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Chapter 8: Q. 63 (page 536)
State the Law of Cosines in words.
The Law of Cosines states that the square of one side of a triangle equals the sum of the squares of the other two sides minus twice their product times the cosine of their included angle.
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An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.
(a) Develop a model that relates the distance d of the object from its rest position after t seconds.
(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.
Given values:
What do you do first if you are asked to solve a triangle and are given two sides and the angle opposite one of them?
The Original Ferris Wheel George Washington Gale Ferris, Jr., designed the original Ferris wheel for the 1893 World鈥檚 Columbian Exposition in Chicago, Illinois. The wheel had 36 equally spaced cars each the size of a school bus. The distance between adjacent cars was approximately 22 feet. Determine the diameter of the wheel to the nearest
foot.
The displacement d (in meters) of an object at time t (in seconds) is given
(a) Describe the motion of the object.
(b) What is the maximum displacement from its resting position?
(c) What is the time required for one oscillation?
(d) What is the frequency?
Landscaping Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one
position on a flat path from the tree is 30掳, and from a second position 40 feet farther along this path it is 20掳. What is the height of the tree?
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