Question 183992
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If the radius of the wheel is 6 inches, then the circumference is *[tex \Large 2\pi\,(6) = 12\pi].  Every time the wheel rolls *[tex \Large 12\pi\ ] inches, the wheel makes one revolution.  So calculate:


*[tex \LARGE \text{          }\math \frac{288\pi}{12\pi}]


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The <i>x</i>-intercept is the <i>x</i>-coordinate of the point where the line intersects the <i>x</i>-axis.  All points on the <i>x</i>-axis have a <i>y</i>-coordinate of 0.  Therefore, the ordered pair describing the point of intersection with the <i>x</i>-axis for an <i>x</i>-intercept of 4 is (4, 0).


Using a similar argument, the intersection point of the line with the <i>y</i>-axis is (0, 2).


Now that you have two points, (4,0) and (0,2), you can use the two-point form of the equation of a straight line to develop your equation:



*[tex \LARGE \text{          }\math y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)]


Where *[tex \Large (x_1,y_1)] and *[tex \Large (x_2,y_2)] are the two given points.  Just substitute the values:


*[tex \LARGE \text{          }\math y - 0 = \frac{2 - 0}{0 - 4}(x - 4)]


Now all you have to do is a little arithmetic and rearranging according to the rules of algebra to put your equation into standard form which looks like:


*[tex \LARGE \text{          }\math Ax + By = C]


Done properly, your <i>A</i>, <i>B</i>, and <i>C</i> should come out to be integers for this problem.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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