#circle

306 messages · Page 1 of 1 (latest)

cedar stagBOT
waxen rapids
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The circle it is referring to with radius 10 is the quarter circle.

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Hope that helps!

orchid drift
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How would you solve it afterwards?

supple python
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I’m actually extremely curious, I know there is another way, but my only idea would be to rotate 45 degrees and use an integral

waxen rapids
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Were you able to solve it?

waxen rapids
livid maple
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https://www.quora.com/The-diagram-shows-a-circle-inscribed-inside-a-square-of-side-length-10cm-A-quarter-circle-of-radius-10cm-is-drawn-with-the-vertex-of-the-square-as-its-centre-What-is-the-shaded-area

Quora
The diagram shows a circle inscribed inside a square of side length...

Answer (1 of 4): Point D is at (0,0). Corners of square are at (1,1), (1,-1), (-1,-1), and (1,-1). A and B are the two intersection points of circles x^2 + y^2 = 1 and (1-x)^2 + (1+y)^2 = 4. Expand the second equation and replace x^2 + y^2 with 1 to get the line y= x + 1/2 which includes points A...

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here’s a solution I found on quora

waxen rapids
orchid drift
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Cough cough

supple python
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im currently looking into it

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and ive got a quartic equation i need the roots of oh god

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im trying to find the two intersection points of the circle so i can integrate distance from a middle point to a circle edge at an angle

swift brook
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Find the area of the quarter circle and then the area of inscribed circle and subtract quarter circle with inscribed circle

supple python
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i dont think that will work

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as they are not perfectly within one another

swift brook
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And the radius of quarter is given

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But

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Wait mb

supple python
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i dont think you can just subtract them lmao

swift brook
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Nah it won’t work srry

swift brook
supple python
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you prob saw wrong or smthn, we all do it every once in awhile

swift brook
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We need an eq

supple python
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im trying to find where the 2 circles intersect

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so i can use an integral to find the area

swift brook
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Local maxima can be used and then the eq for the curve

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But it will make it more complex

supple python
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im gonna be honest with you, i dont know exactly what im doing

swift brook
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xD

supple python
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but i have an idea

swift brook
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Instead of going deep inside it

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There must be another way

supple python
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ye but i could just use an integral with stuff and bam area if i know how to do it

swift brook
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For that particular curve

supple python
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because its a circle

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i can just make a line at an angle and see when it is on the perimeter

swift brook
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It may take time

supple python
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ive already almost got the coordinates of the intersection points

swift brook
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Hmm

supple python
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so those will be our bounds for our angle

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or the arctangent of the thing to make angle stuff

swift brook
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Okay I got it

supple python
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now

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to deal with quartic equation

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oh one of the roots is at the center of the circle

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so thats somewhat convenient

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wait a minute

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how will we find distance from large circle from centerpoint of small circle at an angle

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bro my constant term is 6400

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wait nvm

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wait yeah

swift brook
supple python
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now to find what y is

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using this

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this thing scares me

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bro 💀

image.png
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this hurts my eyes

waxen rapids
supple python
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i had to put it into desmos dude

waxen rapids
supple python
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and then remember which ones are + and -

supple python
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wait oh hell

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i just

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realized something

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i might have to.

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because desmos cannot deal with imaginary numbers.

waxen rapids
waxen rapids
supple python
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I HAVE MADE A GRAVE MISTAKE

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OH NO

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I SIMPLIFIED SOMETHING WRONG

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2 HOURS OF WORK AGO

waxen rapids
supple python
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IVE SPENT MORE LMAO

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I THOUGHT IT WAS INTERESTING

waxen rapids
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Looks like you'll be on this for a while

supple python
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yeah.

waxen rapids
supple python
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im persistent though

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actually tho

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if im gonna be an engineer i gotta deal with this stuff

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so

waxen rapids
supple python
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dude i probably have 3000+ hours in desmos

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ok maybe not that many

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but probably more than a thousand

waxen rapids
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Lol ok

supple python
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i have spent 3 weeks now trying to solve my pronblem

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pronblem

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bor

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nevermind

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there was going to be a point to my rambling

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but i misspelled problem twice

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and forgot

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oh my god its not even quartic

supple python
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found the intersection points

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ill continue tomorrow

swift brook
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Lmao

supple python
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im realizing now there would probably be an easier way to do this

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so i dont have to integrate an angle

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itll just be 2 integrals

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or 3

supple python
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Integral formula finished

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Now to evaluate

waxen rapids
# supple python

That thing looks ghastly, are you absolutely sure you calculated it correctly?

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You wouldn't want to waste time on a dysfunctional integral

supple python
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I modeled it on a program and then got another program to evaluate it and it’s correct

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I just need to understand how to evaluate it

swift brook
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You don’t have to use this much of brain for this

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This problem I guess is an exam related problem and you have to manage time for it

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There maybe a way instead of going to integrals

swift brook
supple python
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its like 14.6

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or smthn

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there is a way without calc

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its just

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way too many separate things

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its like finding a bunch of areas of a circle around a certain point

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here ill just make a graph of it real quick

supple python
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i have to plug in polynomials 💀

supple python
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almost done graph

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sorry for slow

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its 5am

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and i didnt sleep lmao

bold bluff
# supple python its 5am

Bro. I don’t know whether to have immense respect or fear for the fact that you didn’t sleep to do math

supple python
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and its a regular event.

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i have trouble sleeping when i have a problem i havent solved

bold bluff
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Did you sleep at all? I hope you’re okay 🥺

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I just can’t fathom not sleeping to do math

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Usually I just play video games or watch tv

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Or study bio

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Math is not it for me

supple python
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im alr i love math

bold bluff
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That’s good! I wish I was the same because I don’t

supple python
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usually i have more fun when working on an interesting problem

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especially because i can model things on desmos

bold bluff
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Well I can agree that desmos is great

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Best online calculator

supple python
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i spent 30 hours on it over the break

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and still didnt solve my problem lmao

bold bluff
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BRO

supple python
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it was more of a desmos issue tho

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trying to get it to recognize if a square root was rational

bold bluff
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I uh cannot relate

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I try to minimize the time I have to spend on desmos

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I have spent hours searching google scholar and reading articles for a review of the Bee Movie though

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So I understand unnecessary effort

supple python
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yes.

bold bluff
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Just in a different discipline

supple python
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Typing

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Go on

waxen rapids
supple python
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It might also have something to do with insomnia

waxen rapids
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On keyboard I'm decently fast

supple python
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I’m just surprised I caught you while you were typing as I got on discord

waxen rapids
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I always check discord in the morning

supple python
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but i figure to someone who can reliably do integrals

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that the calculus approach is simpler

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which is odd

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but as it turns out calculus is useful

waxen rapids
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Actually even I might be able to solve it that way

supple python
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yeah but you can have a certain fraction of a circle

waxen rapids
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But it's gonna be a lot of steps

supple python
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and then just the triangles

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to get full area

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if you go in the graph you can also drag the line

waxen rapids
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Ya

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I could use tangent to plot lines easy enough

supple python
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the other reason i went calc approach is i didnt have paper

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within close proximity

waxen rapids
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I have to go now but I'll try it using a different approach later

supple python
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and my hands are way too shaky to use an online whiteboard

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alr cya!

swift brook
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This prob solved?

red karma
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.solved?

waxen rapids
bold bluff
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Didn’t someone find a quora answer?

waxen rapids
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Obviously a mod could close the thread but I'm no mod

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So we have to wait for the owner of the thread to do .solved

bold bluff
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Thanks for telling me! I had no idea how the forums worked

waxen rapids
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@supple python I have finally solved this problem so I will post my solution here later. It is indeed a lengthy procedure but I figured it out. Btw, the variable h holds the exact value of the answer if you are still interested.

rn_image_picker_lib_temp_05bb0eae-d519-4230-8bd9-d85eb841aef1.jpg
lyric ginkgo
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@waxen rapids is this what I ended up solving?

waxen rapids
lyric ginkgo
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@median bear here's a breakdown of the solution #math-discussion message

supple python
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ooh

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howd you do it?

lyric ginkgo
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It's discussed in the thread link I shared

supple python
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i do not have access

lyric ginkgo
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Weird...

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Did you get banned or something?

waxen rapids
waxen rapids
lyric ginkgo
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Math discussion shouldn't require any rules

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Ahh

waxen rapids
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Do you know how to do that?

lyric ginkgo
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I did not know that

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No

supple python
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i have no clue

lyric ginkgo
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@supple python here's the solution

image.png
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I just used basic geometry and trig

supple python
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oh

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i just integrated

waxen rapids
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Change your roles here:

Screenshot_20230421-231641.png
supple python
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but i didnt know how to solve final integral

waxen rapids
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You should be able to view the channel after you change your roles

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@supple python you need this

Screenshot_20230421-231752.png
supple python
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yeah i fixed

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i like looking at the desmos graph

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then just microsoft paint labels

waxen rapids
supple python
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yes

waxen rapids
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Oh ok

supple python
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it seems pretty straight forwards

waxen rapids
supple python
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just parts of a circle

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also oh my god

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ive learned integration by power rule

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and somehow didnt realize the ability to find the area of a circular arc

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which somewhat frightens me

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because it should have clicked in my brain immediately

waxen rapids
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This was my longest step although I kept going in circles

Screenshot_20230421-232105.png
supple python
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wait you using chords n stuff

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i found the intersecting points using quadratics

waxen rapids
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The majority of the time I took was wasted on repeated steps lol

supple python
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because circles can also be written as +- sqrt(r^2 - x^2)

waxen rapids
supple python
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i dont know anything about chords

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so far ive just used distances of coordinates

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which might make stuff like this get messy

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i still havent found the exact expression for the lines

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and there are 4 different possibilites

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and im not even sure they quadratic

waxen rapids
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So like for the circles x^2+y^2=25 and (x-5)^2+(y+5)^2=100, the equation of the chord would be y=5/2x, and then you substitute 5/2x in for y in either of the equations for the intersection points.

supple python
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wait what

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where did you get thes

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where did that come from

waxen rapids
supple python
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oh god im gonna have to break out the whiteboard for that one

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when available

waxen rapids
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Dw I calculated the equations of all the lines in this and it definitely took me a while

05bb0eae-d519-4230-8bd9-d85eb841aef1.jpg
supple python
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dang

waxen rapids
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The total time I took is probably 1 to 1.5 hrs

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To solve it

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When I actually sat down to look at it

supple python
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oh thats not that bad

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considering that ive spent like 6 hours on making a table on desmos

waxen rapids
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I'm honestly a little bit surprised because no one at school had any idea how to solve it

waxen rapids
supple python
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nah dude it was worth

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check this out

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its a whole program

waxen rapids
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What does it do?

supple python
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it takes a number that is a product of two prime numbers to certain powers

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so its basically finding all the factor pairs

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with a number which has 2 different numbers as prime factors

waxen rapids
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Oh cool

supple python
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it also tells you if its a perfect square, cube

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and however far you want to go

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with a slider

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you can drag things

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you can move the sliders

waxen rapids
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Nice

supple python
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im proud of it

waxen rapids
supple python
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but multiplying the red number by the blue one will yeild the original one

waxen rapids
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Ok well it's 11:35pm here for me so gn or gm

supple python
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alright

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same

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but my sleep schedule is beyond comprehension

lyric ginkgo
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.solved

cedar stagBOT
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Solved

Post marked as solved by @lyric ginkgo.

Use .unsolved if this was a mistake.

red karma
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hi

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.unsolved

cedar stagBOT
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Unsolved

Post marked as unsolved by @red karma.

Use .solved to mark as solved.

red karma
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lets do record for most discussed helpforum problem

waxen rapids
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This is my unsimplified result. It is also the exact value of the answer.

image.png
waxen rapids
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Wolfram Alpha gave me this:

image.png
lyric ginkgo
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.solved

cedar stagBOT
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Solved

Post marked as solved by @lyric ginkgo.

Use .unsolved if this was a mistake.

waxen rapids
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So you could slightly simplify your answer considering r=5.

lyric ginkgo
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I knew it was r=5. But generalizing is always nicer imo

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I find using actual values can be pretty distracting