help-0

[candid atlas]

cause of the extra

0.3

[modest yew]

ah

[brisk sluice]

can someone help me with this please?

[sleek jewel]

47 110/173

[brisk sluice]

thank you :]

[floral anchor]

Can someone help with #1 on the second page?

<@&286206848099549185>

[candid atlas]

yo

how is the first part wrong?

[restive ember]

x,y and r can be any number greater than one, how would I work out the missing co ordinates? What steps would i need to do. Thanks, its for my programming

[remote heron]

nothing special really

maybe you can work backwards from an example with numbers?

try a unit circle

[restive ember]

its apart of a circle

but i dont know an example

this is the first time im doing this

[remote heron]

let x=0

[restive ember]

okay

[remote heron]

y =0

[restive ember]

r=10

[remote heron]

no

[restive ember]

yes

[remote heron]

r=1

[restive ember]

10 good number

[remote heron]

make it easy on yourself

[restive ember]

okay

[remote heron]

since in this case

(?,?) is just ( cosx, sinx )

[restive ember]

0,0 and 0,1

[remote heron]

well

[restive ember]

cosx what

sinx what

[remote heron]

thats confusing

ill have to type once im home maybe

[restive ember]

i can work out the length of the line

and angle

but not how to get co ord

okay np

[remote heron]

draw a triangle

id say your pic is the hard version

easier for given coordinates, arbitrary angle

[remote heron]

since a point on a circle is really a triangle

[restive ember]

this is all i have to work with

[remote heron]

or can be thought of that way

[restive ember]

for my programming

[remote heron]

sure

wait like uhh

15 min ill be home

i have a tablet can draw

[restive ember]

okay thanks man

[high crest]

Familiar with rotation matrices?

[restive ember]

nope im doing a level maths

so like american high school

[high crest]

No clue what concepts you know then 😅

Trigonometry?

[restive ember]

i know basic trig

sin cos tan

trig identities

pythag

radians

[high crest]

Alright

[restive ember]

primary and secondary solutions

[high crest]

It's basically a isosceles triangle, hence you could calculate the distance between (x,y+r) and (?,?) easily by dividing the triangle in two congruent right triangles.

[restive ember]

okay splitting it

[high crest]

exactly

[restive ember]

but we only have

one side and an angle

for sin rule we need two sides and angle or two angles and side

wait

[high crest]

we have all angles

[restive ember]

i can work out the length

of top line

float length = sqrt((r * r) + (r * r) - (2 * r * r * cos(3.6f)));

this is the code for the top lenth

[high crest]

what language are you using?

[restive ember]

c++

[high crest]

C++ expects radians

[restive ember]

okay ill make it torad

float length = sqrt((r * r) + (r * r) - (2 * r * r * cos(TORAD(3.6f))));

[high crest]

Oh, you know the law of cosines 😅

[restive ember]

that is cos rule

a^2 = b^2+c^2-2bcCos(a)

[high crest]

now draw a right triangle on top of our isosceles triangle

[restive ember]

and $$cos(a) = (b^2+c^2-a^2)/2bc$$

[ocean seal]

zkittlez

[restive ember]

on top

[high crest]

sides should be parallel with x and y axes

[restive ember]

?

or in the middle of

[high crest]

got it?

[restive ember]

ohh ok

i was doing thuis

[high crest]

no, you don't need those anymore

since you calculated the side directly with cosine rule

[restive ember]

im making this in photoshop lol

[high crest]

heh

[restive ember]

okay

so on the triangle

we have

just one side?

[high crest]

yes, but all angles can be determined

[restive ember]

how?

[high crest]

there's another 90° angle at (0,1)

[restive ember]

where

[high crest]

and we know all angles of the isosceles triangle

[restive ember]

looks like an acute to me

[high crest]

the sum of both angles at (0,1) is 90°

[restive ember]

yeah its (180-3.6)/2

okay

so 90 - (180-3.6)/2

gives us top angle?

[high crest]

yes

[restive ember]

i woudlve never came up w that lol

i dont know how its 90 apart from the fact it looks liek its 90

[high crest]

lol

because we said that the two other sides of the right triangle are parallel to x and y axis

and (0,0) to (0,1) is also parallel to y axis

[restive ember]

ahh make sense

yeah

oh shit ye

but this triangle

im gonna have to make copies of it in a loop

cuz im tryna make something like this

but each triangle is 360/100 angle wide of the circle

because health is 100

so its like a health bar

looks like this rn

but its not 3.6 degrees

so one side, two angles

means we can use

sine rule

haha fucked my maths up

omg nice ily

now time to loop it so it fills the whole thing

[high crest]

Because your actual problem is more complicated than the problem you proposed

The approach won't work for subsequent triangles

[restive ember]

bro i dont know what a subsequent triangle even is

[high crest]

since the left side is no longer parallel to y-axis

[restive ember]

it is

the co ordinates are just my screens co ords

so its x,y is the center of my circle

x+r is top of circle

and that thing we did is the point on the circumference of the circle

[high crest]

so you just need that point rather than the actual triangle?

[restive ember]

i have two triangle co ords

bottom and top

just need a way to work out the top right

i think

[high crest]

It will still fall apart when the angle gets too big, won't it?

[restive ember]

nope

im going to

well

draw shit load of triangles

that make up the red fill inside

if ygm

[high crest]

Why even bother with triangles? Why not just draw a sector?

[restive ember]

the drawing api im using

only lets u make circles, triangle or lines

i got happy when i saw sectors

for the circle

but it just makes it sided

@high crest thank you so much bro 👍

[high crest]

Actually, I'm a moron 😅
@remote heron proposal with unit circle is much easier and works for any angle

[high crest]

so (?,?) = (r*sin(a)+x, r*cos(a)+y)

[restive ember]

x + xlength

[high crest]

now

mixed up sin and cos

[restive ember]

and xlength = the length of the side we know/sin(theta) * sin(alpha)

im off my pc now my head is drained

first maths in college

and now maths at home cry 😢

[scarlet kindle]

is -1/4 the same as 1/-4?

[small bear]

yup

[scarlet kindle]

thanks!

[nimble robin]

if you have a set of numbers N=[1, n], how do we calculate the number of permutations of this set in which no two successive values are adjacent

so like if we have N=[1 2 3 4 5], a valid permutation would be 1 3 5 2 4

but an invalid one would be 1 4 3 2 5, because 3 and 4 are successive values

[woeful pulsar]

Sounds interesting hmm

i might try PIE

[nimble robin]

one approach i tried was to calculate
m: # of permutations of n in which elements k and k+1 are adjacent, and no prior pairs of successive elements are adjacent
then add these for 0<k<n-1

in order to calculate the number of permutations with any adjacency

then subtract from the total

[woeful pulsar]

hmm i have an idea

Can you extend a valid permutation of length n-1 to a valid permutation of length n?

oh wait that doesn't fully work though

[nimble robin]

if n > 3 then yes

[woeful pulsar]

like the new number we add in can split apart one adjacent pair

[nimble robin]

i think a better approach is to focus on calculating the number of permutations with any adjacency

i've managed to make a bit more progress with this, but the answer still evades me lol

[woeful pulsar]

I was thinking we try number of permutations of length N with M adjacencies

then using the n-1 -> n idea we can calculate the number easily

how efficient does your solution have to be?

[nimble robin]

just better than brute forcing

[woeful pulsar]

yeah then you can consider this approach I think it can work

[nimble robin]

it intuitively seems that this can be done in O(n^2) runtime complexity, but idk

[woeful pulsar]

i have a feeling it can be done in O(n log n) but idk

[nimble robin]

n-1 -> n only lets us convert invalid n-1 solutions if there is only 1 adjacency

there may be many

[woeful pulsar]

then consider M adjacencies in general

[nimble robin]

so we can have n-m -> n

[woeful pulsar]

not that way

we consider n-1 -> n changing M adjacencies to M-1 adjacencies

or keeping M adjacencies

or increasing it to M+1 adjacencies

$f(N, M)$ be the number of permutations of length N with M adjacencies

We express $f(N, -)$ with a generating function, that is,
$g_N(x)=f(N, 0)+f(N, 1)x+f(N, 2)x^2+...$

We know that
$f(N, M) = f(N-1, M)\times(N-2)+f(N-1, M-1)\times2+f(N-1, M+1)\times(M+1)$

This means we get the differential equation
$g_N(x)=g_{N-1}(x)\times(2x+N-2)+g'_{N-1}(x)$

[ocean seal]

Element118

[nimble robin]

wait what is a generating function

also whered you get the definition for f(N, M)?

[woeful pulsar]

i just defined it

it's for easier notation

[woeful pulsar]

https://en.wikipedia.org/wiki/Generating_function

[nimble robin]

no i mean howd you evaluated it to be f(N-1,M)x(N-2)+f(N-1,M-1)x2+f(N-1,M+1)x(M+1)

[woeful pulsar]

ah just analyse how you can get M adjacencies in the end

hold on oops

I think I made a mistake

[alpine sable]

What’s the easiest way to find the limit in a question like this? With working out pls

[nimble robin]

lhopitals rule

[woeful pulsar]

factor the numerator/denominator to remove (x-4) s

[nimble robin]

bet lhopital is easier

[woeful pulsar]

both are not hard

[nimble robin]

yes

[alpine sable]

Where did they get x not equal to 0,4?

[woeful pulsar]

it depends if you prefer differentiating or factoring

[woeful pulsar]

the original expression doesn't let you plug in

[woeful pulsar]

yeah the recurrence doesn't work whoops

there's not really an easy way to fix

actually there is

we just add one more variable

[alpine sable]

Ic ty

[woeful pulsar]

whether the last one is adjacent

[nimble robin]

i looked at the definition of a generating function. whats the point of using it here?

[charred flint]

generating functions solve everything tbh

[nimble robin]

wait

OHH

[compact meadow]

Nightcrawler or maria I'm drunk

[nimble robin]

solving the differential equation gives us the coefficients of the generating function, which IS the solution for f

so the dash in f(N, -) is a wildcard

[woeful pulsar]

sortof

you still need to add one more variable if the last one is adjacent

[compact meadow]

What's the pattern they doubling ?

[robust granite]

Say is there a theory for AU = lambda^2 U similar to how there is for eigenvalues and eigenvectors, I understand the question is vague but I don't know how else to frame it

[woeful pulsar]

consider the bees immediately below each type of bee

[wanton beacon]

What is a good way to identify midpoint?

On like a vertical number line?

<@&286206848099549185>

[remote heron]

average

you mean in one dimension?

[wanton beacon]

Yeah

[remote heron]

yea just the average

[wanton beacon]

Like this for example

[remote heron]

assuming it runs in order

well i should be clear

average of endpoints

[wanton beacon]

Well let’s assume those are end points

[remote heron]

i dont understand

which?

-6 and -2?

[wanton beacon]

Yeah

2

Not -2

[remote heron]

oh positive 2

[wanton beacon]

Yeah

[remote heron]

so youll take the average

[wanton beacon]

So I get ex.3

[remote heron]

then a sanity check is smart

not quite

[wanton beacon]

No I mean

I understand example 3

Lool

[remote heron]

oh

[wanton beacon]

But not 4

[remote heron]

okay lets look at that number line

[wanton beacon]

Ok

[remote heron]

runs from -6 to 2

then take your average

-6+2

divide by two

[wanton beacon]

Ohh I see

Got it, thank you very much!

[remote heron]

seems like -2

then you gotta make sure it makes sense

-2 is about 4 from -6

and about 4 from 2

[wanton beacon]

Yeah

Thank you!

[remote heron]

np

[lunar ingot]

I'm really confused with how to get the probablity of the 40 round using random walk.

so I understand gambler ruin but I don't understand random walk

[candid thistle]

anyone could help in #help-3?

[thorn kindle]

1 + (cot)/(1-cot)

[wooden wraith]

Determine the sum of the first 10 even numbers from 2 w/ a common quotient of 3.
Can someone help

[thorn kindle]

What does that even mean? A common quotient when divided by what?

[worldly plover]

hello, uhhh if your not doing anything, can you help me 😭

[thorn kindle]

7/5 = 1 + 2/5.
(1+cot)/(1-cot) = 1 + (cot)/(1-cot)

[alpine sable]

Can I solve this by U substitution?

[buoyant kayak]

probably easier to do partial fractions

[empty pike]

send help! I can't really understand the formula well..
Insert a harmonic mean between 1/2 and 1/8.

[alpine sable]

How do I do that?

[buoyant kayak]

https://www.youtube.com/watch?v=6rXByMcuAyI

[astral aspen]

I need help with 41, not quite sure how to do these problems

[sick torrent]

Y’all know a good discord for chem?

[alpine sable]

@buoyant kayak which integration technique is the most useful?

[alpine nacelle]

i is a root and your polynomial has integer coeff so -i is a root too

[muted gulch]

Dont complex numbers come in pairs

Or am i just retarded

So like u would also use the conjugate of x - i

[alpine nacelle]

so P(x) = (x-2)(x²+1) = x^3 - 2x² + x - 2 is a valid answer

[muted gulch]

Yup

Dang im not helpful at all 😫

[empty pike]

send help! I can't really understand the formula well..
Insert a harmonic mean between 1/2 and 1/8.

How to solve this type of questions?

[elder bloom]

can anyone help please

[lost violet]

what is the inverse of $a^x$?

[ocean seal]

alef0

[placid zinc]

$\log_a(x)$

[ocean seal]

Kaynex

[lost violet]

but how can i define it i was trying to do $y=a^x=exp(xln(a)) $ then $y=exp(xlna) $ then $lny=xlna$ and then $x=\frac{lny}{lna}$ but i know that $\log_a(x)=\frac{lnx}{lna}$ but i cant obtain it

[ocean seal]

alef0

[placid zinc]

What's your goal?

[lost violet]

get that inverse of $a^x$ is $\frac{lnx}{lna}$

[ocean seal]

alef0

[placid zinc]

Looks like you did it

Remember to swap x and y for finding the inverse

[fluid knot]

hewo just need help quick me just nub at geometry

[lost violet]

ph right thanks

[marsh fable]

anyone knows the answer for this?

it says its a difference equation

[split oriole]

solve this, first write auxiliry equation

[alpine sable]

suppose that there are n points in the plane and that each of these points is joined to exactly three of the others by straight line segments. what is a possible number of points?

$y=6

#y=6$

$y=6$

[ocean seal]

milk129

[alpine sable]

oh

so thats how u do it.

[thorn kindle]

(1+cot)/(1-cot) = (1+cot-cot+cot)/(1-cot) = (1-cot)/(1-cot) + (cot+cot)/(1-cot) = 1 + (2cot)/(1-cot).
my bad i apologize

[jovial forum]

Can someone check a linear algebra andwer for me in #linear-algebra ?

[upper escarp]

how to do this q?

[raw shard]

@upper escarp i know how to do it i think, i can walk you through it if you want

[alpine sable]

need help

[raw shard]

@alpine sable bruh this channel is in use

[alpine sable]

oh sorry

[upper escarp]

sure

[raw shard]

ok i was getting my supplies ready so give me a few minutes to work it out on my own @upper escarp

[upper escarp]

alr no worries

oh, i think i figured it out and got the ans

thanks for offering tho!

[raw shard]

@upper escarp ok good, did you get 2.5?

[fluid knot]

help

[alpine sable]

need help in #help-1

[fluid knot]

anyone know what number5 mean

[sturdy lake]

beluga

[ocean seal]

alef0

[upper escarp]

yep

[raw shard]

nice

[high badger]

Can someone please explain how we get to this?

[bleak plover]

quadratic formula

[fair cargo]

I have some questions about dimensions could someone help me?

[placid zinc]

In general:

• Feel free to post your question right away, without "asking to ask". Someone can definitely help you.
• Post in the most dead channel. That way, you won't be interrupted.

[fair cargo]

I'm getting a quote for a fish tank

I need the dimensions but am unsure of how to get the dimensions of a shape like this?

I want the fish tank to be a 50 gallon

[placid zinc]

Does that say "wood to hold stuff"?

[fair cargo]

Yes it's a wooden flat place to hold stuff. Let me quickly draw a better drawing

Does this picture help?

[rigid wind]

the fish tank is donut shape?

[fair cargo]

Yes

I need the dimensions of a tank like this to get a quote but I'm unsure of how to calculate the dimensions of a shape like this?

[alpine sable]

ok so I have this function: sqrt(x^2 - 4), Im trying to find the domain of it. I end up with x ≥-+2 but solution actually is "x ≤ −2 or x ≥ 2" makes no sense to me. Nvm im straight up dumb lol

[woeful pulsar]

idk do you have to take into account the thickness of the glass?

do you want it to hold exactly 50 gallons?

is it an annular prism?

[fair cargo]

40-60 gallons would be the range

[woeful pulsar]

okay so there's a lot of leeway in it, so thickness shouldn't matter too much I suppose

is there any maximum sizes in various directions as well?

like if you parametrise it and you can state what constraints you have we can find some feasible solutions probably

[fair cargo]

No bigger 75" length

[woeful pulsar]

hold on (reads up on imperial units to figure how inches relate to gallons)

[fair cargo]

I would probably want it to be 5ft or 60" length

[woeful pulsar]

okay one gallon is 231 cubic inches

okay any height requirements?

looks like you have some preferences on the size as well

can I model the cross section as an ellipse without an ellipse in the middle?

[fair cargo]

Max would be 45" but I would want around 30"

So more like an oval then a doughnut?

[woeful pulsar]

more like a squashed annulus I guess?

is it a squashed annulus (where the outside rim and the inside rim have the same ratios?)

[fair cargo]

I want the thickness of the tank to take up more space then the center

[woeful pulsar]

hmm i have only a vague idea what that means

does that mean that if I scale the tank such that the length and the height are equal, then the distance between the inside rim and the outside rim is more than the diameter of the inside circle?

[fair cargo]

The area of water/glass is more the center empty space

Rather then equal amount of space

[mortal lark]

Hi any1 help

Can u solve this for me

[fair cargo]

How would I get the dimensions of the tank?

[mortal lark]

I keep getting 1 1/3

Books says its 5 1/3

[fair cargo]

Could you ho to a different question area I'm trying to understand dimensions and stuff and need help with that

Go*

[mortal lark]

Ok

[fair cargo]

Thanks

I'm confused

Would I calculate it like this?

Or this?

I'm not really sure how to get the dimensions if a shape like that?

@woeful pulsar

[rigid wind]

i’d guess you work from cylinder volume to get radius

[quasi shale]

Someone help me with this i know its easy but im shit at math "Adrian decorated 16 cupcakes in 28 minutes. If he continues at this pace, how many minutes will it take him to decorate 56 cupcakes?"

[woeful pulsar]

so you want the front area?

what you can do is calculate the area of the large oval - area of the small oval

do you know the formula for the area of an oval?

[fair cargo]

Would this work?

I'm unsure of how to calculate the area of an oval

[alpine sable]

how would i write an interval but without a single number

like from 2 to 5 minus number 3

like [2, 5] - {3}

or how?

[vale niche]

Si alguien necesita ayuda en español me puede mandar mensaje 😃

[alpine sable]

pls speak english.

sorry but we cant understand you

[vale niche]

If somebody need help in Spanish can send me message 😃

[alpine sable]

oh ok

[fair cargo]

How would I calculate the dimensions of the doughnut fish tank idea I had and does it involve calculating the area of an oval?

[alpine sable]

doughnut fish tank?

;-;

[fair cargo]

This design

How do I get the dimensions of it?

[alpine sable]

uh

idk

[vale niche]

You need the area of oval

Send me message

[woven sphinx]

by "oval" do you mean ellipse? if so then the area of an ellipse with length a and height b is $\frac{\pi}{4}ab$ (notably when $a=b=d$ then the formula reduces to $\frac{\pi}{4}d^2$)

[ocean seal]

A Fellow Human

[woven sphinx]

(oval is not accurate mathematical terminology btw)

[fair cargo]

Please can someone give me useful info on how I can measure the dimensions of the design

[woven sphinx]

just did

[fair cargo]

Sorry I was talking to the guy that sent gibberish

[woven sphinx]

oh

e.g. inner oval would have area $\frac{\pi}{4}10\cdot30$ cm^2

[ocean seal]

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

[fair cargo]

Seriously though this guy is waiting I need help with the dimensions

[woven sphinx]

you can then calculate the area of the outer oval and subtract the 2

[fair cargo]

Idk how to calculate oval surface area

[woven sphinx]

oh

surface area?

[woven sphinx]

as in surface area of this?

[fair cargo]

Yes

To get dimensions

How would I write tge dimensions of an oval

[woven sphinx]

sigh the perimeter of an ellipse is a non elementary integral

[fair cargo]

Like this? ||am I dumb?||

[woven sphinx]

so i could send you the answer, but i doubt you would understand

i'll just send you the approximate value ig

what's the thickness of the tape?

what level mathematics are you studying btw?

[fair cargo]

What level is this math at?

[woven sphinx]

i think university? idk i just kinda self learnt this stuff

i guess you might understand if u took ap calc

[fair cargo]

If I sent this photo to the fish tank company would it work?

[woven sphinx]

i dunno i dont make fish tanks for a living

but i'd say that would be understandable

[fair cargo]

How ,any gallons of water are in the design I made?

[woven sphinx]

depends on how tall the fish tank is

[fair cargo]

It's 50"

[woven sphinx]

i told you how to find the area of an ellipse, apply that to find base area, then as you have a prism of sorts you can use that to find the volume

i also calculated the area of the inner ellipse for you

as an example

[fair cargo]

Yeah I'm not that good at math is it possible you could help calculate the amount of gallons in the tank shape I designed?

[woven sphinx]

i dont imperial

what is a gallon

[fair cargo]

About 4 L

[woven sphinx]

all right

[fair cargo]

1 gal = 4 L

[woven sphinx]

~wa pi/4*(8050-3010) in^3 in gallons

hm does texit not work

sry gtg

[fair cargo]

Could you message me the L that could fit in the tank later on

[woven sphinx]

,wa pi/4*(8050-3010) in^3 in gallons

,ask pi/4*(8050-3010) in^3 in gallons

ah there we go

[ocean seal]

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

Requested by A Fellow Human#4859

[woven sphinx]

ugh

[silver current]

How do we put limits in a definite interal
example- i solved ∫cost pi*t dt
which came to be= 1/pi [sin pi * t]

i have upper limit as 3/2 and lower as 0

so do i write** sin pi * 3/2 - sin pi * 0**
or do i write sin pi(3/2-0)

[raw shard]

@silver current first one

i only know the very basics of integrals but i think that’s correct

[silver current]

Oh okay thankyou

[alpine sable]

why is the range x != 0 and x != 1

i get why 0

but why cant y be 1

[raw shard]

@alpine sable y being one would require the other side to be 1/1

[alpine sable]

so 1/x-2 would need to be 0

o makes sense

im dumb lol thanks

[raw shard]

no problem

yeah no value of x will make 1/(x-2) equal 0

just wanted to say that

[alpine sable]

Can someone explain how to solve this

[raw shard]

i might be able to help, but what exactly do you need to do?

[alpine sable]

I been looking for ODEs lessons and I have no idea where to start from

[raw shard]

oh man nevermind

differential equations, scary

[alpine sable]

So confusing…

[raw shard]

@alpine sable can i recommend you a lesson on this from a site i’ve found helpful in learning calculus?

[alpine sable]

yes pls

[raw shard]

ok

[alpine sable]

i have a whole assignment to do so i really need understand them

[raw shard]

https://tutorial.math.lamar.edu/classes/calci/calci.aspx

go to the home page of this site

and find differential equations

[alpine sable]

ty

[raw shard]

you’re welcome

[supple tundra]

This is a seperable differential equation. Have you learned about that?

[alpine sable]

yes but i feel there is something i am missing in the basics

that makes everything else confusing

i will try to relearn from the website i got recommended

[supple tundra]

Basically whenever you have an equation of the form $$\frac{dy}{dx} = g(x)f(y) $$ then you can solve it by doing $ \frac{\frac{dy}{dx}}{f(y)} = g(x) $ and then integrating both sides with respect to x and remembering the chain rule.

[ocean seal]

azeem321

[alpine sable]

where gx

where fy

is fy -5y?

and gx is 1?

[alpine sable]

talking about this

[alpine sable]

just remember that f(y) is in terms of y and g(x) is in terms of x
so you can either consider f(y) as -5y or just y or -y whatever you like and x according to it assume x^0 for g(x)

I see I see

[raw shard]

@alpine sable don’t worry i looked into differential equations a little bit and i also find them confusing lol

[tame kelp]

can someone remove my studying role

[sly mantle]

done. for future reference do ,iam study in #bots

[tame kelp]

Okay, Thanks.

[alpine sable]

how is this possible?

lim as x goes to infinity of 8/x^2 is 0

[crisp grove]

maybe you'll be able to write it as an integral

[vague coral]

look like riemann sum

[woven sphinx]

12.58 gallons

[flat vale]

pretty sure it's 0 🤔

[torn crescent]

Sup guys

[alpine sable]

help

[torn crescent]

I hope everyone is doing good

put it back

[alpine sable]

that's not a riemann sum

riemann sums split intervals

this adds terms

[fleet pollen]

hii, how to do this?

[alpine nacelle]

note that e+i = 180°

[fleet pollen]

so 180/2+13

🤔

[alpine nacelle]

180/(2+13) will be one subdivision of your angle, to adjust to the ratio, yes

180/15 is 12

[fleet pollen]

E is 12?

[alpine nacelle]

nope

[fleet pollen]

180/15=12

[alpine nacelle]

just to be sure, do you see why e+i = 180° ?

[fleet pollen]

yeah its a straight line

[alpine nacelle]

yes, now you have a 2:13 ratio

what does it mean ?

you'll divide e+i in equals parts, such that e is 2 parts, and i is 13 parts

[alpine nacelle]

you figured out one part is 12°

[fleet pollen]

12x2

[alpine nacelle]

yes

[fleet pollen]

🤔 oh

so another part is 2x13

oh

i got it

thx man

[alpine nacelle]

12*13 is i

such that e+i = 2*12 + 13*12 = 15*12 = 180

that's what ratio are

[fleet pollen]

damn such a simple yet hard question

thank you mate

[narrow trench]

hello

I have a doubt.

lemme start asking it

I was trying to calculate s from these 2 kinematic equations.
$v=u+at$
and $v^2=u^2+2as$.
As we all know, the expected result should be $s=ut+\frac{1}{2}at^2$.
First I squared the first equation, $v^2=u^2 + a^2 t^2$.
Then I equated the both $u^2 + a^2 t^2 = u^2 +2as$.
After that I got $a^2 t^2 =2as$.
And I got $s=\frac{1}{2}at^2 $ and the expected $ut$ term wasn't there.
Why?

hello
anybody there?
ping me when you get the solution

[ocean seal]

[🔥IS] X-82

[alpine sable]

v^2= u^2+ (at)^2 ???

[narrow trench]

yes
sqared both sides

oh

I get it

[alpine sable]

lol

[narrow trench]

I guess

[alpine sable]

now try

[narrow trench]

root of squares

[alpine sable]

u will get ut +half at t square

[narrow trench]

$\sqrt{x^2}=|x|$

[ocean seal]

[🔥IS] X-82

[narrow trench]

right?

[alpine sable]

no

a= b+ct , this implies, a^2= (b+ct)^2

[narrow trench]

yes

[silver current]

that is true but i dont think that applies here?

[narrow trench]

;ohk

[alpine sable]

(b+ct)^2=b^2+(ct)^2+2bct

use this

[silver current]

^^

[narrow trench]

can't you use latex?

[alpine sable]

umm, sry

[narrow trench]

oh

understood

[alpine sable]

simple a+b , whole squared

[narrow trench]

$(u+at)^2=u^2+a^2t^2+2uat$

[ocean seal]

[🔥IS] X-82

[alpine sable]

yeah

[narrow trench]

how can I do such a silly mistake?

[alpine sable]

happens

[jovial forum]

Can someone please explain how to take a set of vectors that form a basis and change it to the standard basis in R^3? Struggling to follow my textbook and i think an example will help greatly

[narrow trench]

can you explain in simpler words?

[jovial forum]

Im trying to understand change of basis basically

[tidal trellis]

can someone help me with hegarty maths

[subtle pasture]

whats that lol

[subtle pasture]

270,-90

[pearl lily]

-270, 90

[tidal trellis]

ttyyyyyy

[south warren]

@tidal trellis

Gcse server

[alpine sable]

just line up the graph. look on the y axis where the curve reaches 1 and then see where that is on the x axis

[south warren]

Help pls

[alpine sable]

so you can see that when y = 1, x = -270 for eg

[alpine sable]

I'll help u but I won't tell u

[south warren]

Ok so

What do i do

[alpine sable]

You see line BO

[south warren]

Yeah

[alpine sable]

That is perpendicular to the tangent QBC

ABC

so it must be 90

[south warren]

Yeah

Radius tangent meet at 90

[alpine sable]

OBD AND ODB must be the same

since they are both same distance from centre 0

So they're both 22

[south warren]

And then BOD is isoceles

Yes

Ok

[alpine sable]

So BOD is 136 as angles in triangle are 180

I'll let u do the rest

[south warren]

Thanks

[alpine sable]

np

[pearl solar]

Seems to be easy but i am unable to solve it

[jade birch]

Did you draw it?

[pearl solar]

I tried drawing it and using cosines to get a measure of those but i cannot seem to do it with third one

[jade birch]

Ah tbh I'd need paper for this which I don't have atm ;- ;

[pearl solar]

Ok, maybe someone else would help

[soft zodiac]

I don't know how to solve this any help would be appreciated

[alpine sable]

would this also be correct if I had subtracted 3 on both sides or not? I don't think I can do that with parentheses. So x/a-b = 2/a-b is incorrect right?

[quaint trout]

Yes, that's incorrect

If you subtract 3 from both sides you get

x(a+3-b) - 3 = 5-3

The LHS does not simplify to x(a-b)

[tacit turtle]

Can someone help me with how I can plot the real and imaginary parts as functions of z? I got as far as substitution z = ix and got that Re = exp(3x) and Im = 0. Not sure how to "plot that in terms of z"

[south warren]

\begin{tikzpicture}[scale=1.2]
\draw[thick,color=BlueViolet] (0,0) circle (3cm);
\coordinate[label=below left:$A$] (A) at (-2.4,-1.8);
\coordinate[label=above left:$B$] (B) at (-1.3,2.7);
\coordinate[label=above right:$C$] (C) at (0.3,3);
\coordinate[label=below right:$D$] (D) at (2.1,-2.1);
\draw[thick] (A)--(B)--(C)--(D)--(A);
\coordinate[label=above:$P$] (P) at (-0.6,5.5);
\draw[thick] (B)--(P)--(C);
\node at (-2.1,1) {8};
\node at (1.5,1) {5};
\node at (-1.2,4) {6};
\begin{scope}
\path[clip] (A)--(P)--(D);
\draw[RedViolet] (P) circle (30pt);
\path[clip] (P)--(B)--(C);
\draw (B) circle (17pt);
\end{scope}
\node[color=RedViolet, scale=0.76] at (-0.54,4.8) {$60^o$};
\node[scale=1.4] at (-1.07,2.93) {$\theta$};
\begin{scope}
\path[clip] (A)--(D)--(P);
\draw (D) circle (22pt);
\end{scope}
\node[scale=1.5] at (1.7,-1.8) {$\theta$};
\begin{scope}
\path[clip] (P)--(C)--(B);
\draw (C) circle (16pt);
\end{scope}
\begin{scope}
\path[clip] (P)--(A)--(D);
\draw (A) circle (20pt);
\node[scale=1.5] at (0,3.2) {$\delta$};
\node[scale=1.5] at (-2.1,-1.53) {$\delta$};
\draw[thick,dashed,color=Emerald] (A)--(C);
\end{scope}
\foreach \k in {A,B,C,D,P} \filldraw (\k) circle (1.5pt);

\end{tikzpicture}

[ocean seal]

The 5th Emperor
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[alpine sable]

okay back to here , i know how to get the instantaneous velocity but , what are the values , so what i understood is that the instantaneous velocity is , we draw the tangent line of a point and pick the closest line to it , then find the slope , but not sure how would we get the number , in that example i think the answer would be 15/Ms

[tacit turtle]

do you mind?

[south warren]

Yes i do actually

[tacit turtle]

@south warren you should try #latex-testing

[surreal rune]

need help with add maths

[alpine sable]

i assume this channel is claimed

[surreal rune]

whoops sorry I'm new

[alpine nacelle]

by a lot of people, unfortunately, now it's kinda hard to answer

[surreal rune]

aight which question is free?

[alpine sable]

What are the best mathematics books

Especially for learning logic?

when all the channels are claimed

[magic warren]

how do i go about solving this

[alpine nacelle]

z = 2(-cos(alpha)+isin(alpha))
which angle has the same sin as alpha, but the opposite cos ?

you can put some arbitrary angle alpha on your unit circle and visualize it

it's pi - alpha

[orchid kayak]

Ey, I got a math problem here
Is this chat being used or nop?

[alpine nacelle]

z = 2(-cos(alpha)+isin(alpha)) = 2(cos(pi-alpha)+isin(pi-alpha)) and now it's more obvious @magic warren

[alpine nacelle]

you can use it now

[orchid kayak]

Ayt, so, I've got a math question in my homework

lemme translate it rq

It is known that the trapezoidal terrains ABCD and
PQRS that are found at the intersection of streets to
following are similar.
To get around the two lands, its owner will use 560
meters of wire. Knowing that sides AB = 30 m,
CD = 60 and BC = AD = 25, determine the shortest side of the
PQRS trapeze.

I tried to find ways to make this math

and I couldn't find anything

[magic warren]

@alpine nacelle thanks

[alpine sable]

What's the best mathematics books

[glass lichen]

#book-recommendations

[alpine sable]

i am looking for all whole number solutions to:
129x + 83y = 2000
I put right side equal to 1: 129x+83y=1, got solutions -9 and 14 using bezouts
now want to extend this solution to left side = 2000
note: 129x+83y=1 is a divisor to 2000, any tips on how to get there?

[vale wigeon]

now want to extend this solution to left side = 2000
just multiply the solution to 129x + 83y = 1 by 2000 lol

(x,y) = (-18000, 28000) is a solution to your equation

[alpine sable]

not good enough

x>=0 and y>=0

[vale wigeon]

once you have one solution it's easy to generate them all lol

you will have $x = -18000 + 83k, ; y = 28000 - 129k$ for $k \in \bZ$

[ocean seal]

Ann

[vale wigeon]

find k to make both x and y nonnegative

[alpine nacelle]

note, if you know you need x and y positive, you can make a couple positive from there, and then multiply by 2000, lol

[vale wigeon]

-18000 + 83k ≥ 0 => k ≥ 18000/83

[alpine sable]

x>=0 <=> -18000 + 83 >=0 ill try to figure it out,

yeah

[vale wigeon]

28000 - 129k ≥ 0 => k ≤ 28000/129

[wintry vortex]

hi ann 🙂

[vale wigeon]

,calc 18000/83

[ocean seal]

Result:

216.86746987952

[vale wigeon]

,calc 28000/129

[ocean seal]

Result:

217.05426356589

[vale wigeon]

k=217, it looks like.

hello hiabusha

[alpine sable]

ann

thanks

!

[hushed pasture]

what is the remainder of $16^{2^{1000}}$ by $7$ ?

[ocean seal]

Salah

[vale wigeon]

have you made any progress so far?

[hushed pasture]

I think i did it wrong

[vale wigeon]

show work?

[hushed pasture]

i found that $2^3 \equiv 1 [7] \implies 2^{999} \equiv 1 [7] \implies 2^{1000} \equiv 2 [7]$

[ocean seal]

Salah

[hushed pasture]

and I just compute $16^2 (mod 7)$ but i realise that it's wrong

[ocean seal]

Salah

[cobalt coyote]

Could anyone please help me

Or this I'm not getting

[deep urchin]

Hi I need help in this, Please!! Thank you so so much.

[alpine nacelle]

16 = 2 mod 7 so you're looking at 2^(2^1000) mod 7
2^3 = 1 mod 7 and 2^1000 = 1 mod 3
so 2^(2^1000) = 2^1 = 2 mod 7

[fierce frigate]

help meh

someone said it was
0.4 x 0.6
but i dont know why

[hushed pasture]

OMG thank you man i get it now

[meager pebble]

hi

anyone familiar with numerical methods?

[tawdry sphinx]

if you want both events to take place then you need to multiply the probablities of the events, in this case $P(\text{"both pass the test"})=P(\text{"Joseph passes the test"})\times P(\text{"Daniel passes the test"})=0.6\times 0.4$

[ocean seal]

NoRysq

[fierce frigate]

Why tho

Why do we have to

[tawdry sphinx]

the first event occours with a probablility of 60%

so if we got the event we have a 40% probability of getting the next event happening

meaning we have 60% * 40%

[earnest solar]

is there any channelfor class 8 maths

[sharp barn]

How do we solve this?

[random ocean]

Check the discriminant of the equation 🙂 b^2 - 4ac

If the roots are real and distinct, this should always be positive

[sharp barn]

erm correct me if i am wrong the a =1 b=(k-2) c=-2k

[random ocean]

Mhm

[sharp barn]

I think i did something wrong

[random ocean]

I’m a bit confused by the question since k=-2 clearly gives a repeated root

[opaque trellis]

just solve it with intervals method

[sharp barn]

why cant we just solve it using quadratic formula

[random ocean]

You can do that too

[opaque trellis]

u wrote wrong

[random ocean]

but I think the question is wrong, because you definitely can get a repeated root

[opaque trellis]

k>-2

[random ocean]

Where does it say that?

[opaque trellis]

solve

[sharp barn]

then can you solve it using the method i am using?

if u can can u show?

@opaque trellis u there?

[gusty reef]

Can anyone remind me of the original proof of the harmonic series' divergence?

[sharp barn]

@opaque trellis u helping or nah?

[alpine sable]

send qn

[alpine sable]

find b^2-4ac

[quartz oxide]

Bruh k^2+4k+4 is obv a perfect square
So, must be >0

[alpine sable]

yes

thats it

[sharp barn]

why is it obvious?

[alpine sable]

because it just is

[sharp barn]

bro u got to show it

[quartz oxide]

k^2+4k+4=(k+2)^2

[sharp barn]

u dont get the mark just by saying it just is

[alpine nacelle]

you can factor directly as (x-2)(x+k)

[alpine sable]

(k-2)^2 - 4(1)(-2k) = k^2 + 4-4k+8k = k^2 +4 + 4k = (k+2)^2

but i dont see a reason why roots cant be equal

they have given real and distinct

[sharp barn]

can you use the bot and write it out cuz its kinda of confusing what u wrote

[alpine sable]

@sharp barn

idk how to use it

[sharp barn]

nvm i write it out myself

[alpine sable]

k

[opaque trellis]

root can be taken from odd and even bracket

so can be two same roots

[sharp barn]

ok lets say we found until this k^2 +4 + 4k

[opaque trellis]

3,4,5,6,7

[sharp barn]

then i want to find the value of k

[opaque trellis]

let f(k)= k^2+4k+4

and just find when f(k)>0 and at what values of k

[sharp barn]

sorry but can you show it?

[opaque trellis]

donu know formula x =(-b +root(b^2-4ac))/2a

?

[sharp barn]

oh quadratic formula

[earnest solar]

#help-0 is there channel for class 8 maths

[alpine sable]

@sharp barn do u know that when u square a number its always going to be postive/0 ?

[earnest solar]

hello

[opaque trellis]

when f(x) cross the x-axis on the graphic the sign of value f(x) become from + to - and from - to +

[alpine sable]

k^2 + 4 + 4k = (k+2)^2 , since its the square of (k+2) its always gonna be +ve/0

[sharp barn]

but i got -2

[earnest solar]

hello

[opaque trellis]

yes

its true

[alpine sable]

you should not equate the discriminant to 0

[sharp barn]

mb then what about the -2

[opaque trellis]

i dont understand what kupsrika said

but its normal solution

[alpine sable]

it just means that when k=-2 then that expression equals 0

[random ocean]

The question looks like it’s formulated incorrectly, the roots aren’t distinct for k=-2

[alpine sable]

yes

[random ocean]

You have a repeated root

[alpine sable]

thts what i asked before

[random ocean]

👍

[alpine sable]

but anyways

[sharp barn]

-2 isnt real orea l and distinct right?

[random ocean]

-2 is real

[alpine sable]

-2 is real , and when k=-2 , the roots are real and equal

see dude

[sharp barn]

but i tot real and distinct roots are >0

[alpine sable]

do you know that for roots to be real , b^2 - 4ac > =0 ?

b^2 - 4ac we got it to be (k+2)^2 right ?

and (k+2)^2 is always >=0

hence proved that the roots are always real

the distinct part of the qn is wrong since the roots can be equal

[sharp barn]

ohh so for -2 is the value of k

isit?

[alpine sable]

no no

-2 is one of the values of k

k can be any value

as given in the qn

for k=-2 the roots are equal

for any other k the roots are distinct

[sharp barn]

because it said its real distinct roots so it will be k>-2?

nvm i got it already thanks

[void magnet]

how you I factorise something in the form x^3 - x

[silver current]

What is common in those two terms?

[void magnet]

x

[silver current]

take it outside

what will be the new expression?

[void magnet]

i dont know... x(?^3 - ?)

[silver current]

x^3 means x * x * x

[dry hare]

Find the area of each circle to the nearest tenths. Use 3.14 for . 16 inches Help plsss

[silver current]

if you take one x out how many remain?

[void magnet]

two

so x(x^2 - x)

[silver current]

a little wrong

you can think x as x*1

if you take x out/common of x*1

what will you get

[void magnet]

right so x(x^2)

[silver current]

No

its still in addition

it has not become zero

[silver current]

just use the formula for area of a circle

[void magnet]

oh so x(x^2-1)

[silver current]

correct

Now its not completely factorised

Can you see a pattern inside the brackets?

[void magnet]

yeah

[silver current]

cool, factorise it

[void magnet]

would that be x((x + 1)(x - 1))

[tame oxide]

Hello guys, can anyone help me with a statistics problem?

[silver current]

indeed

therefore you have 3 factors (x)(x+1)(x-1)

[void magnet]

oh i can just write it like that

[silver current]

yep

[glad moon]

Could anyone help me with this question?

[void magnet]

i wish i found out about these help channels sooner I learn so much from them

[silver current]

nice

[rich basin]

why is it that (a) is true

like wouldn't all of them be incorrect

[tame oxide]

I need help with V and VI. Thanks

[coarse axle]

can i have help please

just my exercice is in french

[south warren]

\begin{tikzpicture}
\coordinate (A) at ({4 * cos(50)}, {-4 * sin(50)});
\coordinate (B) at ({2 * sqrt(2)}, {-2 * sqrt(2)});
\draw (0, 0) circle (4);
\draw[dashed] (0, 0) -- (4, 0);
\draw[dashed, green] (0, 0) -- (2, 0);
\node at (1, 0) [above] {$x$};
\draw[dashed, green] (0, 0) -- (0, 4);
\node at (0, 2) [right] {$R$};
\draw[dashed] (2, 0) -- (A);
\draw[dashed] (0, 0) -- (A);
\draw (0.3, 0) arc (0:-35:0.5);
\node at (0.5, -0.25) {$\theta$};
\node at ({0.75 + sqrt(2)}, {-sqrt(2)}) [right, red] {$y$};
\node at (3.5, 3.5) [red] {$y=?$};
\end{tikzpicture}

[ocean seal]

The 5th Emperor

[south warren]

\begin{tikzpicture}[scale=1.2]
\draw[thick,color=BlueViolet] (0,0) circle (3cm);
\coordinate[label=below left:$A$] (A) at (-2.4,-1.8);
\coordinate[label=above left:$B$] (B) at (-1.3,2.7);
\coordinate[label=above right:$C$] (C) at (0.3,3);
\coordinate[label=below right:$D$] (D) at (2.1,-2.1);
\draw[thick] (A)--(B)--(C)--(D)--(A);
\coordinate[label=above:$P$] (P) at (-0.6,5.5);
\draw[thick] (B)--(P)--(C);
\node at (-2.1,1) {8};
\node at (1.5,1) {5};
\node at (-1.2,4) {6};
\begin{scope}
\path[clip] (A)--(P)--(D);
\draw[RedViolet] (P) circle (30pt);
\path[clip] (P)--(B)--(C);
\draw (B) circle (17pt);
\end{scope}
\node[color=RedViolet, scale=0.76] at (-0.54,4.8) {$60^o$};
\node[scale=1.4] at (-1.07,2.93) {$\theta$};
\begin{scope}
\path[clip] (A)--(D)--(P);
\draw (D) circle (22pt);
\end{scope}
\node[scale=1.5] at (1.7,-1.8) {$\theta$};
\begin{scope}
\path[clip] (P)--(C)--(B);
\draw (C) circle (16pt);
\end{scope}
\begin{scope}
\path[clip] (P)--(A)--(D);
\draw (A) circle (20pt);
\node[scale=1.5] at (0,3.2) {$\delta$};
\node[scale=1.5] at (-2.1,-1.53) {$\delta$};
\draw[thick,dashed,color=Emerald] (A)--(C);
\end{scope}
\foreach \k in {A,B,C,D,P} \filldraw (\k) circle (1.5pt);

\end{tikzpicture}

[ocean seal]

The 5th Emperor
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[south warren]

\begin{tikzcd}
\bullet \arrow[out=120,in=60,loop]
\end{tikzcd}\begin{tikzpicture}[scale=1.2]
\draw[thick,color=BlueViolet] (0,0) circle (3cm);
\coordinate[label=below left:$A$] (A) at (-2.4,-1.8);
\coordinate[label=above left:$B$] (B) at (-1.3,2.7);
\coordinate[label=above right:$C$] (C) at (0.3,3);
\coordinate[label=below right:$D$] (D) at (2.1,-2.1);
\draw[thick] (A)--(B)--(C)--(D)--(A);
\coordinate[label=above:$P$] (P) at (-0.6,5.5);
\draw[thick] (B)--(P)--(C);
\node at (-2.1,1) {8};
\node at (1.5,1) {5};
\node at (-1.2,4) {6};
\begin{scope}
\path[clip] (A)--(P)--(D);
\draw[RedViolet] (P) circle (30pt);
\path[clip] (P)--(B)--(C);
\draw (B) circle (17pt);
\end{scope}
\node[color=RedViolet, scale=0.76] at (-0.54,4.8) {$60^o$};
\node[scale=1.4] at (-1.07,2.93) {$\theta$};
\begin{scope}
\path[clip] (A)--(D)--(P);
\draw (D) circle (22pt);
\end{scope}
\node[scale=1.5] at (1.7,-1.8) {$\theta$};
\begin{scope}
\path[clip] (P)--(C)--(B);
\draw (C) circle (16pt);
\end{scope}
\begin{scope}
\path[clip] (P)--(A)--(D);
\draw (A) circle (20pt);
\node[scale=1.5] at (0,3.2) {$\delta$};
\node[scale=1.5] at (-2.1,-1.53) {$\delta$};
\draw[thick,dashed,color=Emerald] (A)--(C);
\end{scope}
\foreach \k in {A,B,C,D,P} \filldraw (\k) circle (1.5pt);

\end{tikzpicture}\begin{tikzpicture}
\coordinate (A) at ({4 * cos(50)}, {-4 * sin(50)});
\coordinate (B) at ({2 * sqrt(2)}, {-2 * sqrt(2)});
\draw (0, 0) circle (4);
\draw[dashed] (0, 0) -- (4, 0);
\draw[dashed, green] (0, 0) -- (2, 0);
\node at (1, 0) [above] {$x$};
\draw[dashed, green] (0, 0) -- (0, 4);
\node at (0, 2) [right] {$R$};
\draw[dashed] (2, 0) -- (A);
\draw[dashed] (0, 0) -- (A);
\draw (0.3, 0) arc (0:-35:0.5);
\node at (0.5, -0.25) {$\theta$};
\node at ({0.75 + sqrt(2)}, {-sqrt(2)}) [right, red] {$y$};
\node at (3.5, 3.5) [red] {$y=?$};
\end{tikzpicture}

[ocean seal]

The 5th Emperor
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rich basin]

<@&286206848099549185>

[prisma prawn]

How do you solve this, whats the first step

[split oriole]

Lcm

[prisma prawn]

what does that mean?

[indigo storm]

Is this correct?

[split oriole]

Lcm of denominator

[prisma prawn]

but how

[split oriole]

Step number 4 , write square outside the squareroot

[prisma prawn]

just multiply each of them with eachother

?

[indigo storm]

Ah got it

Thanks

[alpine sable]

How much time would it take to go thru all of Khan academy maths

[indigo storm]

You mean left side?

[alpine sable]

Like a 1000 hours?

[split oriole]

Yes

[indigo storm]

Got it

[alpine sable]

Algebra can you tell me

[split oriole]

You should ask this question in discussion group, they will definitely help you.

[split oriole]

Can you send full question?

[prisma prawn]

wdym

you need to simplify

[split oriole]

Okkk x^n and x^n, and x^{n-2} lcm?

[crimson cradle]

need help with this ty im struggling

\begin{tikzpicture}[scale=1.2]
\draw[thick,color=BlueViolet] (0,0) circle (3cm);
\coordinate[label=below left:$A$] (A) at (-2.4,-1.8);
\coordinate[label=above left:$B$] (B) at (-1.3,2.7);
\coordinate[label=above right:$C$] (C) at (0.3,3);
\coordinate[label=below right:$D$] (D) at (2.1,-2.1);
\draw[thick] (A)--(B)--(C)--(D)--(A);
\coordinate[label=above:$P$] (P) at (-0.6,5.5);
\draw[thick] (B)--(P)--(C);
\node at (-2.1,1) {8};
\node at (1.5,1) {5};
\node at (-1.2,4) {6};
\begin{scope}
\path[clip] (A)--(P)--(D);
\draw[RedViolet] (P) circle (30pt);
\path[clip] (P)--(B)--(C);
\draw (B) circle (17pt);
\end{scope}
\node[color=RedViolet, scale=0.76] at (-0.54,4.8) {$60^o$};
\node[scale=1.4] at (-1.07,2.93) {$\theta$};
\begin{scope}
\path[clip] (A)--(D)--(P);
\draw (D) circle (22pt);
\end{scope}
\node[scale=1.5] at (1.7,-1.8) {$\theta$};
\begin{scope}
\path[clip] (P)--(C)--(B);
\draw (C) circle (16pt);
\end{scope}
\begin{scope}
\path[clip] (P)--(A)--(D);
\draw (A) circle (20pt);
\node[scale=1.5] at (0,3.2) {$\delta$};
\node[scale=1.5] at (-2.1,-1.53) {$\delta$};
\draw[thick,dashed,color=Emerald] (A)--(C);
\end{scope}
\foreach \k in {A,B,C,D,P} \filldraw (\k) circle (1.5pt);

\end{tikzpicture}

[ocean seal]

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

[dry hare]

A ferries wheel has a diameter of 140 feet. What is the area of the ferris wheel? Use 22
-
7 for pi

help :))

[split oriole]

What is area of a circle?

[split oriole]

Put sin x =t

[old whale]

5x + 3y = 19
2x +2y = 10
by graphical method

[crimson cradle]

Is that the solved equation?

[old whale]

can you describe it for me?

[old whale]

The result is x.y (2,3)

[split oriole]

First draw these lines

On graph

[old whale]

Can you describe it? I don't understand, my teacher didn't explain how to make it

I swear the teacher just sent the file

[split oriole]

https://youtu.be/k-_Z67HFK_A

[lapis stream]

Can I ask here?

[granite raptor]

In what ratio of line x – y – 2 = 0 divides a line segment joining (3, -1) anf (8, 9)

how do i solve this question

[crimson cradle]

https://cdn.discordapp.com/attachments/711377712367009824/803477970361909248/image0.png

[supple jewel]

straight up i got 60 bucks lost im braindead

[crimson cradle]

damn maths discord cant do ez maf

[supple jewel]

its like 11pm im dieing

[alpine sable]

what

can i get some help

You know index/exponents? @alpine sable

no

whats an index again

[supple jewel]

i used my braincells

[crimson cradle]

so what is answer

[alpine sable]

Here, we only need to simplify it.

Look, 1/2×2×2

I,e,.

1/2³
= 2^-3

[supple jewel]

not 60:)

[alpine sable]

are you still looking for help?

[crimson cradle]

yes

[alpine sable]

have you tried anything?

specially differentiating sin^3(x)?

[alpine sable]

oh i thought we had to solve 2x2x2 then write the -3 thing

thanks

[alpine sable]

You're most welcome 😊

[crimson cradle]

ah thank you

[gloomy ermine]

Is there a taylor series for a^x? What I thought would work doesn't seem to when graphing it and when I looked it up, all the results didn't really seem to be answering this question

Well, I mean it only seems to work when the value of a is e

[restive hill]

Hi, can anyone give me three real-life applications of Joint variation and combined variation? Thank you!

[bold panther]

could someone please help?

[shell widget]

@bold panther Try using the formula sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

[bold panther]

ahh ok but what do i do after that?

[rigid wind]

use t in a's place, and pi/2 in b's place

sin(pi/2) and cos(pi/2) can be calculated (or inferred from unit circle)

[bold panther]

ohhh tyyy

also i have one more question does the formula only work for sin and cos or can it work for tan, cot, sec, and csc too?

[ruby current]

sin(t-pi/2)=sin(-(pi/2-t))=-sin(pi/2-t)=-cos(t)

if you want to use the cofactor identity, i.e. sin(pi/2-t)=cos(t)

[alpine sable]

can anyone help me with a statistics question

i have the answer, i just need some help with understanding what to do with it

i dont understand what is going on here....

anyone able to explain why that one part that has e^{-z} is being multiplied by x?

and how that turns into z?

[remote heron]

unfortunate notation

but its jus integration wrt x

think of it just like $\int 4y \dd x$

[ocean seal]

jan Niku

[rigid wind]

x goes from 0 to z

[remote heron]

this is 4yx + c

[rigid wind]

so the difference between the antiderivative at x=z

and at x=0

[remote heron]

just like the derivative of 4yx wrt x is 4y

[alpine sable]

ah its just treating it like a constant

[remote heron]

yea

[alpine sable]

i just dont understand why its being multiplied by x(x)

[remote heron]

theyre using cross notation

[rigid wind]

the cross is multiply