Write the sum using summation notation, assuming the suggested pattern continues. 729 + 1000 + 1331 + 1728 + … + n3 (7 points)

A satellite is to be put into an elliptical orbit around a moon as shown below. The moon is a sphere with radius of 567 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 900 km to 169 km. (5 points)

Please describe how the scientific principle of adaptation applies to YOU with regards to your approach to engaging in fitness activities/working out.  List a specific example of how you have applied this principle appropriately OR not appropriately.  

Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (5 points)

A beam has dimensions of b = 16 in., h = 24 in., and d = 21.5 in. and is reinforced with 3 No. 6 bars. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. Determine the nominal moment capacity, Mn, of the beam.

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

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 5 + 4 cos θ (5 points)

Find the derivative of f(x) = at x = 12. (5 points)

The largest moments in a continuous beam or a frame occur when some spans are loaded with live load and others are not. Influence lines are often used to determine which span should and should not be loaded.

(05.01 MC) Mateo is cooking beef. He must make sure the beef has a minimum internal temperature of 160 degrees so that it is safe to eat. Using a thermometer, he takes the temperature of the beef in five random places. The minimum temperature in the sample is 165 degrees. Identify the population and the sample. (4 points)