2 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 ft22. 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
3 Example 3Given: y varies inversely as x, and y = 4 when x = 10. Write and graph the inverse variation function.kxy =y varies inversely as x.k10Substitute 4 for y and 10 for x.4 =k = 40Solve for k.40xWrite the variation formula.y =
4 Example 3 ContinuedTo 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.xy–2–20–4–10–6–20/3–8–5xy220410620/385
5 5.2 Simplifying Rational Expressions Example 1 Simplify. Identify any x-values for which the expression is undefined.6x2 + 7x + 26x2 – 5x – 5(2x + 1)(3x + 2)(3x + 2)(2x – 3)(2x + 1)(2x – 3)Factor; then divide out common factors.=The expression is undefined at ????
6 Example 2: Multiplying Rational Expressions Multiply. Assume that all expressions are defined.3x5y32x3y710x3y49x2y5x – 34x + 20x + 5x2 – 9A.B.3x5y32x3y710x3y49x2y535x – 34(x + 5)x + 5(x – 3)(x + 3)35x33y514(x + 3)
8 Example 5: Solving Simple Rational Equations Solve. Check your solution.x2 – 3x – 10x – 2= 7(x + 5)(x – 2)(x – 2)= 7Note that x ≠ 2.x + 5 = 7x = 2Because the left side of the original equation is undefined when x = 2, there is no solution.