







Partitions of a set 
20191221 

From Ghani: 1. Are set partition "sets"?
2. If they are so then, why are both {{a}{b,c}} and {{a,b}{c}} said to be valid partitions of A ={a,b,c}
despite them having different elements?
(I understand that set are equal if they have the exact same elements).
Thank you! Answered by Harley Weston. 





The divisors (aliquot parts) of a positive integer 
20191031 

From Kenneth: Is there a fast and simple method that can be used to determine the aliquot parts, whole, positive numbers that can divide into another whole, positive number? Answered by Harley Weston. 





One part in 10^x 
20190626 

From Jim: What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “...to within one part in 10x.” Answered by Penny Nom. 





Margin with commission as part of selling price 
20190213 

From Anni: I need to find selling price to put us at 24% margin.
15% commission is based on selling price and is included in our cost.
I'm trying to do it excel and keep getting a circular reference.
Total cost= cost + commission (15% of selling price)
Selling price=total cost + 24% margin Answered by Penny Nom. 





Heat equation 
20171123 

From Max: What does du\dt=a(triangle)^2u mean. Can it be solved for t. Answered by Penny Nom. 





A road trip word problem 
20160410 

From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom. 





10800 sq. ft equal approx what part of an acre? 
20160227 

From David: 10800 sq. ft equal approx what part of an acre Answered by Penny Nom. 





Partitions into distinct parts 
20150919 

From Brian: Looking for a formula where I can type in a number, 17 for example, and using the numbers 1 through 17 (1, 2, 3, 4 etc....), to come up with all possible combinations, when added, that will equal 17. And each number can only be used once. I've tried a few search engines but my computer stares at me blankly and scratches its head :/. Answered by Chris Fisher. 





Three investment partners sharing the profit 
20140222 

From Ayatullah: Hello;
We are three partners and bought a property at 2050000 and sold at 2300000.
Details of investment of the partners
X= 1500000
Y= 400000
Z = 150000
My questions are
1) How could i calculate percentage of investment of each partner?
2) How could i deduct 30% commission from each partner in profit?
3) How could i distribute the profit amongst the partners?
Thanks in advance Answered by Penny Nom. 





Restricted partitions 
20130325 

From vidya: I am having a series of numbers eg.( 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
I can take any 5 digits eg(15,10,8,6,5) and it should not repeat and the summation should be any predefined static value . eg(44)
That is (15+10+8+6+5=44) . How many summation series will result 44 ?
My problem is how to find this using a formula or any other simpler automation method is there instead of checking one by one all the combinations.
Plz do help me... Thnks in advance Answered by Chris Fisher. 





A bipartite graph 
20121029 

From A student: Suppose that G be a bipartite graph with maximum degree of k.
Prove that:
1)Exists a Kregular bipartite graph that G be subgraph it(H) Answered by Claude Tardif. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





The integral of sqrt(x) * ln(x) 
20091012 

From Oana: Hi! Can you tell me please how much is : ∫ (√x * ln x) ? Answered by Penny Nom. 





Fractional part 
20090401 

From Galina: What fractional part of eight is eight hundredths Answered by Stephen La Rocque. 





Partial derivatives 
20090117 

From Meghan: I have a question I've been working at for a while with maxima/minima of partial derivatives.
"Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed.
Find the dimensions of the rectangular package of greatest volume that can be mailed.
(84 = length + girth = l + 2x + 2y)" Answered by Harley Weston. 





Partial variation 
20081103 

From Diamond: what are the 2 parts of partial variation? Answered by Penny Nom. 





Integration 
20081017 

From hazela: integration of
x sinx cosnx Answered by Harley Weston. 





Integration by parts 
20080130 

From seth: hi i really dont understand integr
ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=cost
for the formula i have uvintegralvu' dx this is all well and good but i cant get it right. Answered by Harley Weston. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





Partial fractions 
20080106 

From taiwo: i copied the question below from john bird's higher engineering mathematics
fourth edition (pg 19) after solving all the partial fraction questions from the book
except this:
x^3 + 4^2 + 20x  7 over (x1)^2 (x^+8). i will appreciate it if you help me out so i can
know whether their answer is correct. thanks alot Answered by Harley Weston. 





Partitioning a clock face 
20071219 

From Kim: Using a clock with a regular circular faced dial, draw two straight lines such that the sum
of the numbers in each of the three areas is equal. Answered by The team at Math Central. 





Dividing a circle 
20071123 

From matt: hi. can you please send me a diagram of how to draw 3 lines in a circle to get 8 sections. Answered by Stephen La Rocque. 





Motion along a line 
20071002 

From Claudette: If the position function of a particle is x(t) = sin^2(2t), find the distance that the particle travels from t = 0 to t = 2 Answered by Harley Weston. 





Integration 
20070202 

From Jenna: How do I integrate ( ln(x) ) / ( x^2 ) ? Answered by Penny Nom and Claude Tardif. 





Can one divide a circle into 4.5 parts 
20060330 

From Chris: If it is possible, can one divide a circle into say, 4.5 parts (with 4 equal parts and a half part)?
Or for that matter, for any integer, n, into n/2 parts as above?] Answered by Walter Whiteley. 





A partial derivative 
20040319 

From Penny Nom: Is it possible to differentiate the following equation, if so could
you please explain.
S=SQRT(T(5/X^2))
I would like the derivative of S with respect to X. Answered by Harley Weston. 





Integrating e^x sin(x) 
20030503 

From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif. 





Two problems 
20021014 

From Eva:
a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Answered by Leeanne Boehm and Penny Nom. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





Integration by parts 
20010409 

From A student: how do you integrate x tan^{1}x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Answered by Claude Tardif and Harley Weston. 





Two integrals 
20010403 

From Jim: I'm having trouble with these integrals. Can you help me out? 1)the integral of:
x^{5} arctan x dx 2)the integral of:
2x^{5} + 9x^{4} + 19x^{3} + 13x^{2}  5x  25  dx x^{4} + 4x^{3} + 5x^{2} Answered by Claude Tardif. 





Part of a part 
20010211 

From Katie: Hello! I was looking at your Fraction questions and since i am pursuing to be an elementry school teacher i feel i don't understand one of your responses. How would you explain this to an elem, midd, and high school student. Even me myselfin college really does not understand. The question was: When you multiply two positive fractions less than 1, how does the answer compare to the size of the fraction? Why? Answered by Penny Nom. 





Congruent parts of congruent figures 
20000310 

From Erica: Yesterday, I recieved a test problem asking to prove two line segments equal. Here is the problem as I was given it: Given: paralleogram ABCD AE is perpendicular to DB CF is perpendicular to DB Prove: AE is equal to CF I answered the problem as follows: . . . Answered by Walter Whiteley. 





Party favors 
20000222 

From Krystina Fernandez: Luanne was making party favors for her little sister's birthday party. Each party favor was in the shape of a cube. Luanne had pink and purple paint to paint the cubes and she could paint each face only solid pink or solid purple (no dots,stripes,ect.).For example, one cube may be all purple, another may have two purple faces and four pink faces. Her little sister wanted to have a different cube for each guest.(A cube is not considered different if it can be turned so that all it's sides match the corresponding sides of another cube.)How many different cubes was it possible for Luanne to make? Answered by Claude Tardif. 





Calculus problems 
19980713 

From Lorraine: I'm stuck again. Can you help? This involves integration using the method of partial fractions the integral of: 7x(to the 5th)  2x(cubed) + 3 dx  x(to the fourth)  81 Do I have to do long division to reduce the numerator to the fourth power? the integral of: 4 16x +21x(squared) + 6x(cubed)  3x(fourth) dx  x(cubed)(x  2)(squared) Lorraine Answered by Harley Weston. 





Les dérivées partielles 
20120516 

From Haddouche: Bonjour,
Je vous demande de bien vouloir m'éclaircir comment on calcule les dérivées partielles généralement étudiées dans les modèles de la concurrence fiscale à titre d'exemple celui de Wildasin ""NASH EQUILIBRIA IN MODELS OF TAX COMPETITION "", dont j'ai essayé toutes les méthodes et aucune d'elle n'est arrivée à trouver le résultat des dérivées de ce dérnier papier, à cet effet, je vous serais reconnaissant de m'éclaicir la méthode afin de résoudre ce problème qui pour moi un vrai mistère à percer.
Je vous remercie infiniment à l'avance.
Et comptant sur votre compréhension, mes salutations les meilleures.
HA Answered by Claude Tardif. 





le prix de départ 
20060910 

From un élève: Une jupe coûte 36 euros après une démarque de 20% quel est le prix de départ moi j'ai trouvé 45 euros mais je n'ai pas la formule de calcul exacte Answered by Claude Tardif. 





Partages inégaux 
20050929 

From Un eleve: Alex et julie ont ensemble 4728 . euro Si Alex donne 538. euro à Julie, ce dernier aurait alors le triple de Julie. Quelle est la somme possédée de chacun? Answered by Claude Tardif. 





Point de partage 
20000221 

From Sebastian Murciano: J'aurais besoin de savoir où je peux trouver de l'informations, ou estce que vous pouvez me donner de l'information sur : Point de partage d'un segment étudié en Secondaire 4. Answered by Claude Tardif. 





Derivées partielle 
19991019 

From Arnaud Flandin: Quel est la definition des derivées partielle Answered by Claude Tardif. 

