A 6-inch tall plastic “bubbleâ€� sits on a flat surface. Any vertical cross section taken through the center of the bubble is given by the curve y = 6 cos x for − π / 2 ≤ x ≤ π / 2 . A can in the shape of a right circular cylinder sits on the surface inside the bubble. Use Newton’s Method to approximate the radius of the can with largest possible volume. What is the volume of the can with this approximate radius?
A 6-inch tall plastic “bubbleâ€� sits on a flat surface. Any vertical cross section taken through the center of the bubble is given by the curve y = 6 cos x for − π / 2 ≤ x ≤ π / 2 . A can in the shape of a right circular cylinder sits on the surface inside the bubble. Use Newton’s Method to approximate the radius of the can with largest possible volume. What is the volume of the can with this approximate radius?
A 6-inch tall plastic “bubble� sits on a flat surface. Any vertical cross section taken through the center of the bubble is given by the curve
y
=
6
cos
x
for
−
π
/
2
≤
x
≤
π
/
2
.A can in the shape of a right circular cylinder sits on the surface inside the bubble. Use Newton’s Method to approximate the radius of the can with largest possible volume. What is the volume of the can with this approximate radius?
the weight W of a steel ball bearing varies directly with the cube of the bearing's radius r according to the formula W= 4/3 pi(p)(r)^3, where p is the density of the steel. The surface area of a bearing varies directly as the square of its radius because A = 4 pi(r^2)
a. Express the weight W of a bearing in terms of its surface area
b. Express the bearing's surface area A in terms of its weight.
c. For steel, p = 7.85 g/cm^3. What s the surface area of a bearing weighing 0.62 g?
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with a diameter of 50m.
A right inverted circular cone has height of 8 meters and base radius of 3 meters. Assuming that the cone is
completely filled with water, how much work does it require to pump all water out of the top of the tank?
Enter the exact value of your answer.
W =
Joules
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