A new set of car tires has a tread depth of 8 millileters. The tread depth decreases 0.12 millimeter per thousand miles driven. Write an equation that gives the tread depth as a function of the distance driven. Then predict what distance the tread depth will be 2 millimeters....
To write an equation that gives the tread depth as a function of the distance driven, we can use the following information:
- The initial tread depth is 8 millimeters.
- The tread depth decreases by 0.12 millimeters per thousand miles driven.
Let's denote the distance driven in thousands of miles as "d". Since the tread depth decreases by 0.12 millimeters per thousand miles driven, the tread depth after driving "d" thousands of miles can be represented by:
Tread depth = 8 - 0.12d
To predict the distance at which the tread depth will be 2 millimeters, we need to solve the equation:
2 = 8 - 0.12d
Let's solve for "d":
0.12d = 8 - 2
0.12d = 6
d = 6 / 0.12
d = 50
Therefore, the tread depth will be 2 millimeters after driving 50,000 miles.
To write an equation that gives the tread depth as a function of the distance driven, let's assume that "x" represents the distance driven in thousands of miles and "y" represents the tread depth in millimeters.
We are given that the tread depth decreases 0.12 millimeter per thousand miles driven. Therefore, we can subtract 0.12x from the initial tread depth of 8 millimeters to find the tread depth at any given distance.
The equation representing the relationship between the distance driven and the tread depth is:
y = 8 - 0.12x
To predict the distance at which the tread depth will be 2 millimeters, we can substitute y = 2 into the equation and solve for x:
2 = 8 - 0.12x
Rearranging the equation, we get:
0.12x = 8 - 2
0.12x = 6
Dividing both sides of the equation by 0.12, we find:
x = 6 / 0.12
x = 50
Therefore, the tread depth will be 2 millimeters after driving a distance of 50,000 miles.
depth=8mm-.12x where x is thousands of miles
2=8-.12x
x=6/.12=50 ?