Chapter 8.2, Problem 38E

a.

To determine

To find: The name of waterfall that drops water from the highest point.

Answer to Problem 38E

Waterfall 1

Explanation of Solution

Given information:

The paths of water from three waterfalls are given below:

Waterfall 1 $h=-3.1d^2+4.8$   ..... (1)

Waterfall 2 $h=-3.5d^2+1.9$   ..... (2)

Waterfall 3 $h=-1.1d^2+1.6$   ..... (3)

Here, h gives the height (in feet) and d represents the horizontal distance (in feet) of the water.

First graph the three given functions by plotting the points as given in the tables below:

  

  

  

The required graph is:

  

From the above graph it is clear that, the waterfall which drops water from the highest point is waterfall 1.

b.

To determine

To find:The name ofwaterfall that follows the narrowest path.

Answer to Problem 38E

Waterfall 2

Explanation of Solution

Given information:

The paths of water from three waterfalls are given below:

Waterfall 1 $h=-3.1d^2+4.8$   ..... (1)

Waterfall 2 $h=-3.5d^2+1.9$   ..... (2)

Waterfall 3 $h=-1.1d^2+1.6$   ..... (3)

Here, h gives the height (in feet) and d represents the horizontal distance (in feet) of the water.

Calculation:

From part (a), the graph representing the above three functions is:

  

From the above graph it is clear that, the waterfall which follows the narrowest path is the waterfall 2.

c.

To determine

To find:The name of waterfall that sends water the farthest.

Answer to Problem 38E

Waterfall 3

Explanation of Solution

Given information:

The paths of water from three waterfalls are given below:

Waterfall 1 $h=-3.1d^2+4.8$   ..... (1)

Waterfall 2 $h=-3.5d^2+1.9$   ..... (2)

Waterfall 3 $h=-1.1d^2+1.6$   ..... (3)

Here, h gives the height (in feet) and d represents the horizontal distance (in feet) of the water.

Calculation:

From part (a), the graph representing the above three functions is:

  

From the above graph it is clear that, the waterfall which sends water the farthest. is the waterfall 3.