Chapter 1: Answers 4 Jack K. Cohen Colorado School of Mines
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r
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 Plot for values of r near 0 in solving the present problem.
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.
- (1.2.24) A sketch reveals some nice right triangles:
d =
.
- It checks.
- No solution given to honor problems.
- (1.2.25) d =
.
- It checks (despite the answer in the back of the book).
- The form
y = mx + b1, y = mx + b2 doesn't include the case of two vertical lines.
-
y = 3x - 2.
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y = 2.1x - 1.1.
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y = 2.01x - 1.01.
- Slope is m = 2, tangent line is
y = 2x - 1.
- Did you notice that the curve for y = x2 was almost linear in the ``zoomed'' plot?
- 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 is a secant line.