Alternate span loading is the common loading pattern for determining maximum shear at the supports between the loaded spans due to dead load.

The elastic beam theory is used in the design of reinforced concrete beams.

Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)  

The symbol Mu represents the _______.

Write the sum using summation notation, assuming the suggested pattern continues. 3 – 15 + 75 – 375 + … (5 points)

Find the fifth roots of 243(cos 240° + i sin 240°). (5 points)

When aligning the body in a neutral spine position which of the following cue should not be followed?  

Find the limit of the function by using direct substitution. (6 points)  

Find the center, vertices, and foci of the ellipse with equation 4×2 + 9y2 = 36. (5 points)

Find the first six terms of the sequence. a1 = -7, an = 2 • an-1 (5 points)