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\markright{Chapter 1: Answers 4}
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\Bf{Chapter 1: Answers 4 \hfill Jack K. Cohen \hfill Colorado School of Mines}

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\item  $r \approx 50,008.33$.  A real pitfall here is getting trapped into investigating the regime where $r < s = 1000$---``obviously'' the radius of the asteroid would sensibly be much larger than $s$.   By the way, the word ``obviously'' in mathematics means ``clear when you think about it for awhile''.  For example, some real smart people have been known to have put up a first \Tt{Plot} for values of $r$ near 0 in solving the present problem.

\noindent Another problem is that we have no idea where to hunt for the ``physically sensible'' root.  As promised in the problem statement, we will develop methods for this in a few weeks.
\item (1.2.24) A sketch reveals some nice right triangles: $d = \sqrt{2}$.

\item  It checks.

\item No solution given to honor problems.

\item (1.2.25)  $d = $ {\Large$\frac{4}{13}$} $\sqrt{26}$.

\item  
        \begin{enumerate}
        \item It checks (despite the answer in the back of the book).
        \item The form $y = mx +b_1, y = mx +b_2$ doesn't include the case of two \Em{vertical} lines.
        \end{enumerate}

\item
        \begin{enumerate}
        \item $y = 3x - 2$.
        
        \item $y = 2.1x - 1.1$.
        
        \item $y = 2.01x - 1.01$.
        
        \item  Slope is $m = 2$, tangent line is $y = 2x - 1$.

        \item  Did you notice that the curve for $y = x^2$ was almost linear in the ``zoomed'' plot? 
        
        \item The precise definition requires calculus concepts that will be discussed soon.  (Attempts to give a definition in terms of only algebra and geometry concepts are sure to be inadequate.)   It \Em{is} a secant line. 
        \end{enumerate} 
        
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