Find the composition. If f(x) = 6x + 5 and g(x) = x + 3, find (g ? f)(x)
A. 6x + 23
B. 6x2 + 23x + 15
C. 6x2 + 23
D. 6x + 8
Answer: D
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Find the average value of 
over the given region.
+ z2 over the rectangular solid in the first octant bounded by the coordinate planes and the planes 
, 
, 
A. 
B. 40
C. 
D. 
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. 3x + y + z - 2w = 10 2x + 3y + 3z + w = -52x + y + 4z + 11w = 11
A. {(7, -1, -6, 2)} B. {(6, -4, -2, 1)} C. {(w + 5, 3w - 7, -4w + 2, w)} D. {(2w + 3, 6w - 7, -10w + 8, w)}
Solve the problem.A rectangular board is 2 by 3 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.
A. 6 B. 4 C. 2 D. 3
Provide an appropriate response.Use Lagrange multipliers to minimize f(x, y) = x2 + y2 - xy subject to x - y = 10.
A. f(2, -1) = 7 B. f(5, -5) = 75 C. f(1, 2) = 3 D. f(5, 5) = 25