An alligators tail length,T varies directly from its body length B. So an alligator with a body length of 7.7 feet has a tail length of 6.3 feet. What is the tail length of an alligator whose body length is 4.4 feet?
Thanks ahead of time.
T = k B
6.3 = k 7.7
k = .818
T = .818 B
T = .818 (4.4)
T = 3.6 ft
In this scenario, since the tail length, T, varies directly from the body length, B, we can set up a proportion to find the tail length of an alligator with a body length of 4.4 feet.
We know that the tail length, T, is 6.3 feet when the body length, B, is 7.7 feet.
So, we can set up the proportion:
T1 / B1 = T2 / B2
where T1 = 6.3 feet, B1 = 7.7 feet, T2 is the tail length we want to find, and B2 = 4.4 feet.
Plugging in the values, we have:
6.3 / 7.7 = T2 / 4.4
Now, we cross-multiply and solve for T2:
6.3 * 4.4 = 7.7 * T2
27.72 = 7.7 * T2
Now, divide both sides by 7.7:
27.72 / 7.7 = T2
T2 ≈ 3.6 feet
Therefore, the tail length of an alligator with a body length of 4.4 feet is approximately 3.6 feet.
To solve this problem, we can use the concept of direct variation. Direct variation means that two variables, in this case, tail length and body length, are directly proportional to each other. In other words, if one variable doubles, the other variable will also double.
In this case, we are given that the tail length (T) varies directly from the body length (B). The problem also states that when the body length is 7.7 feet, the tail length is 6.3 feet.
We can use these given values to find the constant of proportionality (k) by using the formula:
T = kB
To find k, we divide the tail length (6.3) by the body length (7.7):
k = T / B = 6.3 / 7.7 = 0.818
Now that we have the value of k, we can use it to find the tail length (T) when the body length (B) is 4.4 feet:
T = kB = 0.818 * 4.4 = 3.5932
Therefore, the tail length of an alligator with a body length of 4.4 feet is approximately 3.5932 feet.