Determine if the geometric series converges or diverges. If it converges, find its sum.1 + (-8) + (-8)2 + (-8)3 + (-8)4 + . . .
A. converges, 8
B. converges, 64
C. diverges
D. converges, 80
Answer: C
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Solve the problem. If necessary, round to the nearest tenth.The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The restoring force F, in Newtons, acting on a string pendulum is given by the formula F = mg sin ?where m is the mass in kilograms of the pendulum's bob, g ? 9.8 meters per second per second is the acceleration due to gravity, and ? is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when m = 0.5 kilogram and ? = 45°?
A. 3.4 N B. 4.2 N C. 3.5 N D. 3.3 N
Suppose ?C and ?D are corresponding angles of congruent triangles with ?C opposite AB and ?D opposite EF. If AB = 16 and EF = 10 - x, determine x.
If the legs of a right triangle are 7" and 9", then the acute angles of the triangle are approximately
(a) 38° and 52°. (b) 51° and 30°. (c) 32° and 58°. (d) 9° and 81°. (e) None of these is correct.
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set.
A. no solution; ? B. {(2, 1)} C. {(-2, -1)} D. {(1, 2)}