1. Find an angle between 0 and 2𝜋 that is coterminal with the given angle: β 16𝜋/5 Remember to show your work for credit
Posted: Thu Jul 14, 2022 4:01 pm
1. Find an angle between 0 and 2π that is coterminal with the given angle: β 16π/5 Remember to show your work for credit!
2. The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving in miles per hour?
3. The arm and blade of a windshield wiper have a total length of 30 inches from the pivot point. If the blade section is 24 inches long and the wiper sweeps out an angle of 140Β°, how much window area can the blade clean?
5. Determine algebraically whether the function π(π₯) = π₯sin^3π₯ is even, odd, or neither. Work shown must support (prove) your answer! The Guess & Check method will not receive any credit, even if correct.
7. A personβs blood pressure, π, varies with the cycle of their heartbeat. The pressure (in units mmHg) at time π‘ seconds for a particular person may be modeled by the function: π·(π) = 20cos(2πt) + π00 mmHg, π‘ β₯ 0 . According to this model, which of the following statements is TRUE? (Hint: Think of this problem in terms of transformations of a graph. In fact, actually graphing it will help you answer the question!)
(a) The maximum pressure is 100 mmHg.
(b) The pressure goes through one complete cycle in 2 seconds.
(c) The amplitude of the pressure function is 120 mmHg.
(d) The pressure will reach a maximum value at time π‘ = 1 second.
(e) Both statements (b) and (d) are accurate.
2. The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving in miles per hour?
3. The arm and blade of a windshield wiper have a total length of 30 inches from the pivot point. If the blade section is 24 inches long and the wiper sweeps out an angle of 140Β°, how much window area can the blade clean?
5. Determine algebraically whether the function π(π₯) = π₯sin^3π₯ is even, odd, or neither. Work shown must support (prove) your answer! The Guess & Check method will not receive any credit, even if correct.
7. A personβs blood pressure, π, varies with the cycle of their heartbeat. The pressure (in units mmHg) at time π‘ seconds for a particular person may be modeled by the function: π·(π) = 20cos(2πt) + π00 mmHg, π‘ β₯ 0 . According to this model, which of the following statements is TRUE? (Hint: Think of this problem in terms of transformations of a graph. In fact, actually graphing it will help you answer the question!)
(a) The maximum pressure is 100 mmHg.
(b) The pressure goes through one complete cycle in 2 seconds.
(c) The amplitude of the pressure function is 120 mmHg.
(d) The pressure will reach a maximum value at time π‘ = 1 second.
(e) Both statements (b) and (d) are accurate.