it takes julian 12 hour to walk 2 miles. he decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. at which ratio does the constant of proportionality appear?
The constant of proportionality appears in the ratio between the time it takes Julian to walk and the distance he walks. In this case, the constant of proportionality would be the time it takes Julian to walk one mile.
To find this ratio, we divide the total time by the total distance. In this case, since Julian walks 2 miles in 12 hours, the ratio would be:
12 hours / 2 miles = 6 hours/mile
Therefore, the constant of proportionality appears at a ratio of 6 hours/mile.
To determine the constant of proportionality in Julian's walking activity, we can use the formula for direct variation:
y = kx
where y represents the distance and x represents the time. In this case, Julian takes 12 hours to walk 2 miles.
Let's create a data table to represent this relationship:
Time (x) | Distance (y)
----------------|-----------------
12 | 2
To find the constant of proportionality (k), we can use the given values. We know that y = kx, so we can substitute the values from the data table:
2 = k * 12
Now, let's solve the equation for k:
k * 12 = 2
k = 2 / 12
k = 1/6
Therefore, the constant of proportionality appears as 1/6, which implies that for every 1 hour Julian walks, he covers 1/6 of a mile.
To determine the ratio at which the constant of proportionality appears, we need to analyze the given information. Specifically, we know that Julian takes 12 hours to walk 2 miles. Let's represent this relationship using the formula for distance:
distance = rate × time
In this case, the distance is 2 miles, and the time is 12 hours. Now we can rearrange the formula to solve for the rate:
rate = distance / time
Substituting the values, we get:
rate = 2 miles / 12 hours
Simplifying this expression, we find:
rate = 1/6 miles per hour
So, the rate at which Julian walks is 1/6 miles per hour.
Now, let's discuss how the constant of proportionality appears in this scenario. The constant of proportionality represents the ratio between two related variables that remain constant. In this case, we have the distance Julian walks and the time it takes him. We can express this relationship as:
2 miles / 12 hours = k
Where "k" is the constant of proportionality.
Simplifying this equation, we get:
1/6 miles per hour = k
Therefore, the ratio at which the constant of proportionality appears in Julian's case is 1/6.