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A box with a square base of side z is three times higher than it is wide. Express the volume V of the box as a function of z.
Which of the four operations on functions do you think is the easiest to perform? What is the most difficult? Explain why by showing examples for each function.
Use polar coordinates to evaluate the volume of the solid below the paraboloid (z= 4-x^2-y^2) and above the xy plane.
Given the following 3X3 matrix find the eigenvalues and eigenvectors. Please solve by hand before checking with a computer program!
Compare the functions given below by graphing both functions in several viewing rectangles. For what values of x does the graph of g finally surpass the graph of f ? (Give your answer correct to 1 decimal place.)
What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches?
Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product.
Find the slope and the equation of the tangent line to the graph of the function at the given value of x.
If they are taken out seven at a time, no eggs will be left over. Find the least number of eggs that could be in the basket.
a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard.
Consider the following linear mapping from C[-pi,pi] into itself: L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi].
a boat's crew rowed 18 miles downstream, with the current, in 2 hours. The return trip upstream, against the current, covered the same distance, but took 4.5 hours. Find the crew's rowing rate in still water and the rate of the current.
A boat's crew rowed 12 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 4 hours. Find the crew's rowing rate in still water and the rate of the current.
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