91Ó°ÊÓ

Two model rockets are launched at a gathering of the National Association of Rocketry (NAR: www.nar.org). Frank's Apollo II motor burns out at a height of \(500 \mathrm{m},\) at which point the rocket has a velocity of 88.2 meters per second (m/sec). His rocket's height in meters, \(t\) sec after engine burnout, is given by \(f(t)=500+88.2 t-4.9 t^{2}\) Gwen's Icarus Alpha motor burns out at a height of \(600 \mathrm{m}\) at which point the rocket has a velocity of \(78.4 \mathrm{m} / \mathrm{sec} .\) Her rocket's height in meters, \(t\) sec after burnout, is given by \(g(t)=600+78.4 t-4.9 t^{2}\). Use the result from Exercise 7 to find the maximum height of Frank's rocket. This occurs when \(v=0\).

Evaluate the following limits using direct substitution, if possible. If not possible, state why. $$\lim _{x \rightarrow 2} \frac{x^{2}}{5 x-2}$$

Use Heron's formula to find the area of a triangle with sides \(a=5\) in. \(b=8\) in. \(c=9\) in. rounded to two decimal places.

(2.5) If \(p(x)=2 x^{2}-x-3,\) in what intervals is \(p(x) \leq 0 ?\)