Required Homework 3 All graphs must be done on graph paper. Show your work. 1 Write the equation of the line through (0,4) with slope = -1. Then graph the line. 2 Write the equation of the line that passes through (-1, 6) and (4, 3). Then graph the line. 3 Write the equation of the line that passes through the pints (-1, -1) and(5,4). Then graph the line. 4 Write the equation of the line with slope = 3 that passes through the point (0, -1). Then graph the 4 line. 5 Write the equation of the line that is parallel to the line 3x + 5y = 15 and passes through the point (1,1). Then graph both lines. 6 Find the value of x and y where the two lines in problem 5 cross. 7 Graph the line that passes through the points (0, 1) and (5, 1). Then write the equation. What word can be used to describe this line? 8. Graph the line that passes through the points (2, 6) and (2, -3). What word can be used to describe this line? Write the equation of the line. 9 A train station in the Rocky Mountains is 12,000 feet above sea level. When the train leaves the station the altitude (height) increases 0.05 feet for every foot traveled. Write a linear a linear equation (with x = number of feet traveled) and y = the altitude of the train. What will the altitude be when the train has traveled 21,120 feet (exactly 4 miles)? 10 A car dealership finds that when they charge $24,000 per car they sell 500 cars per week but when they charge $25,000 they sell only 400 cars. Write a linear equation that describes the relationship between price and sales. How many cars will they sell if price is $24,200? Math C Spring 2017 Homework 4 All graphs must be done on graph paper. 1. Graph y = x (Yes, it’s in Class Notes 4, but I want to see you do it. 2. Graph y = x + 5 . At a minimum graph the points x = -5, x = -4, x = -1, x = 4, and x = 11, then connect the dots. What is the domain? What is the range? 3. Graph h(x) = -x2 + 1. What is the domain? What is the range? 4. Graph f(x) where f(x) = 1 for x < 1 f(x) = x for 1 < x < 4 f(x) = 4 for x > 4 What is the domain and range for this function? 5. Graph f(x) = (x +2)2 6. Graph g(x) = |x| + 1 What is the domain? What is the range? 7. Graph h(x) = x+2 Hint: if you can’t figure out which numbers make the function easy to work with, use your calculator and let the decimals happen! 8. Calculate 121 and 400 Use your calculator! 9. Graph y = x2 -4 What are the domain and range? 10. What is the domain of f(x) = x + 8 ? What is the range? Homework 5 1 If a person stands on a height, such as a tower, the distance they can see is directly proportional to the height of the tower. If a person is on a tower that is 40 feet high, they can see 8 miles. If a person stands on a tower that is 25 feet high, how far can they see? 2 A water tank has five input pipes, but they are not always all used. The time required to fill the tank is inversely proportional to the number of pipes used. If it takes 25 hours to fill the tank using 2 pipes. How long does it take to fill the tank using 4 pipes? 3 The stopping distance for a car varies directly as the speed of the car. If a car traveling 60 mph can stop in 200 feet, how fast can a car go and stop in 72 feet? 4 The volume of a cylinder is directly proportional to the square of the radius and (jointly) directly proportional to the height. When the radius r = 3 inches and height h = 10 inches the volume is 282.7 cubic inches. What is the volume of a cylinder when radius r = 5 inches and height h = 6 inches? 5 Assume that y varies directly with x and inversely with z. When x = 20, z = 15, y = 4. What is the value of y when z = 5, x = 15? 6 “Electrical resistance” describes the ability of a conductive material to resist electrical current. Electrical current varies directly with voltage and inversely with resistance. (Voltage is measured in volts and resistance is measured in ohms.) With a 12-volt battery and 4 ohms resistance you get 3 amps of current. 4.a Write the equation for the relation of current, voltage, and resistance. 4.b What is the current at 10 volts and 5 ohms resistance? 7 The intensity of a light is inversely proportional to the square of the distance from the light source. At a distance of 9 feet, the intensity of the light is 8 candlepower. (Candlepower is the unit of the measurement of light.) What is the intensity of light from the same source at 6 feet distance? 8 The lifting force, F, under the wing of a plane is jointly directly proportional to the area of the wing and the square of the speed of the plane. A plane with wing area 120 square feet and a speed of 80 miles per hour has a lifting force of of 1600 pounds. What is the lifting force for a plane with a wing area of 150 square feet and a speed of 90 miles per hour? Math C Homework 6 1 A = { 1, 2, ,3, 4, 5, 6, 7, 8, 9, 10, 11, 12} B = { 3, 6, 9, 12, 15, 18, 21 } a. Find A ∩ B b. Find A ∪ B 2 Simplify and graph: 4x + 2 < -10 ∪ 5x – 1 > 9 This can be written: 4x + 2 < -10 and 5x – 1 > 9 3 Solve and graph x + 3 < 9 and –x < 4 4 Graph x < 2 or x > 5 5 What is the solution for x < 2 and x > 10? 6 Solve and graph 3 (x-1) < 12 or x + 7 > 10 7 A student is taking an English class in which there are no exams, just three papers to write. The three papers count equally toward the grade. To get a B in the course the average for the three papers must be at least 80 and less than 90. The score for the first two papers is 85 and 89. Write an inequality for the range of scores on the third paper that will give the student a B. 8 Cars have variable mileage depending on road conditions, wind, speed, etc. Assume that a specfic car can go between 124 to 152 miles on 4 gallons of gas depending on conditions. (Specifically 124 miles < 4 x < 152 miles.) Write an inequality that expresses how far the car can go on one gallon of gas. Graph the inequality. 9 Assume the normal range for height of a three year old boy is between 31 to 37 inches high. (The boundary values x = 31 and x = 37 should be considered part of the normal range.) a. Write an inequality that expresses the normal range of height for a three year old boy in inches. b. The conversion factor from inches to centimeters is 1 inch = 2.54 centimeters. Write an inequality that expresses the normal range of height for a three year old boy in centimeters. 10 The Food and Drug Administration (FDA) recommends that a person’s refrigerator temperature should be more than 32°F and less than or equal to 40°F. a. Write an inequality that expresses the range of acceptable temperatures in degrees Fahrenheit. b. Write an inequality that expresses the range of acceptable temperatures in degrees Celsius.