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, b = 13 in., d = 17 in., and that there are four No. 7 longitudinal tension bars and No. 3 stirrups at 7 in. o.c. The stirrup hooks are 135°.

Find an exact value. (6 points)

Find the zeros of the function. (5 points) f(x) = x2 + 3x + 2  

A combination of horizontal and vertical reinforcement is used to restrain cracks from opening too wide.

The determination of whether a reinforced concrete floor system is classified as a one-way or two-way system is based on the ratio of the span lengths for the floor slab in the two principal horizontal directions.

If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x – ), what should be used for Xmin and Xmax? Explain your answer. (5 points)

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (5 points)4, -8, and 2 + 3i 

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x – 2; 4×2 – 3x + 22 (5 points)

Write a linear factorization of the function. (5 points)f(x) = x4 + 49×2 

If φVc = 50 kip and Vu = 58 kip, are stirrups required?