Question

Part 1 You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person. (An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.) To measure the forearm, measure inside the arm, between the wrist and the elbow. Part 2 Organize your data and find the rate of change. Create a table of the measurements for your data. Label the forearm measurements as your input and the foot measurements as your output. Select two sets of points and find the rate of change for your data. Describe your results. If you had to express this relation as a verbal statement, how would you describe it? Part 3 Compare rates of change. The equation below can be used to find the length of a foot or forearm when you know one or the other. (length of the foot) = 0.860 • (length of the forearm) + 3.302 If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? What is the rate of change of the equation from Part A? Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different? Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer. For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3. Measurement of forearm (x) 10in. , 15in , 10in, 11in. , 12in. Measurement of left foot (y) 9in. 11in. . 8in. 9 11/16in. 11 1/4in.

Answer 1

To measure the foot and forearm length of a person, use a tape measure or ruler. Create a table to organize the data and find the rate of change. The equation y = 0.860x + 3.302 represents the relation between foot and forearm length.

Step-by-step explanation:

To measure the length of a person's left foot and forearm, you can use a tape measure or ruler. Have the person stand on a piece of paper and trace their foot to measure its length. For the forearm, measure the distance between the wrist and elbow on the inside of the arm. For organizing the data and finding the rate of change, create a table with forearm measurements as the input and foot measurements as the output. Choose two sets of points from the table and find the rate of change by subtracting the foot measurement of the first point from the foot measurement of the second point, and dividing it by the difference in forearm measurements. To express this relation as a verbal statement, you can say that the length of a person's foot is 0.860 times the length of their forearm plus 3.302.

If you let y represent the length of the foot and x represent the length of the forearm, the equation becomes y = 0.860x + 3.302. To find the length of a person's foot if their forearm is 17 inches long, substitute x = 17 into the equation and solve for y. The rate of change of the equation is 0.860, which means that for every one unit increase in forearm length, the foot length increases by 0.860 units. When comparing the equation to the data, they may not be exactly the same due to measurement errors or individual variations, but they should have a similar trend. The values could be different because the equation is a general representation whereas the data is specific to the measurements taken. The relation in the data can be considered a function since each forearm measurement corresponds to a unique foot measurement. The equation in Part A can also represent a function since it is a linear equation.