Question

Please answer this fast and here only​

Answer 1

Answer:

1) a) $r_{R,I} = 1150\,m$, b) $r_{R,II} = 3400\,m$, c) $r_{R,III} = 2750\,m$.

2) a) $r_{R,I} = 45,2\,km$, b) $r_{R, II} = 28,15\,km$, c) $r_{R,III} = 51,8\,km$.

Explanation:

The scale factor is defined by the following expression:

$n = \frac{r_{S}}{r_{R}}$ (1)

Where:

$n$ - Scale factor.

$r_{S}$ - Scale distance, in centimetres.

$r_{R}$ - Real distance, in centimetres.

1) If we know that $n = \frac{1}{50000}$, $r_{S,I} = 2,3\,cm$, $r_{S,II} = 6,8\,cm$ and $r_{S,III} = 5,5\,cm$, then the actual distances in metres are:

$r_{R,I} = \frac{r_{S,I}}{n}$

$r_{R,I} = \frac{2,3\,cm}{\frac{1}{50000} }$

$r_{R,I} = 115000\,cm$

$r_{R,I} = 1150\,m$

$r_{R,II} = \frac{r_{S,II}}{n}$

$r_{R,II} = \frac{6,8\,cm}{\frac{1}{50000} }$

$r_{R,II} = 340000\,cm$

$r_{R,II} = 3400\,m$

$r_{R, III} = \frac{r_{S, III}}{n}$

$r_{R,III} = \frac{5,5\,cm}{\frac{1}{50000} }$

$r_{R,III} = 275000\,cm$

$r_{R,III} = 2750\,m$

2) If we know that $n = \frac{1}{50000}$, $r_{S, I} = 90,4\,cm$, $r_{S, II} = 56,3\,cm$ and $r_{S,III} = 103,6\,cm$, then the actual distance in kilometres is:

$r_{R,I} = \frac{r_{S,I}}{n}$

$r_{R,I} = \frac{90,4\,cm}{\frac{1}{50000} }$

$r_{R,I} = 4520000\,cm$

$r_{R,I} = 45,2\,km$

$r_{R,II} = \frac{r_{S,II}}{n}$

$r_{R,II} = \frac{56,3\,cm}{\frac{1}{50000} }$

$r_{R,II} = 2815000\,cm$

$r_{R, II} = 28,15\,km$

$r_{R, III} = \frac{r_{S, III}}{n}$

$r_{R,III} = \frac{103,6\,cm}{\frac{1}{50000} }$

$r_{R,III} = 5180000\,cm$

$r_{R,III} = 51,8\,km$