the equation d=1.2 radical h , gives the distance ,d, in miles a person can see to the horizen from a hieght ,h, in feet.( hint: 1 mile =5,280 ft. A) solve the eqaution for h . B)longs peak in the longs national parkis 14,255 feet in elevation . How far can you see the horizen from the top of longs peak?
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A) To solve the equation d = 1.2√h for h, we need to isolate h on one side of the equation. Let's go through the steps:
1. Start with the equation: d = 1.2√h.
2. Divide both sides of the equation by 1.2: d/1.2 = √h.
3. Square both sides of the equation to eliminate the square root: (d/1.2)² = (√h)².
4. Simplify the equation: (d²/1.44) = h.
So, you can see that the value of h (the height in feet) is equal to the square of d (the distance in miles), divided by 1.44.
B) Now, let's calculate how far you can see the horizon from the top of Longs Peak, which has an elevation of 14,255 feet.
1. Convert the elevation to miles: 14,255 ft ÷ 5,280 ft/mile = 2.7 miles (rounded to one decimal place).
2. Plug the value of d (2.7 miles) into the equation: h = (2.7)²/1.44.
3. Calculate: h = 7.29/1.44 = 5.04 (rounded to two decimal places).
Therefore, from the top of Longs Peak, you can see a distance of approximately 5.04 miles to the horizon.