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Check for Extraneous Solutions 4 EXAMPLE Solve x 13 0 and check for extraneous solutions. Solution x 13 0 Write original equation. x 13 2 (x ) Subtract 13 from each side. (13)2 x 169 ANSWER 䊳 Square each side. Simplify. 169 13 0, so x 169 is not a solution. The equation has no solution because x ≥ 0 for all values of x. Check for Extraneous Solutions Solve the equation. Check for extraneous solutions. 7. x 6 x EXAMPLE Science 8. x 8 2x 9. n 40 Use a Radical Model 5 The centripetal force F exerted on a passenger by a spinning amusement park ride and the number of seconds t the ride takes to complete one revolution are related by the following equation. CENTRIPETAL FORCE t 1620π F 2 Find the centripetal force experienced by this person if t 10. Solution CENTRIPETAL FORCE keeps you spinning in a circle on an amusement park ride. Forces can be measured in newtons. A force of one newton will accelerate a mass of one kilogram at one meter per second per second. t 102 0π 162F 2 Write model for centripetal force. 2 Substitute 10 for t and square each side. 1620π2 F Simplify. 1620π2 100 Solve for F. 1620π2 F 100 F ≈ 160 ANSWER 䊳 The person experiences a centripetal force of about 160 newtons. Use a Radical Model 10. Find the centripetal force exerted on the passenger in Example 5 if the amusement park ride takes 11 seconds to complete one revolution. 706 Chapter 12 Radicals and More Connections to Geometry