8.6 Homework: a bunch of other stuff about radicals

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 $F=G\frac{m_1{m}_2}{r^2}$ , where $F$ is the force of attraction, $G$ is a constant, $m_1$ and $m_2$ are the masses of the two different bodies, and $r$ is the distance between them. Find a formula that would give you $r$ if you already knew $F$ , $G$ , $m_1$ , and $m_2$ .

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

• 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 $s$ feet long, and you build it starting $x$ feet from the bottom of the mountain, how high is the mountain?

Simplify $\frac{\sqrt{28}}{4-\sqrt{7}}$ . Check your answer on your calculator.

Simplify $\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{5}-2}$ . Check your answer on your calculator.

Graph $y=\sqrt{x}–3$ . What are the domain and range?

Graph $y=\sqrt{x-3}$ . What are the domain and range?