Write the expression as the sine, cosine, or tangent of an angle. sin 48° cos 15° – cos 48° sin 15° (6 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 = 6,000 psi, fyt = 40,000 psi, b = 12 in., d = 18 in., and that there are four No. 8 longitudinal tension bars and No. 5 stirrups at 7 in. o.c. The stirrup hooks are 135°.

Determine the casting-position modification factor, ψt, for a rectangular beam with b = 17 in. and d = 23 in., four galvanized No. 7 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 4 Grade 60 stirrups located every 8 in. along the span. Assume 8,000-psi normal-weight concrete and a clear cover of 1.75 in.

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. f(x) = -13×5 – 4×4 – 1 (5 points)

Axial tension tends to increase shear strength.

Determine the function which corresponds to the given graph.(5 points) The asymptote is x = 5.

A rectangular beam with cross section b = 16 in., h = 22 in., and d = 19.5 in. supports a total factored uniform load of 3.80 kips/ft, including its own dead load. The beam is simply supported with a 19-ft span. It is reinforced with four No. 8 Grade 60 bars, two 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 6,900 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 four bars is φMn = 262.9 kip-ft, and the strength of the remaining two bars is φMn = 135.1 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

Determine the size modification factor, ψs, for a rectangular beam with b = 18 in. and d = 24 in., three uncoated No. 7 Grade 60 tension-reinforcement bars placed in the bottom of the beam, and No. 3 Grade 60 stirrups located every 6 in. along the span. Assume 8,000-psi lightweight concrete and a clear cover of 1.75 in.

A simply-supported beam has a 1 kip/ft uniformly-distributed load over the left half of its 9-ft span. What is the magnitude of the shear force at midspan?

Find the domain of the given function. (5 points)f(x) =