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
27 + 𝑡3
Use calculus to approximate the small change in concentration when t changes from
t = 1 to t = 1.5.
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.
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
(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 ?
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