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# graphing inequalities

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The height (in meters) of a shot cannonball follows a trajectory given by $h(t) = -4.9t^2 + 14t - 0.4$ at time $t$ (in seconds). As an improper fraction, for how long is the cannonball above a height of $6$ meters?

Apr 13, 2021

#1
+31586
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put '6' in for height in the equation given    ( which is a dome shaped parablola due to the negative coeeficient of t2)

6 = -4.9 t^2 + 14t - .4

0 = - 4.9t^2 + 14t  - 6.4          now use Quadratic Formula to calculate the two 't values

....the ball is above 6  between thes two values , so calculate the time between these two values of t

a = -4.9     b = 14      c = -6.4

$$t = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

Apr 13, 2021

#1
+31586
+2

put '6' in for height in the equation given    ( which is a dome shaped parablola due to the negative coeeficient of t2)

6 = -4.9 t^2 + 14t - .4

0 = - 4.9t^2 + 14t  - 6.4          now use Quadratic Formula to calculate the two 't values

....the ball is above 6  between thes two values , so calculate the time between these two values of t

a = -4.9     b = 14      c = -6.4

$$t = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

ElectricPavlov Apr 13, 2021