







Deriving the Quadratic Formula 
19970204 

From James: How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it. Answered by Penny Nom. 





Parabolic Mirrors 
19970128 

From Megan Wennberg: Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus. If d1 is the distance from the chord to the point of incidence (x,y) and d2 is the distance from (x,y) to the focus, can you prove that the sum of the distances d1+d2 is constant, independent of the particular point of incidence. Answered by Penny Nom. 





A donkey and his carrots 
19970128 

From Emily Lind: There is a donkey who carries carrots. A farmer has 3,000 carrots to carry to the market. The market is 1,000 miles away. The donkey can only carry 1,000 carrots at a time and he eats 1 carrot every mile that he walks but this is only when he is carrying carrots. How many carrots can the farmer get to market by having the donkey carrying them? Answered by Penny Nom. 





Repeating Decimals 
19970124 

From Grant Reed: Is there a way to tell that the repeating decimal for 1/17 has no more than 16 repeating digits? Answered by Penny Nom. 





Foci of an Ellipse 
19970122 

From David Gilliam: How do I find the focii of the following equation? 4x^2 + 9y^2 = 36 Answered by Harley Weston. 





Mathematics of Schedules 
19970116 

From Byron Krull: I was asked if there was a mathematical method to work with schedules. The problem is this. There are 24 teams playing weekly on 4 sheets at 3 different times of the day as follows... Answered by Denis Hanson. 





Three Spheres 
19970114 

From Alan Schnerch: Three spheres of diameter 2 are placed on a level surface so that each sphere touches the other two. A fourth sphere, also of diameter 2, is placed on top of the other three so that it touches all of the other spheres. The distance from the level surface to the highest point of the top sphere is . . .. Answered by Chris Fisher and Harley Weston. 





A triangle problem 
19961219 

From S. Johnson: Given that Triangle ABC is a right triangle and Circle O is inscribed in it find the radius of Circle O, totally in terms of a, b, and c. Answered by Penny Nom. 





A trig problem 
19961213 

From S. Johnson: sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation. Answered by Harley Weston. 





Roots of a Polynomial 
19961206 

From Paula Miller: Why is the solution called a "root"? Why not just the "xintercepts"? Answered by Chris Fisher and Harley Weston. 





Sides in a Regular Polygon 
19961206 

From Rick Moss: If you are given the measure of each interior angle (162 degrees) of a regular polygon. How many sides does the polygon have? Answered by Penny Nom. 





A balance problem 
19961118 

From Jack N. Bussell: There are 12 coins which look exactly the same, however one of them is heavier or lighter than the rest. Using a pointer balance scale, can you identify the odd coin and whether it is heavy or light in 3 weighings? Answered by Harley Weston. 





Pentominoes 
19961114 

From Sam Maraldo: What is a pentominoe? I need to understand the concept and how/why it is used? Answered by Penny Nom. 





Trigonometry 
19961112 

From Evans: Any idea who came up with some or most of the ideas involved in trigonometry? Answered by Chris Fisher. 





Smith, Rodriguez and Jones 
19961107 

From Rafayel Ambartsumyan: On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones. ..... Who is the engineer? Answered by Penny Nom. 

