Three rollers with diameter of \( 5 \) inches each (radius \( 2.5 \) inches) are placed on the ground. Two rollers diameter \( 4 \) inches (radius \( 2 \) inches) each are placed on top and a final \( 3 \) -inch diameter roller is placed on top. See diagram below. What is the overall height of this stack? Points \( A , B , C , D \) , \( E \) , and F are all the centres of their respective circles. NOTE: \( A , D \) and F are NOT in a line. 

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.

Write the given rate as a fraction in simplest form. Be sure to include the units in your answers. 

\(250\) points in \(100\) minutes 

Select the correct choice below and fill in the answer boxes to complete your choice. (Simplify your answer.) 

A. The rate written as a fraction in simplest form is \(\frac { \square \text { minutes} } { \square \text { points} } \) 

B. The rate written as a fraction in simplest form is \(\frac { \square \text { points} } { \square \text { minutes} } \)

Solve the following: 

1. In the geometric sequence \(2,6,18 , \ldots \) what is the \(9 ^ { \text { th} } \) term? 

2. In the geometric sequence \(- 3,6 , - 12 , \ldots \) what is the \(10^ { \text { th} } \) term? 

3. In the geometric sequence \(32,16,8 , \ldots \) find the \(12 ^ { \text { th} } \) term. 

4. In the geometric sequence \(- 3 / 8 , - 3 / 4 , - 3 / 2 , \ldots \) what is the \(8 ^ { \text { th} } \) term?

5. In the geometric sequence \(2 , - 10,50 , \ldots \) what is the \(7^ { \text { th} } \) term? 

6. In the geometric sequence \(- 1 / 3,1 / 6 , - 1 / 12 , \ldots \) what is the \(6^ { \text { th} } \) term? 

7 . In the geometric sequence \(5 , - 10,20 , \ldots \) what is the \(9^ { \text { th} } \) term? 

8 . In the geometric sequence \(6250,1250,250 , \ldots \) what is the \(8^ { \text { th} } \) term? 

9. In the geometric sequence \(1 / 2 , - 1 / 4,1 / 8 . \ldots \) what is the \(10^ { \text { th} } \) term?

10. In the geometric sequence \(81,54,36 , \ldots \) find the \(7^ { \text { th} } \) term. 

11 . In the geometric sequence \(2,4,8 , \ldots \) what is the \(8^ { \text { th} } \) term? 

12. What is the \(7^ { \text { th} } \) term of the geometric sequence \(3,6,12 , \ldots \) 

13. In the geometric sequence \(- 2 , - 6 , - 18\) , what is \(a_ 8\)? 

14. In the geometric sequence \(2 , - 10,50 , \ldots \) what is the \(7^ { \text { th} } \) term? 

15. What is the \(9^ { \text { th} } \) term of the geometric sequence \(- 1 / 19,1 / 3 , - 1 , \ldots \) ?

\(\left \{ \begin{array} { l } { a ( 1 ) = - 2 } \\ { a ( n ) = a ( n - 1 ) - 5 } \end{array} \right .\) 

Find the \(4^ { \text { th} } \)term in the sequence. 

Complete each conversion by using unit factors. Round to the nearest hundredth. Example: 

\(34 \frac { kg} { hour} = -\frac { punces} { minutes} \) 

1. \(25 \frac { kg} { hour} = \frac { ounces} { minutes} \)

2. \(9\frac { miles} { day} = \frac { meters} { hour} \)

3. \(20777\frac { cm^ 2} { hour} = \frac { in^ 2} { second} \)