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The curves r1 = < 3t, t2, t3 > and r2 = < sin(t), sin(2t), 2t > intersect at the origin. Find their angle of intersection, θ correct to the nearest degree.
Express the retailer's monthly profit from the sale of the cameras as a function of the selling price. Estimate the optimal selling price.
How many ounces of pure zinc must be alloyed with 25 ounces of brass that is 30% zinc and 70% copper to produce brass that is 55% zinc?
Assume debt and common equity each represent50% of the firms capitol structure. Compute the weighted average cost of capitol.
The officejet printer can copy Maria's dissertation in 16 min. The laser Jet printer can copy the same document in 12 min. If the two machines work together, how long would they take to copy the dissertation?
The volume (V) of a gas varies inversely as the pressure (P) upon it. The volume of a gas is 200 cubic centimeters under a pressure of 32 kg per square centimeter. What will be its volume under a pressure of 20 kg per square centimeter?
Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).
Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31
A rectangular carpet has a perimeter of 218 inches. The length of the carpet is 87 inches more than the width. What are the dimensions of the carpet?
What is the greatest number of circular disks, each with a radius of 5.2 cm, that can be printed on a 1-meter square board?
A chef wants to make 1 gallon (128 ounces) of a 35% vinegar-to-oil salad dressing. He only has pure vinegar and a mild 4% vinegar-to-oil salad dressing on hand. How many ounces of each should he mix to make the desired dressing?
You own a portfolio that is 38 percent invested in Stock X, 22 percent in Stock Y, and 40 percent in Stock Z. The expected returns on these three stocks are 10 percent, 15 percent, and 12 percent, respectively.
Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
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