by Marc Bennett

AP Calculus Project

mbennett597 — 2015-01-05 21:59:44 UTC

Marc Bennett and Adam Younce

Problem 1: Optimization

mbennett597 — 2015-01-05 22:00:17 UTC

Find the cheapest way to run electricity from a transformer to a light at a local golf course, without disturbing the course

2 Ways to Dig and their Cost:

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Trench Digger: $19/ft

Underground: $46/ft

A Diagram of the Situation

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Red represents where wiring will have to run

The Nuts & Bolts

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-There is a 400 ft path on a side of the golf course

-The wiring may be installed using a trench system alongside this path

-There is a 150 foot gap between the path and the location of the light

-The underground digger MUST be used under the course itself

Minimizing Cost

mbennett597 — 2015-01-05 22:10:22 UTC

Multiply the cost for each method by the length of wiring (shown on the diagram) where each method will be used. Then take the derivative

Using the Derivative to Find the Absolute Min.

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The Graph of the Derivative

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What are we solving for?

mbennett597 — 2015-01-05 22:18:06 UTC

We are solving for distance x as

notated on the diagram above.

To get the distance that wiring

will be installed using the trench

digger, we will do 400-x.

The Numbers:

mbennett597 — 2015-01-05 22:19:36 UTC

The Trench Digger is best used for around 331.969 Feet.

The Horizontal Digger is best used for 164.706 ft.

A Clarifying Diagram

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How Much Will it Cost?

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Youtube Video

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A tutorial on how we

solved the problem

Youtube Video

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A tutorial on how we

solved the problem

Problem 2: Newton's Law of Cooling

mbennett597 — 2015-01-07 23:19:27 UTC

Given a corpse's temperature at 9:00, and the temperature of the body at 10:00, use Newton's Law of Cooling to

Predict the time of death of a man's wife, and determine if he is indeed the murderer.

Newton's Law of Cooling:

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T(t)=ne^kt +c

Finding n

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Finding k

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The Knowns

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What do we want to accomplish?

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Given two temperatures at two times, we can manipulate Newton's law

of cooling to fit the situation

What's Next?

mbennett597 — 2015-01-07 23:34:59 UTC

Now that we have the entire equation, we will want to find when the body temperature was at the average living

body temperature of 98.6 f

Solving the Equation for Time of Death:

mbennett597 — 2015-01-07 23:37:01 UTC

What was the Time of Death?

mbennett597 — 2015-01-07 23:37:36 UTC

The time of death was 9.825 hours before 9:00 am, the initial time.

Converting this to a Real-Life Time:

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9:00-9 hours is 12 am minus .825(60)

gives us...

Time of Death

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Did The Husband Do it?

mbennett597 — 2015-01-07 23:41:35 UTC

No, assuming that the husband was

at the restaurant at 11:09, he did not

commit murder.

Contributions

mbennett597 — 2015-01-08 02:42:04 UTC

To complete this project, each of us did the worked out one problem, and the other person checked that person's work. We were both in both of the videos,

and each of us was the lead speaker in one of them. We split the duties on the padlet, doing the side of the problem that we attempted. Marc uploaded the

videos and wrote this paragraph.

Marc

mbennett597 — 2015-01-08 02:43:43 UTC

Adam

mbennett597 — 2015-01-08 02:43:48 UTC