In the national park, the distance between the base of two cliffs is 312 feet. The angle of elevation from the base of the shorter cliff to the top of the taller cliff is 35 degrees. The angle of elevation from the base of the taller cliff to the top of the shorter cliff is 27 degrees. The tops of the two cliffs are joined by a bridge of length x, as modeled below. What is the length of he bridge, x, to the nearest foot? Show your work and explain how you determined your answer. (Picture provided)

Step-by-step explanation:

The domain of a function is the set of elements for which the function is defined. In other words, the domain is the range of values ​​of x for which the function exists, that is, it has a result.

"x" in this case represents the number of miles traveled by taxi. If the passenger has enough money to travel a maximum of 20 miles, the domain will be:

Domain = {0 ≤ x ≤ 20}

On the other hand, the image is the range of values ​​of the function for which there is a value of x. In other words, it is the set of values ​​of the variable "y" that is obtained when evaluating in the function all the possible values ​​of x.

In this case the function "y" is evaluated at both ends to determine the range of variation of the image:

In x=0 → y=3.5*0 + 2.8 → y= 2.8

In x=20 → y=3.5*20 + 2.8 → y= 72.8

So,the range of the function is between $2.8 and $72.8

Range = {2.8 ≤ y ≤ 72.8}