We are given the equation:
[tex]d(x)=\sqrt{\frac{3x}{2}}[/tex]
Where x is the height over the sea level, where d is in miles, and x in feet. We want to know the value of the function at x = 18 feet. Thus:
[tex]d(18)=\sqrt{\frac{3\cdot18}{2}}[/tex]
We can now simplify by dividing 18 by 2:
[tex]d(18)=\sqrt{3\cdot9}[/tex]
Now, using properties of radicals:
[tex]d(18)=\sqrt{3}\cdot\sqrt{9}=3\sqrt{3}[/tex]
The answer in simplified radical form is:
[tex]d(18)=3\sqrt{3}\text{ }miles[/tex]
Using the calculator, we can find the answer to the nearest tenth of a mile d(18)= 5.2 miles
