Find the flux of the vector field F across the surface S in the indicated direction.F(x, y, z) = 3i + 9j + 7k , S is the rectangular surface z = 0, 0 ? x ? 1, and 0 ? y ? 9, direction k

A. 27
B. 0
C. 81
D. 63


Answer: D

Mathematics

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Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have.f(x) = x5 + x4 + x2 + x + 6

A. 5; 0 positive zeros; 3 or 1 negative zeros B. 5; 0 positive zeros; 1 negative zero C. 5; 0 positive zeros; 2 or 0 negative zeros D. 5; 0 positive zeros; 0 negative zeros

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Simplify the expression.

A.
B.
C.
D.

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Sketch the graph of f by hand.f(x) = 

A.

B.

C.

D.

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?A firm can produce 100 units per week. If its total cost function is  dollars, and its total revenue function is  dollars, how many units x should it produce to maximize its profit? ?

A. ?1250 units B. ?650 units C. ?97 units D. ?50 units E. ?100 units

Mathematics