A hemisphere-shaped dome of radius 40 ft is to be coated with a layer of rust-proofer before painting. Use differentials to estimate the amount of rust-proofer needed if the coat is to be 0.04 in. thick.
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Round the result to the nearest hundredth, if necessary.
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Hint: The volume of a hemisphere of radius r is 
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__________ ft3
Fill in the blank(s) with the appropriate word(s).
33.51
Mathematics
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Solve the system of equations.5x + 2y + z = -112x - 3y - z = 177x + y + 2z = -4
A. (-3, 0, 4) B. (0, -6, 1) C. (0, 6, -1) D. (3, 0, -4)
Mathematics
Find the derivative of the function using the definition of derivative.f(x) = 
A. f '(x) = - 
B. f '(x) = - 8x2
C. f '(x) = 8
D. f '(x) = 
Mathematics
The graph of an exponential function is given. Match the graph to one of the following functions.
A. f(x) = 2x B. f(x) = -2-x C. f(x) = -2x D. f(x) = 2-x
Mathematics
Suppose g is the inverse function of a differentiable function f and 
If f(4) = 3 and 
find 
Mathematics