This exercise relates to Figure 5(b) on page 60. That

Chapter 1, Problem 61

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This exercise relates to Figure 5(b) on page 60. That figure shows a graph of the equation x y2 0.1y 15. Note that this equation is solved for x rather than y. In the standard Cartesian graphing mode, however, most graphing utilities require that the equation be solved for y. This exercise shows one method for obtaining the graph. (A remark at the end of this exercise mentions a second method.) (a) Rewrite the equation as Then solve for y in terms of x by using the quadratic formula with a 1, b 0.1, and c (15 x). After simplifying, you should obtain y 0.1 160.01 4x 2 y2 0.1y 115 x2 0 G 0 0 y= -6x+8 x y y x y=-6x+8 0 0 . (b) Enter and graph the pair of equations using the viewing rectangle [20, 5, 5] by [10, 10, 5]. Check that your graph agrees with that shown in Figure 5(b). (c) Experiment to find a viewing rectangle in which it is clear that the graph of the equation x y2 0.1y 15 is not symmetric about the x-axis. Remark: A second method for graphing x y2 0.1y 15 requires the parametric mode on your graphing utility. Consult the users manual for your graphing utility to see how to access and operate this mode. Entering the following pair of equations in the parametric mode will yield the graph (or a portion of the graph): x t 2 0.1t 15; y t. 62. Use a graphing uti