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A storage tank has shape of a circular cylinder .Suppose that the radius and height of the tank are measured at 1.5 m and 5m respectively with a possible error in calculating the capacity of the tank
Suppose a particular tissue culture has area AA(tt) at time tt and a
potential maximum area MM. Based on properties of cell division, it is reasonable to assume that
the area AA grows at a rate jointly proportional to �AA(tt) and MM − AA(tt); that is
dddd
dddd = kk�AA(tt) [MM − AA(tt)]
where kk is a positive constant.
1 You may wish to begin your research by consuming the following articles:
Robert Eisner, The Misunderstood Economics: What Counts and How to Count It, Boston, MA: Harvard Business School Press, 1994, pp.
196-199 and Robert H. Frank, Microeconomics and Behavior, 2nd ed., New York: McGraw-Hill, 1994, pp. 656-657.
4 | P a g e
a. Let RR(tt) = AA′
(tt) be the rate of tissue growth. Show that RR′
(tt) = 0 when AA(tt) = MM/3.
b. Is the rate of tissue growth greatest or least when AA(tt) = MM/3? [Hint: Use the first
derivative test or second derivative test.]
c. Based on the given information and what you discovered in part (a), what can you say
about the graph of AA(tt)?
Poiseuille’s law asserts that the speed of blood that is rr
centimeters from the central axis of an artery of radius RR is SS(rr) = cc(RR2 − rr2), where cc is a
positive constant. Where is the speed of the blood greatest?
n the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the
angle α = angle BAD which minimizes the distance L, where L = AD + ED
n the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the
angle α = angle BAD which minimizes the distance L, where L = AD + ED
3. Find the angle of the largest right circular cone which can be inscribed in a sphere of
radius 9 inches.
4. A statue 10 feet high is standing on a base 13 feet high. If an observer’s eye is 5 feet
above the ground, how far should he stand from the base in order that the angle
between his lines of sight to the top and bottom of the statue is a maximum. (How far
should he stand to get the best view of the statue.
5. A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in
width and into a corridor at right angles to the passageway. If the horizontal width of
the girder is neglected, how wide must the corridor be in order that the girder can go
around the corner?
The augmented form of a linear system 𝐴𝑋 = 𝐵 is given by (𝐴|𝐵) = ( 1 0 1 | 1 0 1 1 | 2 0 2 𝜇 | 𝜇 ). Determine the value(s) of 𝜇 that will make the system have (i) no solution, (ii) a unique solution, (iii) infinitely many solutions.
Expand (2x2 + y3)5using combinations.
Find the fourth term of the binomial expansion (x-2y2)5
Verify that the two given functions are inverses of each other
f(x)=x3+1andg(x)=√3 x−1
