An anthropologist can use linear functions to estimate the height of a male or female, given the length of certain bones. A humerus is the bone from the elbow to the shoulder. The height, in centimeters, of a male with a humerus of length x is given by M(x) = 2.89 x + 70.64 . The height in centimeters, of a female with a humerus length x is given by F(x) = 2.75 x + 71.48. A 45- cm humerus was uncovered in some ruins. Assuming it was from a male, how tall was he? Assuming it was from a female, how tall was he? For what height would the lengths of a female humerus and a male humerus be equal.
An anthropologist can use linear functions to estimate the height of a male or female, given the length of certain bones. A humerus is the bone from the elbow to the shoulder. The height, in centimeters, of a male with a humerus of length x is given by M(x) = 2.89 x + 70.64 . The height in centimeters, of a female with a humerus length x is given by F(x) = 2.75 x + 71.48. A 45- cm humerus was uncovered in some ruins.
- Assuming it was from a male, how tall was he?
- Assuming it was from a female, how tall was he?
- For what height would the lengths of a female humerus and a male humerus be equal.
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The length of the humerus is x cm. Let Mx=y1. Then we have, y1=2.89x+70.64.
This gives x=y1-70.642.89.
Let Fx=y2. Then we have y2=2.75x+71.48. Putting x=y1-70.642.89 we get,
y2=2.75x+71.48=2.75y1-70.642.89+71.48=0.95y1-67.108+71.48=0.95y1+4.37y2=0.95y1+4.37
Therefore, the lengths of a female humerus and a male humerus are equal when y2=0.95y1+4.37.
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