Solve the problem.If y varies directly as x, and y = 3 when x = 4, find y when x = 28.
A. 
B. 21
C. 
D. 
Answer: B
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Find all the first order partial derivatives for the following function.f(x, y, z) = x2y + y2z + xz2
A. 
= 2xy + z2; 
= x2 + 2yz; 
= y2 + 2xz
B. 
= 2xy + z2; 
= x2 + yz; 
= y2 + xz
C. 
= 2y + z2; 
= x2 + 2z; 
= y2 + 2x
D. 
= 2xy; 
= x2 + 2yz; 
= y2 + 2xz
Multiply. Simplify if possible.
? 
A. - 
B. -b
C. 1
D. b
Use slack variables to convert the constraints into linear equations.Maximize3x + 5ysubject to:7x + 9y ? 30 x + 6y ? 40with:x ? 0, y ? 0
A. 7x + 9y + u = 30 x + 6y + u = 40 -3x - 5y + M = 0 Maximize M given that x ? 0, y ? 0, u ? 0 B. 7x + 9y + u = 30 x + 6y + v = 40 -3x - 5y + M = 0 Maximize M given that x ? 0, y ? 0, u ? 0, v ? 0 C. 7x + 9y = u + 30 x + 6y = v + 40 3x + 5y + M = 0 Maximize M given that x ? 0, y ? 0, u ? 0, v ? 0 D. 7x + 9y + u ? 30 x + 6y + v ? 40 3x + 5y + M ? 0 Maximize M given that x ? 0, y ? 0, u ? 0, v ? 0
Solve the problem.The area of a triangle is given by A = 
ab sin C,where a and b are the lengths of two of the sides and C is the included angle. If 
and C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.
A. 12.02° B. 155.96° C. 24.04° D. No such triangle exists.