An elliptical plate, major axis 6 feet and minor axis 4 feet, is submerged vertically until its minor axis is 3 feet below the surface of the water (weight density=p lb/ft³). Determine the appropriate integral to be used to determine the force on one side of the submerged portion. 0 ⒸF-3pS (3-y) √/4-y² dy (A) -2 ⒸF-3p ³(3-y) √4-y²dy B 4p (c) F-Lo- F= -S²(3-y) √/9-y²dy 3 -3 -3 4p Ⓒ/- +// 0 D F= (y-3)√9-y²dy 3 0

The gravitational force on a 10 kg object at a distance r meters from the center of the Earth is F = Newtons. Find the work done in moving the object from the surface of the Earth to a height 106 meters above the surface. The radius of the Earth is 6.4 × 106 meters. 4 x 1015 p²

Todd runs around the perimeter of a circular track at 8 ft/sec. The track has a radius of 80 yd. After 30 seconds, Todd turns and runs to the center of the track along a straight (radial) line. Upon reaching the center, he turns and runs away along a different radial line to his starting position on the perimeter. (a) How far has Todd traveled once he has returned to his starting position? distance = 720 v feet (b) How much time will it take for Todd to complete his circuit? time = seconds (c) Find the area of the pie-shaped sector enclosed by path. area = sq-yd

Newton's Law of Gravity says that two objects with masses m, and m2 attract each other with a force F that is jointly proportional to their masses and inversely propor- tional to the square of the distance r between the objects. Express Newton's Law of Gravity as an equation.

2- A constant force of (2kN) pulls a box along a level floor a distance of (10 m) in (50 s). What is the power used?

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y 0.3x² and below the line y 180. (Here, distances are measured in meters.) The water level is 36 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000kg/m³, and the acceleration of gravity is 9.8m/sec².) Answer:

Find the Cross product of P = 2.85i + 4.67j – 8.09k ft and Q = 28.3i + 44.6j = 53.3k lbexplanation not needed

x y ● = Find the dot product of 1 ---A 0 and y = 2 -2 18 1 4 ●

Integrate and be specific.

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region 0.6x² and below the line 2 above the curve y y = 280. (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by kg m³ = water pressure. (Water has a density of 1000- and the acceleration of gravity is 9.8 m sec² .) " Note: Weight density of water is 1000 (9.8)=9800 N/m^3