Math 180 – Applications – Chapters 3 and 4

Show all algebraic steps.

Check your answers using a graph. Label axes with variables names and units. Indicate window values used in the calculator.

1)Maximizing revenue(demand equation)- # 3-6, on page 160

2) Enclosing the Most Area with a Fence -# 7-10, page 160

3) Constructing rain gutters - #15, page 161

4) Throwing an Object on the Earth/Moon

The height of an object which is falling or is projected into the air on the Earth's surface is given by , where h is the height of the object (in feet), is the original velocity of the object (in feet per second), is the original height (in feet), and t is the time (in seconds).

The position equation on the moon is given by

An astronaut standing on the surface of the moon throws a rock into the air at an initial velocity of 27 ft/sec. Assuming his hand is 6 feet from the surface of the moon,

a) What is the maximum height of the rock

b) How long will the rock remain in the air?

If the rock were thrown with the same initial conditions on the surface of the Earth,

a) What is the maximum height of the rock

b) How long will the rock remain in the air?

5) Modeling Population with Rational Functions - # 54, page 201

6) Drug Concentration - # 55, 56, page 211

7) Minimizing Surface Area -# 59, 60, page 212

  • After the semester is over, you discover that the math department has changed textbooks (again) so the bookstore won't buy back your nearly-new book. You and yourfriend Hermandecide to get creative. You go to the roof of a twelve-story building and look over the edge to the reflecting pool 160feet below. You drop your book over the edge at the same instant that Hermanchucks his book straight down at 48feet per second. By how many seconds does his book beat yours into the water?

Our initial launch heights will be the same: we're both launching from 160feet above ground. And the gravity number, since we're working in feet, will be 16. My initial velocity is zero, since I just dropped my book, but my buddy Herman's velocity is a negative48, the negative coming from the fact that he chucked his book down rather than up. So our "height" equations are:

mine: s(t) = –16t2 + 160
his: s(t) = –16t2 – 48t + 160