Question

this is a multi-part item. 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 formula $d = \sqrt{\frac{3h}{2}}, h \geq 0$, with $d$ being the distance they can see in miles and $h$ being their eye-level height in feet. $\sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}}$ $\sqrt{\frac{3(256)}{2}} - \sqrt{\frac{3(400)}{2}}$ $\sqrt{\frac{3(400)}{2}} + \sqrt{\frac{3(256)}{2}}$

Explanation:

Step1: Find Adam's distance

Using the formula \( d = \sqrt{\frac{3h}{2}} \), for Adam \( h = 400 \), so his distance is \( \sqrt{\frac{3(400)}{2}} \).

Step2: Find Pam's distance

For Pam \( h = 256 \), so her distance is \( \sqrt{\frac{3(256)}{2}} \).

Step3: Find the difference

To find how much farther Adam can see, subtract Pam's distance from Adam's distance: \( \sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}} \).

Answer:

\(\boldsymbol{\sqrt{\frac{3(400)}{2}} - \sqrt{\frac{3(256)}{2}}}\) (the first option's expression)