1. Today in Pre-Calculus Go over homework Notes: (need book and calculator) –Modeling Homework

2. Vertical Free Fall Motion The height s and vertical velocity v of an object in free fall are given by s(t) = -½ gt 2 + v 0 t + s 0 and v(t) = -gt + v 0 Where t is time (in seconds), g ≈32 ft/sec 2 ≈9.8m/sec 2 is the acceleration due to gravity, v 0 is the initial vertical velocity of the object, and s o is its initial height.

3. Example Page 184: Number 61 a)s 0 = 83 ft; v 0 =92 ft/sec s(t) = -½ (32)t 2 + 92t + 83 = -16t 2 + 92t +83 So maximum height is 215.25 ft. b)s(t) = 0 (use quadratic formula) 6.543 sec c)v(t) = -32t + 92 v(6.543) = -32(6.543) + 92 = -117.371 ft/sec

4. Example Number 59 a) Revenue = quantity  price R(x) = (26,000 – 1,000x)(0.50 + 0.05x) = 13,000 +800x – 50x 2 b) Graph it so you can see the max and x-intercept c) h = -800/(2  -50) = 8 So Revenue is maximized when x = 8 Price: 0.50 + 0.05(8)= $0.90 Revenue : 13,000 + 800(8) – 50(8) 2 = $16,200

5. Homework Pg. 184: 58, 62, 63