By David Cohen
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Additional resources for Precalculus: A Problems-Oriented Approach, 6th Edition
The calculations are as follows: DE ϭ 2 34 Ϫ 1Ϫ2 2 4 2 ϩ 31 Ϫ 1Ϫ1 2 4 2 ϭ 236 ϩ 4 ϭ 240 EF ϭ 214 Ϫ 3 2 2 ϩ 11 Ϫ 4 2 2 ϭ 21 ϩ 9 ϭ 210 DF ϭ 2 33 Ϫ 1Ϫ22 4 2 ϩ 34 Ϫ 1Ϫ1 2 4 2 ϭ 225 ϩ 25 ϭ 250 Because ( 140)2 ϩ ( 110)2 ϭ ( 150)2, D, E, and F are vertices of a right triangle with hypotenuse DF and right angle at vertex E, and so ^DEF is a right triangle. ) . EXAMPLE y 4 Using the distance formula to ﬁnd a radius (a) Find the radius r of the circle in Figure 8. ) (b) Compute the area and the circumference of the circle.
For each answer, give exact expressions and also calculator approximations rounded to one decimal place. (_3, 2) r x SOLUTION (a) The radius r is the distance from center (0, 0) to the given point (Ϫ3, 2) on the circle. Using the distance formula, we have r ϭ 21Ϫ3 Ϫ 02 2 ϩ 12 Ϫ 0 2 2 ϭ 19 ϩ 4 ϭ 113 units Figure 8 (b) Recall the formulas for the area A and the circumference C of a circle of radius r: A ϭ pr 2 and C ϭ 2pr. 7 units . One of the important applications of rectangular coordinates is in displaying quantitative data.
Figures A and B provide estimates for the number 28 Chapter 1 Fundamentals n 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 t 1995 1996 1997 Year t Figure A Global number n of Internet host computers (thousands) Global number n of Internet host computers (millions) n of Internet host computers, worldwide, for the years t ϭ 1995 –1997 and 1985 –1987. com) 24. Have you or a friend ever run in a 10K (10,000 meter) race? When the author polled his precalculus class at UCLA in Fall 1997, he found that there were ﬁve students in the class (of 160) who said they had run a 10K in under 50 minutes.