Question

question 30 1 pts if the geometric mean of a and 65 is 20√13, find the value of a. 76 73 80 66 none of these answers are correct.

Explanation:

Step1: Recall the geometric mean formula

The geometric mean of two numbers \(x\) and \(y\) is \(\sqrt{xy}\). Here, \(x = a\), \(y = 65\), and the geometric mean is \(20\sqrt{13}\). So, \(\sqrt{a\times65}=20\sqrt{13}\).

Step2: Square both sides of the equation

Squaring both sides gives \(a\times65=(20\sqrt{13})^2\). Since \((20\sqrt{13})^2 = 20^2\times(\sqrt{13})^2=400\times13 = 5200\), the equation becomes \(65a = 5200\).

Step3: Solve for \(a\)

Divide both sides of \(65a = 5200\) by \(65\), so \(a=\frac{5200}{65}=80\).

Answer:

80