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a window has a shape of rectangle surmounted by a equilateral triangle.if the perimeter of the window is 12m, find the dimensions of the rectangle that will produce largest area of the window.
Five schoolchildren are weighed in pairs. The readings (in kilograms) are: 58,60,61,64,64,65,67,68,70 and 71. Find the weights of individual children.
A rectangular page is to contain 54 square inches of printable area. The margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is 2 inches. What should the dimensions of the page be so that..
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
Integral from zero to infinity of cos(x^2) dx = integral from zero to infinity of sin(x^2) dx = 1/2 * (square root of pi/2).
The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have heights that are also approximately Normal, with mean height 69.3 inches and standard deviation 2.8 inches.
Find the least squares approximation of e^x over the interval [0,1] by a polynomial of the form ao+a1x. Find the mean square error of the approximation.
Let K1 and K2 be finite extensions of F contained in the field K, and assume both are splitting fields over F. Prove that their composite K1K2 is splitting field over F.
The integers 1 through 25 are arranged in a 5 x 5 array (we use each number from 1 to 25 exactly once). All that matters is which numbers are in each column and how they are arranged in the columns.
Use a change of variables to find the volume of the solid region lying below the surface f(x,y)=x^2 and above the plane region bounded by the line 2y - x = 1, 2y â?" x = 0, x = 1, and x = 2.
Amy plans to paint both sides of a fence whose base is in the xy-plane and is given by the points (x,y) where x = 30cos^3(t) and y = 30sin^3(t) for 0
Standard deviation, Variance and Covariance. Calculate the standard deviation and variance of each set data, and covariance.
The surface is defined by the equation x^2 - 2y^2 + z^2 +yz = 2. Write equations of the tangent plane and normal line to this surface at the point P(2, 1, -1)
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