Question

A tank with some water in it begins to drain. The function v ( t ) = 46 − 3.5 t determines the volume of the water in the tank (in gallons) given a number of minutes t since the water began draining. What is the vertical intercept of f ? What does your answer to part (a) represent? Select all that apply. The weight of the tank when it is empty. How many minutes it takes for all of the water to drain from the tank. The number of gallons of water in the tank when it starts draining. List all horizontal intercepts (or "roots") of f . What does your answer to part (b) represent? Select all that apply. The weight of the tank when it is empty. The number of gallons of water in the tank when it starts draining. How many minutes it takes for all of the water to drain from the tank.

Answer 1

Answer with Explanation:

Part a)

The volume of water in the tank as a function of time is plotted in the below attached figure.

The vertical intercept of the graph is 46.

Part b)

The vertical intercept represents the volume of water that is initially present in the tank before draining begins.

Part c)

To find the time required to completely drain the tank we calculate the volume of the water in the tank to zero.

$0=46-3.5t\\\\3.5=46\\\\\therefore t=\frac{46}{3.5}=13.143minutes$

Part d)

The horizontal intercept represents the time it takes to empty the tank which as calculated above is 13.143 minutes.