Page 175 - ArithBook5thEd ~ BCC

6.2.1 Exercises

1. Find the area of a rectangle whose length is 4.8 meters and whose width is 3.6 meters. Use the
formula A = lw, where A is the area, l is the length, and w is the width.
2. Find the perimeter of the rectangle in the preceding exercise, using the formula P =2l +2w,
where P is the perimeter and l, w are the length and width, respectively.

3. Find the length of the hypotenuse of a right triangle whose legs are 0.3 yards and 0.4 yards.

4. Straight roads between three towns form a right triangle. The longest road is 17 miles. The next
longest road is 15 miles. How long is the third road?
2
5. How far does an object fall in 3 seconds? Use the formula s =16t , where s is the distance
fallen (in ft), and t is the time (in sec).
9
6. If a thermometer reads 22 C, find the temperature in F. Use the formula F = C +32.
◦
◦
5
!
7. Heron’s formula, A = s(s − a)(s − b)(s − c), gives the area (A) of a triangle (not necessarily
a right triangle) with side lengths a, b and c, and semi-perimeter s. Use Heron’s formula and the
1
semi-perimeter formula s = (a + b + c) to find the area of a triangle with a = b = c =2 ft.
2
8. The formula A = P(1 + r) t gives the amount A of money in a bank account t years after an
initial amount P is deposited, when the annual interest rate is r.Find A after 2 years if the interest
rate is 5% (r =.05), and the initial deposit was P =$500.

9. Find the child’s dosage for a 10-year old, if the adult dosage is 2.2 grams. Use the formula
t
C = · A, where C is the child’s dosage, t is the child’s age, and A is the adult dosage.
t +12

6.3 Functions

Formulae show that one numerical quantity can depend on another. The proper dosage of a child’s
medicine depends on the child’s age; the distance your car can drive (without stopping) depends on the
amount of gas in your tank.
In mathematics, dependence of one quantity (say, y)on another (say, x) is expressed by saying that
y is a function of x. We write
y = f (x),

and say “y equals f of x.” In this notation, f does not denote a number, and the parentheses do
not denote multiplication. f is short for “function.” Another letter might be used, for example, as an
abbreviation for a quantity (d for “dosage,” say). The parentheses are there to receive numerical input
in the form of a value of x.The function acts on the input in a definite way (often given by a formula)
to produce an output, f (x), which is a unique value of y.
A common type of function has the form

f (x)= Ax + B,

where A and B are any two fixed numbers. This is called a linear function; it acts on its input by first
multiplying it by the number A,and then adding the number B.

Page 175