Pre-Calc Homework Solutions 307

# Pre-Calc Homework Solutions 307 - Section 7.3 47(a Solve d...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 7.3 47. (a) Solve d dc [ 0.5, 2.5] by [ 0.5, 2.5] 2 2 2 307 c 4 c 2 2 2 0 0 2 c 0 2 c c 4 The intersection points are 1 1 , 1 , , 2 , and (1, 1). 4 4 1 1 , outer radius R , 4 y2 1 . The volume is 16 2 11 1 y . 48 16 1 1 x (a) A washer has inner radius r and area (R 2 1 This value of c gives a minimum for V because a 2V dc 2 2 r ) 2 1 y4 1 dy 16 1 y4 1 3y 3 2 2 0. 2 2 2 Then the volume is 4 2 2 2 2 2 4 (b) A shell has radius x and height 1 1. The volume is 1 2 x 2 1 1/4 (b) Since the derivative with respect to c is not zero anywhere else besides c at c 0 or c 2 2 (x) 1/4 1 x 1 dx , x f (x) 0 1 x 2 2 3/2 x 3 11 . 48 , the maximum must occur 2 1. The volume for c (3 2 8) 0 is 48. (a) For 0 For x x f (x) x x(sin x) x 2 4.935, sin x. sin x. So (c) and for c 1 it is 2.238. c 0 0, x f (x) sin x for 0 sin 0 . maximizes the volume. (b) Use cylindrical shells: a shell has radius x and height y. The volume is 0 2 xy dx, which from part (a) is 2 cos x 0 2 sin x dx 0 4 . x 12 [0, 2] by [0, 6] 49. (a) A cross section has radius r A(x) 6 0 36 x 2 and area The volume gets large without limit. This makes sense, since the curve is sweeping out space in an ever-increasing radius. 51. (a) Using d C r2 (36x 2 144 (36x 2 x 4). The volume is 144 , and A 144 x 4) dx 12x 3 1 5 x 5 6 0 36 cm3. 5 d 2 2 C2 yields the 4 following areas (in square inches, rounded to the nearest tenth): 2.3, 1.6, 1.5, 2.1, 3.2, 4.8, 7.0, 9.3, 10.7, 10.7, 9.3, 6.4, 3.2. (b) 36 cm3 (8.5 g/cm3) 5 192.3 g 50. A cross section has radius r A(x) r2 (c sin x)2 c sin x and area (b) If C(y) is the circumference as a function of y, then the (c 2 2c sin x sin2 x). area of a cross section is C(y)/ 2 2 The volume is A(y) (c2 0 2c sin x 2c cos x 2c 4 c 1 2 2 sin2 x) dx 1 x 2 1 sin 2x 4 C 2( y) , 4 1 4 6 6 0 and the volume is 0 C 2(y) dy. c2x c c 2 2c . (c) 1 4 6 A( y) dy 0 2 2 1 C 2(y) dy 4 0 1 6 0 [5.42 24 4 2(4.52 10.82 4.42 11.62 2 5.12 11.62 6.32 10.82 7.82 9.42 9.02) 6.32] 34.7 in.3 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online