A railroad tunnel is shaped like a semiellipse, as shown below.   The height of the tunnel at the center is 27 ft, and the vertical clearance must be 9 ft at a point 24 ft from the center. Find an equation for the ellipse. (5 points)

A beam has dimensions of b = 14 in., h = 28 in., and d = 25.5 in. and is reinforced with 4 No. 5 bars. The concrete strength is 4,600 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth to the neutral surface is c = 1.657503 in., determine the strain in the reinforcement.

(04.05 MC)  The 15 most populous states in the United States have an average population of 141.51 million, with a standard deviation of 87.49 million. Virginia and Washington have populations of 83.83 million and 71.70 million, respectively. Texas and Pennsylvania have z-scores of 1.52 and −0.15, respectively. Part A: List these four states in order from smallest to largest populations. (5 points) Part B: Mathematically explain your reasoning and be sure to include all necessary calculations. (5 points) (10 points)

You are considering a beam design that has dimensions of b = 18 in., h = 22 in., and d = 19.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 10,000 psi, and the yield strength of the reinforcement is 60,000 psi. What cross-sectional area of reinforcement is needed to achieve a strain in the reinforcement of 0.0075?

Find the center, vertices, and foci of the ellipse with equation 3×2 + 7y2 = 21. (5 points)

Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4. (5 points)

The sugar present in DNA is aldohexose or aldopentose ?

Recreational drugs are always _________________________________.

Please list all 6 classifications of essential nutrients.  

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