Question

Consider the equation an^2 = 182 where a is any number between 2 and 5 and n is a positive interger. What are the possible values of n?

Answer 1

Step-by-step explanation:

an² = 182

When a = 2, n² = 182/2 = 91, n = 9.539...

When a = 5, n² = 182/5 = 36.4, n = 6.033...

Since 2 <= a <= 5, we have 6.033 <= n <= 9.539.

Therefore our possible values of n are 7, 8 and 9.

Answer 2

The possible values of n are 7, 8, 9

The given equation is:

an²  =  182

Make n the subject of the formula:

$n^2=\frac{182}{a} \\n = \sqrt{\frac{182}{a}}$

Let us consider the minimum and maximum values of a:

when a = 2

$n = \sqrt{\frac{182}{2}}\\n = \sqrt{91} \\n = 9.54$

When a = 5

$n = \sqrt{\frac{182}{5}}\\n = \sqrt{36.4} \\n = 6.03$

We can conclude that 6.03 < n < 9.54

Since n is an integer, the possible values of n are 7, 8, 9

Learn more here: https://brainly.com/question/15816805