College Algebra 3.6 Polynomial and Rational Inequalities 3.7 Variation

3.6 Polynomial Inequalities Obj: solve polynomial and rational inequalities with the critical value method Critical Value Method – Zeros (solutions) of polynomials are called the critical points. – Critical Points of a polynomial divide positive values from negative values.

Example Solve x 2 – 2x – 15 < 0 Factor and solve for x. These are the critical points. Choose a value in each interval. Let x = Plug each value into the factored form ( + or - ). Compare relations. Write solution in interval notation.

Rational Inequalities Steps: 1.Set = to 0 and simplify. 2.Find the zeros of the numerator and denominator to find the critical points. 3.Test the intervals. 4.Compare the relations. 5.Write the solution.

Example Solve

3.7 Variation Obj: to set up and solve problems using variation Direct Variation Inverse Variation Joint Variation Combined Variation

Direct Variation Varies directly or is directly proportional to Meaning as one unit increases, the other increases or as one decreases, the other decreases also y = kx k is the constant of proportionality Examples:

Example The distance d that a ball rolls down an inclined plane is directly proportional to the square of time t. If the ball rolls 5 feet in 1 second, how far will it roll in 4 seconds? Set up the equation using initial info. Solve for k. Set up new equation with k value and new info. Solve.

Inverse Variation Varies inversely or is inversely proportional to Meaning as one unit increases, the other decreases and vice versa. y = Examples:

Example The speed v of a gear varies inversely as the number of teeth t. If a gear that has 48 teeth makes 20 revolutions per minute, how many revolutions per minute will a gear that has 30 teeth make?

Joint Variation more than one variable z = kxy The cost of a concrete patio varies jointly as the area of the patio and the depth of the patio. It costs $500 for a patio with an area of 80 square feet and a depth of 4 inches. Find the cost of a patio with an area of 144 square feet and a depth of 6 inches.

Combined Variation more than one type of variation The volume of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If the volume of the gas is 220 cm 3 when T = 40˚C and P = 20 kg/cm 2, what is the volume when T = 35˚C and P = 10 kg/cm 2 ?

Assignment 3.6page 4201 – 13 eoo, 29 – 45 eoo 3.7 page – 29 eoo