Question

For each planet in a solar​ system, its year is the time it takes the planet to revolve around the center star. The formula Upper E=0.2 x^3/2 models the number of Earth days in a​ planet's year,​ E, where x is the average distance of the planet from the center​ star, in millions of kilometers. There are approximately 686.3 Earth days in the year of Planet Upper D. What is the average distance of Planet Upper D from the center​ star?

Answer 1

Answer: 227.5*10^6 km or 227.5 million km

Explanation:

x^3/2*.02=686.3

686.3/.2=x^3/2*.2/.2

x^3/2=3431.5

x=227.50415642

Answer 2

The average distance of Planet Upper D from the center​ star is 227.5 millions of kilometers (227.5 × 10^6 kilometers)

Explanation:

* Lets explain information to solve the problem

- x is the average distance of the planet from the center​ star, in millions

of kilometers

- The formula of Earth days in the year of Planet is 0.2 x^(3/2)

- The Earth days in the year of Plant D is approximately 686.3

* Lets solve the problem

∵ The number of Earth days in a planet's year = 0.2 x^(3/2)

∵ The Earth days in the year of Plant D is approximately 686.3

- Lets substitute this value in the formula

∴ 686.3 = 0.2 x^(3/2) ⇒ divide both sides by 0.2

∴ 686.3/0.2 = 0.2/0.2 x^(3/2)

∴ 3431.5 = x^(3/2)

- We can use this rule to solve the equation

# If x^n = a, where a is a constant, then x = a^(1/n)

that means we reciprocal the power and take it to the other side

∴ x = (3431.5)^(2/3)

- Now use your calculator to find the answer

∴ x ≅ 227.5

* The average distance of Planet Upper D from the center​ star is

227.5 millions of kilometers (227.5 × 10^6 kilometers)