Examine the Pythagorean theorem below . In this form you can find the length of the hypotenuse (c) of a right triangle if you know the lengths of the two short sides (a & b). Solve this equation for the short side b. If you need to indicate a square root in your answer, type it like this: root * (e + f) to mean the square root of the sum (e + f) . For example, the equation below can be typed as C=root(a^ ^ 2+b^ ^ 2) *

What is the length x of the side of the triangle below? (hint: use the cosine function)

Because light travels in a straight line and casts a shadow, isaac newton hypothesized that light is

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.