3. A company designs spinning toys using the family of functions y = cxv4 x', where c is a positive %3D constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of y = cxy4 x, for some c. Each spinning toy is in the shape of the solid generated when such a region is %3D revolved about the x-axis. Both x and y are measured in inches. (a) Find the area of the region in the first quadrant bounded by the x-axis and the graph of y = cxV4 - x for c = 6. (4 -2:) (b) It is anown that, for y = exV4 – x² For a particular spinning toy, the radius of the V4 - x? xp largest cross-sectional circular slice is 1.2 inches. What is the value of c for this spinning toy? (c) For another spinning toy, the volume is 2n cubic inches. What is the value of c for this spinning toy?
3. A company designs spinning toys using the family of functions y = cxv4 x', where c is a positive %3D constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of y = cxy4 x, for some c. Each spinning toy is in the shape of the solid generated when such a region is %3D revolved about the x-axis. Both x and y are measured in inches. (a) Find the area of the region in the first quadrant bounded by the x-axis and the graph of y = cxV4 - x for c = 6. (4 -2:) (b) It is anown that, for y = exV4 – x² For a particular spinning toy, the radius of the V4 - x? xp largest cross-sectional circular slice is 1.2 inches. What is the value of c for this spinning toy? (c) For another spinning toy, the volume is 2n cubic inches. What is the value of c for this spinning toy?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:AP® Calculus AB Free-Response Questions
3. A company designs spinning toys using the family of functions y = cxV4 - x', where c is a positive
constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of
y = cxy4 x, for some c. Each spinning toy is in the shape of the solid generated when such a region is
2.
%3D
revolved about the x-axis. Both x and y are measured in inches.
(a) Find the area of the region in the first quadrant bounded by the x-axis and the graph of y =
cx/4 – ?
for c = 6.
2.
(b) It is known that, for y = cxv4 x
For a particular spinning toy, the radius of the
%D
xp
4 x2
largest cross-sectional circular slice is 1.2 inches. What is the value of c for this spinning toy?
(c) For another spinning toy, the volume is 2n cubic inches. What is the value of c for this spinning toy?
Write your responses to this question only on the designated pages in the separate Free Response
booklet. Write your solution to each part in the space provided for that part.
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