For each planet in our solar system, its year is the entire time it takes the pl

Question

For each planet in our solar system, its year is the entire time it takes the planet to revolve once around the sun.
The formula E=0.3x^4/3


models the number of Earth days in a planet’s year, E, where x is the average distance of the planet from the sun, in millions of kilometers. Use the formula to solve the following problems:

a) We, of course, have 365 Earth days in our year. What is the average distance of the Earth from the sun? Explain how you would solve this problem. Use a calculator and round to the nearest million kilometers.

b) There are approximately 91 Earth days in the year of the planet Mercury. What is the average distance of Mercury from the sun? Explain how you would solve this problem. Use a calculator and round to the nearest million kilometers.

Explanation / Answer

So for (a), Since E is the number of days in the year, plug in 365 for E, and solve for x.
365 = 0.3x^4/3
365 = 0.3 3x4

365/0.3 =  3x4

(365/0.3)3 = x4

3(365/0.3)3 = x

Plug that into calc and round. (in km.)

Repeat for (b), but use 91 for E.

Therefore for (b), x = 3(91/0.3)3

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