The initial height of the diving board is\( 5 m \). The time at which Jeremiah reaches his maximum height is the\( x \)-coordinate of the vertex.

\(x = \frac { - b } { 2 a } \)

\( x = \frac { \square } { 2 ( \square ) } \)

\( x = \frac { - 8 } { - 9.8 } \)

\( x = 0.82 sec\)

It took Jeremiah\( .82 \)seconds to reach his maximum height.

The maximum height was reached by Jeremiah at\( \square \)seconds. The maximum height is the\( y \)-coordinate of the vertex.

\(h ( t ) = - 4.9 x ^ { 2 } + 8 x + 5 \)

\( h ( 0.82 ) = - 4.9 ( 0.82 ) ^ { 2 } + 8 ( 0.82 ) + 5 \)

\( h ( 0.82 ) = - 3.29 + 6.56 + 5 \)

\( h ( 0.82 ) = 8.27 m\)

The maximum height reached by Jeremiah was\( 18 m \).

An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of\( 8 \)one-bedroom apartments and the data are shown. Complete parts (a) through (f).

Given that\( \vec { A } = 3 \hat { \imath } + 6 \hat { \jmath } , \vec { B } = 2 \hat { \imath } + 6 \hat { k } \), and\( \vec { C } = 3 \hat { \imath } + 2 \hat { \jmath } + \hat { k } \),

(a) determine\( \vec { A } \cdot \vec { B } \); (\( 2 \)marks)

(b)etermine the angle between\( \vec { A } \)and\( \vec { C } \). State whether the angle is an acute (\( 6 \)marks)

Find the partial fraction decomposition for the rational expression.

\( \begin{array} { l} \frac { 8 x+ 36} { ( x+ 6) ( x+ 2) } \\ \\ \frac { 8 x+ 36} { ( x+ 6) ( x+ 2) } = \end{array} \)

Expand the quotient by partial fractions.

\( \begin{array} { l} \frac { x+ 6} { ( x+ 5) ^ { 2} } \\ \\ \frac { x+ 6} { ( x+ 5) ^ { 2} } = \end{array} \)

(Simplify your answer. Use integers or fractions for any numbers in the expression.)