• Go over homework
• Notes: (need book and calculator)
– Modeling
• Homework

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 of the object, and s o is the initial vertical velocity is its initial height.

Page 184: Number 61 a) s
0
= 83 ft; v
0
=92 ft/sec h
 s(t) = -½ (32) t 2 + 92 t + 83 = -16 t 2 + 92 t +83

92

2.875
k
 
16(2.875)
2   
215.25
So maximum height is 215.25 ft.
b) s(t) = 0 (use quadratic formula)
6.543 sec c) v(t) = -32 t + 92 v (6.543) = -32(6.543) + 92 = -117.371 ft/sec

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

• Pg. 184: 58, 62, 63