Mesquite Trees, Anon.
Thorn Avenue
Lubbock, TX 79414

Dear Calculus Student,

Thanks for your help last year. As it turned out, I had to get a different tank after all, due to some minor difficulties with the bank. (A little cash flow problem, purely temporary. Not to worry). It probably works out for the best anyway.

The new tank isn't so lovely -- it looks more like a can of green beans than anything else. (It's mostly made of some hideous green metal, but at least it has one glass wall at one end, so you can see how high the water is). But, hey, the turkeys don't mind the color, right? And it'll do until I resolve this little financial slump.

You'll be glad to know that I used the stuff you sent me even though I didn't need to. (pr² -- Beautiful stuff.) My new tank is 16 feet long and 10 feet high, so the radius is 5 feet, and the storage capacity -- according to your own awesome formula is 9,182 gallons. I was so proud of myself for figuring this out that I even included a diagram of the water gauge I added on the glass wall.

Photograph: The glass wall of my water tank, gallons and all.

Since you guys came through with the goods on the first contract I sent your way, I figured I'd do you a favor and extend our business partnership. I seem to be having difficulty with how much water to let out of this tank.

Now, I don't know if I mentioned this before, but the heart and soul of turkey farming is water. The turkeys get enough water, they're fine. They get too much water, and they go a little loopy. They don't get enough water, and you sell your farm to your brother and get a job as a tele-marketer.

Here's the problem. Sometimes when I let water out of the tank, especially when the tank is full, it seems like there's not as much coming out as there should be. Other times it seems like I'm getting way too much.

It'd be nice to calibrate the gauge I put on the tank. There are two ways to do this, and I'm not sure which will be better, so I'll contract out to you for both types. The first is to keep the hash marks the same, but recalibrate the numbers of gallons at each mark. The second is to keep the numbers all the same, but to recalibrate where they go on the gauge. Since the last work you did for me had that nice formula, I'd like to see the formula for this one, too. Like if the number of gallons is p minus the height squared, or something like that.

I figure that this shouldn't be too much of a difficulty for someone with a good brain like yours. But I'm going to be good to you anyway, since you know my big brother. Let's double your previous fee: up from $150 to $300.

You'll be getting your fee from the previous contract just as soon as my folks clear up a couple of small accounting issues. You'll get the check from us any time now.

Of course I wish you all the best in those classes of yours. Try not to get too caught up in all those guys who argue about whether they exist or not. Remember, it's not what you know; it's who you know. And now you know me.

Sincerely,

Brent Trachte
CEO, Fowl Play, Inc.

P.S. Turkey breeding starts heating up beginning March. I am going to need some hard answers by the 19th of March.

P.P.S. Don't make it too long, otherwise I'll never get through it -- 3--5 pages would be about all that I could take.

P.P.P.S. The attachment below is our standard mumbo-jumbo to make the big bosses upstairs happy. I'm the whole lot of "forewomen and foremen".

All reports submitted to Fowl Play, Inc. should be written so that the forewomen and foremen of the turkey farm implementing the report can understand and apply the information contained therein. Owing to the preeminent position of Fowl Play, Inc. in the field of turkey farming, all of our forepeople have degrees in ag-engineering, and thus have had college level mathematics, including calculus---unfortunately, however, their long experience in the field precludes a ready knowledge of the same. Therefore, the reports should assume a strong precalculus and basic calculus (about half a semester of calculus I) background, but should not expect a knowledge of much more than that.

Reports should further:

• Be written in the first person plural (e.g., "We found the requisite data from the figure...").
• Include mathematical formulas and appropriate graphs in 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.)
• Clearly explain how the mathematical formulas that are included bear on the problem being solved.
• Consist of:
  • An Introduction, describing the problem to be solved, and an indication of the mathematical method used to solve it.
  • A Body, describing the mathematical problem that was solved to answer the question(s) posed in the introduction, and the solution to it.
  • A 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.
  • Be 3--5 pages in length, excluding supporting figures and diagrams in an attached appendix.