Write the sum using summation notation, assuming the suggested pattern continues. -8 – 3 + 2 + 7 + … + 67 (7 points)

Solve the triangle. A = 21°, C = 105°, c = 5 (5 points)

Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -18, 3, , …  (7 points)

(06.07 MC)  Data collected on the discharge of the Colorado River and speed are given in the table:   Discharge (ft3) Speed 1.3 2.3 2.2 0.99 5.8 3.5 11 5 12 16 14 22 16 27 21 14 49 33 Find r2, and interpret the results. (4 points)

Find the sum of the arithmetic sequence. 3, 5, 7, 9, …, 21 (7 points)

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ (5 points)

A beam has dimensions of b = 14 in., h = 30 in., d’ = 2.5 in., and d = 27.5 in. It is reinforced with 2 No. 5 bars on the compression side and 4 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. If the depth of the neutral axis is c = 6.268 in., determine the strain in the compression reinforcement, ε’s.

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

In reviewing for the final exam, what have you discovered are the parts of the course about which you feel most confident? That is, what topics do you understand the best? Why?

Define Osmosis.