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A revolving lighthouse is located 100 m from the nearest point P on a straight shoreline. The light makes one revolution every 30 seconds. Find the speed at which a ray of light from the lighthouse moves along the shore at a point 200 m from P.
a rancher wants to use 300 feet of fencing to enclose a rectangular area of 4400 square feet. what dimensions should the rectangle have?
Assuming exponential population growth, predict the populations of China and the U.S. in the years 2100 and 2200. Assuming exponential population growth, approximately when will China's population double?
A 25-by-33-inch sheet of paper is to be used for a poster, with the shorter side at the bottom. The margins at the sides and top are to have the same width, and the bottom margin is to be twice as wide as the other margins. Find the width of the m..
Answer the following: Assume you have a choice between two annuity contracts. Contract A pays $5,000 per year for 5 years starting one year from today. Contract B pays $5,000 per year for 5 years starting today. The discount rate for each is 6%. W..
A matrix A is said to be skew-symmetric if A^T = -A. Show that any square matrix can be represented as a sum of a symmetric matrix and a skew-symmetric matrix.
Assume that the nonzero complex numbers from group G with respect to multiplication. If a and b are real numbers and i=sqrt -1, the conjugate of the complex number a+bi is defined to be a-bi.
given that a line segment has endpoints (1,2) and (5,10), write a set of parametric equations that passes through these two points.
Assume that n is a positive integer. Use the proof by contradiction method to prove: If 7n + 4 is an even integer then n is an even integer.
Solving probability problems based on combinations
Please solve the following initial value problem: We solve the initial value problem using separation of variables. We use partial fractions to solve for the integral of 1/(x^2-4).
Darla wants to plant strawberries in her rectangular garden. If the dimensions of the garden are ' by ' and each plant must be 3 feet away from any other plant or any edge, what's the maximum number of plants she can plant?
Find an equation for each of the following trig functions
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