Mathematics, 02.01.2020 03:31 taryn1932
Miguel has started training for a race. the first time he trains, he runs 0.5 mile. each subsequent time he trains, he runs 0.2 mile farther than he did the previous time.
a) what is the arithmetic series that represents the total distance miguel has run after he has trained n times?
b) a marathon is 26.2 miles. what is the least number of times miguel must run for his total distance run during training to exceed the distance of a marathon?
Answers: 3
![(0.4+0.1n)n\ge 26.2\\ \\0.1n^2+0.4n-26.2\ge 0\\ \\n^2+4n-262\ge 0\\ \\D=4^2-4\cdot (-262)=16+1048=1064\\ \\n_{1,2}=\dfrac{-4\pm\sqrt{1064}}{2}=-2\pm \sqrt{266} \\ \\n\in (-\infty,-2-\sqrt{266}]\cup[-2+\sqrt{266},\infty)](/tpl/images/0439/5551/39275.png)
, the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon is -2+17=15
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Miguel has started training for a race. the first time he trains, he runs 0.5 mile. each subsequent...
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