Assignment 6 Linear Equations Assignment Name: Thaths:lu Page: 1 2 3 4 Total Marks: 8 10 10 7 35 Score: 1. Exposure to cold weather can cause frostbite and hy- pothermia. Mountain climbers, skydivers, and other Altitude (m) Temperature ('C) high-altitude enthusiasts must protect their skin be- 0 12 cause air temperature, T, in degrees Celsius, de- 4090 -13.6 creases as altitude, A, in metres, increases. This rate 8000 -39.2 of decrease in temperature is nearly constant, up to about 11 000 m. An airplane taking off in Yukon Territory recorded the temperatures in the table above. (a) Sketch a straight-line graph of the data. 13 (b) What is the slope of the line expressed as a fraction in lowest terms? What does 13 the slope represent? (c) What is the T-intercept? What does it represent? /2 Mr. de Jong Page 1 of 4 NDSSAssignment 6 Linear Equations Assignment FMP 10 V (d) Write an equation that describes the relationship between temperature and altitude. [C . - (e) Mount Logan is in Klusne National Park and Reserve, YT- At a height Of 5959 In, Mount Logan is the highest mountain in North America. Predict the temperature 3- climber would experience at the peak of Mount Logan on the day that the airplane g. acollected the data. Assume minimal wind. j, . 1'. '- (f) Most people are at risk of frostbite within 1020 min of exposure to temperatures below 20 'C. Predict the altitudes at which the temperature will be below 20 \"C. 2. Sanding trucks spread a mixture of sand and salt on roads to improve traction in winter. The density of the salt is 1200 kg/m3. The density of the sand is 1800 kg/ma. (a) Write a linear equation to represent the volume, in cubic metres, of salt, 2:, and of sand, y, in a mixture with a mass of 10 000 kg. 1200-" 3 (b) For temperatures below 12 \"C, the volume of sand in 10000 kg of the mixture is - 5.22 1113. What is the volume of salt in the mixture? WW Assignment 6 Linear Equations Assignment FMP 10 (c) By mass, what percent of the mixture is salt? /2 3. The graph shows the linear re- lationship between the speed of Sound Speed sound, V, in metres per second, and V the temperature, t, in degrees Cel- sius, of dry air. At 6.C, the speed 345 of sound is 335 m/s. At 16 .C, it is 341 m/s 340 (a) What is the slope of the line? /2 Speed, V (m/s) 335 330 5 10 15 20 Temperature, t ('C) (b) What rate of change does the slope represent? /2 (c) What is the equation of the line? /2 (d) Determine the speed of sound at 35 .C. /2 Page 3 of 4 NDSS Mr. de JongW (e) What is the air temperature when the speed 0' 3\"nd is 348 mm W e . 1} - 3 i 4. If two lines with slopes of 3 and % are perpendiCUIa-I', What is the value or n? 5. You can monitor your heart rate while you exercise. The Karvonen formula states that the target heart rate during an aerobic workout should be between H = 0.7(220 - A) and H = 0.8(220 - A). In the equations, H represents your target heart rate and A represents your age. Predict whether a. graph of these equations would show parallel lines. Justify your answer. ______________________.f Mr. de Jong Page 4 of 4 NDSS