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The minute hand of a certain clock is 4 in long. Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the hand?
If π=πππππ and π=πππππ calculate:
a) The value of x which will give the maximum volume
b) The maximum volume of the box
c) Comment of the value obtained in part b.
A spherical balloon with radius "r" has a volume as shown. Find a function that represents the amount of air required to inflate the balloon from a radius of "r" inches to a radius of (r+1) inches.
V(r)=4/3pi(r3)
Find the domain and range of the bottom half of the given parabola
y2-x-4y+3=0
Find an expression of the function whose graph is the bottom half of the given parabola
y2-x-4y+3=0
You have been tasked to build a rectangular box. The top and bottom are to be built out of 2 cm thick aluminum. The density of aluminum is 2.7 g per cm^3, and the cost $6 per kg. The front and back walls are to be build out of 1 cm thick stainless steel. The density of stainless steel is 7.5 g per cm^3, and the cost $4 per kg. Finally, the 2 remaining walls are to be built out of 1 cm thick copper. The density of copper is 9.0 g per cm^3, and the cost $9 per kg. Find the measurements and total price of the least expensive such box that has volume 1 m^3
A cellular phone company has the following production function for a smart phone: p(x, y) =
50x
2
3 y
1
3 where p is the number of units produced with x units of labor and y units of capital. a)
Find the number of units produced with 125 units of labor and 64 units of capital. b) Find the
marginal productivities (Hints: Partial derivatives). c) Evaluate the marginal productivities at
x = 125 and y = 64.
Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks
up moisture at a rate proportional to its surface area. Under these circumstances, what will be
the eΒect on the dropβs radius.
