1. Sullivan Algebra and Trigonometry: Section 2.5 Variation Objectives Construct a Model Using Direct Variation Construct a Model Using Inverse Variation Construct a Model Using Joint or Combined Variation

2. Variation refers to how one quantity varies in relation to another quantity. Quantities may vary directly, inversely, or jointly. Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that y = kx. The number k is called the constant of proportionality.

3. For regular unleaded gasoline, the revenue R (in dollars) varies directly with the number of gallons of gasoline sold g. If revenue is $15.00 when the number of gallons of gasoline sold is 12.5, find a formula that relates revenue R to the number of gallons of gasoline g.

4. Let x and y denote two quantities. Then y varies inversely with x, or y is inversely proportional to x, if there is a nonzero number k such that : y = k/x The number k is called the constant of proportionality.

5. The weight of a body varies inversely with the square of its distance from the center of Earth. Assuming the radius of Earth is 3960 miles, how much would a woman weigh at an altitude of 0.5 miles above the Earth’s surface if she weighs 120 pounds on Earth’s surface? So,

6. When a variable quantity Q is proportional to the product of two or more other variables, we say that Q varies jointly with these quantities. Combined variation is a combination of direct and/or inverse variation.

7. The maximum safe load for a horizontal rectangular beam varies jointly with the width of the beam and the square of the thickness of the beam and inversely with its length. If a 10-foot beam will support up to 600 pounds when the beam is 3 inches wide and 4 inches thick, what is the maximum safe load of a similar beam 12 feet long, 4 inches wide and 6 inches thick?