# Mathematics

MathematicsA manufacturer uses a tank to supply water to his machines while they are working. When the machines are on the tank loses 1.5 gallons of water an hour at the same time 1 gallon of water is pumped into the tank from a well. Write an equation that models the amount of water (w) in the tank for any hour (h) that the machines are on. The tank starts full with 150 gallons of water in it.

Describe    some    of    the    earliest    uses    of    the    pigeonhole    principle    by    Dirichlet    and    other    mathematicians

Each    writing    assignment    is    worth

20    points

should    include    the    following    sections

:

Background    (3    points):

This    is    a    discussion    of    how    the

non

-­‐

mathematical    and    mathematical    portions    of    your    topic    fit

together.

You

migh

t    include    a    historical    background    of    the    topic,    definitions    of    terms

,    the

discrete    mathematics

ideas

(e.g.

induction,    logical    fallacy,    etc.

),    and    some    explan

ation    about    why    these    ideas    were    useful.

Examples    (10    points):

In    most    of    your    writing    assignments    you    are    asked    to    discuss    and    describe    an    aspect    of    discrete

mathematics.    Give    two    of    three    examples    or    techniques    of    the    topic    under    discussion.    Give    general

information    and    also

specific    examples    of    the    topic.

Bibliography

(2    points):

List    the    references    you    used    to    complete    this    rep

ort.    J

ust    list    title    and    author    for    any    books

and

articles

you    used.    You    should    also    include    a    list    of    people    that    you    consulted

or    any    other    form    of    help    that    you    received.

For    example,    you    might    obtain    some    of    your    information    from    the    internet;    in    this    case,    you    could    include    the

website.

You’ll    need    at    least    one    book

or    article

as    a    reference,    preferably    two

,    and    a    total    of    at

least    two    reference

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