Re: [分享] 言之有物的廢文範例一
※ 引述《ChinHuiTsao (老兵不死只是黑掉)》之銘言：
: An 8-foot-high fence is located 1 foot from a building. Determine the length
: of the shortest ladder that can be leaned against the building and touch the
: top of the fence.
: 葉 出國前練習吧xdd
根據我google的結果
The ladder, ground, fence, and building make a right triangle inside a
similar triangle.
If the base of the ladder is a distance x from the fence, then it's a
distance (x+1) from the building.
Because the triangles are similar, the height of the top of the ladder is:
h / (x+1) = 8 / x
h = 8(x+1) / x
And the length of the ladder is
L^2 = (x+1)^2 + (8(x+1)/x)^2
L = √(x2 + 2x + 65 + 128/x + 64/x^2)
Minimize this using calculus.
(To make things easier, you can in fact minimize L^2, if you can justify
that that also minimizes L.)
x = 4 is the only positive real solution. Making h = 5 and L = √41
話說我在康橋微積分都考一百
不過是基礎的 科科
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