By Arthur Cayley

This quantity is made from electronic photographs from the Cornell college Library old arithmetic Monographs assortment.

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2, 2] × [−2, 2] b. [−5, 5] × [−5, 5] c. [−10, 10] × [−70, 70] d. [−100, 100] × [−200, 200] 4. Use a graphing device to sketch a graph of x 2 − 10 x2 − 1 with the following viewing rectangles, and determine which gives the best representation for the graph of the equation. y= a. [−5, 5] × [−5, 5] b. [−10, 10] × [−10, 10] c. [−10, 10] × [−100, 100] d. [−5, 5] × [−25, 25] In Exercises 5–10, determine an appropriate viewing rectangle for the graph of each equation, and use it to sketch the graph.

Use equations to describe the problem. (x + 2)2 + (y − 3)2 = 3 + 4 + 9 = 16. The equation of the circle in standard form is (x − (−2))2 + (y − 3)2 = 42 , which describes the circle with center (−2, 3) and radius 4 that is shown in Figure 12. ■ Applications C EXAMPLE 8 A gas pipeline is to be constructed between points A and B on opposite sides of a river, as shown in Figure 13. A surveyor first determines a third point C on the same side of the river as point A so that the lines between A and C and between B and C are perpendicular.

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