Question

The distance d, in miles, of the nth planet from the sun is given by the formula below.

d = 9,275,200[3(2n − 2) + 4]

To the nearest million miles, find the distance of Earth and the distance of Mars from the sun. Give each answer in scientific notation. (Round your answers to the nearest million miles.)
Earth
✕ 10
mi
Mars
✕ 10
mi

Answer 1

To find the distance of Earth and Mars from the sun using the given formula, we need to substitute the respective values of n into the equation and simplify the expression. Let's calculate them:

For Earth (n = 3, as it is the third planet from the sun):

d = 9,275,200[3(2n − 2) + 4]

d = 9,275,200[3(2*3 − 2) + 4]

d = 9,275,200[3(6 − 2) + 4]

d = 9,275,200[3(4) + 4]

d = 9,275,200[12 + 4]

d = 9,275,200[16]

d = 148,403,200

The distance of Earth from the sun is approximately 148,403,200 miles.

For Mars (n = 4, as it is the fourth planet from the sun):

d = 9,275,200[3(2n − 2) + 4]

d = 9,275,200[3(2*4 − 2) + 4]

d = 9,275,200[3(8 − 2) + 4]

d = 9,275,200[3(6) + 4]

d = 9,275,200[18 + 4]

d = 9,275,200[22]

d = 204,055,200

The distance of Mars from the sun is approximately 204,055,200 miles.

Therefore, the distances are as follows:

Earth: 1.48 ✕ 10^8 mi (148,000,000 miles)

Mars: 2.04 ✕ 10^8 mi (204,000,000 miles)