the time x (in days), that it takes a planet to revolve around the sun can be approximated by the equation x=0.407√(d^3),where d is the mean distance of the planet from the sun in millions of miles. It takes Venus approximately 226 days to complete one revolution of the sun. To the nearest million miles, what is the mean distance of Venus from the sun?
Just use the formula provided.
226 = 0.407*d^(3/2)
555.3 = d^(3/2)
555.3^(2/3) = d
d = 67.56 (million miles)
That rounds to 68.
To find the mean distance of Venus from the sun, we can rearrange the equation x = 0.407√(d^3) to solve for d.
Given that x = 226 (the time it takes Venus to complete one revolution), we can substitute this value into the equation:
226 = 0.407√(d^3)
To solve for d, we need to isolate it on one side of the equation. First, we divide both sides of the equation by 0.407:
226 / 0.407 = √(d^3)
Now, let's square both sides of the equation to eliminate the square root:
(226 / 0.407)^2 = d^3
Calculating the left side of the equation:
(226 / 0.407)^2 ≈ 14295.32
Therefore, we have:
14295.32 = d^3
Now, we need to find the cube root of both sides to solve for d:
∛(14295.32) ≈ 24.03
So, the mean distance of Venus from the sun is approximately 24 million miles (rounded to the nearest million miles).