Questions from General Calculus

Q: A storage shed is to be built in the shape of a

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 150 cubic feet. The concrete for the base costs $4 per square foot, the material for the roof costs $2...

Q: A supermarket is to be designed as a rectangular building with a

A supermarket is to be designed as a rectangular building with a floor area of 12,000 square feet. The front of the building will be mostly glass and will cost $70 per running foot for materials. The...

Q: A certain airline requires that rectangular packages carried on an airplane by

A certain airline requires that rectangular packages carried on an airplane by passengers be such that the sum of the three dimensions (i.e., length, width, and height), is at most 120 centimeters. Fi...

Q: An athletic field [Fig. 8] consists of a rectangular

An athletic field [Fig. 8] consists of a rectangular region with a semicircular region at each end. The perimeter will be used for a 440-yard track. Find the value of x for which the area of the recta...

Q: An open rectangular box is to be constructed by cutting square corners

An open rectangular box is to be constructed by cutting square corners out of a 16- by 16-inch piece of cardboard and folding up the flaps. [See Fig. 9.] Find the value of x for which the volume of th...

Q: Draw the graph of f (x) = 1/6

Draw the graph of f (x) = 1/6 x3 - x2 + 3x + 3 in the window [-2, 6] by [-10, 20]. It has an inflection point when x = 2, but no relative extreme points. Enlarge the window a few times to convince you...

Q: A closed rectangular box is to be constructed with a base that

A closed rectangular box is to be constructed with a base that is twice as long as it is wide. If the total surface area must be 27 square feet, find the dimensions of the box that will maximize the v...

Q: Let f (t) be the amount of oxygen (in

Let f (t) be the amount of oxygen (in suitable units) in a lake t days after sewage is dumped into the lake, and suppose that f (t) is given approximately by At what time is the oxygen content incre...

Q: The daily output of a coal mine after t hours of operation

The daily output of a coal mine after t hours of operation is approximately 40t + t2 – 1/15 t3 tons, 0 ≤ t ≤ 12. Find the maximum rate of output (in tons of coal per hour).

Q: Consider a parabolic arch whose shape may be represented by the graph

Consider a parabolic arch whose shape may be represented by the graph of y = 9 - x2, where the base of the arch lies on the x-axis from x = -3 to x = 3. Find the dimensions of the rectangular window o...