Chapter 1.10, Problem 45E

To determine

To Find: A mathematical model for the verbal statement.

Answer to Problem 45E

The mathematical model of verbal statement is $F=\frac{kg}{r^2}$ .

Explanation of Solution

Given information:

‘F’ varies directly as ‘g’ and inversely as $r^2$

Concept and Formula Used:

Direct Variation: It is the relationship between two variable where one variable changes according to other directly at constant rate of vice versa.

Inverse Variation: It is the relationship between two variable where one variable changes in opposite direction of other at constant rate of vice versa.

Calculation:

The given statement is F’ varies directly as ‘g’ and inversely as $r^2$

The statement is mathematically represented as

  $F\propto g\&F\propto \frac{1}{r^2}$

Combining the two equations

  $F\propto \frac{g}{r^2}$

Let ‘k’ be the proportionality constant

Then

  $F=\frac{kg}{r^2}$

Conclusion:

The mathematical model of verbal statement is $F=\frac{kg}{r^2}$ .