You've been asked to calculate the mass of a conical pile of sawdust measuring 8 meters high with a baseradius of 7 meters. From experimental measurements, you've been able to determine that the density of thesawdust depends upon the depth, d, of the sawdust in meters, according to the equation p(d) = 150 + 30dkg/m³. Find the mass of the pile.kg

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Answered: You've been asked to calculate the mass…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 10 cm. Find the rate at which the water level is rising when the water level is 3 cm. cm/sec h b₁ b2
The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.3 lb/ft³. a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full? b. If the water is pumped to ground level with an (8/11)-horsepower (hp) motor (work output 400 ft-lb/sec), how long will it take to empty the tank (to the nearest minute)? c. Show that the pump in part (b) will lower the water level 15 ft (halfway) during the first 20 minutes of pumping. d. What are the answers to parts (a) and (b) in a location where water weighs 62.16 lb/ft³? 62.42 lb/ft³? a. Set up an integral to find the work done. W = Ground 5 ft level 0 30 14 ft
A pyramid of height 500 ft has a square base 700 ft by 700 ft. Find the area A at height h. A(h) = If the rock used to build the pyramid has a weight-density of approximately w = 100 lb/ft3, how much work (in ft-lb) did it take to lift all the rock? Assume there were 10,000 workers each working 10 hours a day, 5 days a week, 50 weeks a year. If the workers, on average, lifted ten 100 lb rocks 2 ft/hr, how long (in months) did it take to build the pyramid
An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 7 cm, and the height is 12 cm. b1 b2 Find the rate at which the water level is rising when the water level is 9 cm. h cm/sec
An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is 11 cm. Find the rate at which the water level is rising when the water level is 2 cm. cm/sec h b₁ b₂
A chamber 27 m beneath the Earth contains hot water with a density of 1000 kg/m³ at a pressure of 955,526 Pa. A narrowing channel leads upwards to a circular vent at the surface having negligible area compared to that of the chamber. At what speed is hot water ejected from the vent? Atmospheric pressure is 1.01 x 105 Pa V = - m/s

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