After learning about rational expressions, we generally discuss direct variation and inverse variation. Direct variation: y varies directly with x, if there is a constant k, such that y = kx. From this we know that if k > 0, then as x ↑ by 1 unit, y↑ by k units; similarly, as x ↓ by 1 unit, y ↓ by k units.
Test Objectives:•Demonstrate the ability to find the value for the constant of variation (k)
•Demonstrate the ability to solve a direct variation problem
•Demonstrate the ability to solve a direct variation as a power problem
Direct Variation Test:
#1:
Instructions: Solve each direct variation problem.
a) If y varies directly with x and y = 30 when x = 7, find y when x = 2/3
#2:
Instructions: Solve each direct variation problem.
a) If q varies directly with z and q = 9.45 when z = 3.5, find q when z = 7.3
#3:
Instructions: Solve each direct variation problem.
a) If y varies directly with x^{4} and y = 3888 when x = 6, find y when x = 3
#4:
Instructions: Solve each direct variation problem.
a) Hooke's law for an elastic spring tells us that the distance a spring stretches varies directly with the force applied: (D = kF). If a force of 150 pounds stretches a spring 32 inches, how much will a force of 225 pounds stretch the spring?
#5:
Instructions: Solve each direct variation problem.
a) The area of a circle varies directly with the square of its radius. A circle with a radius of 5 inches has an area of 78.53in^{2} (approx). What is the area of a circle with a radius of 4.7 inches?
Written Solutions:
Solution:
a) y = 20/7
Solution:
a) q = 19.71
Solution:
a) y = 243
Solution:
a) A force of 225 pounds would stretch the spring 48 inches.
Solution:
a) A ≈ 69.36 in^{2}