4.3++Analyzing+Bones+10-11

May 16, 2011 Noel Oracheski Math 7B


 * 4.3 Analyzing Bones **


 * Answer the following questions according to this table. **


 * ** Bone ** || ** Male ** || ** Female ** ||
 * ** Femur ** || h = 69.089 + 2.238F || h = 61.412 + 2.317F ||
 * ** Tibia ** || h = 81.688 + 2.392T || h = 72.572 + 2.533T ||
 * ** Humerus ** || h = 73.570 + 2.970H || h = 64.977 + 3.144H ||
 * ** Radius ** || h = 80.405 + 3.650R || h = 73.502 + 3.876R ||


 * A. How tall is a female if her femur is 46.2 centimeters long? **

This is the equation to find the height of a female from the length of her femur: h = 61.412 + 2.317F F = Length of Femur = **46.2**

// h // = 61.412 + 2.317 x **46.2** = //168.4574// HEIGHT = 168.4574


 * B. How tall is a male if his tibia is 50.1 centimeters long? **

This is the equation to find the height of a male from the length of his tibia: h = 81.688 + 2.392T T = Length of Tibia = **50.1** // h // =81.688 + 2.392 x **50.1**= //201.5272//

HEIGHT = 201.5272


 * C. If a woman is 152 centimeters (about 5 feet) tall, how long is her femur? Her tibia? Her humerus? Her radius? **

Femur: 39.09710833 cm Tibia: 31.35728385 Hemurus: 27.67907125 Radius: 20.24972

Femur: -61.1412 + ** 152 = 61.1412 + 2.317x ** - 61.1412 ** 90.588 ** / 2.317 ** = 2.317x ** / 2.317
 * 39.09710833 **** = x **

Tibia: -72.572 + ** 152 = 72.572 + 2.533x ** -72.572 ** 79.428 ** / 2.533 ** = 2.533x ** / 2.533
 * 31.35728385 **** = x **

Hemurus: -64.977 + ** 152 = 64.977 + 3.144x ** -64.977 ** 87.023 ** / 3.144 ** = 3.144x ** / 3.144
 * 27.67907125 **** = x **

Radius: -73.502 + ** 152 = 73.502 + 3.876x ** -73.502 ** 78.498 ** / 3.876 ** = 3.144x ** / 3.876
 * 20.249742 **** = x **


 * D. If a man is 183 centimeters (about 6 feet) tall, how long is his femur? His tibia? His humerus? His radius? **

Femur: 50.89857015 Tibia: 42.3545151 Hemurus: 36.8451178 Radius: 28.1082192

Femur: -69.089 + ** 183 = 69.089 + 2.238x ** -69.089 ** 113.911 ** / 2.238 ** = 2.238x ** / 2.238
 * 50.89857015 **** = x **

Tibia: -81.688 + ** 183 = 81.688 + 2.392x ** -81.688 ** 101.312 ** / 2.392 ** = 2.392x ** / 2.392
 * 42.3545151 **** = x **

Hemurus: -73.570 + ** 183 = 73.570 + 2.970x ** -73.570 ** 109.43 ** / 2.970 ** = 2.970x ** / 2.970
 * 36.8451178 **** = x **

Radius: -80.405 + ** 183 = 80.405 + 3.650x ** -80.405 ** 102.595 ** / 3.650 ** = 3.650x ** / 3.650
 * 28.1082192 **** = x **


 * Follow Up: **
 * For one of the bones discussed above, graph the equations for males and females on the same set of axes. What do the x- and y-intercepts represent in terms of this problem? Does this make sense? Why? **


 * Tibia **

x-axis: Length of the Tibia y-axis: Height male x-intercept: -28.65 ** This is where the line crosses the x-axis ** This shows the length of the tibia when the height is at 0 (according to the equation.) male y-intercept: 81.688 This is where the line crosses the ** y-axis ** This shows the length of the height when the length of the tibia is at 0 (according to the equation.)
 * female x-intercept: -34.15 ** This is where the line crosses the x-axis. This shows the length of the tibia when the height is at 0 (according to the equation.)
 * female y-intercept: **** 72.572 ** This is where the line crosses the y-axis This shows the height when the length of the tibia is at 0 (according to the equation.)