Download portfolio problems set 3

PORTFOLIO PROBLEMS SET 3:
Choose 2 of the 3 problems
The 3rd problem can be extra credit.
Choose 2 of the following problems to be completed in the following manner.
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All answers and solutions must be clearly written in a self-contained manner. This means that answers and solutions must
be explained in a manner that can be understood without reference to the question. This does not mean that you should
simply rewrite the questions but should attempt to incorporate the information from the problem into your solution.
Solutions to problems must always be written using complete sentences. In addition, you must use correct units for all
values that are part of your solution. After you have completed any calculations, make sure that you write the solution to
the problem using complete sentences. The purpose of this type of answer is to demonstrate that you understand the point
of the problem and the meaning of your solution.
Your solutions must be neat, well organized, and easy to read. Always use proper grammar, proper sentence and
paragraph structure, and correct spelling.
The solutions must be double-spaced and typed, done on a word processor. Students are strongly encouraged to use
Microsoft Word and its Equation Editor for these solutions.
PROBLEM 1: OOZING LIQUID
A container in the shape of an inverted cone has height 16 cm and radius 5 cm at the top. Its is partially filled with a liquid that
oozes through the sides at a rate proportional to the area of the container that is in contact with the liquid. (The surface area of a
cone is πrl where r is the radius and l is the slant height.) If we pour the liquid into the container at a rate of 2cm3/min, then the
height of the liquid decreases at a rate of 0.3 cm/min when the height is 10 cm. If our goal is to keep the liquid at a constant height
of 10 cm, at what rate should we pour the liquid into the container?
PROBLEM 2: AN INTERESTING DERIVATIVE
Complete the following table to determine the nth derivative of the function f ( x ) 
n
1
x
1 x
f’(x)
2
3
…
48
n
PROBLEM 3: MOVING STEEL PIPES
A steel pipe is being carried down a hallway 9 feet wide. At the end of the hall there is a right angled turn into a narrower hallway
6 feet wide. What is the length of the longest pipe that can be carried horizontally around the corner?
6
θ
9