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Unit 16 – Classwork 4 Thursday, May 19 The word problems on this worksheet were taken directly from Paul Foerster’s Algebra and Trigonometry textbook, copyright 1999, Addison-Wesley Publishing 1. In the graph below, y varies __________________ with the square of x. If the graph contains the point (20, 0.355), find the particular equation expressing y in terms of x. 2. In the graph below, y varies __________________ with the square root of x. If the graph contains the point (16, 10.4), find the particular equation expressing y in terms of x. 3. In 1844 the French scientist J.L. Poiseuille found that the rate at which a fluid such as blood flows through small tubes such as arteries and veins varies directly with the product of the pressure acting on the fluid and the fourth power of the radius of the tube. Assume that you have an artery 0.2 centimeters in radius through which blood flows at 400 cubic centimeters per second when acted upon by the normal pressure of 100 units. a. Write the particular equation expressing flow rate in terms of pressure and radius. b. If the radius of the artery were reduced to 0.16 cm due to the build up of cholesterol, what flow rate would be produced by the normal blood pressure of 100 units. c. If the heart pumped hard enough to restore the flow rate of 400 cubic millimeters per second for the 0.16 cm artery, what would the blood pressure be? 4. The weights of airplanes of similar shape are directly proportional to the cube of their lengths. In order for the airplane to fly, this weight must be directly proportional to the product of the wing area and the flight speed. The wing area varies directly as the square of the length of the airplane. a. Write the general equations from each of the three variation functions above. b. From these equations, derive another equation expressing the speed of the airplane in terms of its length.