Use a calculator to find the approximate value of arccos(0.67). (5 points)

A simply-supported beam has a 3 kip/ft uniformly-distributed load over the left half of its 13-ft span. What is the magnitude of the shear force at midspan?

Simplify the expression. (5 points)

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, d = 23 in., w = 13.5 in., and t = 6 in. There are five No. 7 longitudinal tension bars and No. 5 stirrups at 6 in. o.c.

Find the vertex of the graph of the function. (5 points) f(x) = (x + 4)2 – 1  

Use the Rational Zeros Theorem to write a list of all potential rational zeros. (5 points) f(x) = 2×3 – 5×2 + 7x – 3  

The graph of an exponential function is given. Which of the following is the correct equation of the function? (5 points)

A continuous beam’s flexural reinforcement must extend at least _____ from the point where it is no longer needed to resist tension. Assume f’c = 4,000 psi, fyt = 40,000 psi, d = 23 in., w = 13.5 in., and t = 6 in. There are five No. 7 longitudinal tension bars and No. 5 stirrups at 6 in. o.c.

Find the zeros of the function. (5 points) f(x) = x2 – 6x + 8  

Researchers studying reinforced concrete have considered a mechanical explanation of Vc to be the Holy Grail.