







Selling items at a reduced price 
20150109 

From Kent: I have an item I sell for $19.95 and make a profit of $10.97 for each sale.
If I reduce the price to $14.97, my profit is $5.99 each sale.
Is there a formula to determine how many more I would need to sell
at $5.99 per sale to make the same net cash (profit) as selling at $10.97 per sale? Answered by Penny Nom. 





Reducing by a scale factor of 1/3 
20111121 

From Sandra: A rectangle with the dimensions of 6.3 cm and 5.8 cm is reduced by a scale factor of 1/3. What are the dimensions of the new image? Answered by Penny Nom. 





The rectangle is reduced to 90% of its original size 
20110331 

From stephon: A rectangle has a length of 4cm and a width of 8cm.
If this rectangle is reduced to 90% of its original size what will be the new length Answered by Penny Nom. 





The volume is decreased by 25% 
20081117 

From Wanda: If the volume of a sphere is decreased by 25%, what is the new equation? Answered by Penny Nom. 





A matrix problem 
20050404 

From Alan:
Let A = 

1  1  0 

2  1  2 
a  b  c 
where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]
Answered by Judi McDonald. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





Augmented matrix 
20021231 

From Michelle: I am trying to augment a matrix so that i can find the values of the variables a, b, and c. For the life of me i can't find a solution to the matrix: 3 5 2 ' 22 2 3 1 ' 9 4 3 3 ' 1 I thank you for your help, Michelle Answered by Penny Nom. 





Reduce 79,537/3,623,420 
20011213 

From Eliana: How do you reduce 79,537/3,623,420. Answered by Claude Tardif. 





A system of equations in five unknowns 
20000320 

From Will: I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives . . . Answered by Penny Nom. 

