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Homework: A Bunch of Other Stuff About Radicals

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice word problems which develop concepts related to further uses of radicals.

Exercise 1

Several hundred years before Einstein, Isaac Newton proposed a theory of gravity. According to Newton’s theory, any two bodies exert a force on each other, pulling them closer together. The force is given by the equation F = G m 1 m 2 r 2 F=G m 1 m 2 r 2 , where F F is the force of attraction, G G is a constant, m 1 m 1 and m 2 m 2 are the masses of the two different bodies, and rr is the distance between them. Find a formula that would give you r r if you already knew F F, G G, m 1 m 1 , and m 2 m 2 .

Exercise 2

In the following drawing, m m is the height (vertical height, straight up) of the mountain; ss is the length of the ski lift (the diagonal line); and x x is the horizontal distance from the bottom of the ski lift to the bottom of the mountain.

Figure 1
Ski Lift
An image of a skylift
  • a. Label these three numbers on the diagram. Note that they make a right triangle.
  • b. Write the relationship between the three. (Pythagorean Theorem.)
  • c. If you build the ski lift starting 1,200 feet from the bottom of the mountain, and the mountain is 800 feet high, how long is the ski lift?
  • d. If the ski lift is s s feet long, and you build it starting x x feet from the bottom of the mountain, how high is the mountain?

Exercise 3

Simplify 28 4 - 7 28 4 - 7 . Check your answer on your calculator.

Exercise 4

Simplify 1 5 + 1 5 - 2 1 5 + 1 5 - 2 . Check your answer on your calculator.

Exercise 5

Graph y = x 3 y= x 3. What are the domain and range?

Exercise 6

Graph y = x - 3 y= x - 3 . What are the domain and range?

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