416 CHAPTER 3 Polynomial and Rational Functions Concept Check Match each statement with its corresponding graph in choices A–D. In each case, k 70. A. x y B. x y C. x y D. x y 17. y varies directly as x. 1y = kx2 18. y varies inversely as x. Ay = k xB Concept Check Write each formula as an English phrase using the word varies or proportional. 21. C = 2pr, where C is the circumference of a circle of radius r 22. d = 1 5 s, where d is the approximate distance (in miles) from a storm, and s is the number of seconds between seeing lightning and hearing thunder 23. r = d t , where r is the speed when traveling d miles in t hours 24. d = 1 4pnr2 , where d is the distance a gas atom of radius r travels between collisions, and n is the number of atoms per unit volume 25. V = 1 3pr 2h, where V is the volume of a cone of radius r and height h 26. ƒ = mv2 r , where ƒ is the centripetal force of an object of mass m moving along a circle of radius r at velocity v Solve each problem. See Examples 1– 4. 27. Circumference of a Circle The circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in. 28. Pressure Exerted by a Liquid The pressure exerted by a certain liquid at a given point varies directly as the depth of the point beneath the surface of the liquid. The pressure at 10 ft is 50 pounds per square inch (psi). What is the pressure at 15 ft? 29. Resistance of a Wire The resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K. 30. Weight on the Moon The weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 200-lb astronaut would weigh 32 lb on the moon. How much would a 50-lb dog weigh on the moon? 31. Distance to the Horizon The distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person 144 m above the surface of Earth can see 18 km to the horizon, how far can a person see to the horizon from a point 64 m above the surface? 19. y varies directly as the second power of x. 1y = kx22 20. x varies directly as the second power of y. 1x = ky22
RkJQdWJsaXNoZXIy NjM5ODQ=