SOLUTION: When a softball player swings a bat, the amount of energy E(t), in joules, that is transferred to the bat can be approximated by the function E(t) = −279.67t2 + 82.86t wher

Algebra ->  Inequalities -> SOLUTION: When a softball player swings a bat, the amount of energy E(t), in joules, that is transferred to the bat can be approximated by the function E(t) = −279.67t2 + 82.86t wher      Log On


   

Question 1129339: When a softball player swings a bat, the amount of energy E(t), in joules, that is transferred to the bat can be approximated by the function
E(t) = −279.67t2 + 82.86t
where 0 ≤ t ≤ 0.3 and t is measured in seconds. According to this model, what is the maximum energy of the bat? Round to the nearest tenth of a joule.____joule
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

E%28t%29 is just a parabola. I'm sure you know how to find the vertex, where E%28t%29 is a maximum.
E%28t%29+=+-279.67t%5E2+%2B+82.86t
where 0 ≤ t ≤ 0.3
E%28t%29+=+-279.67t%5E2+%2B+82.86t......complete square to get vertex form
E%28t%29+=+-279.67%28t%5E2+%2B%28+82.86%2F-279.67%29t%2Bb%5E2%29-279.67%28-b%5E2%29
E%28t%29+=+-279.67%28t%5E2+-0.2962778t%2Bb%5E2%29-279.67%28-b%5E2%29
b=0.2962778%2F2=0.148139
E%28t%29+=+-279.67%28t%5E2+-0.2962778t%2B0.148139%5E2%29-279.67%28-0.148139%5E2%29
E%28t%29+=+-279.67%28t+-0.148139%29%5E2%2B6.1374
max ate vertex: (t, E%28t%29)=(0.148139, 6.1374)
so, E%28t%29=6.1374, round to the nearest tenth of a joule:
6.1 joule