1.A 3-meter chain is hanging straight down the side of a building as shown at the bottom of the page. This chain has a variable density of p =x -3x+10 in kg/m. Acceleration due to gravity is 9.8m/s . we are interested in the work to pull all of the chain to the top of the building. (a) Label the sketch with the location of x 0. Your choice for the location of zero must be used for the remainder of the problem. (b) Write an expression for F(xr, ), the force acting on any small interval of chain. (c) Find the expression for the distance any representative part of the chain must travel (distance in terms of x, ). (The exact expression will depend on your location of zero in (a).) (d) Write the expression for W (x,) , the work to raise any small representative part of the chain. (e) Set up (but do not solve) the Reimann sum that approximates the total work done in lifting all of the chain. (f) Set up and solve the proper definite integral to find the total work done in lifting all of the chain to the top of the building. Include all steps of integration and include the proper work unit in your final answer.

A 650-ft equal-tangent sag vertical cuve has its PVC at station 60+50 and elevation 950 ft. The initial grade is -4.5% and the final grade is +3%. Determine elevation of the lowest point of the curve. O A. 803.55 O B. 941.23 O C. 783.71 O D. 835.16

Zack's position on a Ferris wheel can be modelled by the function h(t) = 25.4sin(1.8t + 4.0) + 24.2 Where: • h(1) represents his height in metres • 1 represents the time in minutes. a) What is the maximum height of the Ferris wheel? b) What is the period of rotation of the Ferris wheel, to the nearest tenth of a minute?

5. A ball is launched vertically into the air from a height of h meters and with an initial upward velocity of u meters/second. The ball's height above ground is given by the equation H(t) = -4.9t2 + vt + h, where H is in meters and t is in seconds. (This is the metric version of the gravity model.)