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Pre-Calc Homework Solutions 48

Pre-Calc Homework Solutions 48 - 48 Section 2.2 1 2 65(a f...

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65. (a) f 1 } p 6 } 2 5 sin } p 6 } 5 } 1 2 } (b) The graphs of y 1 5 f ( x ), y 2 5 0.3, and y 3 5 0.7 are shown. [0, 1] by [0, 1] The intersections of y 1 with y 2 and y 3 are at x < 0.3047 and x < 0.7754, respectively, so we may choose any value of a in 3 0.3047, } p 6 } 2 and any value of b in 1 } p 6 } , 0.7754 4 , where the interval endpoints are approximate. One possible answer: a 5 0.305, b 5 0.775 (c) The graphs of y 1 5 f ( x ), y 2 5 0.49, and y 3 5 0.51 are shown. [0.49, 0.55] by [0.48, 0.52] The intersections of y 1 with y 2 and y 3 are at x < 0.5121 and x < 0.5352, respectively, so we may choose any value of a in 3 0.5121, } p 6 } 2 , and any value of b in 1 } p 6 } , 0.5352 4 , where the interval endpoints are approximate. One possible answer: a 5 0.513, b 5 0.535 66. Line segment OP has endpoints (0, 0) and ( a , a 2 ), so its midpoint is 1 } 0 1 2 a } , } 0 1 2 a 2 } 2 = 1 } a 2 } , } a 2 2 } 2 and its slope is } a a 2 2 2 0 0 } 5 a . The perpendicular bisector is the line through 1 } a 2 } , } a 2 2 } 2 with slope 2 } 1 a } , so its equation is y 5 2 } 1 a } 1 x 2 } a 2 } 2 1 } a 2 2 } , which is equivalent to y 5 2 } 1 a } x 1 } 1 1 2 a 2 } . Thus the y -intercept is b 5 } 1 1 2 a 2 } . As the point P
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