Question

Recall that f(v) = 8.35v².6 with f(v) = w and that the lid weighs 8.7 pounds. Assume the tank can hold up to 40 gallons of water. What are the practical domain and range for the function f?

Answer 1

The practical domain for the function f is between 0 and 40 gallons, and the range is any positive value greater than or equal to 8.7 pounds (weight of empty tank)

Step-by-step explanation:

To find the practical domain and range for the function f, let's first understand what the function represents. The function f(v) = 8.35v².6 represents the weight, w, of a tank filled with water of volume v. The lid of the tank weighs 8.7 pounds, so the weight of the tank when empty is 8.7 pounds. The tank can hold up to 40 gallons of water, which is equivalent to approximately 151 liters. Now we can find the practical domain and range:

Domain: Since v represents the volume of water in the tank, the practical domain would be between 0 gallons (empty tank) and the maximum capacity of 40 gallons (full tank).

Range: The weight, w, of the tank with water can be any positive value greater than or equal to the weight of the empty tank (8.7 pounds).