Question

during the summer heat, a 6-mi bridge expands 6 ft in length. assuming the bulge occurs straight up the middle, how high is the bulge? select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. using radicals, b is exactly. the b, up to three decimal places, is approximately. b. the b, is exactly. no approximation is necessary.

Explanation:

Step1: Convert units

Since \(1\) mile \( = 5280\) feet, the original length of the bridge \(L=6\) miles \(=6\times5280 = 31680\) feet. After expansion, the new length is \(L'=31680 + 6=31686\) feet. Half - length of the original bridge \(a=\frac{31680}{2}=15840\) feet, and half - length of the expanded bridge \(c=\frac{31686}{2}=15843\) feet.

Step2: Apply the Pythagorean theorem

Let the height of the bulge be \(b\). According to the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), so \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 15840\) and \(c = 15843\) into the formula:

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Answer:

A. Using radicals, \(b\) is exactly \(\sqrt{95049}\). The \(b\), up to three decimal places, is approximately \(308.300\).