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Mathematics (09) Practice Test - MTELs
Mathematics (09) Practice Test - MTELs
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Mathematics (09) Practice TestOPEN-RESPONSE ITEM ASSIGNMENT #2Use the in<strong>for</strong>mation below to <strong>com</strong>plete the exercise that follows.The machine shown below manufactures various-sized solid spherical rubber balls from acontinuously fed 1" diameter cylindrical rubber stock. For each run, the balls produced areuni<strong>for</strong>m in size. The machine manufactures three balls per second. The total volume ofrubber stock fed into the machine is exactly equal to the <strong>com</strong>bined volume of rubber ballsmanufactured.1" DiameterRubber StockUsing your knowledge of three-dimensional geometry and functions, prepare a response inwhich you analyze this situation. In your response:• calculate the volume V b(d), in cubic inches, of one rubber ball as a function of d, thediameter of the ball;• calculate the volume V s, in cubic inches, of one linear foot of the rubber stock;• derive the function s(d), where s is the speed in feet per second of the rubber feed and d isthe diameter in inches of each rubber ball; and• plot a graph of the function s(d) <strong>for</strong> values of d from 0.5" to 2.5".Be sure to show your work and explain the reasoning you use in analyzing and solving thisproblem.67
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