Q: Consider the situation in Exercise 51 if the cost of laying pipe
Consider the situation in Exercise 51 if the cost of laying pipe under the river is considerably higher than the cost of laying pipe over land ($400,000ykm). You may suspect that in some instances, th...
See AnswerQ: The frame for a kite is to be made from six pieces
The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut with the lengths indicated in the figure. To maximize the area of the kite, how long should the diago...
See AnswerQ: A point P needs to be located somewhere on the line AD
A point P needs to be located somewhere on the line AD so that the total length L of cables linking P to the points A, B. and C is minimized (see the figure). Express L as a function of x = |AP | and...
See AnswerQ: The graph shows the fuel consumption c of a car (measured
The graph shows the fuel consumption c of a car (measured in gallons per hour) as a function of the speed v of the car. At very low speeds the engine runs inefficiently, so initially c decreases as th...
See AnswerQ: Two vertical poles PQ and ST are secured by a rope PRS
Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in the figure. Show t...
See AnswerQ: The upper right-hand corner of a piece of paper,
The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, h...
See AnswerQ: A steel pipe is being carried down a hallway 9 ft wide
A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carrie...
See AnswerQ: An observer stands at a point P, one unit away from
An observer stands at a point P, one unit away from a track. Two runners start at the point S in the figure and run along the track. One runner runs three times as fast as the other. Find the maximum...
See AnswerQ: A rain gutter is to be constructed from a metal sheet of
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the...
See AnswerQ: Write the composite function in the form f ( g(x
Write the composite function in the form f ( g(x) ). [Identify the inner function u = g(x) and the outer function y = f (u).] Then find the derivative dy / dx. y − tan πx
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