







Percentage change in productivity 
20170315 

From Sunni: I'm working on a graph and I need to find the percentage of increase from one figure to another. How do I do that? For instance our department started with a workload of 1773 in Jan and ended with 341 in Dec. In addition to that we received 2088 new items from Jan  Dec with an average of 5 workers. How do I find the percentage of increased productivity if any? Answered by Penny Nom. 





A triple product 
20161003 

From sam: Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,1,1)
And let vector c be a unit vector such that triple product of a,b,c is
minimum . We have to find the value of c.
[Thoughts]
I thought triple product of a b, c means the volume occupied by
parallelepiped. And we have to do volume minimum Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





Expand and simplify [x3][x+3] 
20140716 

From symion: Expand and simplify [x3][x+3] Answered by Penny Nom. 





Dt[sin t tan (t^2+1)] 
20120221 

From Ayu: Ayu
Dt[sin t tan (t^2+1)]
derivatives Answered by Harley Weston. 





A product of 1 000 000 
20101119 

From Sharron: There are many pairs of numbers that when multiplied together give a product of 1 000 000. However, there is one pair, and only one pair, of whole numbers that contain no zero digits and has a product of 1 000 000. What are these two numbers? Answered by Stephen La Rocque. 





Arrays 
20100909 

From Susan: I'm a lawyer but evidently incredibly stupid at 4th grade math. . . .Question: cover a tabletop with 9 rows of square tiles with 9 squares in each row. How many tiles cover the tabletop? Then, the paper shows a 9x9 array and asks how it is used to solve the problem. My daughter wrote 9x9=81. The next question is "what are the products of the two smaller arrays?" ???? There are no other arrays  are we to make smaller arrays from the 9x9? how? Answered by Robert Dawson. 





Adding five positive integers that have a product of 48 
20100427 

From Lorraine: What is the smallest possible sum that can be obtained by adding five positive integers that have a product of 48. Answered by Chris Fisher. 





The product of two integers their LCM and their HCF 
20090215 

From Anonymous: Two numbers have LCM = 60. If their product is 180, what is their HCF? Answered by Harley Weston. 





(a x b) intersect (b x a) 
20090108 

From sean: is it possible to have two sets such that
n((a X b) intersect (b X a) =3 Answered by Harley Weston. 





The product of two numbers is 2400 
20081016 

From belinda: The product of two numbers is 2400, one number is 20 more than the other number. what are the two numbers? Answered by Penny Nom. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





Product of TwoDigit Numbers 
20080731 

From pete: The number 4641 can be expressed as the product of two twodigit whole numbers. What is the sum of these two numbers? Answered by Janice Cotcher. 





Sum and product of the roots of a quadratic 
20080703 

From Gautam: If a and b are the roots of x^2+px+1=0 and c and d are the roots of
x^2+qx+1=0
prove that
(ac)(bc)(a+d)(b+d)=q^2p^2
Regards
Gautam Answered by Harley Weston. 





Product of Two Integers 
20080625 

From devin: two consecutive integer have a product of 240. what are they Answered by Penny Nom. 





The product of the roots 
20080319 

From Rebecca: Determine the product of the roots of the equation
(x1)(x2) + (x2)(x5)=0 Answered by Penny Nom. 





The sum and product of the roots of a quadratic 
20080316 

From Katelyn: Write the quadratic equation....
Sum of the roots = 16
Product of the roots = 80 Answered by Penny Nom. 





The product of two numbers is 1,000,000,000 
20080314 

From Henry: What two numbers that don't in zero when multiplied equals 1,000,000,000 and same with 1,000,000,000,000,000,000. Answered by Penny Nom. 





Percentage change 
20070819 

From nona: If inputs increase by 30% and outputs increase by 15%, what is the percentage change in productivity? Answered by Stephen La Rocque. 





Scalar triple product and volume of a general tetrahedron 
20070803 

From Anurag: how do you prove that
volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c? Answered by Stephen La Rocque. 





If the product of A,B,C is 15834, what is A+B+C? 
20070310 

From rachel: if the product of A,B,C is 15834, what is A+B+C? 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. 





Products with symbols 
20070109 

From Jennifer: Find the product of each (8x)(4) (3x)(5y)(7z) (8x^3y)5X^2) (6a)(3a)(b^2) Answered by Penny Nom. 





The product of of two rotations 
20061217 

From Katie: Is the product of of two rotations over a different center point always a translation? Answered by Walter Whiteley. 





The sum of two numbers is 30 
20061103 

From GG: The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers. Answered by Stephen La Rocque. 





The product of polynomials 
20060713 

From Lynne: If you multiply two polynomials, what can you say about the degree of their product? What exponent applies here? Answered by Stephen La Rocque. 





A product equals a sum 
20050327 

From Tor: Can you please help me with a general formula for the following system:
2+2=2*2
3+3/2=3*3/2
4+4/3=4*4/3
and how will you prove the formula?
Answered by Penny Nom. 





A 3digit product 
20050225 

From A student: I have an odd 3 digit product. My factors are a 1 digit number and either a 2 or 3 digit number. My factors are odd, but neither is 1. Find my factors and my product. Answered by Penny Nom. 





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. 





The product of any n consecutive integers 
20040118 

From Fazia: I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof. Answered by Claude Tardif. 





Pairs of prime numbers 
20031013 

From Nikolas: Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list. Answered by Penny Nom. 





10,000 
20031008 

From Nathan: what two numbers make the product of 10,000. Neither number can end in a zero Answered by Penny Nom. 





The product of four consecutive integers is 3024. 
20030425 

From pillar: The product of four consecutive integers is 3024. What are those numbers. Answered by Penny Nom. 





1575 
20030313 

From Sharyn: find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20 Answered by Penny Nom. 





X times Y equals ten million 
20030226 

From Baneen: Would you be able to tell me which two numbers would compute ten million without any number having zeros in it? 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. 





The solutions of a quadratic 
20010130 

From A student:
 Show that the product of the solutions of ax^{2} + bx + c = 0 is c/a.
 For each equation under the given condition, (a) find k and
(b) find the other solution. kx^{2}  2x + k = 0; one solution is 3 Answered by Penny Nom. 





Multiplying decimals 
20001016 

From Lily: I need help with mutiplying decimals (example) 2.28*0.48( * = times). Answered by Harley Weston. 





10 000 000 = a x b 
20000306 

From Spencer Jaffe: What two numbers that don't end in zero, multiplied equal 10,000,000. Answered by Claude tardif. 





A negative times a negative 
20000229 

From Michael J. Butler: I have reviewed the answer in relation to the question of why (3)x(2)=6; however, I am still not able to properly explain the reasoning to my son, Jonathan, who is in grade 7. I want him to understand the reason for the rule that the multiplication or division of two negative numbers equals a positive number. Can you help? Answered by Chris Fisher. 





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. 





A Sum or Product of Fractions 
19981006 

From Emily Robb: Find a pair of fractions that when they are multiplyed and added the sum /product is the same Answered by Penny Nom. 





Matrices 
19980310 

From Ksya:
 A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ???
 If B^(1) is the inverse of B, where B is a matrices. Can we say [(B^(1))^n][B^n]=I, where I is identity matrices? Any conditions???
Answered by Doug Farenick. 





Mathematical Induction and the Derivative 
19970318 

From Shuling Chong: "Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n." Any educated tries are appreciated. Answered by Penny Nom. 





(3)x(2) 
19951025 

From Azmat: Why is (3)x(2) = 6? Answered by Herley Weston and Ed Giesbrecht. 





Quel serait le cout total de production de 500 entrees 
20060610 

From Suzanne: Chaque operateur traite des donnees pendant 7 heures 1/2 par jour, et peut s'acquitter d'une demande en 3 heures et 3/4. Combien d'operateurs faudratil pour traiter 50 demandes en 1 jour.
Vous etes surveillant a l'entree des donnees. Pour atteindre vos objectifs vous engagez temporairement 2 commis a un salaire de 10$ et a raison de 8 heures par jour. Si chaque personne peut produire 50 entrees par jour, quel serait le cout total de production de 500 entrees.
Answered by Claude Tardif. 

