If everyone had the same body proportions, your weight in pounds would vary directly with the cube of your height in feet. Assume the average height and weight of a female in your math class is 5'5" and 150 pounds. Use this information to write a variation equation then use it to find the weight of the female below if they had the same body type as the average female. Round answer to the nearest pound.
Kelly 5'9"
To write the variation equation, we can use the formula provided: "weight in pounds varies directly with the cube of height in feet."
Let's write the equation, using k as the constant of variation:
Weight = k * (Height)^3
Now, we can use the given information to find the value of k. The average height and weight of a female in your math class are provided as 5'5" and 150 pounds. To convert 5'5" to just feet, we divide by 12 (as there are 12 inches in a foot):
5'5" = 5 + (5/12) = 5.4167 feet (approximately)
Plugging this into the equation, we get:
150 = k * (5.4167)^3
To find the value of k, we divide both sides of the equation by (5.4167)^3:
k = 150 / (5.4167)^3
Now that we have the value of k, we can use it to find the weight of the female named Kelly, who has a height of 5'9". Following the same process, we convert 5'9" to feet:
5'9" = 5 + (9/12) = 5.75 feet
Plugging this value into the equation, we get:
Weight = k * (5.75)^3
Finally, we substitute the value of k we found earlier to determine the weight:
Weight = (150 / (5.4167)^3) * (5.75)^3
Calculating this expression will give us the weight of Kelly if she had the same body type as the average female.
To write a variation equation, we can use the given information that weight varies directly with the cube of height.
Let's assign variables to represent the height and weight of the average female in your math class.
Height: h = 5'5"
Weight: w = 150 pounds
Now, let's write the variation equation using these variables. Weight (w) varies directly with the cube (h^3) of height (h):
w = k * h^3
To find the value of the constant k, we can substitute the values of height (h) and weight (w) for the average female given in the question:
150 = k * (5.42)^3
Simplifying:
150 = k * 157.4648
Now we can solve for k:
k = 150 / 157.4648
k ≈ 0.9527
Now that we have the value of k, we can use it to find the weight of Kelly, who is 5'9" in height. Let's substitute the height of Kelly (h = 5'9" = 5.75 feet) into the variation equation:
w = 0.9527 * (5.75)^3
Calculating:
w ≈ 0.9527 * 195.112
w ≈ 185.872
Therefore, the weight of Kelly, if she had the same body type as the average female in the math class, would be approximately 186 pounds.