Name: 7.6-­‐7.7 7.6 Ratio and Proportion A. Ratios and Proportions A ratio is a comparison of _____________________. When two ratios are ___________ they are in proportion. EX 1: It takes 80 pounds of sodium hydroxide to neutralize 98 pounds of sulfuric acid. At this rate, how many pounds of sodium hydroxide are needed to neutralize 47 pounds of sulfuric acid? EX 2: Triangle ABC and triangle DEF are similar. Find the length of side DF. B. Motion Problem EX: Mike leaves his house traveling 2 miles per hour. Joy leaves 6 hours later to catch up with him traveling 8 miles per hour. How long will it take her to catch up with him? Distance = Rate ·∙ Time Mike Joy Maya Lanzetta MAT 122 I love mathematics…principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game – the encompassing of the infinite. ~Rozso Peter 7.7 Variation A. Types of Variation In Words Direction Variation Equation: Y varies directly with x In Equation Form Inverse Variation Equation: Y varies indirectly or inversely Joint Variation Equation: Combined Variation Equation: Example A skydiver’s speed varies directly with the amount of time spent falling. A sky diver’s speed 2.5 s after jumping from a plane is 24.5 m/s. The volume of gas in a container at a constant temperature varies inversely as the pressure. If the volume is 32 cm3 at a pressure of 8 lbs., find the pressure when the volume is 60 cubic centimeters. The area of a cylinder varies jointly with the radius and height. When the radius is 3 and the height is 6, the area is 36π. What is the area when radius is 4 and height is 5?
The time needed to paint a fence varies directly with the length of the fence and indirectly with the number of painters. If it takes five hours to paint 200 feet of fence with three painters, how long will it take five painters to paint 500 feet of fence? Challenge: If you have a two-­‐in-­‐five chance of winning something, what are your odds?