Business Calc Homework w answers_Part_26

Business Calc - 126 Chapter 3 Review 74 continued 78(a P(0(c One possible answer If the current ridership is less than 40 then the proposed plan

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
74. continued (c) One possible answer: If the current ridership is less than 40, then the proposed plan may be good. If the current ridership is greater than or equal to 40, then the plan is not a good idea. Look at the graph of y 5 r ( x ). [0, 60] by [ 2 50, 200] 75. (a) Since x 5 tan u , we have } d d x t } 5 (sec 2 u ) } d d u t }52 0.6 sec 2 u . At point A , we have u 5 0 and } d d x t }52 0.6 sec 2 0 52 0.6 km/sec. (b) 0.6 } r s a e d c } ? } 1r 2 ev p o r lu ad tion } ? } 6 1 0 m s i e n c } = } 1 p 8 } revolutions per minute or approximately 5.73 revolutions per minute. 76. Let f ( x ) 5 sin ( x 2 sin x ). Then f 9 ( x ) 5 cos ( x 2 sin x ) } d d x } ( x 2 sin x ) 5 cos ( x 2 sin x )(1 2 cos x ). This derivative is zero when cos ( x 2 sin x ) 5 0 (which we need not solve) or when cos x 5 1,which occurs at x 5 2 k p for integers k . For each of these values, f ( x ) 5 f (2 k p ) 5 sin (2 k p 2 sin 2 k p ) 5 sin (2 k p 2 0) 5 0. Thus, f ( x ) 5 f 9 ( x ) 5 0 for x 5 2 k p , which means that the graph has a horizontal tangent at each of these values of x . 77. y 9 ( r ) 5 } d d r } 1 } 2 1 rl } ! } p T § d } § 2 5 1 } 2 1 l } ! } p T § d } § 2 } d d r } 1 } 1 r } 2 52} 2 r 1 2 l } ! } p T § d } § y 9 ( l ) 5 } d d l } 1 } 2 1 rl } ! } p T § d } § 2 5 1 } 2 1 r } ! } p T § d } § 2 } d d l } 1 } 1 l } 2 52} 2 r 1 l 2 } ! } p T § d } § y 9 ( d ) 5 } d d d } 1 } 2 1 rl } ! } p T § d } § 2 5 1 } 2 1 rl } ! } p T } § 2 } d d d } ( d 2 1/2 ) 5 } 2 1 rl } ! } p T } § 1 2} 1 2 } d 2 3/2 2 52} 4 1 rl } ! } p § T d § 3 } § y 9 ( T ) 5 } d d T } 1 } 2 1 rl } ! } p T § d } § 2 5 1 } 2 1 rl } ! } p 1 § d } § 2 } d d T } ( ˇ T w ) 5 } 2 1 rl } ! } p 1 § d } § 1 } 2 ˇ 1 T w } 2 5 } 4 rl ˇ 1 p w d w T w } Since y 9 ( r ) , 0, y 9 ( l ) , 0, and y 9 ( d ) , 0, increasing r , l ,or d would decrease the frequency. Since y 9 ( T ) . 0, increasing T would increase the frequency. 78. (a) P (0) 5 } 1 2 1 00 e 5 } < 1 student (b) lim t P ( t ) 5 lim t } 1 1 20 e 0 5 2 t } 5 } 20 1 0 } 5 200 students (c) P 9 ( t ) 5 } d d t } 200(1 1 e 5 2 t ) 2 1 52 200(1 1 e 5 2 t ) 2 2 ( e 5 2 t )( 2 1) 5 } (1 2 1 00 e e 5 5 2 2 t t ) 2 } P 0 ( t ) 5 5 5 Since P 05 0 when t 5 5, the critical point of y 5 P 9 ( t ) occurs at t 5 5. To confirm that this corresponds to the maximum value of P 9 ( t ), note that P 0 ( t ) . 0 for t , 5 and P 0 ( t ) , 0 for t . 5. The maximum rate occurs at t 5 5, and this rate is P 9 (5) 5 } (1 2 1 00 e e 0 0 ) 2 }5} 2 2 0 2 0 } 5 50 students per day. Note: This problem can also be solved graphically. 79. [ 2 p , p ] by [ 2 4, 4] (a) x ± k } p 4 } , where k is an odd integer (b) 1 2} p 2 } , } p 2 } 2 (c) Where it’s not defined, at x 5 k } p 4 } , k an odd integer (d) It has period } p 2 } and continues to repeat the pattern seen in this window. (200
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

Page1 / 5

Business Calc - 126 Chapter 3 Review 74 continued 78(a P(0(c One possible answer If the current ridership is less than 40 then the proposed plan

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online