Name ___________________________________________________________________ Chapter 6a
1) A man drops a penny off of the Empire State building in New York City. Ignoring air resistance, the
acceleration of the penny is 32 ft/s2 downward. The building is 1250 feet tall.
a) Find the equation for the height of the penny off the ground.
b) Find the distance the penny travels in the first 3 seconds.
𝑡
2) A town of 40 people grows at a rate of 𝑟(𝑡) = 20 − 5 people/year for 0 ≤ 𝑡 ≤ 150.
a) Find an equation for the population of the town after 𝑡 years.
b) How many people does the town have in 20 years?
c) Around 𝑡 = 100 years there was a very contentious political topic that all the townspeople
debated at length. What do you suspect they were talking about?
3) Find the area of the shaded region enclosed by the three curves below. (Answer check: 193)
𝑦 = 4√𝑥
𝑥2
𝑦=
2
𝑦 = −2𝑥 + 6
4) Find the area of the shaded region enclosed by the two curves below. (Answer check: 0.669)
𝑦 = 𝑥2
𝑥 = 2 sin2(𝑦)
The 𝑥-coordinates of the two marked points are:
𝑥 ≈ 0.8
𝑥 ≈ 1.5
5) Use calculus to find the volume of a pyramid whose base is a right isosceles triangle with base length
5. The height of the pyramid is 20. (Answer check: 83. 3̅)
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6) Suppose a football-shaped object is created by rotating the curve 𝑦 = 9 (𝑥 − 3)2 + 1 around the 𝑥axis. Find the volume of this object. (Answer check: 56𝜋
)
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