1 Hàm Só Nào Sau đây Là Hàm Só Lè: A. Y=| - Gauthmath

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Question

Kaylib's eye-level height is 48 ft above sea level, and Addison's eye-level height is 85 1/3 ft above sea level. How much d=sqrt(frac 3h)2 farther can Addison see to the horizon? Use the formula , with d being the distance they can see in miles and h being their eye-level height in feet. sqrt(2) mi 2sqrt(2) mi 14sqrt(2) mi 28sqrt(2) miSHOW LESS163

Solution

user avatar imageAnswer The answer is **2\(\sqrt{2}\) mi**.ExplanationThe question asks to find the difference in the distance to the horizon that Addison can see compared to Kaylib, given their respective eye-level heights and the formula \(d=\sqrt{\frac{3h}{2}}\). This is a calculation-based question. Step 1: **Calculate Kaylib's horizon distance.** Kaylib's eye-level height is given as \(h_K = 48\) ft. Substitute this into the formula: \(d_K = \sqrt{\frac{3 \times 48}{2}} = \sqrt{\frac{144}{2}} = \sqrt{72}\) miles. Step 2: **Simplify Kaylib's horizon distance.** To simplify \(\sqrt{72}\), we find the largest perfect square factor of 72, which is 36. \(d_K = \sqrt{36 \times 2} = 6\sqrt{2}\) miles. Step 3: **Convert Addison's eye-level height to an improper fraction.** Addison's eye-level height is \(h_A = 85\frac{1}{3}\) ft. Convert this mixed number to an improper fraction: \(h_A = \frac{(85 \times 3) + 1}{3} = \frac{255 + 1}{3} = \frac{256}{3}\) ft. Step 4: **Calculate Addison's horizon distance.** Substitute Addison's eye-level height into the distance formula: \(d_A = \sqrt{\frac{3 \times \frac{256}{3}}{2}} = \sqrt{\frac{256}{2}} = \sqrt{128}\) miles. Step 5: **Simplify Addison's horizon distance.** To simplify \(\sqrt{128}\), find the largest perfect square factor of 128, which is 64. \(d_A = \sqrt{64 \times 2} = 8\sqrt{2}\) miles. Step 6: **Calculate the difference in horizon distances.** The question asks how much farther Addison can see. This is the difference between Addison's distance and Kaylib's distance: \(\text{Difference} = d_A - d_K = 8\sqrt{2} \text{ miles} - 6\sqrt{2} \text{ miles}\) \(\text{Difference} = (8-6)\sqrt{2} \text{ miles} = 2\sqrt{2} \text{ miles}\). The options provided are: - \sqrt{2}mi - 2\sqrt{2}mi - 14\sqrt{2}mi - 28\sqrt{2}mi Our calculated difference is \(2\sqrt{2}\) miles, which corresponds to the second option. Click to rate:62.5(255 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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