Questions: For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula E=0.2 x^(2 / 2) models the number of Earth days in a planet's year E where x is the average distance of the planet from the distance of planet 0 from the center star.

For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula E=0.2 x^(2 / 2) models the number of Earth days in a planet's year E where x is the average distance of the planet from the distance of planet 0 from the center star.

Transcript text: For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula $\mathrm{E}=0.2 \mathrm{x}^{2 / 2}$ models the number of Earth days in a planet's year E where $x$ is the average distance of the planet from the distance of planet 0 from the center star.

Solution

Solution Steps

Step 1: Identify the given information

The problem provides the formula $ E = 0.2d^{3/2} $, where $ E $ is the number of Earth days in a planet's year, and $ d $ is the average distance of the planet from the center star in millions of kilometers. We are given that there are approximately 887 Earth days in the year of Planet D.

Step 2: Set up the equation

We need to find the average distance $ d $ of Planet D from the center star. Using the given formula and the value of $ E $: \[ 887 = 0.2d^{3/2} \]

Step 3: Solve for $ d $

First, isolate $ d^{3/2} $ by dividing both sides of the equation by 0.2: \[ d^{3/2} = \frac{887}{0.2} \] \[ d^{3/2} = 4435 \]

Next, solve for $ d $ by raising both sides to the power of $ \frac{2}{3} $: \[ d = (4435)^{\frac{2}{3}} \]