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A manufacturer has been selling lamps at the price of $6/lamp, and at this price they have been selling 3000 lamps a month. The manufacturer wishes to raise the price and estimated that for each $1 increase they will sell 1000 fewer lamps a month. The manufacturer can produce the lamps at a cost of $4 per lamp. At what price should the manufacturer sell the lamp to generate the greatest possible profit?
Suppose that a car normally sells for $16,500 and is now on sale for $14,000. What is the percent of discount? If necessary, round your answer to the nearest tenth.
Explain how the pigeon-hole principle can be used to show that among any 11 integers, at least two must have the same last digit.
Show that the curve with parametric equations x=sin(t), y=cos(t), and z=sin^2(t) is the curve of the surfaces z=x^2 and x^2 + y^2=1. Use this fact to help sketch the curve.
Confirm that the two results are consistent by expressing the derivative in part (a) as a function of x alone.
Find the slope of the tangent line to the graph of y= ln[x*e^x] at the point where x=3.
Computer analysis showed that the surface of a certain drumlin can be approximated by y= 10(1-0.0001x^2) revolved 180 about the x-axis from x= -100 to 100.
Explaining how to derive the formula for the distance between two points -Prepare an essay of 1,000 words explaining how to derive the formula for the distance between two points in analytic geometry 3-space.
A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:
Linear programming problem consisting of only two constraints with one objective function.
A kite 100ft above the ground moves horizontally at a speed of 8fts. At what rate is the angle between the string and the horizontal decreasing when 200ft of string have been let out?
Solve the system of equations graphically. Then classify the system as consistent or inconsistent and the equation as dependent or independent.
For the following algorithm find the number of times the assignment statement (:=) is executed during the running of the program. Answer the question by giving a formula in terms of n:
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