Precal hw

just the ones circled

2.1 LINEAR FUNCTIONS 167 61- y= gar-7, WW) .9: 4Ec\"",1='(1,1) 63. y: 6, P(3,-2) 64. :c = 1, P(5,0) (Perpendicular Lines} Recall from Intermediate Algebra that two non-vertical lines are perpendic- ular if and only if they have negative reciprocal slopes. That is to say, if one line has slope m1 and the other has slope m; then m; - m: = 1. (You will be guided through a proof of this result in Exercise 71.) Please note that a horizontal line is perpendicular to a vertical line and vice versa, so we assume m1 a 0 and ma a 0. In Exercises 65 - 70, you are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point. @ y = a: + 2, P(0,0) 66. y = -59; + 5, P(3,2) w zgs7, P(6,0) 68. y=4;$.P(1$-1) 69. y = 6, P(3. -2) 70. x =1, Pl-5.0l 43. The cross-section of a swimming pool is below. Write a piecewise-dened linear function which describes the depth of the pool, D (in feet) as a function of: (a) the distance (in feet) from the edge of the shallow end of the pool, d. (b) the distance (in feet) from the edge of the deep end of the pool, .9. (c) Graph each of the functions in (a) and (b). Discuss with your classmates how to trans form one into the other and how they relate to the diagram of the pool. a ft. 10 ft.r 415 ft.* In Exercises 44 - 49, compute the average rate of change of the function over the specied interval. 44. f(:r:) =33, [1,2] 45. f(:c)= %, [1,5] 46. f(a:) = , [0,16] .m) = 31:2, {3.3} 48. f(:c) = :i3, [5,7] 49. f(2:)=3$2+2:c7, [4,2} 166 LINEAR AND QUADRATIC FUNCTIONS In Exercises 50 - 53, compute the average rate of change of the given function over the interval [33, a: + h]. Here we assume [:c, a: + h] is in the domain of the function. 50. f(':) = x3 @1133) = % $+4 52. Hrs): 53. le=3$2+2m7 164 LINEAR AND QUADRATIC FUNCTIONS 31. A plumber charges $50 for a service call plus $80 per hour. If she spends no longer than 8 hours a day at any one site, nd a linear function that represents her total daily charges 0 (in dollars) as a function of time t (in hours) spent at any one given location. salesperson is paid $200 per week plus 5% commission on her weekly sales of .1: dollars. ind a linear function that represents her total weekly pay, W (in dollars) in terms of x. What must her weekly sales be in order for her to earn $475.00 for the week? 33. An on-demand publisher charges $22.50 to print a 600 page book and $15.50 to print a 400 page book. Find a linear function which models the cost of a book 0 as a function of the number of pages p. Interpret the slope of the linear function and find and interpret C(O). 55. Using data from Bureau of Transportation Statistics, the average fuel economy F in miles per gallon for passenger cars in the US can be modeled by F(t) = ~0.0076t2 + 0.4515 + 16, 0 5 t g 28, where t is the number of years since 1980. Find and interpret the average rate of change of F over the interval [0, 28]. i 56} The temperature T in degrees Fahrenheit t hours after 6 AM is given by: T(t)=%t2+8t+32, 05:5 12 (a) Find and interpret T(4), T[8) and T(12). (b) Find and interpret the average rate of change of T over the interval [4, 8]. (c) Find and interpret the average rate of change of T from t = 8 to t = 12. (d) Find and interpret the average rate of temperature change between 10 AM and 6 PM. 57. Suppose C(33) = x2 1092+ 27 represents the costs, in hundreds, to produce a: thousand pens. Find and interpret the average rate of change as production is increased from making 3000 to 5000 pens. 58. With the help of your classmates nd several other \"real-world" examples of rates of change that are used to describe non-linear phenomena. (Parallel Lines) Recall from Intermediate Algebra that parallel lines have the same slope. (Please note that two vertical lines are also parallel to one another even though they have an undened slope.) In Exercises 59 - 64, you are given a line and a point which is not on that line. Find the line parallel to the given line which passes through the given point. 59. y = 3a: + 2. P(0.0} E y = -6x + 5, P(3, 2)