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Practice for Quiz Lesson Quiz: Part I Variation 1. The volume V of a pyramid varies jointly as the area of the base B and the height h, and V = 24 ft3 when B = 12 ft2 and h = 6 ft. Find B when V = 54 ft3 and h = 9 ft. 18 ft2 2. The cost per person c of chartering a tour bus varies inversely as the number of passengers n. If it costs $22.50 per person to charter a bus for 20 passengers, how much will it cost per person to charter a bus for 36 passengers? $12.50 Example 3 Given: y varies inversely as x, and y = 4 when x = 10. Write and graph the inverse variation function. y= 4= k x k 10 k = 40 y= y varies inversely as x. Substitute 4 for y and 10 for x. Solve for k. 40 x Write the variation formula. Example 3 Continued To graph, make a table of values for both positive and negative values of x. Plot the points, and connect them with two smooth curves. Because division by 0 is undefined, the function is undefined when x = 0. x –2 –4 –6 –8 y –20 –10 –20/3 –5 x 2 4 6 8 y 20 10 20/3 5 5.2 Simplifying Rational Expressions Example 1 Simplify. Identify any x-values for which the expression is undefined. 6x2 + 7 x + 2 6x2 – 5x – 5 (2x + 1)(3x + 2) (3x + 2)(2x – 3) = (2x + 1) (2x – 3) The expression is undefined at ???? Factor; then divide out common factors. Example 2: Multiplying Rational Expressions Multiply. Assume that all expressions are defined. A. 3x5y3 2x3y7 3 5 3x y3 2x3y7 5 x3 3y5 10x3y4 9x2y5 10x3y4 5 3 9x2y5 B. x–3 4x + 20 x–3 4(x + 5) 1 4(x + 3) x+5 x2 – 9 x+5 (x – 3)(x + 3) Dividing: Example Divide. Assume that all expressions are defined. 2 x2 – 7x – 4 x2 – 9 2x2 – 7x – 4 x2 –9 (2x + 1)(x – 4) (x + 3)(x – 3) (2x + 1)(x – 4) (x + 3)(x – 3) 4(x – 4) (x +3) 4 x 2– 1 ÷ 8x2 – 28x +12 8x2 – 28x +12 4x2– 1 4(2x2 – 7x + 3) (2x + 1)(2x – 1) 4(2x – 1)(x – 3) (2x + 1)(2x – 1) Example 5: Solving Simple Rational Equations Solve. Check your solution. x2 – 3x – 10 =7 x–2 (x + 5)(x – 2) (x – 2) =7 Note that x ≠ 2. x+5=7 x=2 Because the left side of the original equation is undefined when x = 2, there is no solution.