Question 1208014
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Answer: <font color=red>36 million miles</font> (approximate)


Explanation


T = number of days
d = average distance, in millions of miles, the certain planet is from the sun


We can paraphrase the info in the instructions to say:
"Square of T varies directly with the cube of d"
and gives this equation
T^2 = k*d^3
for some constant of variation k.
Why c isn't used instead of k, I'm not sure, but this is common convention used in many textbooks. 


On Earth there are roughly 365 days in a year. 
Of course the reality is a bit more complicated when considering leap years, but I'll try to keep things relatively simple. 
T = 365 pairs up with d = 93
Use these values to find k.
T^2 = k*d^3
365^2 = k*93^3
k = (365^2)/(93^3)
k = 0.165629192013 approximately



We'll use that k value, along with T = 88 to find its paired d value for the planet Mercury.
T^2 = k*d^3
88^2 = 0.165629192013*d^3
7744 = 0.165629192013*d^3
d = cubeRoot( 7744/0.165629192013 )
d = ( 7744/0.165629192013 )^(1/3)
d = 36.025456026483 approximately
d = <font color=red>36</font> 
The average distance from the Sun to Mercury is <font color=red>roughly 36 million miles</font>.


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This is entirely optional, but with science based questions, I find it good practice to verify with reputable sources. 
<a href="https://science.nasa.gov/mercury/facts/">https://science.nasa.gov/mercury/facts/</a>
Quote from the page: "From an average distance of <font color=red>36 million miles</font> (58 million kilometers), Mercury is 0.4 astronomical units away from the Sun."
Notes: 
AU = astronomical units
1 AU = 93 million miles approximately
0.4 AU = 0.4*(93 million miles) = 37.2 million miles, which is fairly close to the 36 mentioned.
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