/sci/ - Science & Math » Thread #11589067

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Mathematics

The Systems Tue 21 Apr 20:20:14 2020 No.11589067 View Reply Original Report

Quoted By: >>11589099 >>11589274 >>11589319 >>11589393 >>11590765

Two quarter circles and a semicircle. What’s the shaded area?

Anonymous

Anonymous Tue 21 Apr 2020 20:26:21 No.11589090 Report

Quoted By: >>11589107

To you have two equations:
x+y=12
(?y^2)/4 + (?x^2)/4 - (?(2x)^2)/2 = Shaded Area
Just plug and chug

Anonymous

Anonymous Tue 21 Apr 2020 20:27:46 No.11589099 Report

Quoted By: >>11589120 >>11589142 >>11589225 >>11589340

>>11589067
Not enough info. You can change the size of the semicircle arbitrarily.

Anonymous

Anonymous Tue 21 Apr 2020 20:29:45 No.11589107 Report

Quoted By:

>>11589090
This makes the assumption that the half-circle has a radius twice the radius of the smaller circle which we don't know to be true so it's wrong so nvm

The Systems

The Systems Tue 21 Apr 2020 20:32:35 No.11589120 Report

Quoted By: >>11589156

>>11589099
Retard detected

Anonymous

Anonymous Tue 21 Apr 2020 20:37:32 No.11589142 Report

Quoted By: >>11589156

>>11589099
HAHAHAHAHA

Anonymous

Anonymous Tue 21 Apr 2020 20:39:17 No.11589147 Report

Quoted By: >>11590567

x+y=12
z=(y-x)/2
(?y^2)/4 + (?x^2)/4 - (?z^2)/2 = Shaded Area
Ok now I think this is right

Anonymous

Anonymous Tue 21 Apr 2020 20:42:24 No.11589156 Report

Quoted By: >>11589159

>>11589120
>>11589142
Freshmen.

Anonymous

Anonymous Tue 21 Apr 2020 20:42:57 No.11589159 Report

Quoted By: >>11589170

>>11589156
How’d you solve it?

Anonymous

Anonymous Tue 21 Apr 2020 20:45:31 No.11589170 Report

Quoted By: >>11589175 >>11589187

>>11589159
If you can't immediately see figure is underdetermined you're a brainless. Just draw two figures where the size are different. Is this your homework?

Anonymous

Anonymous Tue 21 Apr 2020 20:47:19 No.11589175 Report

Quoted By: >>11589191

>>11589170
You haven’t written the solution yet mate, why is your brain going around in circles

The Systems

The Systems Tue 21 Apr 2020 20:49:46 No.11589187 Report

Quoted By:

>>11589170
Jesus Christ

Anonymous

Anonymous Tue 21 Apr 2020 20:50:14 No.11589191 Report

Quoted By: >>11589205

>>11589175
There is no solution you dumb fuck.

If you want people to do your homework go to the homework board >>>/hm/

The Systems

The Systems Tue 21 Apr 2020 20:52:35 No.11589205 Report

Quoted By:

>>11589191
I can post the solution if you want, will that make your brain relax its autism

Anonymous

Anonymous Tue 21 Apr 2020 20:58:29 No.11589225 Report

Quoted By: >>11589246

>>11589099
Is this what they call the Dunning-Kruger effect?

The Systems

The Systems Tue 21 Apr 2020 21:03:41 No.11589246 Report

Quoted By:

>>11589225
The sinking of his skull, and the stepped on soft spot of his brain

Anonymous

Anonymous Tue 21 Apr 2020 21:10:07 No.11589274 Report

Quoted By: >>11589277

>>11589067
Shaded area is 18pi.

The Systems

The Systems Tue 21 Apr 2020 21:11:05 No.11589277 Report

Quoted By:

>>11589274
Beautiful, show worked solutions for retard above

Anonymous

View Same Google iqdb SauceNAO a5.gif, 868KiB, 300x300

Anonymous Tue 21 Apr 2020 21:23:30 No.11589319 Report

Quoted By: >>11589332 >>11589400

>>11589067

Anonymous

Anonymous Tue 21 Apr 2020 21:28:53 No.11589332 Report

Quoted By: >>11589340

>>11589319
And? What makes you think they're any different?

Anonymous

Anonymous Tue 21 Apr 2020 21:31:15 No.11589340 Report

Quoted By: >>11589354

>>11589332
They're not. The gif is to illustrate that the area is invariant, which seems to be confusing people like >>11589099

Anonymous

Anonymous Tue 21 Apr 2020 21:35:28 No.11589354 Report

Quoted By: >>11589366

>>11589340
but how would i know that, trying to calculate the area?
How do you actually calculate it?

The Systems

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The Systems Tue 21 Apr 2020 21:38:42 No.11589366 Report

Quoted By: >>11589387 >>11589394 >>11589400 >>11590427 >>11590508 >>11590810

>>11589354
Dumb fuck

Anonymous

Anonymous Tue 21 Apr 2020 21:45:49 No.11589387 Report

Quoted By: >>11589835

>>11589366
Even easier: make the left quad-circle infinitesimal so that its area becomes zero, we are then left with (pi*12^2)/4 - (pi*6^2)/2 = pi*36 - pi*36/2 = pi*18.

Anonymous

Anonymous Tue 21 Apr 2020 21:46:55 No.11589393 Report

Quoted By: >>11589413

>>11589067
>12
12 what? Centimeters? Nanometers? Kilometers?

Anonymous

Anonymous Tue 21 Apr 2020 21:46:58 No.11589394 Report

Quoted By: >>11589400 >>11589405 >>11589571

>>11589366
assuming CD=DE

Anonymous

Anonymous Tue 21 Apr 2020 21:50:15 No.11589400 Report

Quoted By: >>11589571

>>11589366
So you're basically saying it's impossible without already knowing >>11589319 and changing the initial picture so that >>11589394

Waste of time

Useless shit

The Systems

The Systems Tue 21 Apr 2020 21:52:02 No.11589405 Report

Quoted By: >>11589430

>>11589394
Cock dicks and Dick Empty

The Systems

The Systems Tue 21 Apr 2020 21:53:04 No.11589413 Report

Quoted By:

>>11589393
It doesn’t matter you ADHD retard

Anonymous

Anonymous Tue 21 Apr 2020 21:58:58 No.11589430 Report

Quoted By:

>>11589405
thank you mr systems schizo

Anonymous

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Anonymous Tue 21 Apr 2020 22:45:34 No.11589571 Report

Quoted By:

>>11589394
>>11589400
Perhaps this will help. From the picture, we know that
$r_1 + r_2 = 12$
$r_3 = \frac{r_1 - r_2}{2}$ .
Therefore,
$r_2 = 12-r_1$
$\rightarrow r_3 = \frac{r_1 - (12-r_1)}{2} = \frac{2r_1-12}{2} = r_1-6$ .
The area is of course
$\frac{1}{4}\pi r_1^2 + \frac{1}{4} \pi r_2^2 - \frac{1}{2} \pi r_3^2$
so substituting to get it all in terms of $r_1$ we get
$\frac{1}{4}\pi (r_1^2 + (12-r_1)^2 - 2(r_1-6)^2)$
Expanding this, we can see $r_1$ cancels out:
$\frac{1}{4} \pi (r_1^2 + (144-24r_1+r^2)-(2r^2-24r+72)) = \frac{1}{4} \pi (72) = 18\pi$

Anonymous

Anonymous Wed 22 Apr 2020 00:49:07 No.11589835 Report

Quoted By:

>>11589387
That's what I thought about too. If the area seems to be invariant (which would have to be proven), you could just choose one of the extremes where you have to deal with way less/easier terms.

Anonymous

Anonymous Wed 22 Apr 2020 01:04:50 No.11589864 Report

Quoted By:

is this board infested with highschoolers?

Anonymous

Anonymous Wed 22 Apr 2020 02:52:32 No.11590125 Report

Quoted By:

56.549units^2
Just draw it in some computer program and make the computer calculate the area, then move the points around arbitrarily and see if it changes.

Anonymous

Anonymous Wed 22 Apr 2020 05:11:37 No.11590415 Report

Quoted By: >>11590749 >>11590810

>no one has been able to prove that the area is invariant
>hey i think we need more information
>"HURR DURR SHUT THE FUCK UP DUMB FUCK YOU ARE SUCH A FUCKING RETARD OH MY GOD HOW STUPID CAN YOU BE GOD I AM SO MUCH SMARTER THAN YOU"
>uhhh can you prove the area is invariant?
>DUMB RETARD SHUT THE FUCK UP CAN"T YOU SEE THAT I AM A GOD HERE ON SCI?
yeah, i'll take .9...=1 threads over this pretentious and mentally ill real math shit any day.

Anonymous

Anonymous Wed 22 Apr 2020 05:17:30 No.11590427 Report

Quoted By: >>11590447

>>11589366
>assumes CD=DE
>doesnt prove it
>still spends all thread calling others "dumb fucks"
neck yourself you autistic cancer.

Anonymous

Anonymous Wed 22 Apr 2020 05:28:33 No.11590447 Report

Quoted By:

>>11590427
>assumes CD=DE
It assumes no such thing and the proof is correct.

Anonymous

Anonymous Wed 22 Apr 2020 05:55:39 No.11590508 Report

Quoted By: >>11590514

>>11589366
DE=(12-r) not (12-2r)

Anonymous

Anonymous Wed 22 Apr 2020 05:56:41 No.11590514 Report

Quoted By:

>>11590508
wait im actually retarded

Anonymous

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Anonymous Wed 22 Apr 2020 06:22:23 No.11590567 Report

Quoted By:

>>11589147

Anonymous

Anonymous Wed 22 Apr 2020 06:26:09 No.11590577 Report

Quoted By:

the smaller quarter circle radius is r
the bigger quarter circle radius is q
the other one's diameter is d
the shaded area is then:
(r^2 + q^2 - 2(d/2)^2)*pi/4

we want to get the equation in terms of r so...
d/2=6-r
q=12-r

the area is then:
(r^2 + (12-r)^2 -2(6-r)^2) * pi/4

if we graph this over the interval 0 <= r <= 12 we see that it is unchanging. The area is then 18*pi for any value r chosen

Anonymous

Anonymous Wed 22 Apr 2020 07:07:09 No.11590680 Report

Quoted By: >>11590748 >>11590757

Your all fuckin retards. I printed it out, cut out a square with 12 being the side of the square. Weighed it: 3.1 grams. Next up, cut out only the shaded region, weigh that: 1.217 g.

Ok, now some fucking simple ass math:
(3.1/144) = (1.217/Area)

area = (144/3.1)*1.217 = 56.5316

Now, because I'm not a fucking moron, I did that 9 more times and averaged them all.

Final result: 56.55

The Systems

The Systems Wed 22 Apr 2020 07:31:58 No.11590748 Report

Quoted By:

>>11590680
This is absolutely incorrect mate, ignorance is truely bliss

The Systems

The Systems Wed 22 Apr 2020 07:33:01 No.11590749 Report

Quoted By:

>>11590415
>it gets me to think, and I do so poorly, so therefore I am angry

It’s ok, we are all your friends, but I think it’s time you grow up

Anonymous

Anonymous Wed 22 Apr 2020 07:43:34 No.11590757 Report

Quoted By: >>11590763

>>11590680
That is uncannily accurate, anon. The exact value is 18pi, or approximately 56.5487, which means you are off by less than one part in ten thousand. I almost find it hard to believe you can cut that accurately.

Anonymous

Anonymous Wed 22 Apr 2020 07:46:29 No.11590763 Report

Quoted By: >>11590778

>>11590757
Oh man that's crazy.

In all seriousness though, talk to some old experimental physicists, we use to really do this shit lol, back when computers were not so easily available.

Anonymous

Anonymous Wed 22 Apr 2020 07:47:21 No.11590765 Report

Quoted By:

>>11589067
$\frac{9 \pi}{2} \approx 14,137$

Anonymous

Anonymous Wed 22 Apr 2020 07:55:27 No.11590778 Report

Quoted By:

>>11590763
I guess cutting out a drawing and weighing it is a pretty accurate method for numerically approximating an integral if you don't have any computation device more powerful than a four-function pocket calculator.

Still, I would not have expected one in ten thousand accuracy. I would have thought the consistency of your drawing paper would already be less homogeneous than that.

Anonymous

Anonymous Wed 22 Apr 2020 08:20:49 No.11590810 Report

Quoted By:

>>11590415
He literally gave you the solution, you retarded cumbrain. >>11589366

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