Fiction

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Fiction

On Bathroom Lighting

Epilogue: The Woman and the Trough, by Abby Schoneboom

A serf girl from the village of Hemsk noticed her reflection in a stinking horse trough and fell weeping by the roadside, lamenting the loss of her bloom. Towards evening, a kindly traveller came by and, seeing the fair lass in her distress, inquired about the nature of her woe.

"Kind sir, my face is grey and craggy, though I am but two-and-twenty years," the girl wept. The clever traveller, guessing the source of the girl's sorrow, reached in his pouch and drew out a silvery mirror, holding it up to the girl's fair complexion. "Dear wench, your blemishes were merely lumps of floating crud and your wrinkles muddy ripples in the trough water."

In the glow of sunset, the girl gazed upon her soft, beautiful face and laughed with joy. The girl never feared looking in the horse trough again, and would have lived happily ever after except that her tragic stupidity led her into a continual series of other disasters.

Thanks to Abby Schoneboom and the good people at Bonkworld for permission to reproduce this story from Bathroom Lighting

But now it's time for some serious trough stuff, with many thanks to Roger E. Griffiths

Math 182 Practice Exam 2 Name

October 25, 1996 Show all work

Problem	1	2	3	4	5	6	7	Total
Possible	15	15	15	15	8	12	20	100
Score

Mass density of water in a horse trough = 1000 kg/m³, weight density of water = 9800 N/m³.

1. A mathematician designs a funnel to fill his horse trough. The funnel is infinitely long. In fact, it can be described by rotating the curve about the x axis for x between 1 and infinity. Find the volume of the funnel.

2. A mathematician designs a horse trough of infinite length whose cross sections are rectangles of width one

centimeter and height centimeters. If the trough is filled with water, is the mass of the water infinite or finite? Hint, the mass of water in the trough in grams is given by . If the integral converges, estimate its value to within 3 decimal places.

3. The ends of a horse trough 319 meters long are equilateral triangles having sides of length 2 meters. If the horse trough is full of water, find the hydrostatic force on one end of the trough.

4. The ends of a horse trough 10 meters long are semi-circles of radius 2 meters. If the horse trough is full of water, find the work required to pump all of it into another horse trough 10 meters above the top of the trough.

5. You were kicked out of your dorm because you had a horse trough full of ice in your room for chilling beverages. Now you are homeless and must sleep in your horse trough. However, a manufacturer of horse troughs offers you a job if you can just evaluate the improper integral .

6. You are driving your pickup, with a horse trough in the back, when suddenly you see a four car pile up
ahead. (No horse troughs were injured.) Compute the improper integral . If it diverges just say so, if it converges, find its value.

7. The region bounded by the curves y = x and y = x2 is rotated about the line y = 3. Compute the volume of the resulting solid (note the following would make a poor horse trough, cuz there's a hole in it.)

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