A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t≥0. The initial position of the yo-yo at time t = 0 is x = 3. Part A: Find the average value of v(t) on the interval Part B: What is the displacement of the yo-yo from time t = 0 to time t = πT? Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π.

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.