. Some of the highest tides in the world occur in the Bay ofFundy on the Atlantic Coast of Canada. At Hopewell Capethe water depth at low tide is about 2.0 m and at high tideit is about 12.0 m. The natural period of oscillation is alittle more than 12 hours and on June 30, 2009, high tideoccurred at 6:45 AM. This helps explain the following modelfor the water depth (in meters) as a function of the time t , (in hours after midnight) on that day:  D (t ) = 7 + 5 cos [ 0.503 (t - 6.75)] How fast was the tide rising (or falling) at the following times?(a) 3:00 AM (b) 6:00 AM(c) 9:00 AM (d) Noon

The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 88 square centimeters? cm/min

4. While visiting Newfoundland, Ray notices that that the water level at a town dock changes during the day as the tides come in and go out. Marking on one of the piles supporting the dock show a high tide of 3.3 m at 6:30 am., a low tide of 0.7 m at 12:40 p.m., and a high tide again at 6.50 pm. a) Estimate the period of the fluctuations in the water level at the town dock. b) Estimate the amplitude of the pattern. c) Sketch the function.

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole? 16/3 X ft/s Enhanced Feedback Please try again. Draw a diagram for this problem. Draw a right triangle with horizontal and vertical edges. Let the vertical edge be the pole. Draw another vertical line with one end on the hypotenuse: and the other end on the horizontal edge depicting the man. Label the distance between the man and the pole x and the distance between the man and the tip of the shadow y. Use properties of similar triangles to find a relation among x, y, the height of the man, and the height of the pole. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the rate at which the tip of the shadow is moving, (x + y). Then, use the values from the exercise to evaluate the rate of change of the distance between the…