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Suppose the short-run production function for a particular product is represented by:
Q = 60,000L2 - 1,000L3
a. Find the marginal product and show mathematically that labor is subject to diminishing returns.
b. Beyond what labor usage, the marginal product becomes negative.
c. Show mathematically that when the average product is at maximum, marginal product is equal to it?
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.
From the top of a 165 ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse?
?Using the same equation from #5, you have traveled 25 miles in 2 minutes and come to a standstill. What was your initial velocity? (This time, final velocity is 0 miles/hour.)
Use green's theorem to calculate the area of the region between the x-axis and one arch of the cycloid with parametric equations x = a(t - sin t), y = a(1 - cos t).
Find an expression for the time he will take to get from A to B, in terms of theta.
Consider the area A of the triangle with vertices [a1 a2]^T [b1 b2]^T [c1 c2]^T. Express A in terms of.
A heavy rope, 60 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 150 ft high.
One professor grades homework by randomly choosing 5 out of 15 homework problems to grade.
passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 6 seconds later?
A karate match is held on a square mat that has an area of 676 square ft. what is the length of the mat?
a carpenter is building a rectangular room with a fixed perimeter of 104 ft. what dimensions would yield the maximum area? what is the maximum area?
a rectangle has a baserepresented by x+5 and a height represented by 3x-2. Write a binomial representing the perimeter of the rectangle.
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