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?

227.5*10^6 km or 227.5 million km

Step-by-step explanation:

x^3/2*.02=686.3

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

x^3/2=3431.5

x=227.50415642

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

Step-by-step 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)

first off what is to the power of eight? If its 12 then see part 1 is its the whole thing then see part 2.

Step-by-step explanation:

1. 5x+12^2=

5x+144=

x=28.8

2.( 5x+12)^2

    5x^2+12^2(cancel out the power of 2 since it has no effect on the expression)

    5x+12

     x=2.4