Question

pam’s eye–level height is 256 feet above sea level and adam’s eye–level height is 400 feet above sea level. what expression shows how much farther adam can see to the horizon?
use the for $d = \sqrt{\frac{3h}{2}}$
$\bigcirc\quad \sqrt{\frac{3(256)}{2}} - \sqrt{\frac{3(400)}{2}}$
$\bigcirc\quad \sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}}$
$\bigcirc\quad \sqrt3{\frac{3(400)}{2}} + \sqrt{\frac{3(256)}{2}}$

Explanation:

Step1: Define distance for Adam

Substitute $h=400$ into $d=\sqrt{\frac{3h}{2}}$:
$d_{Adam} = \sqrt{\frac{3(400)}{2}}$

Step2: Define distance for Pam

Substitute $h=256$ into $d=\sqrt{\frac{3h}{2}}$:
$d_{Pam} = \sqrt{\frac{3(256)}{2}}$

Step3: Find difference in distances

Subtract Pam's distance from Adam's:
$d_{Adam} - d_{Pam} = \sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}}$

Answer:

$\boldsymbol{\sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}}}$ (the second option)