







Constructing a cross country district schedule 
20151213 

From David: Retired math teacher trying to help soninlaw schedule a cross country district schedule. The would like to have four trimeets each week for five weeks and one week of dual meets. The score the trimeets as three duals, i.e. 1v2, 2v3, 1v3 constitutes one trimeet. After many hours, not sure its possible, but I have forgotten a great deal! Thanks Answered by Victoria West. 





The volume of a cylinder 
20090218 

From jim: given the volume of a cylinder at 565m^3 and the height of 20m how do i calculate the cross section area in order to determine the compression strength of the cylinder Answered by Harley Weston. 





Moving grain across the river 
20080312 

From Janice: Wesley needs to move 820 kg of grain across the river in a canoe that can carry no more than 120 kg. Wesley has a mass of 70 kg. What is the fewest number of trips he will have to make? A. 17 trips; B. 18 trips; C. 32 trips; D. 33 trips. Answered by Penny Nom. 





Crosssectional area of a fire hose 
20080127 

From Tom: My question is this I know the equations for the final answer but the book skips how to get to one section of the equation. Q=(a)(v)
A= The crosssectional area of the conduit in square feet (ft2). So if you have a 5 inch hose how do they get A=0.136 ft2 ? And I know the velocity already v= velocity in ft per second. Answered by Stephen La Rocque. 





Comparing flow rates of two pipes 
20070714 

From Kenneth: If two water pipes are 3 feet long, but one of them has a 1 foot diameter and the second has a 1 1/2 foot diameter, what simple mathematical method can be used to determine how much faster one pipe can drain water than the other pipe? Answered by Stephen La Rocque. 





Comparing two fractions 
20070118 

From Kayla: Why does eight over twelve compared to one half work when you use cross multiplication. Answered by Penny Nom. 





An octagonal bird house 
20070113 

From Soren: I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew! Answered by Harley Weston. 





A perpendicular intersection of two barrel vaults 
20060721 

From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings.
A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults).
A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semicircular arch.
The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault.
Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle. 





Crossword math puzzle 
20040914 

From Joyce and Tiffany: The puzzle name was real number vocabulary and the question is (a number that divides evenly into another what is it?). (Space in between ticmarks on a number line). Answered by Harley Weston. 





Crossing a river 
20040909 

From Barb: Nine men and two boys, trekking through the jungle, need to cross a river. They have a small inflatable boat and it's easy enough to row it across the river. The boat, however, can hold no more than one man or the two boys. How can they all get across? (Hint. suppose there was only one man and two boys) Does it make math sense and what would the answer be Answered by Penny Nom and Claude Tardif. 





Vectors 
20040706 

From Annie: a=3ij+2k and b=i+3j2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k. Answered by Chris Fisher. 





A project about crosses 
20030610 

From Joel:
I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)? Cross Number  Area sq cm  1  5  2  13  3  25  4  41  5  61  I also need to know what the formula is for it? Answered by Penny Nom. 





The crosssection of a football field 
20030525 

From Francis: Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly. height from base to highest point 45.75 centimetres distance of the field 50 metres a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the crosssection is a parabola, find the algebraic model that describes this shape. b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line. Answered by Harley Weston. 





The cross country team 
20020612 

From Denae: In cross country, a team's score is the sum of the first five finishers on the team. The captain of the team finished 2nd in the meet. The next four finishers on the team placed in consecutive order. The team score was 40. in what places did the other members finish? Answered by Penny Nom. 





The distance across a circle 
20020118 

From Douglas: If you know how far around a circle is (say earth) 25000 miles how do you calculate the distance across? Answered by Penny Nom. 





Multiplying vectors 
20011022 

From Murray: Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Answered by Harley Weston. 





Cross multiplication 
20000216 

From J E Swinton: Why does cross multiplication work? How come canceling work? Answered by Penny Nom. 





Crossing number 
19991106 

From Christian: The crossing number of a graph G, denoted cr(G) is defined to be the minimum number of (pairwise) crossings of edges among all drawings of the graph in the plane. For example, cr(K5)=1 and cr(K3,3)=1. What is cr(K7,7)? I figured out that the answer is 81. Now I am trying to figure out if K7,7 can be drawn in the plane with less than 81 crossings? I'm not sure how to approach this one. Other than actually drawing it out and checking by trial and error, I am not sure how to approach this problem. Please help! Answered by Denis Hanson. 





Area of a triangle from vertex coordinates 
19990421 

From Mark Tyler: I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too. I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula: A = abs((x1x2)*(y1y3)(y1y2)*(x1x3)) for triangle (x1,y1)(x2,y2)(x3,y3) I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long. Regardless, it may be fun for the kids, even if it's not on the curriculum. Answered by Walter Whitley. 





Crosssectional area of a cylinder 
19990412 

From Rebecca Connor: What is the formula to find the crosssectional area of a cylinder? Answered by Chris Fisher. 

