The scale of a map says that 4 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?
What is the actual number of kilometers that is represented by 5 centimeters on the map?
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Ответ:

jakails828

14.05.2020

Mathematics

Same parameterization as in the provided link, which I'll reproduce correctly here:

$\mathbf s(u,v)=\langle u,3\cos v,3\sin v\rangle$

and this time $0\le u\le5$ and $\cos^{-1}\dfrac23\le v\le\dfrac\pi2$

We get the same surface element,

$\mathrm d\mathbf S=3\,\mathrm du\,\mathrm dv$

and the area is

$\displaystyle3\iint_{v=\cos^{-1}(2/3)}^{v=\pi/2}\int_{u=0}^{u=5}\mathrm du\,\mathrm dv=\dfrac{15\pi}2-15\cos^{-1}\dfrac23$

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The scale of a map says that 4 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 4 kilometers? What is the actual number of kilometers that is represented by 5 centimeters on the map? 3.2 (Just type the number into the text boxes.)