Question

Please answer this fast and here only​

Answer 1

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`.

Step-by-step explanation:

The scale factor is defined by the following expression:

`n = (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 = (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) = (r_(S,I))/(n)`

`r_(R,I) = (2,3\,cm)/((1)/(50000) )`

`r_(R,I) = 115000\,cm`

`r_(R,I) = 1150\,m`

`r_(R,II) = (r_(S,II))/(n)`

`r_(R,II) = (6,8\,cm)/((1)/(50000) )`

`r_(R,II) = 340000\,cm`

`r_(R,II) = 3400\,m`

`r_(R, III) = (r_(S, III))/(n)`

`r_(R,III) = (5,5\,cm)/((1)/(50000) )`

`r_(R,III) = 275000\,cm`

`r_(R,III) = 2750\,m`

2) If we know that
`n = (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) = (r_(S,I))/(n)`

`r_(R,I) = (90,4\,cm)/((1)/(50000) )`

`r_(R,I) = 4520000\,cm`

`r_(R,I) = 45,2\,km`

`r_(R,II) = (r_(S,II))/(n)`

`r_(R,II) = (56,3\,cm)/((1)/(50000) )`

`r_(R,II) = 2815000\,cm`

`r_(R, II) = 28,15\,km`

`r_(R, III) = (r_(S, III))/(n)`

`r_(R,III) = (103,6\,cm)/((1)/(50000) )`

`r_(R,III) = 5180000\,cm`

`r_(R,III) = 51,8\,km`