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\textbf{---Homework 2---}

\textbf{\#35}  Determine the zeroes of $D(x) = x^2-8x+5$.  (Hint:  Use the
	quadratic formula.)

\textbf{\#36}  Determine the zeroes of $B(y) = y^2+2y-5$.  (Hint:  Use the
	quadratic formula.)

\textbf{\#39}  Determine the zeroes of $R(t) = \sqrt{16-t^2}$.

\textbf{\#40}  Determine the zeroes of $R(x) = \frac{3}{4}\sqrt{x^2-12}$.

\textbf{\#44}  A ball is thrown upward from an initial height of $h_0$
feet with an initial velocity of $v_0$ feet per second.  Its height
(in feet) above ground level, $t$ seconds after it is thrown, is given
by the function
$$
	h(t) = -16t^2 + v_0t + h_0.
$$
Suppose that a ball is thrown upward from a tower such that $v_0=64$ and
$h_0=24$.

\textbf{(a)}  How high was the ball after 3 seconds?

\textbf{(b)}  When did the ball hit the ground (to the nearest 0.01 second)?

\textbf{(c)}  Compute
$$
	\frac{h(2) - h(0)}{2}.
$$
What is the significance of this number?

\textbf{\#45}  A ball is dropped from the top of the Empire State Building
(1250 feet tall) in New York City.  Its height $t$ seconds after it is dropped
is given by $h(t) = 1250t-16t^2$.  After $t_0$ seconds, it hits the ground.

\textbf{(a)}  What is the value of $t_0$ (to the nearest 0.01 second)?

\textbf{(b)}  Compute
$$
	\frac{h(t_0)-h(0)}{t_0}
	\quad\textrm{and}\quad
	\frac{h(t_0)-h(t_0-1)}{1}.
$$
Suppose that you were standing on the ground, waiting to catch the dropped
ball.  Which of these two numbers would be most important to you?

In exercises 46-49, a table of values has been generated with function $f$
of the form
$f(x)=nx$,
$f(x)=n/x$,
$f(x)=x^n$, or
$f(x)=n^x$ ($n$ is constant).
Determine $f$ for each table.

\textbf{\#48}
\begin{tabular}{|l||l|l|l|l|l|}
\hline $x$    & 0 & 1 & 2 & 3 & 5 \\
\hline $f(x)$ & 1 & 3 & 9 & 27 & 243 \\
\hline
\end{tabular}
\textbf{\#49}
\begin{tabular}{|l||l|l|l|l|l|}
\hline $x$    & 4 & 6 & 10 & 12 & 16 \\
\hline $f(x)$ & 6 & 9 & 15 & 18 & 24 \\
\hline
\end{tabular}

\vspace*{0.1in}
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\textbf{---Homework 2---}

\textbf{\#35}  Determine the zeroes of $D(x) = x^2-8x+5$.  (Hint:  Use the
	quadratic formula.)

\textbf{\#36}  Determine the zeroes of $B(y) = y^2+2y-5$.  (Hint:  Use the
	quadratic formula.)

\textbf{\#39}  Determine the zeroes of $R(t) = \sqrt{16-t^2}$.

\textbf{\#40}  Determine the zeroes of $R(x) = \frac{3}{4}\sqrt{x^2-12}$.

\textbf{\#44}  A ball is thrown upward from an initial height of $h_0$
feet with an initial velocity of $v_0$ feet per second.  Its height
(in feet) above ground level, $t$ seconds after it is thrown, is given
by the function
$$
	h(t) = -16t^2 + v_0t + h_0.
$$
Suppose that a ball is thrown upward from a tower such that $v_0=64$ and
$h_0=24$.

\textbf{(a)}  How high was the ball after 3 seconds?

\textbf{(b)}  When did the ball hit the ground (to the nearest 0.01 second)?

\textbf{(c)}  Compute
$$
	\frac{h(2) - h(0)}{2}.
$$
What is the significance of this number?

\textbf{\#45}  A ball is dropped from the top of the Empire State Building
(1250 feet tall) in New York City.  Its height $t$ seconds after it is dropped
is given by $h(t) = 1250t-16t^2$.  After $t_0$ seconds, it hits the ground.

\textbf{(a)}  What is the value of $t_0$ (to the nearest 0.01 second)?

\textbf{(b)}  Compute
$$
	\frac{h(t_0)-h(0)}{t_0}
	\quad\textrm{and}\quad
	\frac{h(t_0)-h(t_0-1)}{1}.
$$
Suppose that you were standing on the ground, waiting to catch the dropped
ball.  Which of these two numbers would be most important to you?

In exercises 46-49, a table of values has been generated with function $f$
of the form
$f(x)=nx$,
$f(x)=n/x$,
$f(x)=x^n$, or
$f(x)=n^x$ ($n$ is constant).
Determine $f$ for each table.

\textbf{\#48}
\begin{tabular}{|l||l|l|l|l|l|}
\hline $x$    & 0 & 1 & 2 & 3 & 5 \\
\hline $f(x)$ & 1 & 3 & 9 & 27 & 243 \\
\hline
\end{tabular}
\textbf{\#49}
\begin{tabular}{|l||l|l|l|l|l|}
\hline $x$    & 4 & 6 & 10 & 12 & 16 \\
\hline $f(x)$ & 6 & 9 & 15 & 18 & 24 \\
\hline
\end{tabular}

\end{document}
