Answer:
1) a) [tex]r_{R,I} = 1150\,m[/tex], b) [tex]r_{R,II} = 3400\,m[/tex], c) [tex]r_{R,III} = 2750\,m[/tex].
2) a) [tex]r_{R,I} = 45,2\,km[/tex], b) [tex]r_{R, II} = 28,15\,km[/tex], c) [tex]r_{R,III} = 51,8\,km[/tex].
Explanation:
The scale factor is defined by the following expression:
[tex]n = \frac{r_{S}}{r_{R}}[/tex] (1)
Where:
[tex]n[/tex] - Scale factor.
[tex]r_{S}[/tex] - Scale distance, in centimetres.
[tex]r_{R}[/tex] - Real distance, in centimetres.
1) If we know that [tex]n = \frac{1}{50000}[/tex], [tex]r_{S,I} = 2,3\,cm[/tex], [tex]r_{S,II} = 6,8\,cm[/tex] and [tex]r_{S,III} = 5,5\,cm[/tex], then the actual distances in metres are:
[tex]r_{R,I} = \frac{r_{S,I}}{n}[/tex]
[tex]r_{R,I} = \frac{2,3\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,I} = 115000\,cm[/tex]
[tex]r_{R,I} = 1150\,m[/tex]
[tex]r_{R,II} = \frac{r_{S,II}}{n}[/tex]
[tex]r_{R,II} = \frac{6,8\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,II} = 340000\,cm[/tex]
[tex]r_{R,II} = 3400\,m[/tex]
[tex]r_{R, III} = \frac{r_{S, III}}{n}[/tex]
[tex]r_{R,III} = \frac{5,5\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,III} = 275000\,cm[/tex]
[tex]r_{R,III} = 2750\,m[/tex]
2) If we know that [tex]n = \frac{1}{50000}[/tex], [tex]r_{S, I} = 90,4\,cm[/tex], [tex]r_{S, II} = 56,3\,cm[/tex] and [tex]r_{S,III} = 103,6\,cm[/tex], then the actual distance in kilometres is:
[tex]r_{R,I} = \frac{r_{S,I}}{n}[/tex]
[tex]r_{R,I} = \frac{90,4\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,I} = 4520000\,cm[/tex]
[tex]r_{R,I} = 45,2\,km[/tex]
[tex]r_{R,II} = \frac{r_{S,II}}{n}[/tex]
[tex]r_{R,II} = \frac{56,3\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,II} = 2815000\,cm[/tex]
[tex]r_{R, II} = 28,15\,km[/tex]
[tex]r_{R, III} = \frac{r_{S, III}}{n}[/tex]
[tex]r_{R,III} = \frac{103,6\,cm}{\frac{1}{50000} }[/tex]
[tex]r_{R,III} = 5180000\,cm[/tex]
[tex]r_{R,III} = 51,8\,km[/tex]
