% (c) 1996 Gavin LaRose (glarose@NebrWesleyan.edu)
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\centerline{\bf Math 105---Calculus I\quad Project 2}
\centerline{\bf a leg up on legal issues\dots }
\centerline{\sevenrm \copyright 1996 Gavin LaRose
(glarose@NebrWesleyan.edu), Nebraska Wesleyan University}
\centerline{\sevenrm permission granted to use and distribute for 
free in an academic setting.}

\bigskip
After your successful ``debut'' as mathematicians at the eminantly
successful IMC, Inc. contracting firm, accolades have poured in.  And,
equally as promising, there appear to be additional contracts arriving
as well.  The latest to which you have been assigned is one that
arrived just recently from Hangemhi, Inc. (a legal consulting company
known to have some affiliation with the world-wide MPC,
Inc. conglomerate).  This has been referred to you on the basis of
your past 
success with medically related contracts\dots\  The letter you
received from them follows.

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\logo
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\longindent Suite 101, Boldledge Business Park\par
\longindent Lonlinc, SK\par
\longindent 04685\par
\medskip
\longindent 26 February, 1996\par

\bigskip
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\noindent Independent Mathematical Contractors, Inc.\par
\noindent Suite 2, Strawmarket Business Plaza\par
\noindent Lonlinc, SK 04685

\bigskip
\bigskip

\noindent Dear IMC:
\medskip
\noindent
As you may know, Hangemhi, Inc. recently won a case that received
national attention---the infamous ``case of the rapidly plummeting
client,'' in which it was alleged that our client had lept from a
window to a busy street below.  Following its resolution, however, we
find ourselves in the position of addressing the legal needs of a
series of ``copy-cat'' clients who are accused of placing untoward
stresses on their respective bodies in the course of activities which,
as you will understand completely, we are not in a position to
speculate with you at this juncture.

\medskip
\noindent
As in the infamous ``plummeting client'' case, we are first attacking
the scientific feasibility of the alleged activities.  In particular,
one of our clients is purported to have succeeded in a series of
maneuvers which are wholly unlikely to have been possible given their
recent hip replacement.  A partial diagram of the replaced joint
appears below in figure 1.
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\noindent
We were able to discover from a medical research company with which we
have ties that the stresses that the joint would sustain in course of
the alleged maneuvers are related to the rate at which the gap between
the ``ball'' and ``socket'' of the joint changes as different
positions in the joint are considered.  Therefore, we need an analysis
from you of how large this rate of change is likely to be at various
positions in the joint, and an estimate of what the maximum rate is
likely to be.
\medskip
\noindent
As specified in your contract, your report should be submitted by the
11th of next month, as the case is to go to court sometime around the
close of that week.\par
}
}

\medskip
\noindent
If you should find in the course of your
investigation that you have questions regarding this project, you
are to contact Dr.\ Gavin LaRose, our firm's consulting scientist (who
is, unfortunately, only working for us part-time around his job with
Chemproc, Inc., and hence is unable to resolve this problem for us
directly) with the other members of your investigative team; he will
be more than willing to assist you.  You should further contact him
(also as a team) by the 4th of March to report on your progress---{\it
failure to do so will result in a 5\% reduction of your contract
payment\/}.

\bigskip

\longindent Yours sincerely,
\bigskip
\bigskip
\bigskip
\longindent Claire N. ``C.D.'' Arro, Partner\par
\longindent Hangemhi, Inc.
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\noindent Encl: Technical report requirements

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\centerline{\bf Technical Report Requirements}
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\noindent
\noindent 
All reports submitted to Hangemhi, Inc. should be written so that 
all members of the legal team using the
report can understand and apply the information contained therein.
These legal team members are all experts in law, but have little
recent experience in mathematics.  They should therefore be assumed to
remember essential precalculus and algebra concepts, but, sadly,
little more.

\bigskip
\noindent Reports should further:
\bigskip
 
\item{$\bullet$} Be written in the first person plural (e.g., ``We
found the requisite data from the figure\dots'').
\medskip
\item{$\bullet$} Include mathematical formulas in the the text of the
body of the report as appropriate to describe the methods and results
obtained.  (While the report must be typewritten, it is fine to neatly
hand-write formulas if that significantly simplifies its generation.)
\medskip
\item{$\bullet$} Clearly explain how the mathematical formulas that are
included bear on the problem being solved.
\medskip
\item{$\bullet$} Consist of
\smallskip
\itemitem{$\bullet$} An {\sl Introduction\/}, describing the problem
to be solved, and an indication of the mathematical method used to
solve it.
\smallskip
\itemitem{$\bullet$} A {\sl Body\/}, describing the mathematical
problem that was solved to answer the question(s) posed in the
introduction, and the solution to it.
\smallskip
\itemitem{$\bullet$} A {\sl Conclusion\/}, summarizing the results
obtained from the solution described in the body and clearly stating
their relevance to the original problem as described in the
introduction. 
\medskip
\item{$\bullet$} Be 2$1\over 2$--5 pages in length.
 

\bye
