Lesson%2027%20HW%20handout

Lesson%2027%20HW%20handout - r = 0 when t = 0. (Solution)...

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MA153 JIN NOTE for HW 27 1. Let and . Find . (Solution) 2. Use and to evaluate the expression. (Solution) 3. Solve the equation: if . (Solution) Hence the equation is Hence . 4. A fire has started in a dry open field and is spreading in the form of a circle. If the radius of this circle increases at the rate of 2 ft/min, express the total fire area as a function of time (in minutes). (Solution) The radius after minutes: The area of the circle after minutes: 5. The volume of a conical pile of sand is increasing at a rate of 243 ft 3 /min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes), assuming that
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Unformatted text preview: r = 0 when t = 0. (Solution) Recall that the volume of the cone of radius of base and of height is Here since the , . The volume after minutes: Hence after minutes, 6. A hot-air balloon rises vertically from ground level as a rope attached to the base of the balloon is released at the rate of 6 ft/sec (see the figure). The pulley that releases the rope is 24 feet from a platform where passengers board the balloon. Express the altitude of the balloon as a function of time . MA153 JIN (Solution) Let be the height after seconds. The hypotenuse of the right triangle after seconds is . By Pythagorean theorem, we have...
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Lesson%2027%20HW%20handout - r = 0 when t = 0. (Solution)...

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