The independent variable in the image is the distance of the car from the midline (y=0), and the dependent variable is the angle that the camera must have with respect to the midline (y=0) in order to focus on the car. The relationship between the independent and dependent variables can be modeled using the following function:
where d is the distance between the camera and the car.
In the image, we are asked to model the angle that the camera must have with respect to the straight line that connects it to the road (y=0), so that for an arbitrary car moving down the driveway, and its position y with respect to y=0, the camera focuses on it at all times.
Independent variable: The independent variable is the distance of the car from the midline (y=0). We will use the symbol y to represent this variable, and the units are kilometers.
Dependent variable: The dependent variable is the angle that the camera must have with respect to the midline (y=0) in order to focus on the car. We will use the symbol θ to represent this variable, and the units are radians.
Relationship between the independent and dependent variables:
We can model the relationship between the independent and dependent variables using a mathematical function. One possible function is:
where d is the distance between the camera and the car.
This function works as follows:
The camera must be tilted downwards to focus on a car that is closer to the midline (y=0).
The camera must be tilted upwards to focus on a car that is further away from the midline (y=0).
The camera must be level to focus on a car that is directly in front of it.
We can use the table of measurements provided in the image to verify that this function works well. For example, when the car is 0.15 kilometers away from the midline, the camera must be tilted at an angle of 0.1 radians downwards to focus on it. This matches the value in the table.