/sci/ - Science & Math » Thread #12420323

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Anonymous Fri 04 Dec 22:02:50 2020 No.12420323 View Reply Original Report

Quoted By: >>12420464 >>12420475 >>12420483 >>12420512 >>12420522 >>12420750 >>12420763 >>12420870 >>12422510 >>12422568 >>12424680 >>12424893 >>12426128

Oh, you think you like math?
Calculate the average value of sin^100(x) to 20% precision without using a calculator.
(this shouldn't take you much more than 5 minutes)

Anonymous

Anonymous Fri 04 Dec 2020 22:50:25 No.12420464 Report

Quoted By: >>12420499 >>12420789

>>12420323
And x is? Dumbfuck?

Anonymous

Anonymous Fri 04 Dec 2020 22:53:15 No.12420475 Report

Quoted By:

>>12420323
Easy OP, just use the taylor series for sine. Ask a question that doesn't requires math more advanced than high school

Anonymous

Anonymous Fri 04 Dec 2020 22:54:26 No.12420483 Report

Quoted By: >>12420512

>>12420323
Easy OP, just use the taylor series for sine. Ask a question that requires math more advanced than high school

Anonymous

Anonymous Fri 04 Dec 2020 22:59:00 No.12420499 Report

Quoted By:

>>12420464
>average value
Unfortunately it appears you are the dumb fuck

Anonymous

Anonymous Fri 04 Dec 2020 23:01:34 No.12420512 Report

Quoted By: >>12420704

>>12420483
That makes no sense for this question.

>>12420323
Just integrate from 0 to 2pi, divide by 2pi. Ezpz

Anonymous

Anonymous Fri 04 Dec 2020 23:06:30 No.12420522 Report

Quoted By:

>>12420323
The answer is X

Anonymous

Anonymous Sat 05 Dec 2020 00:12:05 No.12420704 Report

Quoted By: >>12420751

>>12420512
>integrating sin^(100)(x) by hand

Anonymous

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Anonymous Sat 05 Dec 2020 00:27:21 No.12420750 Report

Quoted By: >>12420754 >>12420759

>>12420323
Wouldn't it just be 0?

Anonymous

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Anonymous Sat 05 Dec 2020 00:28:16 No.12420751 Report

Quoted By:

>>12420704
>using complex exponentials to integrate sin^100(x)dx

Anonymous

Anonymous Sat 05 Dec 2020 00:29:11 No.12420754 Report

Quoted By: >>12420762 >>12420778

>>12420750
it's strictly positive and at x=0 sin^100(x)=1 so it can't be 0, but 0 is probably within the bounds that OP gave.
I'd say like .05 or something

Anonymous

Anonymous Sat 05 Dec 2020 00:30:59 No.12420759 Report

Quoted By:

>>12420750
Ah wait, never mind. I forgot that exponential function notation doesn't mean composition in this context

Anonymous

Anonymous Sat 05 Dec 2020 00:31:22 No.12420762 Report

Quoted By: >>12420767 >>12420777

>>12420754
The average is 0 when you set X to range from 0 to 0

Anonymous

Anonymous Sat 05 Dec 2020 00:31:23 No.12420763 Report

Quoted By: >>12420777

>>12420323
0 for all values except when x is.too close to multiples of 2?

Anonymous

Anonymous Sat 05 Dec 2020 00:32:30 No.12420767 Report

Quoted By: >>12420785

>>12420762
I took average to mean global average

Anonymous

Anonymous Sat 05 Dec 2020 00:35:06 No.12420777 Report

Quoted By: >>12422487

>>12420762
>>12420763
It's an even function, you dumb cunts. Name me a single even function that vanishes over a symmetric domain.

Anonymous

Anonymous Sat 05 Dec 2020 00:35:09 No.12420778 Report

Quoted By: >>12420788

>>12420754
>at x=0 sin^100(x)=1
Doubt

Anonymous

Anonymous Sat 05 Dec 2020 00:37:01 No.12420785 Report

Quoted By:

>>12420767
That's where you were wrong, you gotta read the question more carefully in the future.

Anonymous

Anonymous Sat 05 Dec 2020 00:37:22 No.12420788 Report

Quoted By:

>>12420778
fuck you know what I mean. at pi/2

Anonymous

Anonymous Sat 05 Dec 2020 00:37:56 No.12420789 Report

Quoted By:

>>12420464
sin goes from -1 to 1 anon...

Anonymous

Anonymous Sat 05 Dec 2020 00:42:59 No.12420802 Report

Quoted By: >>12420818

X = somewhere between 0 and 1
>20% precision

I answer .2, as low numbers are more common than high numbers and I can cover the lower 40% of possibilities with .2 as my answer

Anonymous

Anonymous Sat 05 Dec 2020 00:48:49 No.12420818 Report

Quoted By: >>12420830

>>12420802
He thinks 20 percent of 0.2 is 0.2

Anonymous

Anonymous Sat 05 Dec 2020 00:50:48 No.12420830 Report

Quoted By: >>12420839

>>12420818
No 20% of 1(1-0=1) is .2

20% of 1 is .2, a 20% range of .2 allows for a 20% swing in either direction aka 40% coverage

Anonymous

Anonymous Sat 05 Dec 2020 00:54:49 No.12420839 Report

Quoted By: >>12420843

>>12420830
you have to be within 20% of the correct answer, mongrel. not of the possible values

Anonymous

Anonymous Sat 05 Dec 2020 00:56:05 No.12420841 Report

Quoted By:

Ok so this is a little sloppy reasoning, but just to get an idea of whats going on.

sin is -1 to 1. When we square we get 0 to 1. Ok so we have a number between 0 and 1, and raise it to a big power, 50. This will tend to push it to 0. So I expect a small but positive average.

Anonymous

Anonymous Sat 05 Dec 2020 00:56:21 No.12420843 Report

Quoted By: >>12420848

>>12420839
Yeah and theres a 40% chance im within 20%

Anonymous

Anonymous Sat 05 Dec 2020 00:58:09 No.12420848 Report

Quoted By: >>12420882 >>12422340

>>12420843
if the correct answer is 0.05 you need to be between 0.051 and 0.049. your logic is dogshit

Anonymous

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Anonymous Sat 05 Dec 2020 01:03:50 No.12420870 Report

Quoted By: >>12421760 >>12422220 >>12422568

>>12420323
here's the precise answer because I'm not an engineercuck.

Anonymous

Anonymous Sat 05 Dec 2020 01:06:59 No.12420882 Report

Quoted By:

>>12420848
I had a correct answer and you are mad that I am not wrong, in a many worlds hypothesis I get the answer correct 100% of the time that I am aware of the commonality of low numbers

Anonymous

Anonymous Sat 05 Dec 2020 06:59:00 No.12421760 Report

Quoted By: >>12423926

>>12420870
> because I'm not an engineercuck.
I doubt you can solve even 20% (heh) of problems in the book where the OP problem came from (which was written by a mathematician btw)

Anonymous

Anonymous Sat 05 Dec 2020 10:22:30 No.12422220 Report

Quoted By:

>>12420870
Marks off for not simplifying the final answer. Total grade 0/100

Anonymous

Anonymous Sat 05 Dec 2020 11:08:50 No.12422340 Report

Quoted By:

>>12420848
So in other words, to maximize coverage, that anon should've picked .909090... Since 20% is an increasing function. That way 10% up would give the max: 1. Specifying 20% as a tolerance range is stupid from the get-go. Instead you should've said "within +- .01" or something along those lines.

Anonymous

Anonymous Sat 05 Dec 2020 11:12:32 No.12422354 Report

Quoted By:

Is that you Arnold?

Anonymous

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Anonymous Sat 05 Dec 2020 12:12:16 No.12422472 Report

Quoted By: >>12422502 >>12424431

I'll do a half decent approximation for the average given any even power of sine, here ya go

Anonymous

Anonymous Sat 05 Dec 2020 12:17:48 No.12422487 Report

Quoted By:

>>12420777
0

Anonymous

Anonymous Sat 05 Dec 2020 12:28:20 No.12422502 Report

Quoted By:

>>12422472
>can anyone check this? it gives an upper bound on the average

Anonymous

Anonymous Sat 05 Dec 2020 12:32:52 No.12422510 Report

Quoted By: >>12423385

>>12420323
linearization of the value range for four ranges or better three ranges, since the same linear equation applies from pi/2 to 3pi/2
express x in number of pi
n*2*pi + x_eff = x blah blah regulation
done

Anonymous

Anonymous Sat 05 Dec 2020 13:02:19 No.12422568 Report

Quoted By: >>12424431

>>12420323
Actually, how to do that under five minutes. Say I start with the product from this anons post
>>12420870
how to estimate it fast?

Anonymous

Anonymous Sat 05 Dec 2020 17:51:28 No.12423385 Report

Quoted By:

>>12422510
+

building on what I wrote earlier
with second degree polynomial for the sectional description, you get an error of 69%(model max difference was about 5E-3), maybe even less.
so 3rd polynome might already work.

Anonymous

Anonymous Sat 05 Dec 2020 20:39:32 No.12423926 Report

Quoted By:

>>12421760
cope and seethe

Anonymous

Anonymous Sat 05 Dec 2020 23:07:30 No.12424431 Report

Quoted By: >>12426060

>>12422568
>How to estimate fast
Say it's less than ?/4 , more than 1/2
>Alternatively, use
>>12422472

Anonymous

Anonymous Sun 06 Dec 2020 00:08:24 No.12424680 Report

Quoted By:

>>12420323
0,08

Anonymous

Anonymous Sun 06 Dec 2020 01:17:21 No.12424893 Report

Quoted By:

>>12420323
>average value of sin
The wages of sin are death

Anonymous

Anonymous Sun 06 Dec 2020 09:25:42 No.12426060 Report

Quoted By:

>>12424431
Ok smartass, how do you quickly find x_0 and x_1 from that pic?

Anonymous

Anonymous Sun 06 Dec 2020 10:09:30 No.12426128 Report

Quoted By: >>12426138

>>12420323
Just use Laplace's method.
$<br />\frac{1}{\pi} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \mathrm{d}x \cos(x)^{100} \approx \frac{1}{\pi} \int_{-\infty}^{\infty} \mathrm{d} x e^{-100 \frac{x^2}{2}} = \frac{\sqrt{\frac{2 \pi}{100}}}{\pi} = .1 \sqrt{\frac{2}{\pi}} \approx .1 \sqrt{.6} \approx .1 \cdot .8 = .08<br />$

Anonymous

Anonymous Sun 06 Dec 2020 10:17:46 No.12426138 Report

Quoted By:

>>12426128
Laplace's method is to solve by inspection.

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