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 given information.
Let's assume the distance driven is represented by 'x' in thousands of miles.
Given that the tread depth decreases by 0.12 millimeters per thousand miles driven, we can calculate the decrease in tread depth as:
0.12 millimeters * x (thousands of miles) = 0.12x millimeters
Therefore, the equation that gives the tread depth as a function of the distance driven (in thousands of miles) is:
Tread Depth = 8 millimeters - 0.12x millimeters
Now, to predict the distance at which the tread depth will be 2 millimeters, we can set up the equation and solve for 'x':
2 millimeters = 8 millimeters - 0.12x millimeters
Rearranging the equation, we have:
0.12x millimeters = 8 millimeters - 2 millimeters
0.12x millimeters = 6 millimeters
Now, to solve for 'x', we divide both sides of the equation by 0.12:
x = 6 millimeters / 0.12 millimeters
x = 50
Therefore, the tread depth will be 2 millimeters after driving a distance of 50,000 miles.