Math 060 Quiz 3 Answer Key

MATH 060 _______________ANSWER KEY_______________

TTh 1:30-3:35, Room A-107

QUIZ 3 September 11, 2008 1. (5 points) Recall the formula for a lever system: Given the beam is of length d; the fulcrum is at a distance of x from one end; a weight of F1 is placed at that end; and a weight of F2 is placed at the other end. Then the system balances if F1 x = F2 (d − x) . Using the above formula, solve this problem: A lever of 30 feet long is used with a child of 50 lbs. on one end, and her 100-lb. mother on the other end. Where must the fulcrum be placed so that the system balances? (Specify whether the distance you calculated is from the child or from the mother.) Let x be the distance from the child to the fulcrum. Then: d = 30 feet; F1 = 50 lbs.; F2 = 100 lbs. The lever system balances when: 50 x = 100 (30 – x) 50 x = 3000 – 100x ⇒ 150 x = 3000 ⇒ x = 20 To be balanced, the fulcrum must be placed at 20 feet from the end where the child is. (If you had set x = distance from where the mother is, the answer would have been 10 feet.)

2. (2 points) Graph the line:

y=

2 x −1 3

There are many ways of figuring out this graph. One way is to find two points. If x = 0, then y = –1 ; so (0, –1) is one point. If x = 3, then y = 2 – 1 = 1 ; so (3, 1) is another point.

3. (3 points) Calculate the slope of the line containing the points (2, –4) and (–3, –1).

Slope =

y Difference (−1) − (−4) − 1 + 4 3 3 = = = = − or –0.6 x Difference (−3) − 2 −3−2 −5 5