Page 54 - How To Solve Word Problems In Calculus
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(a) What is the projectile’s average velocity for the first 2 seconds
of travel?
(b) What is the projectile’s initial velocity?
(c) What is the projectile’s velocity after 5 seconds? What is its
position?
(d) What is the maximum height reached by the projectile?
(e) When does the projectile hit the ground and with what velocity
does it hit?
5. A rod of length 5 ft has a linear density proportional to the cube of
the distance from one end. If the total mass of the rod is 500 slugs,
compute
(a) The average density of the rod
(b) The density of the rod at its midpoint
6. Boyle’s law states that when a gas is compressed at constant
temperature, the product of its pressure and volume remains
2
constant. If the pressure of a gas is 80 lb/in when the volume is
3
40 in , find the rate of change of pressure with respect to volume
3
when the volume is 20 in .
7. If x items of a commodity are sold to a wholesaler, the price per
2
item is 500 − 2x − 0.1x dollars. Compute the marginal revenue
derived from the sale of the 11th unit.
Solutions to Supplementary Problems
1.
y
x
y
x x
x x
The surface area of the boxis the sum of the areas of its sixsides.
2
S = 2x + 4xy
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