A drug's concentration in a patient's blood, in micrograms per milliliter, can be modeled by the function C(t) = 8t 0.01t2+5.3 where t is the time, in minutes, since the drug is injected. The drug's concentration will be milligrams per milliliter 25 minutes since the injection. Round your answers to two decimal places if needed. When the drug's concentration decreases to 9.23 milligrams per milliliter, it's time to give the patient another injection. The nurse should wait for minutes before another injection. Round your answers to an integer if needed. If no re-injection is applied, in the long term, the drug's concentration will be milligrams per milliliter.
![The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s](https://www.doubtrix.com/uploads/editor/9947714394TPgahcSJtp.png)
![The normal monthly precipitation at the Seattle-Tacoma airport can be approximated by the model shown below, where R is measured in inches and t is the time in months, with t = 0 corresponding to January 1. (Round your answers to two decimal places.) R = 2.876 + 2.202 sin(0.576t + 0.847) (a) Determine the extrema of the function over a one-year period. relative minimum (t, R) = ( ), relative maximum (t, R) = ( ), (b) Use integration to approximate the normal annual precipitation. (Hint: Integrate over the interval [0, 12].) in (c) Approximate the average monthly precipitation during the months of June, July, and August. in](https://www.doubtrix.com/uploads/editor/2944063509AgmljYiKFe.png)