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Review 5.1 to 5.3 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. k y= y varies inversely as x. x k Substitute 4 for y and 10 for 4= 10 x. k = 40 Solve for k. 40 y= 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 y x y –2 –20 2 20 –4 –10 4 10 –6 –20/3 6 20/3 –8 –5 8 5 5.2 Simplifying Rational Expressions Example 1 Simplify. Identify any x-values for which the expression is undefined. 6x2 + 7 x + 2 6x2 – 5 x – 5 (2x + 1)(3x + 2) (2x + 1) = Factor; then divide out common (3x + 2)(2x – 3) (2x – 3) factors. The expression is undefined at ???? Example 2: Multiplying Rational Expressions Multiply. Assume that all expressions are defined. 3 x 5y 3 10 x3y4 x–3 x+5 A. B. 2 x 3y 7 9 x 2y 5 4x + 20 x2 – 9 3 3x y 5 3 5 10x3y4 x–3 x+5 2 x 3y 7 3 9 x 2y 5 4(x + 5) (x – 3)(x + 3) 5 x3 1 3 y5 4(x + 3) Dividing: Example Divide. Assume that all expressions are defined. 2x2 – 7 x – 4 4 x 2– 1 ÷ x –9 2 8x2 – 28 x +12 2x2 – 7 x – 4 8x2 – 28x +12 x –9 2 4 x 2– 1 (2x + 1)(x – 4) 4(2x2 – 7x + 3) (x + 3)(x – 3) (2x + 1)(2x – 1) (2x + 1)(x – 4) 4(2x – 1)(x – 3) (x + 3)(x – 3) (2x + 1)(2x – 1) 4(x – 4) (x +3) Example 5: Solving Simple Rational Equations Solve. Check your solution. x2 – 3 x – 10 =7 x–2 (x + 5)(x – 2) =7 Note that x ≠ 2. (x – 2) x+5=7 x=2 Because the left side of the original equation is undefined when x = 2, there is no solution.

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posted: | 3/5/2014 |

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