Find the curvature of the curve r(t).r(t) = (6 + cos 6t - sin 6t)i + (10 + sin 6t + cos 6t)j + 5k
A. ? = 
B. ? = 3
C. ? = 
D. ? = 3
Answer: A
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Find all the first order partial derivatives for the following function.f(x, y) = sin2 (8xy2 - y)
A. 
= 16y2sin (8xy2 - y) cos (8xy2 - y); 
= 2sin (8xy2 - y) cos (8xy2 - y)
B. 
= 2sin (8xy2 - y) cos (8xy2 - y); 
= (32x - 2) sin (8xy2 - y) cos (8xy2 - y)
C. 
= 16y2sin (8xy2 - y) cos (8xy2 - y); 
= (32xy - 2) sin (8xy2 - y) cos (8xy2 - y)
D. 
= 2sin (8xy2 - y) cos (8xy2 - y); 
= 2sin(8xy2 - y) cos(8xy2 - y)
Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.log45 3 + log45 15
A. 15 B. 1 C. 3 D. 45
Solve the problem.The function A = Aoe-0.0099x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 300 pounds of the material are initially put into the vault, how many pounds will be left after 150 years?
A. 70 pounds B. 68 pounds C. 321 pounds D. 217 pounds
Solve the problem.The Windmill Harbour Marina purchased a boat hauling rig for $235,000. Its estimated life is 16 years, at which time it will have a scrap value of $6200. Use the straight-line method of depreciation to find the annual amount of depreciation. Find the book value at the end of 9 years.
A. $14,688, $363,700 B. $14,300, $106,300 C. $14,300, $128,700 D. $14,688, $132,192