The time taken by the satellite to fall on the planet Mars is 8 hours.
Explanation:
Given that the satellite falls from the outer space onto Mars, its distance in miles from the planet is given by the formula,
[tex]d=-9t^2+776[/tex]
where t is the number of hours it has fallen.
We need to determine the time taken by the satellite to fall on the planet Mars when the satellite is 200 miles away from Mars.
To determine the number of hours taken by the satellite to fall on Mars, let us substitute [tex]d=200[/tex], we get,
[tex]200=-9 t^{2}+776[/tex]
Subtracting both sides of the equation by 776, we have,
[tex]-576=-9t^2[/tex]
Dividing both sides by -9, we get,
[tex]64=t^2[/tex]
Taking square root on both sides, we have,
[tex]t=8, t=-8[/tex]
The value of t cannot be negative.
Hence, [tex]t=8[/tex]
Therefore, the time taken by the satellite to fall on the planet Mars is 8 hours.
