Page 145 - Calculus Workbook For Dummies

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Chapter 8: Using Differentiation to Solve Practical Problems

5. A farmer’s hog trough is 10 feet long, and 6. A pitcher delivers a fastball, which the
its cross-section is an isosceles triangle batter pops up — it goes straight up above
with a base of 2 feet and a height of 2 feet 6 home plate. When it reaches a height of 60
inches (with the vertex at the bottom, nat- feet, it’s moving up at a rate of 50 ft/sec.
urally). The farmer is pouring swill into the At this point, how fast is the distance from
trough at a rate of 1 cubic foot per minute. the ball to 2nd base growing? Note: The
Just as the swill reaches the brim, her distance between the bases of a baseball
three hogs start violently sucking down the diamond is 90 feet.
swill at a rate of ⁄2 cubic foot per minute for
1
each hog. They’re going at it so vigorously Solve It
that another ⁄2 cubic foot of swill is being
1
splashed out of the trough each minute.
The farmer keeps pouring in swill, but
she’s no match for his hogs. When the
depth of the swill falls to 1 foot 8 inches,
how fast is the swill level falling?

Solve It