Let the position of a swinging pendulum in simple harmonic motion be given by s(t) = a cos(t) + b sin(t) where a and b are constants, t measures time in seconds, and s measures position in centimeters. If the position is 3.1 cm and the velocity is -5.1 cm/s when t = 0, find the values of a and b. a. a = -2.5500 and b = 1.5500 O b. a = -(3.1) and b = -(-5.1) c. a = -(-5.1) and b = -(3.1) d. a = -5.1 and b = 3.1 e. a = -10.2000 and b = 6.2000 O f. a 3.1 and b = -5.1 =

The electric power P (in W) as a function of the current i (in A) in a certain circuit is given by P = 12i2 + 60i. Find the instantaneous rate of change of P with respect to i for i = 0.75 A. The instantaneous rate of change of P is WIA for i = 0.75. (Simplify your answer.)

Simplify cos(x – or difference of angles identity. T) to a single trig function using the sum -

The velocity v of blood at a valve in the heart of a certain animal is modeled by the equation v= -2 cos (5xt) + 2, where v is in centimeters per second and t is time in seconds. a. What are the maximum and minimum velocities of the blood at this valve? b. What is the animal's heart rate in beats per minute? a. The maximum velocity of the blood at this valve is cm/sec and the minimum velocity of the blood at this valve is b. The animal's heart rate in beats per minute is cm/sec.