[lime river]

Got*

[midnight haven]

So c’ =-2a/sqrt(a^2+b^2)

c’(t)=-2*24/sqrt(24^2+10^2) (the sub here is wrong)

W8 what

[lime river]

Looks like u have done some mistake
While differentiating
b² + c² = a²
2c × c' = 2a × a'
So c ' = a×a'/c
c' = 24 × 13/25

[midnight haven]

What mistake?

I use c to be the hypotenuse

[lime river]

Yea so ur differentiating wrt to time so a' will also come

[midnight haven]

Yep

[pearl pond]

@naive dirge Has your question been resolved?

[midnight haven]

I see where I missed up

[pearl pond]

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[midnight haven]

my channel was deleted guy

[acoustic path]

take powers of A

[midnight haven]

ok

thanks

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[glass remnant]

why is this 3?

[glass remnant]

if youyr plugging it in

would you not get 0 over one

[sonic patrol]

so first of all, $\sin 0 = 0$

[jolly parrot]

Pseudonium

[sonic patrol]

so “plugging in 0” would get ya $\frac 0 0$

[jolly parrot]

Pseudonium

[sonic patrol]

ofc the way you actually do the limit is not exactly by plugging in 0

what you want to notice is that, for $x$ small, $\sin x \approx x$

[jolly parrot]

Pseudonium

[glass remnant]

something like this right

[sonic patrol]

mhm

so what you can do is take the constant “3” out of the limit

so $\lim_{x \to 0} \frac{3 x}{\sin x} = 3 \times \lim_{x \to 0 } \frac{x}{\sin x}$

[jolly parrot]

Pseudonium

[glass remnant]

ah

i see

thank you!

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[prisma vortex]

Ik this isnt maths but logic is a part of maths i think so i was wondering if anybody could help me with this :>

[autumn fossil]

Each of those columns basically gives you order in which the fossils appeared

[dapper kraken]

new pfp!

[acoustic path]

notice that if a layer appeared anywhere except for the top layer, then whichever layer(s) above it would be younger

therefore, you can conclude that you want to look the column with a layer that uniquely appears at the top

[autumn fossil]

A < B < C < D
F < E < A < D
G <A < B < C
E < G < A < B

You could even transform it into this, and now it's a math problem

[acoustic path]

that is fully unnecessary

[autumn fossil]

Idk the names of the fossils, so I just assigned letters to them, so that it's easier to refer to them

[pearl pond]

@prisma vortex Has your question been resolved?

[noble heath]

So whats the oldest, is it the jalapeno

Or tower of pis

Pisa

[pearl pond]

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[zenith basin]

can someone please help me with this

[pearl pond]

@zenith basin Has your question been resolved?

[zenith basin]

<@&286206848099549185>

[midnight haven]

Have you tried calculating its derivative?

[zenith basin]

thats a good idea

imma try that

[autumn fossil]

btw it might be easier to first multiply it by 2 + cos(x)

[gray heart]

which is the solution?

[zenith basin]

This what I got

[zenith basin]

they dont give solutions for proof questions

@midnight haven @autumn fossil im not really sure how to prove thats always negative

[midnight haven]

It's not always negative

[zenith basin]

isn't that what you want though

to show its always gonna be decreasing

[autumn fossil]

,w d/dx (x(2+cos(x)) - 3sin(x)))

[jolly parrot]

Results provided by WolframAlpha

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

Requested by methisalwaysright

[autumn fossil]

this looks easier to work with

[autumn fossil]

try starting by rearranging it a bit

[zenith basin]

oh damn

[autumn fossil]

x(2+cos(x)) > 3sin(x)

x(2+cos(x)) - 3sin(x) > 0

now differentiate

[autumn fossil]

and you should get this

maybe some taylor series stuff could work there

[zenith basin]

ohh

that makes sense

[zenith basin]

ngl bro i have no clue what that is

[gray heart]

i think it can be solved without derivatives, but i m not sure

[autumn fossil]

do you have the solution?

I actually don't have many ideas outside of taylor series

[gray heart]

i found that 0<x< pi, but i'm probably wrong

[autumn fossil]

how?

it should work for all x > 0

the larger x is, the larger the difference will be

for sufficiently large x, this is actually trivial

[gray heart]

I' m in high school and i don' know calculus yet so i solved that as a goniometry inequality

[autumn fossil]

How?

[gray heart]

i think I did something wrong, I need to check again all the passages

which solution do you expect?

[pearl pond]

@zenith basin Has your question been resolved?

[zenith basin]

Wdym

[gray heart]

in this exercise you need to find a solution or you need to prove something?

i' m not an english native speaker, so sometimes i don't understand

[pearl pond]

@zenith basin Has your question been resolved?

[zenith basin]

You need to prove the inequality

[pearl pond]

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[white creek]

Hi, so I just want to clarify something, so I’m solving f(x)/g(x) which is f(x) is 2x^2+5 and g(x) is 3x-5. With that, if I divide them do I cancel out 5 in the numerator and denominator??

[next dove]

no

you can't

[white creek]

So basically this is already good?

No need to cancel out anything?

[next dove]

uh, you could try long division

synthetic division

whatever they taught you

[white creek]

Alright then, thanks for the help then mate

[pearl pond]

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[brisk steeple]

he don't know you lil bro

[brisk steeple]

.close

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[thin mural]

Would someone mind checking if I got these right

[thin mural]

<@&286206848099549185>

<@&286206848099549185>

[midnight haven]

can you enlarge it

i only see your cup or whatever that blue thing is

[thin mural]

Uh let me try

Oh really weird

Hold on

,rotate

[thin mural]

Better?

@midnight haven

[midnight haven]

yes much better

if it isnt a polynomial there are no degrees

[thin mural]

Oh

I thought that it had to be a whole number

Can it be negative

[midnight haven]

no it cant

as mentioned in your question it says

if yes, degree?

your answer to the top one is no

so

[thin mural]

I knew what the first one was

The second one is weird

Cause there’s an X as an exponent

So I said no

Cause it’s not a whole number

[midnight haven]

wait

the second one is a polynomial of degree 2

[thin mural]

But doesn’t the X make this not a poly

[midnight haven]

nono

oh wait you mean the x in that indice

sorry i read it as a 2

[thin mural]

Yea

So would that make it not a poly

[pearl pond]

@thin mural Has your question been resolved?

[pearl pond]

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[uncut rover]

What steps or formula do I need to use to solve this? I’m guessing plugging in 1 for x isn’t the right move

[midnight haven]

is 0.45 the wrong answer you got or

[uncut rover]

Yea that’s what I got

[midnight haven]

what about you try substitutign f(1)

as 1

like f(x) = f(1) = 1

and than solve for x

?

[uncut rover]

Ok I’ll try that

Am I at a dead end or did I mess something up

[midnight haven]

i just calculated

and it leads to -11.70820393

and 1.708203932

what 💀

[uncut rover]

I don’t know either

Wait if I showed another example could you like reverse explain how the answer is .12

[versed ledge]

@uncut rover you need to find derivative with respect to x

That is what called rate of change

[versed ledge]

For this question
f(x) = 0.03(8x-x²)
f(x) = 0.24x - 0.03x²
Now find derivative
d/dx(f(x)) = d/dx(0.24x+0.03x²)
....
Then at last put value of x , you will get 0.12

[uncut rover]

Could you explain the derivative step

[versed ledge]

Do you know derivatives? I mean have you studied yet

[uncut rover]

I’ve seen it mentioned once but it hasn’t been elaborated on

[versed ledge]

Well then you should not try questions related to derivatives as per my opinion because you won't understand what's happening .you should be aware what is
d/dx(x), d/dx(x²) etc else you won't be able to solve. Let me show the 2nd question

For this question
f(x) = 0.03(8x-x²)
f(x) = 0.24x - 0.03x²
Now find derivative
d/dx(f(x)) = d/dx(0.24x-0.03x²)
d/dx(f(x)) = 0.24 * dx/dx - 0.03 * 2x * dx/dx
d/dx(f(x)) = 0.24 -0.06x

Now x is given in your question

Put the value of x and find d/dx(f(x))

That is your rate of change

@uncut rover ^^

[pearl pond]

@uncut rover Has your question been resolved?

[pearl pond]

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[midnight haven]

how to solve this

[dapper kraken]

what forms of an eqhation of the circle do you know

[frosty frigate]

do u know the equation of a circle

[midnight haven]

(x-h)^2+(y-k)^2=r^2

[frosty frigate]

now

coefficient of x^2 and y^2 is not 1

so first make it 1 and try

[midnight haven]

complete the sqs and shit?

[frosty frigate]

no no

divide by 36

[midnight haven]

whole eq?

alrighty

[frosty frigate]

yes

[dire wolf]

Yeah

[dapper kraken]

basically after you make coef of x^2 y^2 1

[dire wolf]

^

You don't want anything in front of (x-h)^2 + (y-k)^2

[frosty frigate]

but u can also use x^2 + y^2 + 2gx + 2fy + c = 0

[dire wolf]

Which is why you divide by 36 in the beginning

[frosty frigate]

if u know that

[dire wolf]

https://cdn.discordapp.com/emojis/1209604890268278835.webp?size=48&quality=lossless&name=Gasper

[dapper kraken]

is bro a vencord user

[midnight haven]

x^2+y^2-x/3-27/36y-8/36=0

[frosty frigate]

yeah

now if u want u can complete square

or

use this one

[dire wolf]

Yes :(

[frosty frigate]

x^2 + y^2 + 2gx + 2fy + c = 0

[dire wolf]

Im sorry

Im poor

!

[midnight haven]

use this one? tf u mean?

[dapper kraken]

wtf guessed it 🔥 same

[midnight haven]

8/36

[frosty frigate]

x^2 + y^2 + 2gx + 2fy + c = 0

this one

[dire wolf]

Me when r=sqrt(g^2+f^2-c)

[midnight haven]

sqrt 8/36 is the answer?

[frosty frigate]

no

that is c

radius is root(g^2 + f^2 - c)

[dire wolf]

Did i not say that

Or was that for phelps

[frosty frigate]

phelps

[dire wolf]

Kk

Btw phelps

You should use whatever the teacher teaches

[midnight haven]

they taught this stuff 2 years back

[dire wolf]

Ohhh

[midnight haven]

i don't really remember now

in some tests i need this

[void glen]

complete the square

[midnight haven]

🤡

[void glen]

twice

[dire wolf]

Yea if u just need the radius just put it in standard form or use the formula

[midnight haven]

is there any faster way? calculator is allowed

[dire wolf]

My bad 😭

[void glen]

^ this is faster

[midnight haven]

x^2+y^2-x/3-27/36y-8/36=0

this is the eq right?

now

swrt of this?

*sqrt

[dire wolf]

Need to multiply g and f by 2

$x^2 + y^2 + 2(g)x + 2(f)y + c = 0$

[jolly parrot]

avelia

[dire wolf]

Idk if that makes it easier to separate

But you need a coefficient of 2 in front for it to wor

k

[midnight haven]

https://tenor.com/view/elmo-shrug-idk-i-dont-know-who-knows-gif-17348455

i have no idea what you guys are trying to teach me

[dire wolf]

Like 14 = 2*7

So you would write 2(7)x instead of 14x

[worldly glacier]

should we start from the beginning again?

[dire wolf]

HOLY SHIT

[midnight haven]

can anyone try it with more simpler steps

[midnight haven]

yes pls

[dire wolf]

NO FUCKING WAY

[worldly glacier]

BRO IS STRUGGLING

and ur yapping

[dire wolf]

SQL????

[worldly glacier]

if im being honest

[dire wolf]

My bad!

UMich boy

[worldly glacier]

I forgot

WAIT TRANSFER

[dire wolf]

Help the kid

😭

[worldly glacier]

btw how did it go

or don't wanna talk about it

[dire wolf]

Dms

[midnight haven]

guys

[worldly glacier]

guys

i gotchu

[midnight haven]

okay look

now, i want to get the exact radius

calculator is fucking allowed

[dire wolf]

WHAT

[worldly glacier]

mf 😭

[dire wolf]

What calculator you have

[midnight haven]

desmos

[dire wolf]

Okay we're just going to use the standard forme equation

$(x - h)^2 + (y - k)^2 = r^2$

Where ((h, k)) is the center of the circle and (r) is the radius

Original equation
$36x^2 + 36y^2 - 12x - 27y - 8 = 0$

Factor out 36:

$36(x^2 + y^2) - 12x - 27y - 8 = 0$

Divide by 36:
$x^2 + y^2 - \frac{12}{36}x - \frac{27}{36}y - \frac{8}{36} = 0$

Simplify
$x^2 + y^2 - \frac{1}{3}x - \frac{3}{4}y - \frac{2}{9} = 0$

Completing the square for x and y:
$\left(x - \frac{1}{6}\right)^2 - \frac{1}{36} + \left(y - \frac{3}{8}\right)^2 - \frac{9}{64} - \frac{2}{9} = 0$

Combine constants:
$\left(x - \frac{1}{6}\right)^2 + \left(y - \frac{3}{8}\right)^2 = \frac{225}{576}$

Radius:
$r = \sqrt{\frac{225}{576}} = \frac{15}{24} = \frac{5}{8}$

Bleh

[jolly parrot]

avelia

[worldly glacier]

the dedication 😭

[dire wolf]

Or smth dk

[frosty frigate]

i swear ikr

dedication ++

[dire wolf]

Format is ass

[void glen]

(36x² - 12x + 1) + (36y² - 27y + 81/16) - 8 - 1 - 81/16 = 0
(6x - 1)² + (6y - 9/4)² = (15/4)²
(x - 1/6)² + (y - 9/24)² = (5/8)²

is this so hard

[dire wolf]

Be chill w it cyclic

Some people might have bad teachers

Always blame the skill gap on the teacher

[frosty frigate]

💀

[midnight haven]

yeah for me

[dire wolf]

Phelps lmk if you don't understand part of my work

[midnight haven]

got it guys

thxx

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[sullen gate]

Help

[sullen gate]

Hello

I will semd a picture

Y=1 side of the red sphere

The distance between the red and the black

Is 2m

I need to find the perimeter of the black one

<@&286206848099549185>

[vague prism]

i think i might know how to solve this one

first construct a triangle with one point in the center and the base at one of the black lines

then a red line will be in the triangle

so it constructs similar triangles

and the top angle of the triangle is 45 degrees

[sullen gate]

Give me a second

Ok

Then?

[vague prism]

since they are similar triangles you will be able to find the ratio between (length from center to red line)/(length from center to black line) and it will equal 1/(length of black line)

[sullen gate]

Wait

I’m stupid

I don’t. Get it

[vague prism]

i'll send a pic

wait

[sullen gate]

Ok

But how does this got to do with algebra

Please ping me when u reply

I am currently walking home

[vague prism]

so (green line)/(yellow line) = (big red line)/(black line)

[sullen gate]

Ohh I see

I SEE

[vague prism]

its just ratios

[sullen gate]

so (green line)/(yellow line) = (big red line)/(black line)

How big is yellow compare to green

Because I need to figure out the perimeter

[dapper kraken]

is trig allowed

actually i dont think you need it?

[sullen gate]

This is a year 8 question

According to my teacher

The bus is gonna be on my exam

[dapper kraken]

wtf ok

[sullen gate]

He also said it’s gotta do sowmthing with algebra

[dapper kraken]

what exactly is 2m in distance?

[sullen gate]

Y=1m

Metre

[dapper kraken]

ornge or black

(the 2m)

[sullen gate]

Orange

[dapper kraken]

ok

[sullen gate]

I have another question after this one btw

Orange is the distance between red sphere and black sphere

[dapper kraken]

you have to find the green some way

[sullen gate]

Lemme think

[dapper kraken]

without trig, best bet is to somehow use pythagoras+kite

so like take 2 of those diagonals, they are right angles, green=x, d1×d2/2=(x×xsqrt2)/2
the kite is also the same as 2 of those triangles, so height×base×2/2= sqrt(x^2-1/4)×1

this is ugly af, you can let x^2 be y and solve quadratic then solve x

alternatively if you know trig, 2x^2-2x^2cos(45)=1

[dapper kraken]

this maybe the algebra your teacher talked about

[vague prism]

i got an answer of about 29.25 for the perimeter

might be wrong tho

[dapper kraken]

dont tell em

!noans

[pearl pond]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[vague prism]

i didnt even give the full answer

[sullen gate]

How did u even get 29.25

[dapper kraken]

eh ok faie

[vague prism]

youll probly need to get more decimal points than just two

[sullen gate]

LEMEM read ur thing

[dapper kraken]

lemme work it out myself aswell

[sullen gate]

Where is the kite

[dapper kraken]

uh i got 20.25

[vague prism]

huh

[dapper kraken]

lets talk in dms

[sullen gate]

What grade r u 2

I see

What’s sqrt

[vague prism]

square root

i feel like we're just overthinking this and theres an easier solution

[sullen gate]

Let me email my teacher

Hope he give us a small clue

Let me draw a better one

Hold up

[dapper kraken]

small clue: cos rule :p

[sullen gate]

What’s cos

[dapper kraken]

ignore that

im just playin

[sullen gate]

I will draw a better example

How long had it been bro

I may have figured it out

[vague prism]

what is it

[sullen gate]

The distance between red and black

Calculate

How much it increase

So if it’s 2m

Wait nvm

What am I thinking

[vague prism]

what the

i used calculator this time and got a whole different answer

and i did everything correctly

[pearl pond]

@sullen gate Has your question been resolved?

[sullen gate]

Just close it

I’ll do it with my friend d

[pearl pond]

@sullen gate Has your question been resolved?

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[pastel widget]

i need help again

[pastel widget]

idk what to do since its /12

i thought that it would maybe be the same as sin(pi/6)/2

which gives me 1/4

then idk what angle gives 1/4 for cos

[spare lark]

It is not

[pastel widget]

it was a stretch ik

but i didnt know what to do

[tropic blade]

you carried the division outside of the function or did another thing?

[pastel widget]

thats besides the point guys

idk what i did 😂

my point is i dont know how to solve it

[tropic blade]

well

[spare lark]

Do you know the addition formula for sin ,

[pastel widget]

i dont think so...?

what is it

[spare lark]

Sin(a-b) = sin(a)cos(b) - sin(b)cos(a)

[pastel widget]

oh we didnt learn that

[spare lark]

Ok

[pastel widget]

there must be a way to do it with what i learnt

we learnt

reciporacal functions

cot cosec sec

pythagorian identity thing

[tropic blade]

there is

[pastel widget]

sin(theta) = cos(pi/2 - theta) or whatever

[tropic blade]

you know sin((pi/2)-x)=cos(x) right?

[pastel widget]

yea

[tropic blade]

sin(pi/12) = cos(pi/2 – pi/12)

[pastel widget]

oh?

how do u know to use it

like

i dont see any resemblance

[tropic blade]

so we can both turn into cos

if you want we can turn the cos into sin function

there are lot of ways

[pastel widget]

im a bit confused

can u explain how u came to this

[pastel widget]

.

like why did u insert pi/2-pi/12

the cos(pi/2-pi/12) bit

i know its in the identity but isnt it just x

[tropic blade]

sin(x)=cos(pi/2 – x)

[pastel widget]

oh shit

x = pi/12

[tropic blade]

ya

[pastel widget]

ah ok

and then from there

sin(pi/12) = cos(5pi/12)

so theta = 5pi/12

[tropic blade]

imagine we have an equation f(a)=g(b)

we gotta turn these into the same function to see the relation between a and b right?

This is what are we doing right now.

Turn the sin into cos or turn the cos into sin function so we can solve for theta

[pastel widget]

ohhhhhhhhhhhh

i see

thank you for your help

[tropic blade]

now we get cos(theta)=cos(5pi/12)
thats it

theta is obviously 5pi/12

there are infinite solutions, since it said theta is between 0 and pi/2
that's the only solution for theta

[pastel widget]

Ok that makes sense

thank you

what if they made the domain larger

like 0 to pi

[tropic blade]

for the general solution

theta= 5pi/12 +2pi•k
or
theta -5pi/12 +2pi•k

where k is an integer of course

2pi•k because cos is a periodic function

-5pi/12 because cos is also an even function.
cos(x)=cos(-x) coming from this feature

plug some integer values for “k” and take the ones between 0 and pi

for the first one, theta= 5pi/12 + 2pi•k

the equation only hold for values between 0 and pi when k=0

[pastel widget]

oh so + and -

[tropic blade]

obv it'll be larger than pi or smaller than 0 if you put other values like +1,+2… or -1,-2,…

[pastel widget]

ok sweet

[tropic blade]

for the second one
theta= -5pi/12 + 2pi•k
we don't get any value between 0 and pi for any value of k

[pastel widget]

wait why are you adding 2pi*k?

maybe this was a little too complicated of a question for me to ask 😂 sorry, we only really just started this topic

[tropic blade]

.

[pastel widget]

so howcome we didnt add that for the original question

[tropic blade]

the first question, told you to find the value of theta

it didn't say anything about other values if they exist

only one value, I suppose

we found that theta is 5pi/12 which is obviously between 0 and pi/2

[pastel widget]

so if they extended the domain it would allow for multiple possible values for theta

im following so far

[tropic blade]

I suppose there's only one value for this, so I stopped at there

there's another solution if you want to solve it quick without making sin or cos the same function

we both know the relation between sin and cos

if sin(x)=cos(y)

x+y=90 degrees

pi/12 + theta = pi/2
you can solve in this way too

[pastel widget]

oh

that might be easier

[tropic blade]

its actually the same with cos(pi/2 – pi/12)=cos(theta)

just with more steps

[pastel widget]

theres so many ways 😂

thank u for showing me

i appretiate the help bro

[tropic blade]

https://tenor.com/view/oppenheimer-oppenheimer-movie-walk-walking-gif-3311223081607307352

[pastel widget]

The sigma himself

LCR8

.close

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[golden fjord]

Is there a way to determine if a fraction is larger or smaller than another without extending each fraction by the common denominator?

[golden fjord]

ex: 11/12 and 12/13

Which is greater than the other?

[tropic saddle]

well in this specific case they are 1-1/12 and 1-1/13 so you can compare them using that

[dusky glen]

There isn't a good general method other than that I don't think

But as denascite says there are specific cases where you can use tricks

[golden fjord]

Mm mm

I think I ran into some where you an use tricks

Aside from saving time on the ones you can use tricks on, you said there was no general method?

[tardy reef]

generally rather than gcd we just do: a/b < c/d as ad < bc

but other than that, theres nothing simpler

[golden fjord]

Wait so in the given example, if 11 * 13 < 12 * 12, then the first fraction (11/12) is greater than the second (12/12)

[golden fjord]

using this "rule" I mean

if I understood how to use the rule at all

[tardy reef]

?

you clearly used <

which means less than

[golden fjord]

oh yeah

[tardy reef]

if ad > bc, then its greater than

[golden fjord]

ah

that was silly

but i understand what i did wrong

if I had said "less than the second"

it would be correct?

[tardy reef]

yes

[golden fjord]

okay thank you, that's useful I didn't know about that

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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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[finite perch]

How is the answer B? When I factor 3x^2 +10x - 8, I get x = 4, and x = -2/3

[finite perch]

Factored the following way:

3 * -8 = -24

(ac)

factors of -24 that add to 10 are -12 and 2

3x^2 - 12x + 2x - 8 = 0

3x(x-4) + 2(x-4)

(3x + 2) (x-4)

x = 4

x = 2/3

-2/3*

[midnight haven]

,w solve 3x^2 +10x - 8 = 0

[jolly parrot]

Results provided by WolframAlpha

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Requested by iamstupid4304

[finite perch]

bruh what

How is my factoring wrong then

[versed ledge]

-12x+2x = -10x not 10x

[finite perch]

OH

so its -2 and 10

3x^2 - 2x + 10x - 8

?

[versed ledge]

What

[finite perch]

wait nvm\

[versed ledge]

Its 12 ,-2

[finite perch]

yea sorry

3x^2 - 2x + 12x - 8

x(3x - 2) 4(3x - 2)

ok ok that works

thanks

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[indigo flower]

hi i need help

[indigo flower]

problem says u have 4 boxes that each has 3 coin in it

coins are gold and silver

first box has 3 gold coins second has 1 silver and 2 gold ones 3 same as second but has higher amount of silver coins and last one has 3 silver coins

and u take a coin from 1 of the boxes and its silver u dont put it back if u take a second coin out of same box, whats the probability that it will be silver

<@&286206848099549185>

[topaz lichen]

how does box 3 have higher amount of silver coins but same as second box if it can only have 3 coins

u mean 2 silver 1 gold?

[indigo flower]

oh sry

[strange fox]

are you trying to describe Bertrand's box paradox

[indigo flower]

yea so second box has for example 2 gold and 1 silver and third has 2 ilver 1 gold

[topaz lichen]

oh okk

[strange fox]

this sounds similar to that

[indigo flower]

no its random problem

[indigo flower]

it may be tho

[strange fox]

https://en.wikipedia.org/wiki/Bertrand's_box_paradox

this it?

[indigo flower]

yea but boxes have 3 coins each

[topaz lichen]

wdym by u dont put it back if u take a second coin?

[indigo flower]

so u pick that coin and its silver u dont put it back into the box and u take the second coin out of the same box

and whats the probability of that second coin to be silver

u still here?

<@&286206848099549185>

.close

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[indigo flower]

.close

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[meager rune]

Can someone please help me with this?

[autumn fossil]

p is some number?

[meager rune]

?

[autumn fossil]

What is p?

[meager rune]

I have no idea

[autumn fossil]

Okay, let's just treat it as some variable then

[meager rune]

Alright

[autumn fossil]

Can you rewrite 16 as a^b where a is a prime number?

[meager rune]

2^4??

[autumn fossil]

Okay, so now we have $\left(\left(2^4\right)^p\right)^4$

[jolly parrot]

MæthIsAlwaysRight

[meager rune]

Ohhh

[autumn fossil]

Do you know what to do now?

[meager rune]

p * 4 * 4??

[autumn fossil]

yes, that will be the new exponent of 2

[autumn fossil]

so this is the b

[meager rune]

Alright just finished writing it down

So the answer is 2^16p

??

[autumn fossil]

Correct

[meager rune]

Hell yeah jigsaw

That was a good explanation thanks for that

.close

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[unborn field]

I have a quick question regarding this task. I was able to find out that the slope of the level curve through 1;1 has a slope of -2 at that point. But I am confused about the query "find its equation".

I thought this equation can simply be found by plugging 1;1 into the function, check what the output is and then plug it into the function I used when applying IFT. So my answer would be that the equation for the level curve is 5 = 2x^2y+2x^2+y^2.

But the solution is different. There they used the point 1;1 and the slope and stated that the equation is y=-2x+3. But I dont understand - isnt this something different from the level curve?

If somebody could explain how this "find its equation" should be correctly interpreted Id be thankful. Let me know if the question is not clear.

[midnight haven]

do they not mean the first derivative?

so somethings like
4xy + 4x + y^2 ? could be wrong though

[unborn field]

Not sure what you mean by that to be honest.

[proud valve]

It's asking for the slope from the gradient vector id imagine

[unborn field]

The slope part of the question I managed to do, its -2. But I am confused about the "find its equation" part. Unless I am misunderstanding your idea

[proud valve]

It's been a while since i've done these but i believe it's asking for the tangent of the level curve, which is in 2d, so the function y(x) is what it wants. which would be y-y_1=-2(x-x_1) => y=-2x+3

[unborn field]

This is also what the solution shows yes. But I fail to see how the question addresses this, since the tangent of the level curve is not the same as the level curve, right. Maybe the "its equation" refers to "slope" though, so finding the equation of the slope would yield 2x+3. Do you understand my confusion?

But thanks, most likely your interpretation is the correct one.

[proud valve]

It's weirdly written yeah, but the tangent of the level curve is the rate of change between y and x, since Z is held constant. and the function of a tangent is simply ax+b.

[pearl pond]

@unborn field Has your question been resolved?

[pearl pond]

@unborn field Has your question been resolved?

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[karmic sluice]

Hi so i have a q about this over here

I know that
A: Red Flash (R)
B: Blue flash (B)
C: R R
D: B B
E: B R
F: R B
G: RRR
H: RRB
I: RBR
J: BRR
K: BBB
L: BBR
M: BRB
N: RBB

is there some factorial notation or statstics method

that i can use

to know how many different combinations of flashes I can have for the letters O to Z

or do i have to list them all out

[sweet bone]

you're effectively counting in binary; there are 2^4 = 16 binary strings of length 4, and only 12 letters in O to Z, so you have enough to encode all those letters with 4 digits each

[karmic sluice]

ah i see

so cuz there r two options 0 and 1

every time you add an extra spot

so _ _ _

ur adding another ^2 column?

so for 0 1 you can arrange them in 2^2 ways

for 3 slots u can do it in 8 ways

but 4 slots wld it not be 2^4 = 16?

[karmic sluice]

when wld i use factorial notation? and when do i know to raise to the power

<@&286206848099549185>

[pearl pond]

@karmic sluice Has your question been resolved?

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[weak cipher]

can someone explain how you get a?

[hallow raven]

plug in t = 2 on the graph

[weak cipher]

but why plug in t=2 if it says v(2)?

[twin hedge]

because on this graph the y axis is the velocicty and the x-axis is time

so to find velocity at t=2 we need to look at what the y-value is there

[weak cipher]

ok, also how do you find x(1)? its not even on the graph

oh nbm

nvm

but if it wasnt given, how would you find x(0)?

[weak cipher]

this is so confusing lol

[twin hedge]

x=v*t

wait no

distance is area under the curve

so find the area of the triangle

up until t=2

[weak cipher]

and thats what x(0)=?

[twin hedge]

sorry misread

at x=0

the velocity is 0

so no distance travelen

traveled

so x(0)=0

[weak cipher]

it says x(0)=-3.....

so idk how to find that

[twin hedge]

i think you misread and it says x(9)

d) right?

[weak cipher]

i wanna know how youd find x(0) if it isnt given

[twin hedge]

you can't

[weak cipher]

ok cool thanks

so to find x(9) its -3 plus all the areas up to 9?

[twin hedge]

correct

[weak cipher]

and then the thing i never comprehended but my teacher wants us to do is convert whatever those graphs are called into velocity v time graphs

sorry heres an example

of one

[twin hedge]

which one?

[weak cipher]

how you convert the graph at top to the bottom

and vice versa

[twin hedge]

what is the y-axis of the graph on top?

like velocity?

or distance

[weak cipher]

at what point?

[twin hedge]

no just what are the values on the y-axis, are they velocities or distances

[weak cipher]

velocities

right?

[twin hedge]

so if the top one is velocity-time and the bottom one is, what do they want to convert

[weak cipher]

no i dont know

they want to convert the top one into a velocity versus time graph

and idk how to

but the answer is right there

i just dont know the method

[twin hedge]

but the top one already is velocity versus time you just said right?

[weak cipher]

i dont know😭

idk what its called

[twin hedge]

idk then either

[weak cipher]

<@&286206848099549185> 🙏

[weak cipher]

question is how do you convert the top graph into the bottom graph

[pearl pond]

@weak cipher Has your question been resolved?

[weak cipher]

<@&286206848099549185>

[crystal plaza]

Yea

That u in the pic

[weak cipher]

yes please help me

how do you convert the top graph into the lower graph?

[crystal plaza]

What is y axis

[weak cipher]

y(t)

velocity verse time graph

i think right?

[weak cipher]

how tf is this found @twin hedge

[twin hedge]

see how in the top graph the y axis has unit (cm)

that means it’s distance

oh wait

so u now at III?

[weak cipher]

just perusing thru

im so confused lmao

[twin hedge]

do you want me to first explain II?

[weak cipher]

sure

[twin hedge]

so, the top graph is distance-time and the bottom graph is velocity vs time

do you agree?

[twin hedge]

bc of this

[weak cipher]

one second

[twin hedge]

take ur time

[weak cipher]

yes i agree

[twin hedge]

okay, so in the velocity-time graph the y at say t=0 to t=1 would be the slope of the top graph, because in a distance-time graph, the velocity is slope

[weak cipher]

the y at what?

[twin hedge]

the y in the bottom graph

is the velocity

[weak cipher]

ok, and the bottom is distance

is that not the same thing for the top one?

[twin hedge]

top graph is distance vs time

[weak cipher]

ohhh

i see

ok

[twin hedge]

so, you understand this part?

[weak cipher]

when you say slope of the top graph what does that mean because the slope constantly changes

[twin hedge]

the slope between t=0 and t=1

because there its constant

[weak cipher]

ok i see

and the slope from there is 3

right

-3

[twin hedge]

-4

[weak cipher]

oh im dumb LOL

ye

-4 yes

[twin hedge]

so thats why in the bottom graph the y is also -4

for t between 9 and 1

0 and 1

[weak cipher]

OHHH and the point ends where the point ends from t=0 to t=1 right?

[twin hedge]

yes

[weak cipher]

because on the dist time graph it ends at 1, so on the v-t graph it also ends at 1?

[twin hedge]

yess

[weak cipher]

bro thank you so much

just so i can write it down ima list the steps tell me if correct

[twin hedge]

sure

[weak cipher]

1. Determine slope on given interval on dist-time graph
2. The slope there will determine the v(t) value on the velocity time graph
3. Where the interval ends on the dist-time graph, the interval ends on the velocity time graph
4. Repeat until all intervals are done

[twin hedge]

very good!

[weak cipher]

https://tenor.com/view/thank-you-thank-you-so-much-thank-you-so-very-much-thank-you-so-so-much-thnx-gif-9180115347613668927

genuinely

bro bout to save my grade

[twin hedge]

ur welcome

lol

[weak cipher]

so for three real quick

how is v(4) determined if there is no given?

[twin hedge]

determine the slope at t=4

and because its linear

its the same as taking from t=3 to t=7

[weak cipher]

slope from 3 to 5 is -10 so at 4 is it -5?

[twin hedge]

no, see how it’s a straight line, so the slope doesn’t change

so at t=4 its the same as t=3 and t=5

[weak cipher]

so just -10?

[twin hedge]

well no at t=3 there is no slope actually but besides the point

[twin hedge]

yes

[weak cipher]

ok ye

alright so -10

OH

its just -10?

i didnt realize

my teacher is doing to much with allat

[twin hedge]

yes sorry forgot to comfirm

[weak cipher]

so if i get a question about velocity (time) on a distance-time graph, I just look for the slope at the t value in v(t)?

[twin hedge]

yeah

[weak cipher]

alright y(6)

my guess was to find 6 on y axis and match it up to x axis

but clearly that was wrong

[twin hedge]

very good

no its correct

wait no

find 6 on x axis

and match y

almost

[weak cipher]

thats so trippy😭

[twin hedge]

theyre just asking what the y value is at t=6 so we look what the y value is for t=6 (on x axis)

[weak cipher]

ill only keep you captive for a bit longer; just need some help w these

so for v(11), youd look at 11 on the graph, but its obviously not there

so im lost

[twin hedge]

how do you mean its not there?

[weak cipher]

like its not visibly on the graph provided

[twin hedge]

draw a line up at t=11 and see what v corresponds to it

[weak cipher]

omg bruuu

makes sense

[twin hedge]

haha np

[weak cipher]

but for x(12)

[twin hedge]

the distance at a point in a velocity vs time graph is the area under the curve up until that point

we calculated that area for 1)

but they say at t=0, x=-8

8*

so we need to add that

[weak cipher]

right

[twin hedge]

to the sum of areas

[weak cipher]

where does it say that?

[twin hedge]

on top

next to IV

also marked

[weak cipher]

oh ok, so what does that mean in relation to x(12)?

[twin hedge]

it means that at x=12, the distance is (sum of areas up until 12)+(8)=0+8=8

[weak cipher]

ohhhh

i get it

i think that concludes my conquest

[twin hedge]

nice

[weak cipher]

thank you bro🙏

[twin hedge]

great

[weak cipher]

.close

[pearl pond]

Channel closed

Closed by @weak cipher

Use .reopen if this was a mistake.

[pearl pond]

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[tranquil badger]

sup

[tranquil badger]

https://cdn.discordapp.com/attachments/1231703608198692946/1277466773075263499/aura_flow.jpg?ex=66d090e4&is=66cf3f64&hm=0e783b8a74231f31c05e80077bb4b83e568b079a98fc0a0a411856f22b1ca90b&

Explain in English the concept behind the factoring process they used

[finite gulch]

https://www.youtube.com/watch?v=zjjPgCWs6F0

[tranquil badger]

They wanted to know if 1 would add or multiply to make 2.

[tranquil badger]

Explain within a few words what the AC method is and if it differs from that method.

[finite gulch]

learn the method and do it urself

[tranquil badger]

Anyone else willing to give an answer?

[pearl pond]

@tranquil badger Has your question been resolved?

[pearl pond]

@tranquil badger Has your question been resolved?

Channel closed

Closed by @tranquil badger

Use .reopen if this was a mistake.

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.

[candid bone]

How to start to solve this

[worldly glacier]

find the limit as x ->0 of h(x)

[candid bone]

Wdym by that just sub in 0?

What does limit mean

can we clear that up

[worldly glacier]

oh you should know what a limit is

to define continuitity

https://www.youtube.com/watch?v=riXcZT2ICjA

[vestal raft]

sin(5x)/x

this is a special identity.

sin(x)/x =1

so you multiply by 5/5 to match the identity.

[candid bone]

Got it

[vestal raft]

5sin(5x)/5x

so answer is 5

[candid bone]

thats the limit?

[vestal raft]

yes

[candid bone]

limit at what

lim as x=0

?

[vestal raft]

yeah

Do you have any other questions?

[candid bone]

Ok bet but question is asking to make a piecewise function

[vestal raft]

okay, piecewise just means you are looking at more than one function. like x^2 and x at the same time but on different intervals.

[candid bone]

Yup

ik what piecewise is but idk how to imply it ehre

[pearl pond]

@candid bone Has your question been resolved?