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)

A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 408 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 781 km to 562 km. (5 points)

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 56°, a = 16, b = 17 (5 points)

Quote a sentence from the article correctly in MLA format, remembering all parts of the “citation sandwich.” Then quote the same sentence correctly in APA format, remembering all parts of the “citation sandwich.”

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)

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 10 No. 8 bars at a depth of 20 in. The top row contains 7 No. 5 bars at a depth of 16 in. Determine the effective (centroidal) depth, d, of the steel.