A cheetah ran 9.6 miles in 8 minutes and 18 miles in 15 minutes hint use the distance formula if needed what is the independent value what is the dependent value what is the constant of proportionality K what is the constant of proportionality K what is the proportion
In this scenario, the independent value is the time, while the dependent value is the distance covered by the cheetah.
Let's use the distance formula (d = rt) to find the constant of proportionality (K) for each case:
For the first scenario, the cheetah ran 9.6 miles in 8 minutes. Using the formula, we have:
9.6 = r * 8
Solving for r, the rate or speed of the cheetah, we get:
r = 9.6 / 8 = 1.2 miles per minute
Therefore, the constant of proportionality (K) in this case is 1.2.
For the second scenario, the cheetah ran 18 miles in 15 minutes. Using the formula, we have:
18 = r * 15
Solving for r, we get:
r = 18 / 15 = 1.2 miles per minute
Again, the constant of proportionality (K) in this case is 1.2.
Hence, the constant of proportionality (K) is the rate or speed of the cheetah, which is 1.2 miles per minute in both scenarios.
The proportion relating time and distance can be expressed as:
d1 / t1 = d2 / t2
Where d1 and t1 are the distance and time for the first scenario (9.6 miles and 8 minutes), and d2 and t2 are the distance and time for the second scenario (18 miles and 15 minutes).