Page 33 - How To Solve Word Problems In Calculus

Supplementary Problems

1. The difference of two numbers is 15. Express their product as a
function of the smaller number, x.
2. A rectangle has an area of 200 square meters. Express its perimeter
as a function of its width.
3. Caren wants to fence in a rectangular vegetable garden and
subdivide it into three regions by using two additional sections of
fence parallel to one side, x, of the rectangle. The total enclosed
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area is to be 1000 ft . Express the total length of fencing as a
function of x.
4. A rectangle is inscribed in a semicircle of radius 10 with the base of
the rectangle lying along the bottom of the semicircle. Express the
area of the rectangle as a function of its width and determine its
domain.
5. An open boxis to be constructed from a rectangular piece of sheet
metal 8 × 12 inches by cutting away identical x-inch squares from
each of the four corners and folding up the sides. Express the
volume of the resulting boxas a function of x.
6. A church window is to be in the shape of a rectangle surmounted
by a semicircle. If the perimeter of the window is 100 inches,
express its area as a function of its semicircular radius r .
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7. An open boxhas a square base. If its surface area is 200 cm ,
express its volume as a function of its base dimension x.
8. A right circular cylinder is inscribed in a sphere of radius 10.
Express its volume and surface area as functions of its height h.
9. If 500 apple trees are planted in an orchard, each tree will produce
800 apples. For each additional tree planted, the number of apples
produced per tree diminishes by 20. Find a function that represents
the total number of apples produced in the orchard.
10. It costs $800 to manufacture a certain model of personal computer.
Overhead and other fixed costs to the company are $2000 per
week. The wholesale price of a computer is $1500 but, as an
incentive, the company will reduce the price of every computer by
an additional $10 for each computer purchased in excess of 10.
(Thus if 13 computers are purchased, each will cost $1470.) Express
the company’s weekly profit as a function of the number of
computers sold.

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