Question

Hello! I just need help with how to work this problem out

Answer 1

Explanation:

`88=0.2x^{(3)/(2)}\\x^{(3)/(2) } =(88)/(0.2) =440\\squaring\\x^3=440 * 440=193600\\taking~cuberoot\\x\approx 57.85\\x\approx 58 ~million~kilometers`

Answer 2

Rounded to the nearest million kilometers, the average distance of Mercury from the center star is approximately 58 million kilometers.

Explanation:

The average distance of Mercury from the center star can be determined using the formula E(x) = 0.2x^(3/2), where "E(x)" represents the number of Earth days in a planet's year and "x" represents the average distance of the planet from the center star in millions of kilometers. Given that the year of Mercury consists of approximately 88 Earth days, we need to find the corresponding average distance, "x."

Given that there are approximately 88 Earth days in the year of Mercury, we can set up the equation as follows:

⇒ E(x) = 0.2x^(3/2)

⇒ 88 = 0.2x^(3/2)

To find "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.2 and then raising both sides to the power of 2/3:

⇒ 88 = 0.2x^(3/2)

⇒ 440^(2/3) = x

∴ x ≈ 58 million km

Therefore, the average distance of Mercury from the center star is approximately 58 million kilometers.