Calculus Questions

Question 7 . The concentration C (in milligrams/milliliter) of a drug in a patient’s bloodstream t hours after injection into muscle tissue is modelled by 𝑐 = 3𝑡 27 + 𝑡3 Use calculus to approximate the small change in concentration when t changes from t = 1 to t = 1.5. Question 9. A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 8 m. w h 2w Question 10 . Water is flowing at a rate of 6 𝑚3 /min from a reservoir shaped like a hemispherical bowl of radius 13 m, shown below. The volume of water in a hemispherical bowl of radius R is 𝑉 = 𝜋 3 𝑧 2 (3𝑅 − 𝑧) when the water is z meters deep. (a) At what rate is the water level changing when the water is 8 m deep ? (b) What is the radius of the water’s surface when the water in z m deep ? (c) At what rate is the radius changing when the water is 8 m deep ?