it takes trillion 1/2 hour to walk 2 miles and decides to start walking in his spare time but because he wants to make sure he has enough time to get in desired distance he created the data table at which ratio does constant of proportionality appear?
hours miles walked
1/4. 1
1/2 2
3/4 3
1 4
The constant of proportionality in this scenario represents the ratio of miles walked to the number of hours. To find this constant, we can look for a consistent ratio between the miles walked and the hours in the data table.
If we examine the ratios between miles and hours for each row:
1/4 hour --> 1 mile
1/2 hour --> 2 miles (ratio = 2 miles / 1/2 hour = 4 miles/hour)
3/4 hour --> 3 miles (ratio = 3 miles / 3/4 hour = 4 miles/hour)
1 hour --> 4 miles (ratio = 4 miles / 1 hour = 4 miles/hour)
We can see that for each row, the ratio of miles walked to hours remains constant at 4 miles/hour. Therefore, the constant of proportionality appears at the ratio of 4 miles/hour.
To determine at which ratio the constant of proportionality appears in the data table, we need to observe the relationship between the hours and the miles walked.
In this case, the person takes "trillion 1/2" hour to walk 2 miles. Let's convert this into a mixed number for better understanding.
A trillion is equivalent to 1,000,000,000,000. Therefore, "trillion 1/2" hour can be written as 1,000,000,000,000 1/2 hour.
Now, let's analyze the given data table:
Hours Miles Walked
1/4 1
1/2 2
3/4 3
1 4
We can start by observing the ratio between the hours and the miles walked:
1/4 hour / 1 mile = 1/4
1/2 hour / 2 miles = 1/4
3/4 hour / 3 miles = 1/4
1 hour / 4 miles = 1/4
From the calculated ratios, we can see that the hours divided by the miles walked consistently give us 1/4. This constant ratio of 1/4 indicates the constant of proportionality, where the time it takes to walk certain miles remains the same.
Thus, the constant of proportionality appears at a ratio of 1/4 in the given data table.
To determine the constant of proportionality, we need to find the ratio between the hours and the miles walked. Let's calculate this ratio for each data point in the table:
For the first data point, when 1/4 hour is walked, we have 1 mile. The ratio is 1 mile / (1/4) hour = 4 miles per hour.
For the second data point, when 1/2 hour is walked, we have 2 miles. The ratio is 2 miles / (1/2) hour = 4 miles per hour.
For the third data point, when 3/4 hour is walked, we have 3 miles. The ratio is 3 miles / (3/4) hour = 4 miles per hour.
For the fourth data point, when 1 hour is walked, we have 4 miles. The ratio is 4 miles / 1 hour = 4 miles per hour.
As we can see, the ratio remains constant at 4 miles per hour for all the data points. Therefore, the constant of proportionality appears at a ratio of 4 miles per hour.