what is the advantage of a paralell circut overa series circut?
599671
If one load fails, the others remain on whereas in a series, if one load fails, they all fail (remember the old Christmas lights?)
297111
Think of the first as the area of a flat round plate sweeping out the inside of the figure you get from the rotation.  What will be its area? πr² where the r is the y value of √(9 + X²).  That changing area will sweep out the volume from whatever the limits are (you don't say), so it's the integral of π(√(9 + X²))², or π(9 + X²).\n\nIn the second case, the thing sweeping out the volume is the surface area of a cylinder as its radius grows.  Thats the circumfrence of the base times the height.  The circumfrence is 2πr where r is the X value and the height is the difference between Y = x and Y = X/2.  So it's the integral from 0 to 2 of:\n\n   2πX(X-X/2).\n\nThinking of an area sweeping thru the volume helps.
322159
Are you kidding me? Sin(x) is awesome! I totally love sinx-ing  those sexy numbers :)\n\nI sinxed pi the other day, and it totally melted away.
307198
It is linear on intervals, on (- infinite, 0) and on (0, +infinite) but not on the whole R. \n\nTry plotting it, you get a reversed V, not a straight line.
266644
I've just answered this in your previous question: "Statistics: Variability & SRS Samples of Population?"\n \nIf you look there, you'll find the formula for the s.d. of p_hat. So that increasind n by multiplying it by "m", reduces (devides) sd (or se) by sqrt(m).\n \nFor example, lets say the sd is 0.2 and the sample size is 100. If you increase the sample to 400 (multiply it by 4), the sd is devided by sqrt(4) = 2, i.e., sd = 0.1.
967058
It depends on what you are wanting to prove. Generally speaking, when you substitute numbers, you are restricting to a specific example. You cannot prove a general result by only looking at specific examples (unless you somehow show those specific cases give *all* the possibilities). However, you *can* show a result is false, if it is false for some specific example, so to show a general result is false, it is enough to 'plug in numbers'.
846910
No. They do not share the same dimensions.\n\nYou can multiply them though.
379220
Nice history of it with a mathematical explanation here :\n\nhttp://mathworld.wolfram.com/GoldenRatio.html
782532
there is no built-in at-the-nth-power operator in c++,\n\nsimply use \n#include <math.h>\ndouble z = pow(3,2);
400641
There's a difference.  It refers to (sin x)^2.  Plug in a few numbers and you can easily tell the difference.
853022
It should be a function because one x input value gives only one y output value. Try the vertical-line test. But the function does not have an inverse though.
935998
Just add them together sample by sample. Squaring them is destroying the negative values. (Just think of a sine wave.) \n The distortion must be terrible!\n\n Note however if when you add them the sum exceeds a certain value you will get some overload. If the sample values are modest to start with this will not happen.
263227
This integral does not have an indefinite closed form of elementary functions. It can be evaluated numerically by either integrating the series representation of e^(-x^2) or using integral approximation methods like Simpson's rule.\nIt also has an interesting value if evaluated over its entire domain; by changing coordinates to polar coordinates, one can easily show that the integral over the entire real line is equivalent to Sqrt[Pi].\nThis fact is used in statistics to normalize the Gaussian distribution to have area 1 under the curve. The integral of your expression on the interval [0,t] is then known as the error function. See the source for details.
510352
The solution by a_ebnlhaitham is not quite correct in that he omitted the 2 from the power of r (i.e.(teta)).The answer should be 1/(1 - r^2) not 1/(1 - r). The series converges because r lies in the open interval (-1,1).
937394
Let the first term of the series be a.Therefore,the second term would be ar,r being the common ratio.and the fifth term is ar^4\nDividing ,the fifth term  ar^4 by the second term ar,we get.\nar^4/ar=(81/64)/3  or,r^3=27/64.Therefore r=3/4.\nPutting the valu of r in the secon term i.e. ar=3,we get a=3/r=3/(3/4)=4.\nTherefore,the series is 4,3......81/64.......\nit is apparent that the trms of the series would have the values increasing and it would not come to an end because it has attained the value of  more than an unity.\nThe sum of the series would be infinity.\nAs the sum of the series is infinity,the sum of firs 10 trms of sum of any number of trms for that matter,and the sum of the complete sries would be infinity as any number subtratd from infinity gives  result of infinity.
124077
centripital and centrifigal
506532
Ahhhhhhh... isn't it great to be 30 going on 10.  Life it too short to be grown up.  Greatest shaped object huh.... okay well lets see.... you have limited my choices here, that is not fair btw. :p ~ How about a circle.  You can not invert it mathematically.  It has no beginning nor ending.  You can do so many wonderful things with it, such as foot ball, balloons, rings and what not.  It is perfect, yet can not be computed to the last digit (PI) and last but not least, because I say so.  LOL  :)