Name Date Credit. Homework #48: Direct Variation and Proportion Read p

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1 Name Date Credit Homework #48: Direct Variation and Proportion Read p p / In Exercises 1~4, several ordered pairs of a function are given in a table. Tell whether the function is a direct variation. If it is, give the constant of variation. Oral Ex w z s t For each direct variation, give an equation that relates the two variables and includes the value of the constant of variation. 5. The circumference (C) of a circle varies directly as the radius (r). 11. The distance (d) a car travels at 90 km/h is directly proportional to the time (t) traveled. Solve. Written 3. If p is directly proportional to q, and p = 9 when q = 7.5, find q when p = If s varies directly as, and s = 12 when r = 2, find s when r = If p is directly proportional to r 2, and p = 20 when r = 6, find p when r = 12. p / Solve. Problems 3. A real estate agent made a commission of $5400 on a house that sold at $120,000. At this rate, what commission will the agent make on a house that sells for $145,000?

2 9. The stretch in a loaded spring varies directly as the load it supports. A load of 15 kg stretches a certain spring 3.6 cm. What load would stretch the spring 6 cm? 15. The distance an object falls from rest varies directly as the square of the time it has fallen. If the object fell 4 ft during the first half second, how far did it fall during the next two seconds? 19. The volume of a sphere is directly proportional to the cube of its diameter and is 288π cm 3 when the diameter is 12 cm. Find the constant of proportionality in terms of π. Then write the formula for the volume of a sphere in terms of its diameter. p. 357 / Solve each equation over the real numbers. Mixed Review 2. 6.

3 Name Date Credit Homework #49: Inverse and Joint Variation Read p p / In Exercises 5 10, give an equation of the variation described. Use k for the constant of variation. OE 5. V varies directly as the cube of r. 9. w varies jointly as x and y and inversely as z. Written 1. If y varies inversely as x, and y = 3 when x = 6, find x when y = If w is inversely proportional to the square of v, and w = 3 when v = 6, find w when v = If z is jointly proportional to x and y, and z = 18 when x = 0.4 and y = 3, find z when x = 1.2 and y = If s varies directly as r and inversely as t, and s = 10 when r = 5 and t = 3, for what value of t will s = 3 when r = 4? 9. Suppose that z varies jointly as u and v and inversely as w, and that z = 0.8 when u = 8, v = 6 and w = 5. Find z when u = 3, v = 10 and w = 5.

4 p / Problems 3. The heat loss through a glass window varies jointly as the area of the window and the difference between the inside and outside temperatures. If the loss through a window with area 3 is 720 BTU when the temperature difference is 15 C, what is the heat loss through a window with area 4.5 when the temperature difference is 12 C? In Problems 5, and 6, use the fact that the intensity of light, measured in lux, is inversely proportional to the square of the distance between the light source and the object illuminated. 5. A light meter 7.5 m from a light source registers 24 lux. What intensity would it register 15 m from the light source? 9. The stretch in a wire under a given tension varies directly as the length of the wire and inversely as the square of its diameter. A wire having length 2 m and diameter 1.5 mm stretches 1.2 mm. If a second wire of the same material (and under the same tension) has length 3 m and diameter 2.0 mm, find the amount of stretch. p. 357 / Solve each equation over the real numbers. Mixed Review 7. 9.

5 Name Date Credit Homework #50: Arithmetic Sequences Read p p. 509 / Find the formula for the nth term of each arithmetic sequence. Written 1. 24, 32, 40, 48, 3. 3, 10, 17, 24, 5. 7, 11, 15, 19, Find the specified term of each arithmetic sequence. 7. 4, 9, 14, 19, 11. 2, 11, 20, 15., Find the arithmetic mean of each pair of numbers , 7 21.

6 Insert (a) two, (b) three, and (c) four arithmetic means between each pair , 33 a. b. c. 27. How many terms are in the sequence 18, 24, 30,..., 618?

7 Name Date Credit Homework #51: Geometric Sequences Read p p. 513 / Find the formula for the nth term of each geometric sequence. Written 1. 2, 6, 18, 54, 3. Find the specified term of each geometric sequence. 7. 2, 6, 18, 54, , 80, 20, 5, 13., Find the geometric mean of each pair of numbers , 8 Insert the given number of geometric means between each pair. 23. Three; 5, 80

8 Tell whether each sequence is arithmetic or geometric. Then find a formula for the nth term , 33, 41, 49, , 100, 50, 25, p / The following problems involve arithmetic and geometric sequences. A calculator may be helpful in solving these problems. Problems 1. Allysa has taken a job with a starting salary of $17600 and annual raises of $850. What will be her salary during her fifth year on the job? 7. A culture of yeast doubles in size every 4 hours. If the yeast population is estimated to be 3 million now, what will it be one day from now? (Challenge) 14. There are 12 steps in the chromatic scale from the A below middle C to the next higher A. This scale can be played by playing the white and black keys of a piano in order from left to right. The frequency of a note is given in hertz (Hz). For example, the A below middle C has a frequency of 220 Hz, which means the piano string vibrates 220 times per second. Notice that the frequency of the A above middle C is twice as great, 440 Hz. If the frequencies of the notes in the chromatic scale form a geometric sequence, show that the common ratio is and then find the frequency of middle C.

9 Name Date Credit p. 521 / Write each series in expanded form. Homework #52: Series and Sigma Notation Read p Written Write each series using sigma notation

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11 Name Date Credit Homework #53: Sums of Arithmetic and Geometric Series Read p p. 527 / Find the sum of each arithmetic series. Written 1.,, 3.,, The first 100 terms of the series Find the sum of each geometric series. 13.,, 15.,, 17.

12 19. Find if the series is (a) arithmetic; (b) geometric. a. b. p / Solve. A calculator may be helpful. Problems 5. Kurt can trace his ancestors back through 10 generations. He counts his parents as the first generation back, his four grandparents as the second generation back, and so on. How many ancestors does he have in these 10 generations? 9. a. Which of the two jobs described below will pay you the higher salary during the fifth year of employment? b. Which will pay you the greater total amount for all five years? Job A: Make $20,000 the first year with annual raises of $1500. Job B: Make $18,000 the first year with annual raises of 10%.

13 Name Date Credit Homework #54: Recursive Definitions of Sequences Read p (AMSCO book) p. 251 (AMSCO) / In 19 30: a. Write an algebraic expression that represents for each sequence. b. Find the ninth term of each sequence , 4, 6, 8, 21. 1, 4, 7, 10, , 6, 3, 1.5, i, 8i, 6i, 4i, , In 31 39, write the first five terms of each sequence

14 p. 514 (Dolciani) / The following problems involve arithmetic and geometric sequences. A calculator may be helpful in solving these problems. Problems 3. The cost of an annual subscription to a magazine is $20 this year. The cost is expected to rise by 10% each year. What will be the cost 6 years from now? 5. A carpenter is building a staircase from the first floor to the second floor of a house. The distance between floors is 3.3 m. Each step rises 22 cm. Not counting either floor itself, how many steps will there be?