Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 46°, a = 12, b = 11 (5 points)

Let u = , v = . Find -4u + 2v. (5 points)

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 19 feet and the height from the ground to the front doors is 4 feet, how long is the ramp? (Round to the nearest tenth.) (5 points)

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -1 – 3 sin θ (5 points)

Express the complex number in trigonometric form. 4i (5 points)

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 12, 3, , …  (7 points)

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. (5 points)

Find the first six terms of the sequence. a1 = -1, an = 2 • an-1 (7 points)  

A gluten is: 

A beam has dimensions of b = 14 in., h = 28 in., d’ = 2.5 in., and d = 25.5 in. It is reinforced with 2 No. 5 bars on the compression side and 5 No. 8 bars on the tension side. The concrete strength is 2,500 psi, and the yield strength of the reinforcement is 60,000 psi. For the results given below, determine the strength Mn for this beam.a = 6.767 in. (depth of concrete stress block)Cc = 200.0 kips (compressive force in concrete)Cs = 37.0 kips (compressive force in steel)T = 237.0 kips (tensile force in steel)