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Chapter 10: Q. 70 (page 644)
Searchlight - A searchlight is shaped like a paraboloid of
revolution. If the light source is located 2 feet from the base
along the axis of symmetry and the depth of the searchlight
is 4 feet, what should the width of the opening be?
The width of the opening is.
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Uniform Motion A Cessna (heading south at 120 mph) and a Boeing 747 (heading west at 600 mph) are flying toward the same point at the same altitude. The Cessna is 100 miles from the point where the flight patterns intersect, and the 747 is 550 miles from this intersection point. See the figure.
(a) Find parametric equations that model the motion of the Cessna and the 747.
(b) Find a formula for the distance between the planes as a function of time.
(c) Graph the function in part (b) using a graphing utility.
(d) What is the minimum distance between the planes? When are the planes closest?
(e) Simulate the motion of the planes by simultaneously graphing the equations found in part (a).
Semi elliptical Arch Bridge The arch of a bridge is a semi ellipse with a horizontal major axis. The span is feet, and the top of the arch is feet above the major axis. The roadway is horizontal and is feet above the top of the arch. Find the vertical distance from the roadway to the arch at -foot intervals along the roadway.
Fireworks Display Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time, the first person standing at point A hears the burst. One second later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point A, where did the fireworks display occur?
Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river meters wide. The center of the arch is meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.
Solar Heat - A mirror is shaped like a paraboloid of
revolution and is used to concentrate the rays of the sun at
its focus, creating a heat source. See the figure. If the mirror
is 20 feet across at its opening and is 6 feet deep, where will
the heat source be concentrated?
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