Suppose that the functions \( u \) and \( w \) are defined as follows. 

\( u ( x ) = 2 x \) 

\( w ( x ) = x ^ { 2 } + 1 \) 

Find the following. 

\( ( w \circ u ) ( 2 ) = \) 

\(( u \circ w ) ( 2 ) = \) 

The third \(( 3^ { rd} ) \) and seventh \(( 7^ { th} ) \) terms of an arithmetic sequence are seven \(( 7 ) \) and fifteen \(( 15 ) \) respectively. i. Write two linear equations showing the relationships between the terms and the first term \(a\) and the common difference \(d\) . [ \(2\) marks ] ii. Solve the equations ( part i) for the first term \(a\) and the common difference \(d\) . iii. Using the values derived for \(a a d\) determine the sum of the first one hundred \(( 100 ) \) terms of the sequence. 

Let \(U = \{ \text { all sode pops} \} ; A = \{ \text { all diet sode pops} \} ; B = \{ \text { all cola soda pops} \} ; C = \{ \text { all sode pops in cans} \} ; \text { and } D = \{ \text { all caffeine- free soda pops} \} .\) Describe the given set in words. A' \(\cap \) C Select one: a. All non-diet soda pops and all soda pops in cans b. All non-diet soda pops in cans c. All diet soda pops in cans d. All diet soda pops and all soda pops in cans Let \(U = \{ \) all soda pops \(\} ; A = \{ \) all diet soda pops \(\} ; B = \{ \) all cola soda pops \(\} ; C = \{ \) all soda pops in cans \(\} \) ; and \(D = \{ \) all caffeine-free soda pops \(\} \) . Describe the given set in words. 

\(A ^ { \prime } \cap C\) 

Select one:

 a. All non-diet soda pops and all soda pops in cans 

b. All non-diet soda pops in cans 

c. All diet soda pops in cans 

d. All diet soda pops and all soda pops in cans 

Solve the system. Use any method you wish. 

\(x + y + 2 = 0     \)       (1)

\(x^ 2 + y^ 2 + 4y - 3x = - 4\)        (2)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 

A. The solution set is \(\{ \} \) .

    (Simplify your answer. Type an ordered pair. Type exact answers, using radicals as needed. Use a comma to separate answer as needed.)

B. There is no solution. 

9.5 Solve Applications of Quadratic Equations 

Question \(13\) 

An rock is thrown downward from a platform that is \(158\) feet above ground at \(75\) feet per second. Use the projectile formula \(h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \) to determine when the rock hit the ground. [Recall that \(v _ { 0 } \) is the initial velocity of the object and \(h _ { 0 } \) is the inital height of the object.]

Answer: The rock will hit the ground after \(\square \)

Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.

Explain why the function is discontinuous at the given number a. (Select all that apply.) 

\(f ( x ) = \{ \begin{array} { l l } { \frac { x ^ { 2 } - 2 x } { x ^ { 2 } - 4 } } & { \text { if } x \neq 2 } \\ { 1 } & { \text { if } x = 2 } \end{array} a = 2\) 

\(\square \lim _ { x \rightarrow 2 ^ { + } } f ( x ) \) and \(\lim _ { x \rightarrow 2 ^ { - } } f ( x ) \) are finite, but are not equal. 

\(\square \lim _ { x \rightarrow 2 } f ( x ) \) does not exist. 

\(\square f ( 2 ) \) is undefined. 

\(\square f ( 2 ) \) is defined and \(\lim _ { x \rightarrow 2 } f ( x ) \) is finite, but they are not equal. 

\(\square \) none of the above