A pipe tapers 0.75 inches for every 30 inches of length.Use a constant of direct variation to determine the amount of taper of a 105 inches length.
I need help with finding a constant of direct variation.
To find the constant of direct variation, you need to identify two variables that are directly proportional to each other. In this case, the length of the pipe and the amount of taper are the two variables.
Let's assume L represents the length of the pipe in inches, and T represents the amount of taper in inches.
According to the given information, the pipe tapers 0.75 inches for every 30 inches of length. This means that for every 30 inches increase in length, there is a corresponding increase of 0.75 inches in taper.
So we can write the following proportion:
L/30 = T/0.75
Now, we need to find the constant of direct variation. To do this, we cross-multiply and solve for the constant.
L * 0.75 = 30 * T
0.75L = 30T
Divide both sides of the equation by 30:
(0.75L) / 30 = T
0.025L = T
Therefore, the constant of direct variation is 0.025. This means that for every inch increase in length, there will be a corresponding increase of 0.025 inches in the taper.