Chapter 8.1, Problem 14PSA

a

To determine

To calculate:The arithmetic means and geometric mean of given pair i.e.8 and 50 and note which one is greater.

Answer to Problem 14PSA

Arithmetic mean is greater

Explanation of Solution

Given information Pair of number as 8 and 50

Formula used Arithmetic mean in between, A and B is $\frac{A+B}{2}$ and

Geometric mean in between A and Bis $\sqrt{A.B}$

Calculation

Arithmetic mean for the given pair of number

  $\begin{array}{l}=\frac{A+B}{2}\\ =\frac{8+50}{2}\\ =\frac{58}{2}\\ =29\end{array}$

Geometric mean for the pair of given numbers

  $\begin{array}{l}=\sqrt{A.B}\\ =\sqrt{5\times 80}\\ =\sqrt{400}\\ =20\end{array}$

Hence, Arithmetic mean is greater

b

To determine

To calculate:The arithmetic means and geometric mean of given pair i.e.6 and 12and note which one is greater.

Answer to Problem 14PSA

Arithmetic mean is greater

Explanation of Solution

Given information Pair of number as 6 and 12

Formula used Arithmetic mean in between, A and B is $\frac{A+B}{2}$ and

Geometric mean in between A and B is $\sqrt{A.B}$

Calculation:

Arithmetic mean for the given pair of number

  $\begin{array}{l}=\frac{A+B}{2}\\ =\frac{6+12}{2}\\ =\frac{18}{2}\\ =9\end{array}$

Geometric mean for the pair of given numbers

  $\begin{array}{l}=\sqrt{A.B}\\ =\sqrt{6\times 12}\\ =\sqrt{72}\\ =6\sqrt{2}\end{array}$

Hence, Arithmetic mean is greater