Write the expression as the sine, cosine, or tangent of an angle. cos 107° cos 42° + sin 107° sin 42° (6 points)

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 1.60 kips/ft, including its own dead load. The beam is simply supported with a 18-ft span. It is reinforced with five No. 5 Grade 60 bars, three of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 4,200 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. The strength of the five bars is φMn = 130.3 kip-ft, and the strength of the remaining two bars is φMn = 53.5 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

What are “Unique Benefits” in a value proposition?

Use basic identities to simplify the expression. (6 points)

Write the expression as the sine, cosine, or tangent of an angle. sin 5x cos x – cos 5x sin x (6 points)

Write the quadratic function in vertex form. (5 points) y = x2 – 2x + 5  

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b = 13 in. and d = 61 in. There are four No. 9 longitudinal tension bars and No. 3 stirrups at 6 in. o.c.

Write the expression in standard form. (5 points) 

Find the zeros of the polynomial function and state the multiplicity of each. (5 points)f(x) = 3(x + 9)2(x – 9)3  

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 26 in., b2 = 10 in., d1 = 8 in., d2 = 13 in., and that there are three No. 7 longitudinal tension bars and No. 3 stirrups at 12 in. o.c. The stirrup hooks are 90°.