Answer :
Answer:
t is between 0.47 seconds and 4.02 seconds
Step-by-step explanation:
Given
[tex]Inequality: -4.9t^2+22t+0.75>10[/tex]
Required
Determine the values of t
[tex]-4.9t^2+22t+0.75>10[/tex]
Subtract 10 from both sides
[tex]-4.9t^2+22t+0.75 - 10 >10 - 10[/tex]
[tex]-4.9t^2+22t-9.25 >0[/tex]
Multiply through y -1
[tex]4.9t^2-22t+9.25 <0[/tex]
Solve t using quadratic formula:
[tex]t = \frac{-b \±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 4.9[/tex]
[tex]b = -22[/tex]
[tex]c = 9.25[/tex]
So, we have:
[tex]t = \frac{-(-22) \±\sqrt{(-22)^2 - 4*4.9*9.25}}{2 * 4.9}[/tex]
[tex]t = \frac{22 \±\sqrt{484 - 181.3}}{9.8}[/tex]
[tex]t = \frac{22 \±\sqrt{302.7}}{9.8}[/tex]
[tex]t = \frac{22 \±17.40}{9.8}[/tex]
Split the equation
[tex]t = \frac{22 + 17.40}{9.8}[/tex] or [tex]t = \frac{22 - 17.40}{9.8}[/tex]
[tex]t = \frac{39.4}{9.8}[/tex] or [tex]t = \frac{4.6}{9.8}[/tex]
[tex]t = \frac{39.4}{9.8}[/tex] or [tex]t = \frac{4.6}{9.8}[/tex]
[tex]t = 4.02[/tex] or [tex]t = 0.47[/tex]
Hence; the range is
[tex]0.47 < t <4.02[/tex]