The fuel of a rocket is launched is given by -x^2 - 140x +2000. During what period of time is the mass of the fuel greater than 500t?

1 Answer
Jun 19, 2018

The time period is:

0" s" <= x < 10" s"

Explanation:

I am assuming that the function gives the weight of the fuel (in tons) and that the time variable x has the domain x>= 0.

w(x) = -x^2 - 140x +2000, x >=0

Please observe that at x = 0 the weight of the fuel is 2000" tons":

w(0) = -0^2 - 140(0) +2000

w(0) = 2000" tons"

Let's find the time where the weight of the fuel is 500" tons":

500 = -x^2 - 140x +2000, x >=0

0 = -x^2 - 140x +1500, x >=0

0 = x^2 + 140x -1500, x >=0

Factor:

0 = (x-10)(x+150), x>=0

Discard the negative root:

x = 10" s"

The time period is:

0" s" <= x < 10" s"