Use synthetic division to determine whether the number k is an upper or lower bound (as specified for the real zeros of the function f). k = 4; f(x) = 4×4 – 3×3 – 2×2 – 5x – 4; Upper bound? (5 points)

Alternate span loading is the common loading pattern for determining maximum negative moments at supports due to live load.

Determine the transverse reinforcement index, Ktr, for a rectangular beam with b = 17 in. and d = 23 in., five galvanized No. 9 Grade 60 tension-reinforcement bars placed in the top of the beam, and No. 3 Grade 40 stirrups located every 6 in. along the span. Assume 7,000-psi lightweight concrete and a clear cover of 2 in.

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)

It’s a good idea to spread your marketing budget across many platforms and try to reach everyone.

Find cot θ if csc θ = and tan θ > 0. (6 points)

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)