Chapter 4.1, Problem 39IP

a.

To determine

Find the minimum area of each playing field.

Answer to Problem 39IP

The minimum area is $36,400\text{sq}\text{.ft}\text{.}$

Explanation of Solution

Calculation:

Calculate each power and multiply them.

Field hockey:

  $\begin{array}{l}{2}^6\cdot {10}^3\\ =2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 10\cdot 10\cdot 10\\ =64.1000\\ =64,000\text{sq}\text{.ft}\end{array}$

Man’s lacrosse:

  $\begin{array}{l}{3}^2\cdot 7\cdot {10}^3\\ =3\cdot 3\cdot 7\cdot 10\cdot 10\cdot 10\cdot \\ =9\cdot 7\cdot 1,000\\ =63,000\text{sq}\text{.ft}\end{array}$

Women’s soccer:

  $\begin{array}{l}{2}^4\cdot 5^2\cdot 7\cdot 13\\ =2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 5\cdot 7\cdot 13\\ =16\cdot 25\cdot 7\cdot 13\\ =36,400\text{sq}\text{.ft}\text{.}\end{array}$

Thus the minimum area is $36,400\text{sq}\text{.ft}\text{.}$

b.

To determine

Order the areas from least to greatest.

Answer to Problem 39IP

The areas from least to greatest is $36400<63000<64000$

Explanation of Solution

Calculation:

Order from least to greatest have field hockey, Men’s lacrosse, Women’s soccer.

  $36400<63000<64000$

Thus, the areas from least to greatest is $36400<63000<64000$

c.

To determine

How much the area of a field hockey field than the area of a men’s lacrosse field.

Answer to Problem 39IP

The field hockey field is $1000$ square feet larger than the men’s lacrosse field.

Explanation of Solution

Calculation:

Subtract men’s lacrosse from field hockey,

  $64000-63000=1000$

Thus the field hockey field is $1000$ square feet larger than the men’s lacrosse field.