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?

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Answer 1 · 2018-06-19T00:07:45

The time period is:

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

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:

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

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