Determine As,min for the following beam given that f’c = 7,750 psi and fy = 60,000 psi.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 6 No. 6 bars at a depth of 20 in. The top row contains 4 No. 8 bars at a depth of 14 in. Determine the effective (centroidal) depth, d, of the steel.

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. C = 71°, a = 27, c = 26 (5 points)

A beam has dimensions of b = 18 in., h = 12 in., and d = 9.5 in. and is reinforced with 5 No. 8 bars. The concrete strength is 3,500 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.207 in., does the reinforcement yield?

Find the derivative of f(x) = 7x + 9 at x = 6. (6 points)

(05.04 MC)  A researcher has conducted a survey using a simple random sample of 500 golf club members to create a confidence interval to estimate the proportion of golf club members favoring a 1% annual increase in dues to remodel the clubhouse. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 125 people instead of 500 golf club members. Which of the following statements best describes how the confidence interval is affected by this change? (3 points)

Let u = , v = . Find u – v. (5 points)

Find the derivative of f(x) = -4×2 + 11x at x = 10. (6 points)

Find a ⋅ b. a = 6i – 6j, b = 4i + 2j (5 points)

Briefly reflect on the process you have followed to write your rough draft. Where are you in the process? What is left to do? What is your plan for completing the draft and/or revising it in the coming weeks? Try to capture your thoughts and what you have learned over the past few weeks about constructing a large research project.