A company designs spinning toys using the family of functions y = cxv4 – x, where e 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 – x², for some c. Each spinning toy is in the shape of the solid generated when such a region is 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 for c = 6. (4 - 21) dy (b) It is known that, for y = cx\4 – x². dx -. For a particular spinning toy, the radius of the V4 – x? 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 2z cubic inches. What is the value of c for this spinning toy?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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A company designs spinning toys using the family of functions y = cxv4 – x², where e is a positive
constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of
y = cxv4 – x², for some c. Each spinning toy is in the shape of the solid generated when such a region is
revolved about the x-axis. Both xr and y are measured in inches.
(a) Find the area of the region in the first quadrant bounded by the xr-axis and the graph of y = cxv
for c = 6.
dy
(b) It is known that, for y = cxv4 – x“
dx
(4 - 21)
-. For a particular spinning toy, the radius of the
%3D
V4 - x?
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 27 cubic inches. What is the value of c for this spinning toy?
Transcribed Image Text:A company designs spinning toys using the family of functions y = cxv4 – x², where e is a positive constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of y = cxv4 – x², for some c. Each spinning toy is in the shape of the solid generated when such a region is revolved about the x-axis. Both xr and y are measured in inches. (a) Find the area of the region in the first quadrant bounded by the xr-axis and the graph of y = cxv for c = 6. dy (b) It is known that, for y = cxv4 – x“ dx (4 - 21) -. For a particular spinning toy, the radius of the %3D V4 - x? 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 27 cubic inches. What is the value of c for this spinning toy?
Expert Solution
Step 1

The design of spinning toys is given by the below family of functions.

y=cx4x2

Here c is a positive constant

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