Answer:
She shot a dangerous ball.
Step-by-step explanation:
According to the statement, we must prove that [tex]h(t) < 1\,m[/tex] for all value [tex]t[/tex]. We know that height of the ball ([tex]h(t)[/tex]), measured in metres, is represented by the following function:
[tex]h(t) = -5\cdot t^{2}+10\cdot t[/tex] (Eq. 1)
Where [tex]t[/tex] is the time, measured in seconds.
Which means that following inequation must be met:
[tex]-5\cdot t^{2}+10\cdot t < 1[/tex]
[tex]-5\cdot t^{2}+10\cdot t -1 < 0[/tex]
[tex]5\cdot t^{2}-10\cdot t +1 > 0[/tex]
[tex](t-1.894)\cdot (t-0.106) > 0[/tex]
From Algebra we know that product of either two positive numbers or two negative numbers is equal to a positive number, meaning that solution of inequation is:
[tex]0\,s \leq t < 0.106\,s[/tex] and [tex]t> 1.894\,s[/tex]
By graphing the give
Which means that ball is a dangerous ball at [tex]0.106\,s\leq t \leq 1.894\,s[/tex].
Lastly, we present the graph of the function as attachment.
