(a) Find the solution u(x, y) of Laplace's equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the following boundary conditions u(0, y) = 0, u(a, y) = f(y), 0 < y < b, u(x, 0) = h(x), u(x, b) = 0, 0 ≤ x ≤ a. Hint: Consider the possibility of adding the solutions of two problems, one with homogeneous boundary conditions except for u(a, y) = f(y), and the other with homogeneous boundary conditions except for u(x, 0) = h(x).

Needmax recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Which expressions are equivalent to -7+3(-4e-3)? choose all answers that apply: choose all answers that apply: a -4(3e+4)? 4(3e+4) b 12e12e c none of the above

Thanh and her crew are building a stage in the shape of a trapezoid for an upcoming festival. the lengths of the parallel sides of the trapezoid are 14 ft and 24 ft. the height of the trapezoid is 12 ft. what is the area of the stage? enter your answer in the box. ft²