Please Help Me!
The equations below express the relationship between a person's height, H, and femur (thigh bone) length, F. Both measurements are in inches.
Males : H=27.5+2.24F
Females: H=24+2.32F
a) If a man's femur is 20 inches long, about how tall is he?
b) If a woman's femur is 15 inches long, about how tall is she?
c) If a man is 65 inches tall, about how long is his femur?
d) If a woman is 68 inches tall, about how long is her femur?
e) What do the numbers 2.24 and 2.32 tell you about the relationship between femur length and height for males and females?
Just plug in your numbers.
(a) H = 27.5 + 2.24*20
(d) 68 = 24+2.32F
(e) as femurs lengthen, men grow more slowly
a) To find out how tall a man is when his femur is 20 inches long, we can substitute the value of F into the equation for males: H = 27.5 + 2.24F.
Replacing F with 20, we get: H = 27.5 + 2.24 * 20.
Now we can simplify this equation to find the answer:
H = 27.5 + 44.8
H = 72.3
Therefore, a man with a femur length of 20 inches is approximately 72.3 inches tall.
b) To determine the height of a woman with a femur length of 15 inches, we can use the equation for females: H = 24 + 2.32F.
Substituting F with 15, the equation becomes: H = 24 + 2.32 * 15.
Simplifying the equation, we have:
H = 24 + 34.8
H = 58.8
Thus, a woman with a femur length of 15 inches is approximately 58.8 inches tall.
c) If a man is known to be 65 inches tall, we can use the equation for males: H = 27.5 + 2.24F to determine his femur length.
Rewriting the equation with H as 65, we get: 65 = 27.5 + 2.24F.
Now we can solve for F:
65 - 27.5 = 2.24F
37.5 = 2.24F
Dividing both sides by 2.24, we find:
F ≈ 16.74
Hence, a man who is 65 inches tall will have a femur length of approximately 16.74 inches.
d) Similarly, if a woman is 68 inches tall, we can use the equation for females: H = 24 + 2.32F.
Replacing H with 68, we have: 68 = 24 + 2.32F.
Next, we can solve for F:
68 - 24 = 2.32F
44 = 2.32F
Dividing both sides by 2.32, we obtain:
F ≈ 18.97
Therefore, a woman who is 68 inches tall will have a femur length of approximately 18.97 inches.
e) The numbers 2.24 and 2.32 in the equations represent the rate of change or the slope of the relationship between femur length (F) and height (H) for males and females, respectively.
For males (H = 27.5 + 2.24F), the slope is 2.24, indicating that for every 1-inch increase in femur length, the height increases by 2.24 inches.
Similarly, for females (H = 24 + 2.32F), the slope is 2.32, indicating that for every 1-inch increase in femur length, the height increases by 2.32 inches.
In other words, these numbers represent the ratio of femur length to the corresponding change in height.