Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be h = 256+16t-16t². During what time interval will the ball at least 64 ft above the ground?


Mathematics

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Solve the problem.Find the mass of the region of density  bounded by the hemisphere  and the xy-plane.

A. 16? B. 32? C. 8? D. 4?

Mathematics

Simplify the expression. Write the answer with positive exponents only. Assume that all variables represent positive real numbers.2

A.
B.
C.
D.

Mathematics

Express the sum using summation notation.3 + 6 + 9 + ... + 21

A.

B.

C.

D.

Mathematics

A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.It costs the company $1.44 to make each dog and $1.67 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the dual objective function?

A. 1.44, 1.67 B. 1, 4, 1 C. 300, 700, 230 D. 1, 2, 1.44

Mathematics