Buried Treasure 2: Suppose you seek a treasure that is buried in the side of a mountain

Chapter 3, Problem 6

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Buried Treasure 2: Suppose you seek a treasure that is buried in the side of a mountain. The mountain range has a sinusoidal vertical cross section (Figure 3-7h). The valley to the left is filled with water to a depth of 50 m, and the top of the mountain is 150 m above the water level. You set up an x-axis at water level and a y-axis 200 m to the right of the deepest part of the water. The top of the mountain is at x = 400 m. a. Find a particular equation expressing y for points on the surface of the mountain as a function of x. b. Show algebraically that the sinusoid in part a contains the origin (0, 0). c. The treasure is located beneath the surface at the point (130, 40), as shown in Figure 3-7h. Which would be a shorter way to dig to the treasure, a horizontal tunnel or a vertical tunnel? Show your work. Figure 3-7h

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