Page 37


Problem 1


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Problem 2


4, 7, 9, 12, 15. Any others?



Problem 3


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Problem 4


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Angle DMP is 72 degrees, not 62; that way angle MPR and PRM are 36 degrees, making all triangles have a total of 180 degrees from interior angles. - Max



Problem 5


Make a careful sketch of five or six sides of a arbitrary regular polygon, starting at A. Look at triangle ABC. What kind of triangle is this? If angle CAB=12 degrees, what is angle ACB? What is the measure of angle ABC? What is the measure of the EXTERIOR angle at B? What do all the exterior angle (according to the SENTRY THEOREM) add up to? Use this to find the number of exterior angles, which, in turn, is the same as the number of sides.



Problem 6


In one hour, the UFO moves along the vector [5,10,10]. The length of this vector is 15 units (how did I get this?). In one-third of an hour (where did this come from?) the UFO travels 5 units (why?). The UFO was at




To find out when the UFO left the ground, you need to notice that the y-coordinate can be described parametrically by 10+10t where t is the time in hours. Solving the equation 10+10t=0 yields t=-1, or one hour before noon, or 11:00 am.



Problem 7




Problem 8


Before you even LOOK at the picture, you should plug in some numbers for r and try to generate som data and a feel for the problem.

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Problem 9


Use the result from Problem 8 above. What would happen if the angle bisectors intersected perpendicularly?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 10


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Problem 11







Page 38


Problem 1


Each interior angle in a regular pentagon is 108 degrees (how?). That means that the uncovers acute angle at P is 360 - 108 - 108 - 108 = 36.



Problem 2


If the shaded pentagon were removed, that would leave an angle of 144. IF there exists a regular polygon with a 144 degree angle, then an exterior angle would be 36 degrees. According to the Sentry Theorem, the exterior angles sum to 360 degrees, so this polygon must have 10 sides.



Problem 3


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Problem 4


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Problem 5


The zero in the z-coordinate means the airplane took off from "ground level" as represented by the xy-plane.

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Problem 6


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Problem 8


2011-01-12_0002.jpg



Problem 9


2011-01-12_0001.jpg



Problem 10


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Problem 11


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