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A hemisphere of radius 7 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
I will use * to symbolize a partial derivative. For example, u*x denotes the partial derivative of u with repsect to x. Here is the problem, D'Alembert's solution for the one-dimensional wave equation for a semi-infinite string.
A regression analysis
Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.
Conduct the appropriate analysis of these data and determine whether there are any significant differences.
Two trains leave stations 384 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 75 miles per hour. How long will it take for the two trains to meet?
A cylindrical drill with radius 2 is used to bore a hole throught the center of a sphere of radius 7. Find the volume of the ring shaped solid that remains using polar coordinates.
Vectors as linear combinations of the vectors
A boat travels 72 miles upstream in the same time that it takes to travel 120 miles downstream. The speed of the boat in still water is 32 mph. Find the speed of the current.
What is the probability of getting a score of 68 or less on this exam?
Develop a model to represent the total profit for selling x necklaces. How many necklaces will the student have to sell to break-even?
College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 95% confident that the sample percentage has a margin of error of 2 per..
Modeled the word problem mathematically like system of equations and solve by the matrix method - Determine the augmented matrix that represents the three equations
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