What is the shortest distance between circle A defined by (x − 5)2 + (y − 4)2 = 4 and circle B defined by (x − 1)2 + (y − 1)2 = 1? There is some point P on circle A closest to B, and there is another point Q on circle B closest to A. What are the coordinates of P and Q?
A circle of radius 1 is tangent to the parabola y=x^2 as shown. Find the gray area between the circle and the parabola?
The temperature on a unit sphere x^2 + y^2 + z^2 = 1, is given by a temperature distribution
T(x,y,z) = 50.(xy + yz)
What is the temperature difference between the coldest and warmest point on the sphere?
Let A be a 2x3 matrix and B a 3x2 matrix. If AxB and BxA both defined and determinant of the matrix AxB is 4, then evaluate the determinant of the matrix BxA.
