Important When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: 0 Provide full solutions, showing all of your steps. 0 Make sure that there is one step or idea per line. 0 Use one equal sign per line. 0 Make sure that equal signs line up vertically. 0 Don't use self-developed short form notations. 1. The Louvre museum in Paris features an inverted La Pyramide Inverse square pyramid with a height of 10 m. The side of the square is 13 m. Super-villains decide to fill the pyramid with water, and do so at a rate of 10 m3 per second. How quickly is the water level rising when it reaches the top? (10 marks) 2. A girl of height 120 cm is walking toward a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light. How is the size of her shadow changing when she is 1.5 m from the light? (10 marks) 3. Water is leaking from a trough at the rate of 0.8 US. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85 cm, and the height is 25 cm. The length of the trough is 3 m. Find the rate at which the height is changing when the depth of water is 11 cm. (10 marks) 4. An oil rig lies 20 km 011 the coast of Newfoundland. A town lies 80 km along the coast from the nearest point on land to the rig. A pipe is to be drilled from the rig to the town. The cost per km of the pipe under water is $2.5 million, but on land is $1.5 million. Find the route that results in the cheapest pipeline, and determine that lowest cost. (10 marks)