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The hypotenuse of a right triangle has one end at the origin and one end on the curve y(x) = X3e-5x, with x ≥0 . One of the other two sides is on the x-axis, the other side is parallel to the y-axis.
(a) Express the area of the triangle in terms of x only.
(b) Find A '(x)
(c) Find the critical point for x > 0.
(d) Find the maximum area of the triangle. Give an exact answer.
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What is the value of v?
A bacteria population starts with 400 bacteria and grows at a rate of r(t) bacteria per hour. How many bacteria n will there be after three hours? (Give your answer to the nearest bacterium.) r(t) = 450.266 e^(1.12567 t)
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds
You are to solve Problem 30 in Chapter 4 on page 158 of your textbook. It's about publishing three weekly magazines. You can use QM for Windows to perform a sensitivity analysis for Objective function coefficients and the RHS values of the constraint..
It takes 5 hours to fill an empty tank when both outlet pipes are open. When one outlet pipe is closed, it takes 3 hours to fill the tank. Find the flow rates (in gallons per hour) in and out of the pipes.
The Rourke family traveled 20 kilometers farther than the Clarke family. How many hours did each family spend on their boat trip?
You walk 88 yards due south, then 124 yards due west, and then 44 yards due north. How far are you from your staring point?
A car traveling along a straight road at 51 ft/sec accelerated to a speed of 65 ft/sec over a distance of 330 ft. What was the acceleration of the car, assuming it was constant?
Two balls are chosen randomly from a basket containing 8 white, 4 black and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings.
Determine the production level that gives maximum profit, and determine the amount of the maximum profit. (Round your answers to two decimal places.)
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