Question 1182154
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You can use a graphing tool such as GeoGebra or Desmos to graph {{{y = 40-5x-5x^2}}} (note I'm using x in place of t)


Then click on the location where the curve crosses the x axis to determine the coordinates of that point. The location is approximately (2.372, 0)
You'll only worry about cases when x > 0.


Desmos Link
<a href = "https://www.desmos.com/calculator/hlyqda56a1">https://www.desmos.com/calculator/hlyqda56a1</a>
That's the graph I set up. It's basically a parabola that's upside down.


The x coordinate of the x intercept is what we want. The 2.372 rounds to <font color=red>2.37</font> which is the only answer.


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If you're not allowed to use a graphing tool, then the quadratic formula is the next best thing


y = 40 - 5x - 5x^2
y = -5x^2 - 5x + 40
We have something in the form y = ax^2+bx+c where
a = -5
b = -5
c = 40


Those three values are plugged into the quadratic formula below

{{{x = (-b+sqrt(b^2-4ac))/(2a)}}} or {{{x = (-b-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-5)+sqrt((-5)^2-4(-5)(40)))/(2(-5))}}} or {{{x = (-(-5)-sqrt((-5)^2-4(-5)(40)))/(2(-5))}}}


{{{x = (5+sqrt(825))/(-10)}}} or {{{x = (5-sqrt(825))/(-10)}}}


{{{x = (5+28.7228132326901)/(-10)}}} or {{{x = (5-28.7228132326901)/(-10)}}}


{{{x = (33.7228132326901)/(-10)}}} or {{{x = (-23.7228132326901)/(-10)}}}


{{{x = -3.37228132326901}}} or {{{x = 2.37228132326901}}}


{{{x = -3.372}}} or {{{x = 2.372}}}


We ignore the negative x value because we cannot have a negative time value. The only practical solution is roughly {{{x = 2.372}}} which rounds to <font color=red>2.37</font> as we found earlier.


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Answer: <font color=red>2.37</font>
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