Solve the problem.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 = 0.8 kilogram and ? = 25°? If necessary, round the answer to the nearest tenth of a Newton.

A. 3.1 N
B. 3.3 N
C. 7.1 N
D. 1 N


Answer: B

Mathematics

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Evaluate the integral.

A. - csc 7t cot 7t - ln +  + C
B. - csc 7t cot 7t + ln + C
C.  csc 7t cot2 7t - ln + C
D. - csc 7t cot 7t - ln + C

Mathematics

The concentration C, in milligrams per deciliter, of a certain drug in the bloodstream t hours after injection is given in the following table.  t0123 C36.0030.2425.4021.34? A: Make a table of successive ratios to show that the concentration of the drug can be modeled by an exponential function. Round your answer to two decimal places.B: Find an exponential model for the data. Round your answer to two decimal places.C: Plot the graph of the data points along with the exponential model. Include up to 10 hours.D: According to the model, how long will it take for the drug concentration to decay to 14.00% of the initial amount? Round your answer to two decimal places.

What will be an ideal response?

Mathematics

Find the probability.A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 26 that have no defects. What is the probability that at least one of the calculators is defective?

A. 0.140 B. 0.164 C. 0.836 D. 0.821

Mathematics

Simplify the square root. Assume all variables represent nonnegative real numbers.

A. x4
B. 4x4
C. 4
D. 4x4

Mathematics