Two rocks are lauched straight up in the air. The height of Rock A is gived by the function \(f\), where \(f( t) = 4+ 30t- 16t^ 2\). The height of Rock B is given by \(g\), where \(g( t) = 5 + 20t - 16t^ 2\). In both function, \(t\) is time measured in seconds and height is measured in feet.

a. determine which rock hits the ground first.

b. Rock A, modeled by f(t) hits the ground at about ____ seconds.

c. Rock B, modeled by g(t) hits the ground at about ____ seconds.

Mei and Anju are sitting next to each other on different horses on a carousel. Mei's horse is \(3\) meters from the center of the carousel. Anju's horse is \(2\) meters from the center. After one rotation of the carousel, how many more meters has Mei traveled than Anju?

\(\pi \) more meters 

\(2 \pi \) more meters 

\(4 \pi \) more meters 

\(5 \pi \) more meters 

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp's incline? 

\(\frac { 1 } { 3 } \) inch up per foot across 

\(\frac { 1 } { 2 } \) inch up per foot across 

2 inches up per foot across 

3 inches up per foot across 

Purchase \(6\) new cars - \(\$ 18,990\) each less an \(8 \% \) fleet discount. 

Driver wages (1 driver per new vehicle) - $45,000 salary. 

Fuel/Maintenance - $8,500 per vehicle, per year. 

Total Cost after 3 years: $

A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed? 

A. \(\frac { 6,000 } { 3 x - 10 } \) 

B. \(6,000 ( 3 x - 10 ) \) 

C. \(\frac { 1,000 } { x } + \frac { 5,000 } { 2 x - 10 } \) 

D.\(\frac { 1,000 } { x } + \frac { 5,000 } { 2 x } - 10\)