SECTION A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A73 Now Work problem 57 Since the volume of the box is to be 144 cm ,3 we have Discard the solution = x 14 (do you see why?) and conclude that the sheet metal should be 22 centimeters by 22 centimeters. Check: If we take a piece of sheet metal 22 centimeters by 22 centimeters, cut out a 9-centimeter square from each corner, and fold up the edges, we get a box whose dimensions are 9 cm by 4 cm by 4 cm and whose volume is ⋅ ⋅ = 9 4 4 144cm,3 as required. ( ) ( ) − = − = − = ± = ± = = x x x x x x 9 18 144 18 16 18 4 18 4 22 or 14 2 2 Divide both sides by 9. Use the Square Root Method. = V 144 Applications and Extensions In Problems 9–18, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 9. Geometry The area of a circle is the product of the number π and the square of the radius. 10. Geometry The circumference of a circle is the product of the number π and twice the radius. 11. Geometry The area of a square is the square of the length of a side. 12. Geometry The perimeter of a square is four times the length of a side. 13. Physics Force equals the product of mass and acceleration. 14. Physics Pressure is force per unit area. 15. Physics Work equals force times distance. 16. Physics Kinetic energy is one-half the product of the mass and the square of the velocity. 17. Business The total variable cost of manufacturing x dishwashers is $150 per dishwasher times the number of dishwashers manufactured. 18. Business The total revenue derived from selling x dishwashers is $250 per dishwasher times the number of dishwashers sold. 19. Financial Planning Arik’s friend bought him a lottery ticket for his birthday that won $10,000. Arik decided to give half to his friend and invest the other half. With his investment, Arik is planning to take a trip to Europe when he retires. He contacted a travel agent and has determined he will need $500 in extra income each year to save enough money for the trip. He can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should Arik invest in each to realize exactly $500 in interest per year? 20. Financial Planning After 2 years, Arik (see Problem 19) decided to add an extra week to his European vacation. He estimates that he will now require $700 per year. Assuming that the remaining information is the same, how should the money be reinvested? A.8 Assess Your Understanding Concepts and Vocabulary 1. The process of using variables to represent unknown quantities and then finding relationships that involve these variables is referred to as . 2. The money paid for the use of money is . 3. Objects that move at a constant speed are said to be in . 4. True or False The amount charged for the use of principal for a given period of time is called the rate of interest. 5. True or False If an object moves at an average speed r , the distance d covered in time t is given by the formula = d rt. 6. Multiple Choice Suppose that you want to mix two coffees in order to obtain 100 pounds of a blend. If x represents the number of pounds of coffee A, which algebraic expression represents the number of pounds of coffee B? (a) −x 100 (b) −x 100 (c) x 100 (d) + x 100 7. Multiple Choice Which of the following is the simple interest formula? (a) = I rt P (b) = I Prt (c) = I P rt (d) = + I P rt 8. Multiple Choice If it takes 5 hours to complete a job, what fraction of the job is done in 1 hour? (a) 4 5 (b) 5 4 (c) 1 5 (d) 1 4 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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