







How to calculate percentage change 
20070803 

From Galland: I am working on graphs and I need to find the percentage of increase from one figure to another. How do I do that? For instance staff hours for 2006 were 28011 and for 2007 were 31230. How do I find the percentage of increase? Answered by Stephen La Rocque. 





logbase4 (sin x) = 0.5 
20141026 

From Susan: Solve for x: logbase4 (sin x) = 0.5 Answered by Penny Nom. 





Find the nth term 
20141026 

From Kenneth: According to the pattern of the following sequence. Find it's nth term:
3,9,27,81,243,.......... Answered by Penny Nom. 





A truncated squarebased pyramid 
20141022 

From Beth: How do you find the height of the original squarebased pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)? Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom. 





Division in base 3 
20140930 

From Nnubia: 1021 in base 3 divided by 2 in base 3 Answered by Penny Nom. 





Continuity on a closed interval 
20140921 

From Pragya: The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval,
but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's
limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help... Answered by Penny Nom. 





Base 6 
20140910 

From Amanda: using base 6, what is the next number after 25? 35? 55? and 455?
I need to be able to show the base 6 material. Answered by Penny Nom. 





35 base 6 
20140910 

From Amanda: Sorry I am having trouble understanding base,
35 in base 6 means 3 10's and 5 ones, which is the same ____ in base 10? Answered by Penny Nom. 





211(base x)=152(base 8) 
20140909 

From Vaidehi: Find the base value (i.e. x):
211(base x)=152(base 8) Answered by Penny Nom. 





A second grade word problem 
20140909 

From Beth: How do I explain to my second grader how to find the answer to the problem:
My tens digit is 8 more than my ones digit. My ones digit can not be zero. Answered by Penny Nom. 





A secret number 
20140908 

From jai: it is smaller than half of 100, it is more than 4 tens and less than 5 tens, the tens digit is two more than the ones digit , together the digits have a sum of 6..... What is my secret number? Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





The inverse of f(x) = x^2  x 
20140822 

From Tyler: Find the Inverse function of:
f(x) = x^2  x Answered by Robert Dawson. 





A price increase and a consumption decrease 
20140816 

From sujan: If the price of petrol increases by 25% and Rajesh intends to spend only 15% more on petrol then by how much % should he reduce the quantity of petrol he buys? Answered by Penny Nom. 





Multiplication in base five 
20140807 

From Alise: Hi Maths Central!
I was wondering if you could help me with multiplying in base 5. I have read a question previously answered by you in regards to this but got fairly confused by it and was hoping you could help me with my question.
My question is: Multiply 1422 base 5 by 21 base 5 keeping these numbers and answer in base 5.
Would you also be able to explain how to get to the answer?
Thanks! Answered by Penny Nom. 





The sum of the first 50 terms of an arithmetic progression 
20140726 

From Joshua: Hello ...my is Joshua...I'm a grade 11 student...I got a question
Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84 Answered by Penny Nom. 





60% as much as $30. 
20140718 

From Kenneth: Question from Kenneth:
Hello:
Do you know why some "as...as" phrases indicate multiplication?
For example, ? is 60% as much as $30. This is equivalent to 60% X $30 = $18. How does this make sense?
I saw this example in an old textbook on business mathematics, but the author did not explain why it is equivalent
to multiplication.
I thank you for your reply. Answered by Robert Dawson. 





Selecting a meal at a school cafeteria 
20140718 

From Gil: A school cafeteria offers 2 main entrees, 3 fruits, 4 vegetables, and 3 drinks. If a plate consists of 1 entree, 2 vegetables, 1 fruit, and 1 drink, how many different plates can a cafeteria manager make? Please explain how you derived at answer. Thank you Answered by Penny Nom. 





How can eight eights be 1000? 
20140620 

From Aamir: The digit 8 if we add it 8 time in it the answer should be equal to 1000.it may possible.i.e.,
8+8+8+8+8+8+8+8=1000 Answered by Penny Nom. 





A reversed curved on a railroad track 
20140619 

From cherrielyn: Assuming that earth is a sphere of radius 6380 km,
what is the difference in the latitudes of two cities 270 miles apart
positioned on the same meridian?
Thank you in advanced po! :) Answered by Penny Nom. 





Forming a cylinder from a square 
20140608 

From kalyani: the curved surface of a cylinder is a square of diagonal 2*square root of 2. What is the area of the base of the cylinder? Answered by Penny Nom. 





6 inches of dirt in a baseball field 
20140601 

From Mary: The baseball field is 20,000 Square feet, 6 inched deep
I need to know how many cubic yards of dirt this will generate. Answered by Penny Nom. 





Overlapping sets 
20140523 

From daniel: motors inc manufactured 325 cars with automatic transmission,216 with power steering ,and 89 with both these options. How cars were manufactured if every car has at least one option? Answered by Penny Nom. 





A piecewise graph 
20140510 

From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0500 units cost 17 cents per unit
5001500 units cost $85 plus 10 cents for each unit in the excess of 500
1500 or more units cost $185 plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units Answered by Penny Nom. 





Percentage change 
20140509 

From hi: the hw club had 46 members in sept. in april, the
club had 24 members. what was the percent of change in the hw club's membership from sept. to apan increase or decrease in membership?
ril? what is Answered by Penny Nom. 





What was the selling price? 
20140425 

From Con: Apple built 40 32GB wifi iPads, gave away two in a contest, and sold the rest at two times the manufacturing price. If the company's total profit was $10,782, what is the selling price of one of these iPads? Answered by Penny Nom. 





A circle is divided into three sectors 
20140417 

From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom. 





Converting to base 5 
20140410 

From Usama: Convert the numbers used in the following expressions into those of basefive and solve :
21+34108+62
Convert the result so obtained into decimal system and thus check your answer? Answered by Penny Nom. 





The locus of a point 
20140404 

From srishti: A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c . what is the locus of the point? Answered by Penny Nom. 





9,4,6,8,3,... 
20140331 

From Alynna: You are given the following pattern: 9,4,6,8,3,...
Create a formula for the nth figure.
I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom. 





Graphing piecewise functions 
20140329 

From Rayven: Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to
graph piecewise functions. I know that you have already answered a question similar to this
(I did my research first) but it didn't completely help me on my homework. I have to graph
piecewise functions for the specified domains, and create a table for the absolute values.
I know that two bars around a number means absolute value (two bars around 2 makes it +2)
, but how do I graph and chart the absolute value for the following:
f(x)= x+3  for 5≤x≤3
And then graph and chart: (on a separate graph):
f(x)= {x if x≤0
{x+1 if x <0
thank you!
~Rayven Answered by Penny Nom. 





Percentage increase of the population of a town 
20140328 

From hunter: The population of a certain town in 1984 was 2900 people. The percent increase was 2.5% each year. What is the town's population in 2002? Answered by Penny Nom. 





An arithmetic sequence 
20140320 

From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom. 





40 meters increased by 20% 
20140314 

From Kyle: I need help finding out this question:
40 meters increased by 20%
Is the answer 800 or is it 8? Answered by Penny Nom. 





Three consecutive whole numbers 
20140313 

From Abhishek: Three consecutive whole numbers are such that if they be divided by 5,3 and 4 respectively, the sum of the quotient is 40. What are the numbers? Answered by Chris Fisher. 





Determine the selling price 
20140308 

From augustine: knowing an auctioneer charges a 7% fee and I know I want $74,400 what is the formula to determine selling price. Answered by Penny Nom. 





What are the possible lengths of the hypotenuse? 
20140307 

From audrey: The three sides of a right angles triangle measure x2, x+5, and 2x1 in length.
What are the possible lengths of the hypotenuse?
... I'm doing the equation c2=a2+b2 and subbing in the numbers but nothing makes sense Answered by Penny Nom. 





The inverse of y = 5^x 
20140307 

From Melody: how do you find the inverse of y = 5^x Answered by Penny Nom. 





The diameter of the base of a cone 
20140223 

From elwin: i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone.
and what is the diameter of the angle is changed to 180. Answered by Harley Weston. 





Selecting a card 
20140216 

From Akarsh: Cards numbered 1 to 1000 were put in a box.Ali selects cards at random.What is the probability that Ali selects a card containing at least one'3'? Answered by Penny Nom. 





A sequence 
20140210 

From Joshua: hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms. Answered by Penny Nom. 





Conics 
20140201 

From Kassidy: Hey, I have searched through all the questions about conics and how
people use them in the real world, but none of them were very specific
on how they are applied and the process, why it's so important etc.
I have a project due asking these questions and it's been very difficult
finding the right answer, if you could name jobs, how they are use and
specifically applied that would be greatly appreciated. Answered by Penny Nom. 





A sequence 
20140130 

From joshua: hi...really struggle with one question that the teacher gave us...
The sequence is 1,2,1,5,8,1,11,___,___ Answered by Penny Nom. 





Counting in base five using words not digits 
20140125 

From Randy: We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure  in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow  how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems? Answered by Harley Weston. 





An arithmetic sequence 
20140106 

From paris: find the twentyfifth term of an arithmetic sequence whose first term is 12 and whose common difference is 6 Answered by Penny Nom. 





An infinite geometric series 
20131224 

From Muhammad: The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Answered by Penny Nom. 





Find the next 3 terms of the sequence 
20131219 

From Lanelyn: Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__ Answered by Robert Dawson. 





Base 5 arithmetic 
20131127 

From samuel: Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations? Answered by Penny Nom. 





The popcorn box problem 
20131107 

From Dave: We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4corners of a sheet of card and then folding up.
What I want is to find the sizes of card that lead to integer solutions for the size of the cutout, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.
I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1. Answered by Walter Whiteley. 





A union and interception problem 
20131019 

From Zakir: Sir, I have some problem in union there is a Question in a book
find B set if A={2,4,6,8} , AUB={2,4,5,6,7,8} and A intersection B={6,8}
plz tell me how can I find the B set Answered by Penny Nom. 





Base 5 arithmetic 
20131012 

From Obassy: (4 2 4 3)(1 3 x 4)=( Y 3 4 4),find the value of x and y in the subtraction above carried in base five? Answered by Penny Nom. 





Base 5 
20130930 

From Zakir: Sir I wanna know something about base 5 number system
Why we use it and who use this ? and what is the purpose of it Answered by Robert Dawson. 





The markup on a country maple bedroom set 
20130926 

From steven: Bargain Furniture sells a fivepiece country maple bedroom set for $1299. The cost of this set is $700. What are the markup on the bedroom set? Answered by Penny Nom. 





Intersection points and diagonals 
20130911 

From Kenneth: I was wondering, is there a relationship between the number of sides of a regular ngon and the number of times its diagonals intersect?
Ie:
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on. Answered by Chris Fisher. 





The sum of all whole numbers from 1 to X 
20130906 

From Tim: How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this Answered by Penny Nom. 





A sequence or a series? 
20130905 

From Rahul: Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)).
I am confused. It looks like a series to me. Please help.
Regards,
Rahul Answered by Robert Dawson. 





8 numbers from 80 
20130904 

From susan: Out of 80 numbers how many combinations of 8 are there and what are they. Answered by Penny Nom. 





More than half of the people said... 
20130826 

From Lucy: Hi,
The question is:
Samoa 23%
Brazil 41%
Sri Lanka 52%
Senegal 39%
Armenia 37%
Croatia 20%
Why is the following statement true for the data above: More than half of the people said they were interested in Sri Lanka. The reason I don't understand the problem is that because the percentages add up to be greater than 100%, that means that the 500 people(as stated in the question) who participated in the survey got to pick more than once. Therefore, it is not 52% out of 100% anymore.
Thanks for taking the time to answer my question. Answered by Robert Dawson. 





Tesseract 
20130822 

From Dan: I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help.
The question is: for a tesseract of side length = 1
what is the distance of the center of each cube from the center of the tesseract ?
I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me.
(anyone not having a clue what I am talking about can brush up here http://en.wikipedia.org/wiki/Tesseract )
Thanks in advance  Dan V Answered by Robert Dawson. 





Consecutive Numbers Question 
20130811 

From Lucy: Hello,
I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use
2x+1, 2x+3, 2x+5 or just x, x+2, x+4.
Also, the same question for even numbers. Would you use:
2x, 2x+2, 2x+4 or just x, x+2, x+4.
My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct?
Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),.
For the question: the sum of 4 consecutive odd integers must be:
Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16.
Thank you so much for taking the time to answer my question. Answered by Harley Weston. 





Practical uses of trigonometry 
20130806 

From tharindu: use of trigonometry Answered by Penny Nom. 





Slicing through a cone to form an ellipse 
20130806 

From Pulkit: we get an ellipse on slicing through a cone. Is there a relation between central axis of the cone and this ellipse?
Does it pass through the any of the foci of the ellipse? Answered by Chris Fisher. 





The area of a semicircle 
20130728 

From Lucy: Find the area of the the figure described: a semicircle with arc length 3 pi. Answered by Penny Nom. 





A geometric sequence 
20130716 

From Relebohile: Find the n^th term of 3,6,9,12,24,48... Answered by Penny Nom. 





Three consecutive odd integers 
20130708 

From sparsh: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: Answered by Robert Dawson. 





Inverse trig functions 
20130519 

From ky: hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5.
And find the measure of all three angle using sin1, cos1, tan1.
I got really confuse, I'm taking the SAT pretty soon and it would be great
to get this... THANX Answered by Penny Nom. 





Points of intersection 
20130502 

From Bianca: Find the sets of values of k for which the line y=kx4 intersects the curve y=x^22x at two distinct points. Answered by Penny Nom. 





How do i reverse this formula? 
20130420 

From MK: I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit.
Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut.
The current formula is X15%X = Y where X = 22,000,000 and Y = 18,700,000
Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X15%X = 22,000,000.
How do i reverse this formula to find the value of X
Thanks Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





If 4 cooks can bake 8 pies in 6 hours????? 
20130318 

From Kenneth: Hello:
I want to determine which quantities are directly and inversely proportional in order to determine the answer for the following:.
If 4 cooks can bake 8 pies in 6 hours, 2 cooks can bake how many pies in 4 hours?
Answer: 2 2/3 pies
Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above?
I thank you for your reply. Answered by Robert Dawson. 





Increasing and decreasing sales 
20130306 

From Meghan: Pace Design's sales increased by 30% in the first year, increased by 60% in the second year, decreased by 60% in the third year and increased by 90% in the fourth year. What was the cumulative change in sales over the 4 years? Answered by Penny Nom. 





Your profit should be 20% of your cost 
20130221 

From anis: if the customer says your profit should be 20% of your cost..
1) my selling value should be cost +20% of cost = SP
or
2)cost / 0.80 = SP which is correct...if the second answer is right how should i justify my customer Answered by Penny Nom. 





Write a rule for the sequence 
20130220 

From Angelia: Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ¾, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________ Answered by Penny Nom. 





How can I teach how to change bases? 
20130220 

From Tammy: How can I teach how to change bases? For example 80 base 10 changed to base 3.
Thank you! Answered by Harley Weston. 





A curve in 3space 
20130214 

From pardeep: we have to show that the curve r(t)=(cos t)i+(sin t)j+(1cos t)k ,0<=t<=2pie;
is an ellipse by showing it to an intersection of a right circular cylinder and a plane.
i got the eqn. of the cylinder but did not get the eqn of plane. Answered by Harley Weston. 





Is a line lying in a plane an open or a closed region? 
20130213 

From pardeep: please help with this question on the open and closed intervals ::
Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? Answered by Harley Weston. 





Multiplication in base two 
20130201 

From Michael: multiply in the indicated base
110two*11two Answered by Penny Nom. 





The multiplication table for the different bases 
20130201 

From sylvia: I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers. Answered by Penny Nom. 





A triangular island 
20121229 

From Udit: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Penny Nom. 





A raised bed in the shape of an octagon 
20121122 

From pat: I want to make raisedbed gardens  usually 4' square, but want to be more creative by creating octagonal boxes. The ideal size for square beds is 4'x4'. The boards are 8' long, so I want to get as much out of a board as I can. If I want an octagon with a diameter of 4', I think the sides would be (rounded off) about 1.5' each using 2 full boards with a little waste and the growing space would be less than a 4' square (16 square feet). If I want to increase the length of each side to 2' each (getting the max from a board), what will the diameter of this octagon be so I can determine the growing space of the box. (The reason a 4' square is important in gardening, besides maximizing the wood, is that a person can reach into the center to plant and pick veggies without stepping on the soil, so diameter is important). My math days are long over and I'm having trouble working with octagons! Thank you! Answered by Harley Weston. 





Difference of squares 
20121119 

From Qelibar: Please factorise x^2y^2  4 Answered by Penny Nom. 





Factor (6a^25a+1)(8a^26a+1)(12a^27a+1) 
20121116 

From bailey: Factorise f(a)=(6a^25a+1)(8a^26a+1)(12a^27a+1)
thus find [f(a)]^1/2 Answered by Penny Nom. 





Stairs for the new community center, part 2 
20121113 

From Emily: Plans for a set of stairs for the front of a new community center use the ratio of rise to run of 2 units to 5 units.
B. Sketch a set of stairs that meets the risetorun ratio of 2 units to 5 units. Answered by Penny Nom. 





A function with 3 asymptotes 
20121019 

From rimoshika: find a function that have 3 Asymptotic : y=x/y=sinx/x=1 Answered by Penny Nom. 





The nth term of a sequence 
20121019 

From Emily: I don't understand how to do this question:
Nth term for 9, 7, 5, 3, 1
Is there a fast way to do nth term for this question? Or in fact any question? Answered by Penny Nom. 





Revolutions per second 
20121018 

From Crystal: Suppose a car wheel is 26 inches in diameter.
a) If the tire completes one rotation, how far would the car travel?
b) If the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second? Answered by Penny Nom. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Equivalent sets 
20120913 

From asif: show that (1,1)~(1,1) or give its counter example Answered by Harley Weston. 





The hypotenuse 
20120906 

From Jeevan: how can i find the height and base of a right angle triangle if i have the hypotenuse only ? Answered by Penny Nom. 





A security code 
20120901 

From Breanna: The code is made up of five two digit numbers from 01 to 20 entered in a certain order. How many different security codes are possible with this system Answered by Penny Nom. 





Minutes and seconds 
20120829 

From Casey: I have to write a variable equation. The questions says there are 60 seconds. but we need to write and equation to solve for minutes. Is it 1/60 or 1/s Answered by Robert Dawson. 





An arithmetic progression 
20120822 

From A student: the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term. Answered by Penny Nom. 





John's electronic store 
20120725 

From Jora: Electronic Store
John opened an electronic store in December. During his first month,
He sold 10 LCD TVs and 20 Plasma TVs. His income during that
month was $12800. In January, he sold 25 LCD TVs and 40 Plasma
TVs for an income of $27600.
In February he projects to sell 30 LCD TVs and 50 Plasma TVs.
If John expenses are $28900 in February, how much money will he
have after paying the expenses? Answered by Penny Nom. 





A cylinder is to be filled with peas. 
20120612 

From Silje: Hi! How can I solve the following question without the use of a calculator?
"A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on.
This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?" Answered by Robert Dawson. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





A geometric sequence 
20120610 

From vicki: The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is fortyfive. What is the first term of the sequence? Answered by Penny Nom. 





The area of a semicircle 
20120528 

From Rebecca: how do you find the area of a semi circle and then how do you add the area of a semi circle and the area of a rectangle? Answered by Penny Nom. 





Division in base eleven 
20120527 

From Zoe: How do you divide numbers that are in base 11?
For example;
9A7A6A divided by A Answered by Penny Nom. 





The nth term 
20120505 

From Justin: Which expression can be used tofind the nth term in this sequence?
94,75,56,37,18,.....
My choices are
A. 19n=113 B. 21n+115
C. 19+75 D. 21n+73
Please explain how to get the correct answer. I think it is A. but I am not sure, Answered by Penny Nom. 





How to find the base length of a isosceles triangle if only the sides are given? 
20120425 

From aqilah: how to find the base length of a isosceles triangle if only the sides are given? Answered by Chris Fisher. 





The inverse of y = x^2  2x 
20120420 

From Shona: How do I Find the inverse of the function y= x^2  2x ? Answered by Penny Nom. 





A semicircular roof gutter 
20120409 

From Kyle: A semicircular roof guttering contains some water.
The crosssection of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm.
What is the depth of water in the gutter? Answered by Penny Nom. 





1+2+4+8....= 1 
20120402 

From Andy: In this minutephysics video, it's claimed that 1+2+4+8....= 1
Is this true, and if so, how?
< href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8Rg Answered by Robert Dawson. 





The power set of A 
20120324 

From rashdin: Can you find a set A, A=4 and define a bijective function between A and P(A)? Answered by Penny Nom. 





The length is inversely proportional to the width 
20120318 

From David: For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is12 and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9 Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





An increase/decrease in profit 
20120313 

From Thanikasalam: It is understood that increase/decrease in profit for current year compared to the previous year is done by the formula (xy)/y, with x=profit on current year and y=profit on previous year. How do we derive this formula?
If we work on this formula of calculating increase/decrease in profit, we get x/y1
* = (xy)/y
= x/y  y/y
= x/y  1
How do you justify the 1 in the equation above. How to derive the formula and how do i prove it? Answered by Penny Nom. 





Four digit combinations from 1,2, ..., 9 
20120226 

From Errol: show me a list with all four digit combination numbers from 0 9 Answered by Penny Nom. 





A geometric sequence 
20120224 

From Camille: Find x if the sequence 5,10,x+2 is geometric. Answered by Penny Nom. 





If x ix directly proportional to y then ... 
20120219 

From Crystal: I understand that we say x and y are proportional, then y = kx.
Generally when we say x is proportional to y, we think that when x increases y increases.
Now I am questioning whether that is actually true.
If k is negative, then when x increases, y DECREASES.
My question is does this mean this statement is incorrect:
If x is proportional to y, when x increases, y increases proportionally.
Is it more correct to say:
If x is proportional to y, when x increases, y either increases proportionally or decreases proportionally.
Along the same line of reasoning, when x is inversely proportional to y,
we think that when x increases y decreases, but that is true only if k is positive.
Is that correct? Answered by Harley Weston. 





Figures with dots 
20120215 

From A: Okay so my daughter came home and had this question for homework from her teacher. I have no idea what it means HELP!!
The question shows a figure that is a square. It has 5 dots on the top, bottom and on the sides looks similar to this:
. . . . .
. .
. .
. .
. . . . .
they want to know 3 more ways to show the number of dots in the figure. They have already shown one with just counting them
and the other one that they showed was circling the four corner dots and then taking the dots in between with a number sentence set up
like this: 4+4*(52) = 4+4*3= 16. They also besides giving 3 ways want us to write a number sentence and an algebraic sentence to show the number of
dots in the figure with "n" sides. Please help! So confusing ! I don't know if my square turned out or not but it should be 5 across the top and bottom and
on the sides and no dots in teh middle it is just the outside. Answered by Penny Nom. 





Can the result of the calculation be 2? 
20120209 

From Thomas: You have the digits 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 in a random order side by side and put randomly between two digits a colon, so that a division comes into existence. Can the result of the calculation be 2? Answered by Robert Dawson and Chris Fisher. 





A tree growth modelled by a geometric series 
20120208 

From Steph: Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres Answered by Penny Nom. 





Notation for the second derivative 
20120206 

From Shafira: In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2? Answered by Robert Dawson. 





Two sectors of a circle 
20120203 

From Wayne: I am not even sure what to ask. I have to two lengths of feet and an angle of degrees, and I have to find the area?
**Problem attached
Thanks,
Wayne Answered by Penny Nom. 





Properties of real numbers applied to subsets 
20120201 

From Mark: Hello 
The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

From Vicki: I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





Two shapes 
20120106 

From muhammad: Question from muhammad, a student:
a boy has two pieces of wire each 99cm long .he bends them into the shapes shown below.calculate the radius of each figure,giving each answer to two decimal places.figures are one is semicircle and other on is half of the semicircle. Answered by Harley Weston. 





A 46% increase 
20120103 

From kabilan: increase a price of £8.24 by 46% and give the answer to the nearest penny Answered by Robert Dawson. 





The number of digits in a number base m 
20111222 

From Jash: Assume there is a number system of base m.
The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).
In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.
Find m. Answered by Robert Dawson. 





Three consecutive numbers 
20111129 

From Michael: Find three consecutive numbers such that the second number squared
is equal to the first and third added together Answered by Penny Nom. 





Converting from base 4 to base 10 
20111129 

From anjg: How to convert base 4 number 2^11 to base 10 number? Answered by Penny Nom. 





Four carpenters can build eight houses in 10 days. 
20111123 

From Kenneth: Four carpenters can build eight houses in 10 days.
Two carpenters can build how many houses in 15 days? Answered by Penny Nom. 





What was the cost price of the article? 
20111110 

From tashana: By selling an article for $320,the profit was 20% of the cost price.what was the cost price of the article. Answered by Penny Nom. 





The sum of a series 
20111107 

From Rattanjeet: Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series. Answered by Penny Nom. 





A scale drawing 
20111030 

From aretha: i have a scale drawing of a house floor plan, don't understand how
to find the answer. the drawing is 1in: 3ft. need to find the length /
width/and the actual length/width of the living room,kitchen, 3bedrooms
deck,sitting room, entry, and closet Answered by Penny Nom. 





Three consecutive terms of an arithmetic sequence 
20111030 

From Juliette: Find X when x, 1/2x + 7, 3x 1 are consecutive terms of an arithmetic sequence. Answered by Penny Nom. 





Expanded form 
20111012 

From Chris: Write this number in expanded form
4 326 180 501
Thanks!!! Answered by Penny Nom. 





Three consecutive odd integers 
20111007 

From Muneera: Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one? Answered by Penny Nom. 





A reservoir has the shape of an inverted cone 
20111003 

From Roger: a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters? Answered by Penny Nom. 





58 choose 4 
20110826 

From Jean: Using only the numbers 159, how many times would the
number 23 appear in combinations of 5 numbers?
... Can a list be provided as well?
Thank you very much,
Jean Answered by Penny Nom. 





Two line segments in the plane 
20110815 

From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.
Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points. Answered by Chris Fisher. 





A sequence 
20110814 

From intesar: how do i figure this out 0,1/6,2/9,3/12 Answered by Penny Nom. 





The third term of a sequence 
20110813 

From sammantha: Find the 3rd term of the sequence, an=1.5(4)n  1. Answered by Penny Nom. 





Infinite Logarithmic Series 
20110808 

From Sourik: Dear Expert,
In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between 1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof.
Thanking you,
Sourik Answered by Robert Dawson. 





The nth term of a sequence 
20110701 

From Rachel: I am trying to help my son get ready for our Aims test and I am not much help. The sequence is 2,5,10,17 The question is which equation represents the rule for finding the nth term for this sequence
a. an=n + 1
b. an=2n2
c. an=n2+1
d. an=2n+1 Answered by Penny Nom. 





The nth term 
20110430 

From Samantha: predict the general term, or the nth term, An for the sequence.
1/2,2/3,3/4,4/5,5/6 Answered by Penny Nom. 





Find the rate at which the searchlight rotates 
20110417 

From Meredith: A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Answered by Penny Nom. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





A true or false trig question 
20110324 

From Abeth: True or False: Since cot (theta) = cos (theta)/sin (theta), if cot (theta) = 1/2, then cos (theta) =1 and sin (theta)=2.
My answer before was true, but not my answer is false. Can you give me a solution on this matter. thanks. Answered by Penny Nom. 





A 15% increase 
20110322 

From Abeth: Bobby dela Cruz is the purchasing agent for school supplies of a certain university. Because of new research projects, Bobby ordered an additional 32,500 worth of supplies this month. This is a 15% increase from last month. What was the value of the school supplies that Bobby ordered last month? Answered by Robert Dawson. 





Three consecutive odd numbers 
20110311 

From George: Write an equation three consecutive odd numbers whose sum is 75 Answered by Penny Nom. 





A family of circles 
20110301 

From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Answered by Penny Nom. 





Converting base 3 to 5 
20110228 

From Harry: Hey Math Central, I came across your website and im in need of help on my maths c assignment. I have to convert base 3 to 5 without converting back to ten. I heard that you can use patterns in 3 and 5 to make an equation but im not sure how to and i also heard you can use logarithms but i dont know how to use those so im kinda stumped. Answered by Robert Dawson. 





An imaginary infinite geometric tree 
20110218 

From Elise: An imaginary infinite geometric tree grows 1m the first day.
2nd day 2 branches and right angles to each other and each 0.5 m long.
3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of rightangled triangles and high school level knowledge of geometric series to show
the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m. Answered by Robert Dawson. 





Reversing the digits 
20110208 

From rejie: if the digits are reverse , the number is 9 less than the original number.what is the equation? Answered by Penny Nom. 





Three consecutive numbers 
20110131 

From parth: name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisibel
by 5 and the largest divisible by 4 Answered by Penny Nom. 





A player runs from second base to third base 
20110130 

From Marie: A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5
Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First.
I have found dA/dt in a previous problem. Answered by Penny Nom. 





The perimeter of a semicircle 
20110129 

From Keith: I have the perimeter of a semi circle of 37 but how do I calculate the diameter from this.
This is all the information I have. Answered by Penny Nom. 





The sequence 2,3,5,5,8,7,11 
20110119 

From taylor: number relationship in number sequence 2,3,5,5,8,7,11 Answered by Chris Fisher and Penny Nom. 





tanθ=1.192 
20110115 

From Adori: Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation.
a) tanθ=1.192
I do not understand how to find the second value of θ. Answered by Harley Weston. 





What is next in the sequence? 
20110113 

From jodi: what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25 Answered by Penny Nom. 





Set notation 
20110110 

From Ron: The question asked in a handout:
8k  5 < 35, keI
I believe the answer to k is 5. But what does the k e(E) I mean in this? Answered by Harley Weston. 





Semicircles and the Pythagorean Theorem 
20110109 

From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:
****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??
I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom. 





A sector of a circle 
20110107 

From Alice: the radius of a circle is 7cm the angle of the sector is 68 how do you find the Answered by Penny Nom. 





Line segments 
20110104 

From Izsak: What is the formula to find the number of segments that can be named by a given number of points on a line? Answered by Penny Nom. 





[sec^2x]*[sec^2x] 
20101216 

From Hari: [sec^2x]*[sec^2x]=...? Answered by Penny Nom. 





A geometric progression 
20101215 

From Abeth: find the value of x so that 2(x1), x+3, x will be a geometric progression. Answered by Penny Nom. 





A sector of a circle 
20101129 

From Mel: Find the area of a sector of a circle that has a central angle of 13pi/18 and a radius of 12cm. Round answer to nearest 10th degree Answered by Penny Nom. 





Hours minutes and seconds 
20101126 

From beket: I need to turn 1.486588292 into real time hours minutes and seconds. I keep getting multiple answers. Online conversions give me 1 hour 29 minutes and either 11 or 12 seconds. On the calculator I get 1 hour 29 minutes and 20 seconds. Can you explain how to turn this decimal into time? Answered by Robert Dawson and Penny Nom. 





Intersecting polygons 
20101117 

From Laura: How can I estimate the amount of intersection (area or better a normalized number) between two polygons if I have the cartesian coordinates of their vertices?
Thank you in advance,
regards,
Laura Answered by Robert Dawson. 





The perimeter of a semicircle 
20101111 

From gayathri: the area of semicircle is 1925sq.cm find perimeter Answered by Stephen La Rocque. 





Three consecutive odd integers 
20101107 

From karen: find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first Answered by Penny Nom. 





How far must the pitcher travel to get to the ball? 
20101104 

From ken: A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball. Answered by Penny Nom. 





The base of an isosceles triangle 
20101024 

From Brian: how can I find the base of an isosceles triangle from the height and the perimeter? Answered by Penny Nom. 





Four consecutive integers 
20101021 

From Mickey: Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer.
I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3 Answered by Penny Nom. 





A division sentence for an array 
20101005 

From Laura: On a math test Grace needs to look at an array and write a division sentence for the array. Grace writes 18/3=6 on her answer sheet. Describe what the array on Graces test looks like. Answered by Penny Nom. 





A Taylor polynomial for (lnx)/x 
20100929 

From Dave: I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, 3, 11, 50, 274... Ok, so the negative is an easy fix > (1)^n1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this?
Thanks! Answered by Chris Fisher. 





rat sequence 
20100924 

From Vishal: this is known as rat sequence. I want to know the logic pf this :
1,2,4,8,16,77,145 Answered by Chris Fisher. 





A reverse PST calculation 
20100923 

From Manning: Hi, I'm a manufacturing contractor in Saskatoon. The way to calculate PST for us is using total contract amount x 70% then 5%.
For example, contract amount of $100 x 70% x 5% = $3.5 (PST). The subtotal is using contract amount + PST.
$100 + $3.50 = $103.50.
If you only know the subtotal is $103.50 including PST, how do you reverse calculation to get the contract amount?
Thank you very much for your help. Answered by Harley Weston. 





A taxi ride 
20100922 

From Jack: A taxi ride costs you $2 for the first km and 10 cents for each tenth of a km thereafter.
Sketch a graph of the total cost $C(x) for a ride of xkm, for 0 < x < 2. Hint: The
graph is not smooth.
How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth, Answered by Stephen La Rocque. 





Find the point of contact of the circles 
20100920 

From Sandra: If the center of circle A = (1,3) and the radius of it is √20,
the center of circle B = (5,9) and the radius of it is √80.
Find the point of contact of the circles A and B. Answered by Janice Cotcher. 





The nth term 
20100914 

From Anna: The problem is 2n2. find the nth term. I'm lost as how to even begin Answered by Penny Nom. 





Differentiable on an interval 
20100812 

From Dave: Hi
I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help. Answered by Robert Dawson. 





An 18ft round pool 
20100719 

From christine: will an 18ft round pool fit on a 12x16 ft rectangular cement slab? Answered by Tyler Wood. 





Remainders 
20100717 

From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher. 





A pattern in a puzzling sequence 
20100709 

From Martha: A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15
USE THIS PATTERN SUGGESTED TO HELP YOU FIND
THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#$ where @ + # + $ = 258 Answered by Tyler Wood. 





The product of 2 consecutive integers 
20100628 

From Sharon: the product of 2 consecutive integers is 6 less than the square of the larger number.
find the smaller number Answered by Penny Nom. 





The intersection of two graphs 
20100627 

From Austin: In depth explanation of how to find the intersection points of functions y=4t+300 and y=4.9(t5)^2+300 Answered by Stephen La Rocque. 





Selling price, cost and profit 
20100622 

From Alex: The profit on a certain television set is 16.5% of the cost price. If the profit is $330,
Find:
a) the cost price
b)the selling price of the television Answered by Penny Nom. 





The area of a circle 
20100612 

From grier: please,
what is the area of a semicircle with arc length 3pi? Answered by Penny Nom. 





A cylindrical vessel with belled ends 
20100601 

From George: surface area of a vessel with a cylindrical length of 60 feet, a diameter of 10 feet, and with belled ends of 5foot radius Answered by Penny Nom. 





Math in the workplace: nursing 
20100524 

From Taylor: How is math used in the workplace  Nurse Anesthetist? Answered by Penny Nom. 





The number of gallons of water in a basement 
20100523 

From George: A basement with dimensions 68 ft long by 42 ft wide by 10 ft deep is flooded to the ceiling calculate the number of gallons of water in the basement. 70 Answered by Penny Nom. 





Divisibility by 3 
20100523 

From Cathleen: To math central. I have to do a maths extension question that I don't understand. At first I thought I did.
It is about the dividing by three. In one part of the question, it asks me to show that the rule of division by three does not work for 23142 with a little 5 down the bottom.
What doe base 5 mean? We first thought that the little 5 down the bottom meant multiplying y the power of five.
Can you please tell me what it means so I can finish this question? Answered by Penny Nom. 





The hypotenuse of a triangle 
20100522 

From linda: find the length of the hypotenuse of a triangle with legs of 12in. and 17in. round to the nearest hundredth Answered by Tyler Wood. 





Percentage increase 
20100520 

From Rebecca: Question from Rebecca:
In 2008 my land was valued at $84,000. In 2009 my land was revalued at $235,000.00. What is the
percent increase between the two values? I want to be able to express "the
value was increased by x%." Answered by Harley Weston. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





The nth term 
20100509 

From Jessica: what is the nth term of 3, 9, 19, 33, 51
please help Answered by Walter Whiteley. 





A geometric progression 
20100430 

From Kalyani: sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is? Answered by Chris Fisher. 





Sales taxes in Quebec 
20100428 

From carole: I work at a company where we use transport companies and we often get credits
on their invoices. I need to know how to subtract the sales taxes from these credit amounts.
(5% TPS and 7.5% TVQ).
Is the equation: Amount / 1.05 = then this amount / by 1.075=? Answered by Penny Nom. 





4 + 10 + · · · + (6n − 2) 
20100421 

From Lan: Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How? Answered by Penny Nom. 





The area of semi circle 
20100416 

From sagir: how to find the area of semi circle? Answered by Penny Nom. 





A sequence 
20100413 

From Essence: hello,
I am having trouble doing my math homework. It asks me to write the first five terms of each sequence .I can not figure it out because it is a fraction.
The Problem Is:
{2n+1/2n} Answered by Penny Nom. 





A geometric sequence 
20100413 

From glen: A geometric sequence has a first term of 0.1024, a second term of 0.256,
and a middle term of 156.25. how many terms are there in the whole
sequence?
i know that r=2.5 but i dont know how to find how many terms there are. Answered by Penny Nom. 





Counting by sevens 
20100413 

From Larry: Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted
three of the following numbers, which number did Lee NOT count?
a. 107
b. 184
c. 534
d. 641
Answered by Robert Dawson and Penny Nom. 





The area of a field of view 
20100407 

From Frank: I know we have a field of view of 90 degrees and the distance we can cover is 6 miles. What is the area we can cover/view?
A formula would be nice to have since the diameter or distance of the wedge area can change and the degree of the field of view can also change.
Thank you and I look forward to hearing from you.
Frank Answered by Penny Nom. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





1/1+1/2+1/3... 
20100331 

From Mohd: you explained the way of getting the summation of 100 series numbers
but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100 Answered by Robert Dawson. 





The angle of intersection between two lines 
20100325 

From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher. 





Water in a culvert 
20100318 

From Chip: Hello,
I have a problem to which I know there must be an analytical solution  but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it.
Thank you Answered by Penny Nom. 





Angular velocity 
20100317 

From Lindsay: Determine the angular velocity, in radians per second, of a 14inch car wheel, if the car is traveling at 60 miles per hour Answered by Harley Weston. 





A 14 side well house cover 
20100312 

From Kenneth: I am 35 yr I am wanting to build a well house cover. I'm trying to figure out how long the pieces need to be and what angle they need to be for a 4 ft dia with 14 side well house. I would love an answer but would also like to know how to figure it in the future. Thanks Kd Answered by Harley Weston. 





Prove A intersect B =X iff A = X and B = X 
20100306 

From Gloria: how would you prove A intersect B =X iff A = X and B = X Answered by Tyler Wood. 





The base area of rectangular prism 
20100305 

From Desiree: How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ? Answered by Penny Nom. 





2+3 =10 and 7+2=63 and ... 
20100301 

From brenda: if 2+3 =10 and 7+2=63 and 6+5 =66 and 8 +4 = 96 then 9+7+ ??????
its driving me crazy !! Answered by Penny Nom, Claude tardif and Melanie Tyrer. 





The hypotenuse 
20100227 

From Dannielle: how do you find the hypotenuse if a=8 and b=6? Answered by Penny Nom. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





The first five terms of a sequence 
20100214 

From Joanne: Find the first five terms of the sequences with the nth term given as follows.
n^2+3n Answered by Penny Nom. 





Can a line segment curve over two planes? 
20100214 

From Graham: I am working on a math fair project.
Can a line segment curve over two planes?
Such as, if I had a three dimensional L bracket and I drew a line segment
on it with a marker starting on the bottom of the L and had it curve
around the corner and up the top, would it still be considered one line
segment? Or is that two line segments?
Is there a rule that a line segment can only occupy one plane?
Thank you.
Graham Answered by Chris Fisher. 





A square corner 
20100211 

From Trevor: I am building a new house and wish to set it out on site with the use of
profile boards and string. I want to be certain it is correct in terms of
squareness. I have a vague idea that the square on the hypotenuse should
be equal to the sum of the squares of the other two sides.
I get a little lost here and need some help. The building is a rectangle
measuring 40x30 feet to exterior brickwork. I guess that the length
of the hypotenuse should be exactly the square root of the combined
squares of the two sides.
Using the above measurements could you give me calculations from nuts
to soup as to the correct length of the diagonal. And what adjustments
are needed if everthing is not in accord.
Trevor. Answered by Robert Dawson. 





A sequence 
20100207 

From Shalev: hi,
i had a job interview yesterday. it had mathematical questions. couldn't solve 1. i m obsessed with it. please find out what the answer is..
it goes like this:
2,4,5,5,8,6,_,_,14,8
thank u very much Answered by Claude Tardif. 





The perimeter of a semicircle 
20100204 

From Sarah: The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle. Answered by Tyler Wood. 





A sector of a circle 
20100204 

From trisha: Given a circle with a radius of 6 inches. Find the area of the sector that is formed by an arc of 36 degrees. Round your answer to the nearest tenth of an inch. Answered by Penny Nom. 





Consecutive even integers 
20100203 

From cassandra: find 2 consecutive even integers whose sum is 34
find 3 consecutive even integers such that 3 time the middle interger is 10 more than the greatest. Answered by Tyler Wood. 





A sequence 
20100127 

From Haku: if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula? Answered by Penny Nom. 





A sequence 
20100122 

From brahmaji: 0 7 26 63 _ 215 342 fill the blank? find the missing number Answered by Robert Dawson. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





Percentage increase from a negative to a positive 
20100112 

From Greg: If a company had a net lost in 2005 of $11,234 and net income of $3231 in 2006, what is the percentage annual growth in income between the two years? Answered by Robert Dawson. 





Improper fractions 
20100112 

From Blanca: Between which two consecutive natural numbers does the improper fraction 57/56 lie? Answered by Robert Dawson. 





The domain, range and inverse of a relation 
20100108 

From Nazrul: Given that A={2,1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details.
Thank you. Answered by Penny Nom. 





The area of a sector 
20100107 

From angelkem: how do you get the area of the circle, the sector, the shaded sector, non shaded sector and its total area if the diameter is 20 cm and each area of the circle is 45 degrees? Answered by Penny Nom. 





Consecutive odd intergers 
20100106 

From keyanna: list five consecutive odd integers, starting with 3 Answered by Robert Dawson. 





Holiday for 7 golfers 
20100105 

From Andy: I am having difficulty scheduling pairings for a forthcoming Golf holiday. There are 7 players and we will be playing 7 rounds  each round will be a 3 ball and a 4 ball. I am trying to work out a schedule that means everyone plays with each other roughly the same number of times (with a minimum of, say, 3 times if possible). Also, we are looking to ensure everyone plays in roughly the same number of 3 and 4 balls. Any suggestions would be much appreciated (we leave in 10 days time). Thank you. Answered by Victoria West. 





Profit increase from 10% to 15% 
20100103 

From taha: A shopkeeper sold a pen for $13.20 to a make a profit 10 percent.In order to earn a profit of 15 percent,he should have sold it for? Answered by Penny Nom. 





Triangles on a base of 2.4 meters 
20091226 

From Allan: Please,How do I calculate the height of a triangle when I only know the width of the base line,It is 2.4 mtrs. Thankyou very much. Answered by Penny Nom. 





The acute angle formed by intersecting lines 
20091217 

From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x  2y = 2. Was is necessary to find the intersection point? Answered by Robert Dawson. 





The second derivative of y = x³ (x² + 5) 
20091214 

From Kyrie: Find d²y/dx² for this function:
y = x³ (x² + 5) Answered by Penny Nom. 





A circle problem 
20091214 

From Fawad: AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm.
Find the length, in cm of AQ. Answered by Chris Fisher. 





Bases larger than ten 
20091214 

From Nick: For numbers in bases larger than ten, what are the digits by mathematicians' conventions?
I assume the first 10 are always 09. I know two computer science conventions (for hexadecimal (AF caseinsensitively) and for base 85 (casesensitivity plus 23 other characters)) and as a school student I learned that base 12 uses either T and E (which confused me when I thought they stood for Eleven and Twelve) or A and B, the latter as capitals only. Clearly, these conventions are in conflict.
I saw your reply in http://mathcentral.uregina.ca/QQ/database/QQ.09.99/magin1.html as accessed a few minutes ago but hope that in the 10 years since then mathematicians have arrived at a convention. Have they?
Thank you.

Nick Answered by Claude Tardif. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





7 36 14 18 28 9 56 x y 
20091206 

From lisa: what is the sequence of x and y
7 36 14 18 28 9 56 x y Answered by Penny Nom. 





What number comes next? 
20091125 

From Mark: Can someone help and give me the break down of how to solve. 5,3,1,1 Answered by Penny Nom. 





The point of intersection of the pair of straight lines 
20091119 

From Stephanie: Find the point of intersection of the pair of straight lines:
y=3x9
y=4x+2
x = _______ and y = ________
I am totally confused. Please help Answered by Robert Dawson. 





A baseball diamond 
20091118 

From maelee: the official distance between home plate and second base in baseball diamond is 120ft. Find the area of the official ball diamond & the distance between the bases. Answered by Robert Dawson, Chris Fisher and Penny Nom. 





6 numbers from 53 numbers 
20091117 

From MIGUEL: IM A STUDENT IN HIGH SCHOOL AND IM HELPING THE SOCCER COACH WITH PLAYS
SO I NEED ALL THE POSSIBLE NUMBER COMBINATIONS OF NUMBERS 1 53 IN SETS OF SIX
THE NUMBER CAN ONLY BE USED ONCE IN EACH SET. Answered by Penny Nom. 





A sequence of letters and numbers 
20091110 

From Maria: What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old.
J1F8M1A0M1J0J1 Answered by Robert Dawson, Claude Tardif and Harley Weston. 





A drawing of a baseball diamond 
20091109 

From Beth: My husband has a drawn diagram on a piece of paper of a baseball diamond. He knows that on the paper 1 1/16" (1.6875") = 90 actual feet. How do we calculate how many feet 5 7/8" on the paper would be? Answered by Penny Nom. 





Consecutive odd integers 
20091109 

From Erin: I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2
and so on, but if its odd then do the numbers change to odd ones? i don't know
the question is: the sum of four consecutive odd integers is 72. write an equation to model
this situation and find the values of the four integers Answered by Robert Dawson and Penny Nom. 





What's the next term? 
20091103 

From bharat: if
1=5
2=25
3=325
4=4325
5=? Answered by Robert Dawson and Penny Nom. 





The extended real numbers 
20091102 

From Justin: Hello there, I was wondering is the set of extended real numbers a closed set or an open set?
Justin Answered by Robert Dawson. 





Consecutive positive integers 
20091101 

From Madi: I'm doing my homework, and there are questions on Consecutive Positive Integers. I was just wondering, what is a consecutive integer?
Or to be more specific, what is a consecutive POSITIVE integer? Answered by Penny Nom. 





The intersection of two graphs 
20091030 

From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. Answered by Penny Nom. 





Graphing y=(4x^2)^5 
20091025 

From natalie: I want to graph the curve of y=(4x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8.
Thank you so much,
natalie Answered by Harley Weston. 





Four consecutive odd integers 
20091024 

From Tonya: the sum of four consecutive odd intergers 2008 what are the intergers Answered by Penny Nom. 





What jobs use conics? 
20091022 

From denise: i have to type a paper on what jobs use conics and i can not find anything can you help
thanks
Denise Answered by Penny Nom. 





The inverse of f(x)=1/x^2 
20091022 

From Jasmine: how to solve f(x)=1/x^2 > find f1[x], than state if its a function Answered by Harley Weston. 





A sequence 
20091020 

From Alyce: The rule of this sequence is k=1/8n. Find the 8th term of the sequence.
1/8, 1/4, 3/8, 1/2, ...
Thanks! Answered by Penny Nom. 





The hypotenuse of a right triangle 
20091018 

From steven: the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse. Answered by Penny Nom. 





The next three terms 
20091016 

From Shawn: I'm a parent and don't know how to help my 6th grader solve for this problem.
Name the next tree terms in this sequence and tell the rule used to find each:
1,0,1,0,1,2,3,8,25,..... Answered by Chris Fisher. 





What is the next term? 
20091004 

From julia: patterns
18 46 94 63 52 61 what is the next one? Answered by Penny Nom. 





How many terms are there in this sequence? 
20090928 

From tabby: How many terms are there in this sequence?
5,1,3,...,111 Answered by Penny Nom. 





Seven circles 
20090920 

From Bobbi: try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circlesvertical, horizontal, and diagonal  add up to 12. Each number can be used only once. Answered by Stephen La Rocque. 





Segments of a ring gasket 
20090920 

From Robert: I am in the process of making an Excel spreadsheet in which our sales
team just needs to enter the outside diameter, inside diameter, and
number of segments to price ring gaskets that are too big to fit on a
sheet of material and need to be cut into segments. With your help I
was able to create a spread sheet that can calculate the Chord lengths,
and Segment height on a single gasket segment. I am now stuck trying to
come up with a formula to figure out the height of the second segment
when it is stacked on the first segment, then use it to add more
depending on the quantity of segments needed. I have an illustration
below showing 2 segments (of a gasket that was segmented into 4 pieces)
stacked together. I need to find a formula to get the dimension from
"A" to "B". Answered by Harley Weston. 





A sequence 
20090919 

From Oliver: I am struggling to work out the missing terms in the following sequence:
1, 3, _, 7, 11, 18, _ Answered by Chris Fisher. 





Cubes and squares 
20090916 

From Stanley: What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square? Answered by Robert Dawson. 





A sequence 
20090915 

From Derek: what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2... Answered by Penny Nom. 





The nth term of a sequence 
20090911 

From Michael: My son has this question as part of his key stage 3 maths homework
The nth term of a different sequence is n  2/n^2.
We've got to find the first three terms of the sequence. Answered by Claude Tardif. 





Bisecting rays 
20090909 

From frank: Ray OC bisects angle AOB, ray OD bisects angle AOC, ray OE bisects angle AOD, ray OF bisects angel AOE, and ray OG bisects angle FOC: if angle BOF=120 degrees, then find angle DOE? Confused! Answered by Penny Nom. 





The intersection of two graphs 
20090902 

From Jaqueline: Find the points of intersection of the graphs of the equations
x^(2 )+ y^2=25 and 2x + y = 10 Answered by Penny Nom. 





Price increases and decreases 
20090902 

From craig: I work for an industry that bases it price increases and decreases on commodity pricing  Customer get confused on how/why we calculated new prices due to movement in the market 
Price go up x% for every $10 of movement in the market 
For this example
Movement went down by $30 and it is 2% for every $10  so price decrease was 6%.
Customer's price is currently $100.
We say  $100/1.06= new price of $94.3
Customer says  $100*.94= new price of $94.
They don't understand that if board went back up $30 which would be 6% increase, they wouldn't be back at $100 if they multiplied on the price decrease.
$94*1.06=$99.64 vs. $94.3*1.06=$100 (Back to the original price)
What is the best way to explain to customer besides using this example?
Any help or info is appreciated.
Craig Answered by Victoria West. 





Arithmetic Sum & Sequence 
20090901 

From Alice: Find the 24th term of this sequence
6.8,8.0,9.2...
Find the sum of the first 21 terms Answered by Janice Cotcher. 





Cardinality of infinite sets 
20090901 

From Brian: I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong.
I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers.
Please correct me if I am wrong, but I believe those two sets are  pardon the expression  equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa.
For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321  I could write it out algebraically, if you want, but you get my point)
Am I wrong?
Thanks,
Brian Answered by Victoria West. 





Sequence problem 
20090818 

From James: I have the equation: t_{n} = (n)(n+1)/2
Which gives the sequence: 1, 3, 6, 10, 15 etc.
However, I'd like to be able to solve for n.
So that a t of 6 would give me the answer of 3, and t of 10 would give me the answer 4 etc. Answered by Stephen La Rocque and Victoria West. 





Subtraction base 5 
20090809 

From Nikki: can you help me how to do subtraction in base 5 notation. example is 3434  51?
how do you do this in base 5?
can you please explain how you do this & the answer as i have no idea.
Thank you kindly
Nikki Answered by Harley Weston. 





An infinite set 
20090807 

From Islam: How can I prove that the set of all odd natural numbers is an infinite set. Thank you. Answered by Robert Dawson. 





Percentage decrease 
20090804 

From Bill: How to calculate the Percentage Increase or Decrease of a $ value.
Example 
Site Spend for 01012008 thru 073108 was $ 3,465,660
Site Spend, 2009 YTD as of 073109, was $ 1,673,405
Site Spend down what % between these two amounts ? Answered by Penny Nom. 





Angular speed 
20090804 

From Mary: The engine of a sports car rotates at 5000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution. Answered by Penny Nom. 





Intersection of Two Curves 
20090727 

From Amarah: Find the coordinates of the point A( this point is where the two lines intersect). Justify answer
question : here is a curve x^y =y^x (for x,y>o) Answered by Janice Cotcher. 





How can I trisect an angle? 
20090727 

From Nazrul: How can I trisect an angle? Answered by Robert Dawson. 





The inverse of F(x)=x^26x+13, for x>3 
20090726 

From Juan: The function F is given by F(x)=x^26x+13, for x>3.
A. Write F(x) in the form (xa)^2+b
B.Find the inverse function F^1
C.State the domain of F^1 Answered by Penny Nom. 





Finding the Common Difference and Number of Terms of an Arithmetic Sequence 
20090724 

From Juan: In an arithmetic sequence, the first term is 2, the fourth term is 16 and the nth
term is 11,998
A. What is the common difference?
B. What is the value of n. Answered by Janice Cotcher. 





A sundial on an elliptical cylinder 
20090722 

From Leo: I want to build a sundial where the shadow falls on an elliptical cylinder. I can
calculate the coordinates of the points on the cylinder that I want to mark.
My problem is that I will have to make the surface as a flat sheet and bend it
into an elliptical shape. However, I cannot work out a scheme to transfer
the coordinates I know into a distance that will work when I bend the shape.
Help! Answered by Robert Dawson. 





Annular sector 
20090720 

From Ed: What is the name for the section of a flat ring (annulus)? Similar to a section on a radar screen, a quadrilateral but the top and bottom are curved. Answered by Robert Dawson. 





Finding the Line Joining Perpendicular Feet 
20090716 

From mukulu: Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x3y4= 0 and 3x+y6=0. Answered by Janice Cotcher. 





A sequence 
20090711 

From jamie: what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _ Answered by Penny Nom. 





A base 7 number and a base 9 number 
20090709 

From koteawarao: Find a base 7 threedigit number which has its digits reversed when expressed in
base 9.
ans: (281) base 7 and (182) base 9 Answered by Harley Weston. 





A binary equation 
20090707 

From Chinonyerem: Find a bitwise solution (i.e find xi so that each xi E {0,1}) to
32 = x1 + 2x2 + 4x3 + 9x3 + 20x5 Answered by Harley Weston. 





The retail price for an ice cream scoop 
20090705 

From Patricia: Hi  I am trying to figure out the fairest retail price for an ice cream scoop. We have an ice cream parlor
and the cost of the ice cream we buy by the bulk container has recently been increased so now we must charge
more for our scoops. We pay a wholesale price of $25.40 for 242 ounces of ice cream. The cost per ounce is
$0.105. What is the formula for figuring out how much to charge retail per scoop? This is probably so simple
but confusing to me. Please help. Thank you! Answered by Harley Weston. 





Prove that the set of all positive odd integers is an infinite set 
20090620 

From Nazrul: How can I prove that the set of all positive odd integers is an infinite set.
Thank you in advance. Answered by Victoria West. 





Successive differences 
20090618 

From Jonathan: I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help. Answered by Robert Dawson and Penny Nom. 





Subsets 
20090616 

From Tracy: Suppose C is the subset of D and D is the subset of C.
If n(c)=5, find n(D)
What other relationship exists between sets C and D? Answered by Penny Nom. 





Two ships and a lighthouse 
20090527 

From Chelsey: I have a question in regards to how do I know when to use tangent or cosine when determining angles. The question is: Looking north from the observation deck of a lighthouse 60 m above the sea, a lighthouse keeper sees two ships. The angles of depression to the ships is 5 degrees and 10 degrees. How far apart are the ships?
I don't understand which one to use when solving the equation. Answered by Harley Weston. 





A sequence 
20090526 

From Jay: what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20 Answered by Stephen La Rocque. 





What type of conic section is this? 
20090522 

From Donna: What type of conic section is 3x² + 3y²  4y  8 = 0 Answered by Penny Nom. 





An infinite geometric series 
20090518 

From terri: find the sum of the infinite geometric series
14 7 +7/2 7/4 +.....
A. 7007/13 B. 2002 C. 28/3 D.5005/7 Answered by Stephen La Rocque. 





A sequence 
20090518 

From Richard: This is my question about sequences.
Write down the nth term of the following sequences.
1/2, 3/4, 9/8, 27/16
Plz help me solve the question! Answered by Penny Nom. 





A number sequence 
20090508 

From alicia: what is the next number 1,2,6,42,1806? is it 1954? Answered by Robert Dawson, Chris Fisher, Penny Nom and Claude Tardif. 





How do you convert 1248 to base 6? 
20090502 

From Tamara: How do you convert 1248 to base 6? Answered by Penny Nom. 





Stairway construction 
20090502 

From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs.
Rule 1: x+y=43 and x+y=46 (cm)
Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length)
I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe.
Did i explain it ok? Thanks for your help.
olivia Answered by Penny Nom. 





2+6+12+20+30+42 
20090424 

From fredy: what is the sigma notation for the series 2+6+12+20+30+42? Answered by Stephen La Rocque. 





Miles per hour and feet per second 
20090422 

From mary: A car traveling at 60 miles per hour, how many feet per second has it traveled? Answered by Robert Dawson. 





Percent increase from a negative number to a positive number 
20090421 

From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = 110,333.00
2008 Net Profit = 66,054.00
Brian Answered by Harley Weston. 





The center of an ellipse 
20090421 

From Nae: what is the ellipse center of 5x^2+3y^2=15 Answered by Stephen La Rocque. 





$65.09 is 70% greater than the average price 
20090411 

From Kelly: Hello!
I know you might be thinking that I didn't look through your previous answers, but I really did.
Here's my dilemma I have a percent increase equation that is missing the 'old" value.
I know that $65.09 is 70% greater than the average price, but I do not know the average price. How do I go about finding that?
I tried to set up an equation, but its throwing me off because the unknown variable is in there twice, and it's been a long time since I've taken math
Thank you for your help...greatly! Answered by Penny Nom. 





The axiom of choice and constructibe sets 
20090410 

From sydney: The axiom of choice asserts the existence of certain sets, but does not construct the set. What does "construct" mean here? For example, does it require showing the existence and uniqueness of some function yielding the set? In general, what does it mean to require the existence of a mathematical object be tied to a construction of it? Answered by Claude Tardif. 





Direct and inverse relationships 
20090406 

From allison: A piece of string is cut into n pieces of equal lengths L
(1) does n vary directly or inversely with L Answered by Penny Nom. 





Three consecutive odd integers 
20090402 

From Brian: Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first. Answered by Robert Dawson. 





A 25 team league 
20090331 

From brad: 25 teams are in a league in which each team plays everybody once how many games must be scheduled ? Answered by Penny Nom. 





Adding in base six 
20090329 

From Lucy: If you are working in base 6,
what do you have to add to 4(base 6) to get 10(base 6)???? Answered by Penny Nom. 





Uses of Pythagorean theory 
20090327 

From Britta: Please, give me some complex real life situation examples where the pythagorean theory is used. It must be a grade 8 or grade 9 level of thinking as that is what is my teacher's demands. Answered by Robert Dawson. 





The base of a triangle 
20090325 

From yinna: how do I find the base of a triangle who's height is 2 times the base and the area is 9? Answered by Penny Nom. 





The base and height of an isosceles triangle 
20090323 

From Chris: How do you find the base and height of an isosceles triangle that has 2cm legs? Answered by Harley Weston. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





A plane cuts a line segment 
20090317 

From Manis: Find the ratio in which the line joining (2,4,16) and (3,5,4) is divided by the plane 2x3y+z+6=0. Answered by Robert Dawson. 





License plates and poker hands 
20090314 

From CC: You have a license plate it can have 6 numbers/letters you can use the numerals 09 and the letters AZ how many combos are possible and how did you figure it out?
Question 2,
Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards. Answered by Harley Weston. 





A sequence 
20090313 

From Shelly: Which sequence satisfies the rule n/4? Answered by Stephen La Rocque. 





Three consecutive odd integers 
20090311 

From Susan: Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70 Answered by Penny Nom. 





A sequence 
20090311 

From Vly: 2; 6; 26;126;626 find the nth term Answered by Harley Weston. 





The angles of a triangle 
20090311 

From Marissa: The angles in a triangle measure 7x1, 18x+2, and 5x+10. Determine whether the
triangle is acute, obtuse, or right. State your reasons clearly. Answered by Robert Dawson. 





Trifecta 
20090309 

From Annie: I want to know how many combinations are there for the first 3 horses in
a race of 20 horses. For example, the horses can come in 1, 5, 7 or
7, 5, 1 which are totally different combos. I've only found formulas
where the 1, 2, 3 and 3, 2, 1 are counted as the same combo.
In horse racing every combo is different.
Thank you. Answered by Penny Nom. 





A property that decreases in value every year by 10 percent 
20090307 

From PEter: there is a competition problem where a cottage is worth 25000 years, but it decreases in value every year by 10 percent. Without a calculator, is there a way to find after how many years, the cottage will be worth 2500? (besides multiplying it out and besides logs) Answered by Stephen La Rocque. 





The ratio test 
20090306 

From Haley: Use the ratio test to determine whether the series in convergent or divergent.
(2/5)+(4/10)+(8/15)+... Answered by Harley Weston. 





Infinite sets and infinite limits 
20090306 

From Justin: Hello, I know I have asked a similar question before but I was just wondering if set theory applies to the lim x>0, y=1/x=infinity and if so, what type of infinity would it be? Thanks a lot for your help with this question!
Regards,
Justin Answered by Robert Dawson and Harley Weston. 





Direct, inverse and indirect proportionality 
20090304 

From Brian: My 14 year old is confused about indirectly proportional and inversely proportional. On searching on the internet we were directed to:
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/ellis1.html
Here leanne starts explaining indirectly proportional and ends up describing inversely proportional. Has Leanne got it wrong ?
What is indirectly proportional.
Thanks
Brian Answered by Chris Fisher. 





Convergent or divergent? 
20090303 

From Betsy: Use the ratio test to determine if the series is convergent or divergent.
1+1/2^2+1/3^3+1/4^4
I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1)
but I can't simplify r=lim(n>inf.)=n^n/(n+1)^(n+1) Answered by Robert Dawson. 





An array with 2 more rows than columns 
20090228 

From Mario: Write a division sentence modeled by an array that has 2 more rows than the number in each row. Answered by Penny Nom. 





Where do X, Y and Z go? 
20090227 

From Aj: A E F H I K L M N T V W
B C D G J O P Q R S U
where do X, Y and Z go? Answered by Robert Dawson. 





1 3 6 10 15.... 
20090226 

From Allie: 1 3 6 10 15....
i know the pattern is +2 +3 +4 +5 and so on...but i dont know how to write an equation to find the nth term. help! Answered by Robert Dawson and Claude Tardif. 





Multiplying in different bases 
20090225 

From Susan: 11 base 2 X 22 base 3 + 33 base 4 = _________ base 5 Answered by Robert Dawson. 





wo consecutive numbers with a product of 9506 
20090225 

From sofie: find two consecutive numbers with a product of 9506 Answered by Penny Nom. 





Pressure at Given Depth 
20090222 

From Tamara: A sea is 3km deep. The average density of sea water there is 1020 kg/m^3. What is the water pressure at the bottom? Answered by Janice Cotcher. 





One vertex angle of a regular octagon is trisected 
20090219 

From Chelsy: Suppose one vertex angle of a regular octagon is trisected as shown in the figure. Each side of the octagon measures 4 units. Find the area of the shaded area. Answered by Robert Dawson. 





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. 





More on infinity and Set Theory 
20090217 

From Justin: I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x>0, y=infinity?
Justin Answered by Robert Dawson. 





Miles per hour to kilometers per second 
20090217 

From Tamara: If a car goes 60 miles in an hour how many kilometres will it go in a second? Answered by Penny Nom. 





Infinity and Set Theory 
20090217 

From Justin: I was just wondering is the limit x>0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory?
Justin Answered by Robert Dawson. 





The second derivative of h(x)=f(g(x)) 
20090216 

From Kristina: If h(x)=f(g(x)), and is differentiable, then find h"(x). Answered by Robert Dawson. 





In what base is 3x3= 10? 
20090214 

From David: In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one? Answered by Penny Nom. 





y = p q^t 
20090212 

From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0
a) find p and q
b) hence find y when t=4 Answered by Stephen La Rocque. 





A semi circular room 
20090211 

From Taylor: being 450pi (the area of a semi circle)
how much money would it cost to lay carpet at $2.57 per foot???
if the area of a semi circular room is 450 pi ft
then what is the volume being that the diameter is 60 feet
and the ceiling is 16 feet tall Answered by Robert Dawson and Penny Nom. 





Seating around a circular table 
20090209 

From Jenny: A committee of 15  9 women and 6 men  is to be seated at a circular table (with 15 seats). In how many ways can the seats be assigned so that no two men are seated next to each other? Answered by Victoria West. 





Congruent line segments 
20090205 

From casie: marica drew oneline segment on a graph with endpoint of (0,9) and (0,4). she drew another line segment with endpoints (1,1) and (6,1). are the line segment congruent?explain Answered by Penny Nom. 





The sequence 5, 12, 19, 26, ... 
20090204 

From Vickie: Hello,
Here's the question. Ryan wanted to play basketball on a team, He started practicing shooting everyday to improve his skills. The first day he make 5 shots, the second day he made 12 shots, the third day he made 19 shots, and the fourth day he makde 26 shots. If the first day was March 1 and the pattern continues, how many shots will Ryan make on the last day of April and the last day of July? My daughter's answers were 425 for April and 1069 for July. Are these correct and what would be the formula for this question? ? +N=? I don't know please help.
Thank you,
Vickie Answered by Robert Dawson and Penny Nom. 





A piecewise function for monthly salary 
20090203 

From Josh: A sales rep for a drug company is paid on the following scale. His base salary is $1600 per month. He is also paid a commission of 2% of sales over $20,000. When his gross sales reach $30,000 he is then paid 4% on the amount above that until his sales reach $50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over $100,000 for the month. Set up a piecewise function for the information above. Answered by Harley Weston. 





Calculating markup 
20090203 

From Tonya: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my cut to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my cut once I pay the commission and I don't want it to do that. Thanks Answered by Penny Nom. 





What do I need to pass the course? 
20090202 

From Lynnette: If I received 100% on my assignment which is worth 20% of my total mark and 87% on my midterm which is worth 40% of my total mark what would I need to get on the final exam which is worth 40% of my mark. To pass the course I must have 80% or above. Thanks. Answered by Penny Nom. 





The sequence 2n!  1 
20090201 

From Penny: I am trying to help my son with this problem. Find the first five terms of the sequence that can be written from the formula A= 2n !1. Answered by Penny Nom. 





The intersection of two lines 
20090130 

From kaylee: how do you find and graph the intersect of these two equations:
y=2x4 (and) 2y=x
thanks,
kaylee Answered by Stephen La Rocque. 





Ambitious 7th Grader 
20090128 

From John: I have been asked to tutor a 7th grader who is very good in math. He is taking the most advanced course that his school offers to 7th graders. This course will cover Algebra 1 over a period of two years, using McDougal Littell's Algebra, Structure and Method, Book 1, a book I like a lot.
I have been hired not to help him with his schoolwork, which is too easy for him, but to guide him through something in math beyond his schoolwork. This was his idea, an idea which surprised his parents, but one which they support.
Do you have a suggestion for me? If so, I would be very grateful to hear from you. I think this could be a lot of fun for me and my new student, if I pick the right path.
Thanks and best regards,
John
John Answered by Robert Dawson, Victoria West and Walter Whiteley. 





Percentage increase 
20090119 

From Destiny: In 1990 there were 25 springs in the park. This year there are 35 springs
in the park. What is the percent increase? Answered by Penny. 





The point of intersection of the straight lines 
20090118 

From Kieran: Find the point of intersection of the straight lines
y=2x+4, and y+2x16=0 Answered by Robert Dawson and Penny Nom. 





Segments of a sphere 
20090116 

From Herman: How do I solve for a segment of a sphere so that the orange peel or pie shaped section is converted to a flat surface with dimensions. I form large diameter domes, elliptical and sphere heads on a press. I enter the diameter say 30 feet with two segments above and below the equator and the total number of segment around the circumference at say 18 so the widest part of the pie shaped section will fit my press. How do I take the upper or lower course above or below the equator and figure the height of the orange peel shape, the chord length at top and bottom, and solve for the right angle at 2 degree increments down the arc length of the pieces so I can layout the flat plates prior to pressing. Thanks for your help. Answered by Robert Dawson. 





A seven card poker hand 
20090112 

From Sean: from a standard card deck, seven cards are chosen at random.
find the probability that the set chosen contains exactly three of each
of two different face values.
the second part of the problem asks the probability that the card hand contains
exactly three 2's and exactly three 5's. Answered by Robert Dawson. 





(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. 





A union B and A intersect B 
20090107 

From Jim: Suppose A and B are sets and (A union B) = (A intersect B). Is it true that A=B. Answered by Penny Nom. 





y varies jointly as x and the square of z and... 
20090105 

From peter: I don't really get the terms in this problem. Could you explain it: If y varies jointly as x and the square of z and inversely as the cube of w, by what factor is y increased when z is doubled and w is divided by 3 and x remains the same? Answered by Harley Weston. 





The area enclosed by a curve and the xaxis 
20090104 

From Rogerson: Find the area, S, enclosed by the curve y = x^2 + 6x  5 and the xaxis in the interval 0≤x≤4. Answered by Harley Weston. 





Determine y'' by implicitly differentiating twice 
20090104 

From Walter: Given x^3  3xy + y^3 = 1 , determine y'' by implicitly differentiating
twice. I cannot solve this. Would you be kind enough to perform the
mathematics and show the steps involved in obtaining the solution? Answered by Harley Weston. 





What is f^1(3) when f(x)=2x1? 
20090103 

From Peter: how do you do functions like f^1(3) when f(x)=2x1? Answered by Penny Nom. 





Jon's bank account 
20090103 

From Abigail: Hi, i have an exam soon (monday =[ )
in my revison book, it shows two peoples bank accounts and then it says
"write a formula to show the balence of Jon's bank account after n weeks of 2003"
this is the table show
Jon's Bank account
Weeks 
Week 1 
Week 2 
Week 3 
Week 4 
Week 5 
Balance(£) 
970 
1035 
1100 
1165 
1230 
Answered by Penny Nom. 





A spill of oil on a flat surface 
20081219 

From Phillip: Hello, my question is: If I spilled 25 gallons of diesel fuel on a flat surface how much area would the spill cover?
How would I mathematically figure it out?
Thanks! Answered by Robert Dawson and Harley Weston. 





The inverse function for F(x)=x^3+x 
20081218 

From alireza: I want inverse function for F(x)=x^3+x Answered by Robert Dawson. 





The middle term of an arithmetic sequence 
20081215 

From Leigh: Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92 Answered by Penny Nom. 





Annual percent growth 
20081213 

From Joe: If WallMart had sales of $58,200,000,000 in the year 2002 and $90,800,000,000 in the year 2006.
1. Find what percent that increase is of the 2002 sales? I came up with (9.08*10^10  5.82*10^10) / 5.82*10^10 * 100 = 56.01% increase. Is this correct?
2. What was the percent GROWTH in WalMart's sales from 20022006? I am having trouble figuring out how to do the Growth problem. I would appreciate any help. Answered by Harley Weston. 





The third vertex of a right triangle 
20081210 

From prashant: how to calculate coordinates of third vertex in a right angle triangle given the coordinates of hypotenuse as (1,3) and (4,1) Answered by Robert Dawson. 





Division in different bases 
20081202 

From MICHELLE: DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5 Answered by Penny. 





A log base 2 problem 
20081126 

From dave: solve for x
(log base 2 of x)  (log base 2 of (x2)) = 3 Answered by Penny Nom. 





Sec(2x) 
20081123 

From Evan: Prove that this is an identity...
sec2x = sec^2x / 2  sec^2x Answered by Harley Weston. 





The nth term of a sequence 
20081120 

From kim: Find the next 2 terms of the sequence.
11n+2.5 Answered by Harley Weston. 





The height, base and perimeter of a triangle 
20081117 

From Zack: How would i calculate the height of a triangle if the base is 10cm and the area is 50cm²?
If possible how would i calculate the length around the the triangle. Answered by Penny Nom. 





License plates 
20081117 

From Clayton: Okay, so in this situation a license plate must have four letters (AZ) and four numbers (09), ex. ABCD1234, where repeating a letter or number is allowed ex. AAAA1234, or ABCD1111, or AAAA1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD1234 from New York, and ABCD1234 from Minnesota are considered different combinations, how many different license plates could there be? Answered by Penny Nom. 





The nth term of a sequence 
20081116 

From Robin: How do I solve for the next term in the following sequence, I just don't want the answer...I want how to do it to. x,x 1, x 2
Also, how do I solve for the nth term? I can't understand the explanations I've found. He has numbers subscripted in his equations. Answered by Victoria West. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





A crosssectional area 
20081113 

From David: I am doing a science project examining the tensile strength of seaweed fronds. I need to calculate the crosssectional area from the major and minor diameters of the elliptical central axis of the seaweed frond. What formula would I use to get this.
The strength of the segments is expressed in terms of crosssectional area of the frond at the test site. Answered by Penny Nom. 





1/8, 2/7, 1/2, 4/5, ..., ... 
20081106 

From katie: Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence. Answered by Penny Nom. 





An arch is in the form of a semi ellipse 
20081103 

From jessica: An arch in the form of a semi ellipse has a span of 10 meters and a
central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis. Answered by Penny Nom. 





A sequence 
20081026 

From Nicole: what is the rule to this sequence 3,6,12,24,48..... Answered by Penny Nom. 





The sequence 49,48,46,43,39... 
20081026 

From Kyle: What number comes next in the series 49,48,46,43,39...? Answered by Stephen La Rocque. 





The sequence 6,1,6,2,6,4,6,8,6, 
20081026 

From Kyle: What number comes next in the series 6,1,6,2,6,4,6,8,6,? Answered by Stephen La Rocque. 





The amount of diesel fuel in a tank 
20081026 

From Mike: I have an cylinder shaped oil tank that holds approx. 283 gals of diesel fuel. The tank is laying on on its side, (like taking a garbage can and laying it down on its side). What is the formula to calculate how much oil is in the tank at any given time. If the tank was sitting on end it would be easy to figure out, but it is not. Answered by Stephen La Rocque. 





nth term 
20081022 

From jen: what is a nth term and how do i find the nth term of any sequence Answered by Penny Nom. 





A canal with cross section a semicircle 
20081019 

From Connor: a canal with cross section a semicircle is 10m deep at the centre.
Find an equation for the semicircle and use it to find the depth 4m
from the edge Answered by Penny Nom. 





An arithmetic series 
20081017 

From Laura: In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have?
What formula do I use? Answered by Penny Nom. 





Bags of wheat seed 
20081016 

From Gayle: If you want to plant 26 seed per square foot (wheat) on one acre of land and the seed comes in 50 lb bags and there are 13,500 seed per pound (675,000) per 50 pounds, how many bags do you need to plant per acre? Answered by Penny Nom. 





Bags of pennies 
20081011 

From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West. 





The volume of fluid in a semi circular trough 
20081010 

From Kerry: How do I find the volume of fluid in a semi circular trough? Answered by Penny Nom. 





A 10% increase in supply 
20081010 

From Irena: How do you find begining inventory if after 10% increase in supply you got 27.5 units Answered by Penny Nom. 





Three consecutive integers 
20081007 

From pam: Find three consecutive integers such that the greatest increased by twice the least is 293. Answered by Penny Nom & Chris Fisher. 





The rise over the run 
20081007 

From Mak: what is the ratio of the rise to run? Answered by Penny Nom. 





Area of a semicircle 
20081006 

From Benjamin: How do you find the area of a semicircle if the diameter is a variable. Answered by Penny Nom. 





Does an oval have sides? 
20081002 

From reid: My 6 yo neice came home with her math homework and she was supposed to identify which objects had sides.One of the objects was an oval.I don't believe it has sides because it is curved and I don't think that would make it an object with sides.What would be the correct answer?Thanks,Reid Answered by Janice Cotcher. 





The empty set 
20080929 

From wahab: Why a null set is called a set?
the definition of set includes that a set is a collection of well defined objects
But a null set is having no value. Answered by Harley Weston. 





The nth term 
20080929 

From shauna: The first five numbers in a sequence are
40, 37 34, 31, 28
Find an expression for the nth number in the sequence. Answered by Penny Nom. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





The area of an arched transom 
20080928 

From Ivan: What is the formula for figuring out the square footage of arched transom windows & doors? Answered by Harley Weston. 





Increase pricing by 5% 
20080928 

From Adrian: I am working to increase pricing by 5%. If the price is 100, I would typically use the formulas 100 * 1.05 = 105, which is a $5 increase. An associate suggests I divide to get the desired increase. For example, using $100 with a 5 percent increase. I would use the forumula 100/.95 = 105.26. Thas is a 5.26 increase. Can you explain this method to me an why the different increases? Which one is correct. Answered by Penny Nom. 





Two consecutive numbers 
20080921 

From tomas: what is the two consecutive numbers with a product of 4160? Answered by Penny Nom. 





The area of a garden 
20080920 

From Hannah: How do you find the area of a semi circle when no measurement is given?
The question is find the area of the garden which is semi circular.
The measurements are 24m and 26m and the semi circle's height is 10m! Answered by Penny Nom. 





Finding the Pattern in a Sequence 
20080916 

From sjp: please could you help me find the nth term for
8 4 0 4 8
and
4 1 4 11 20
Thank you Answered by Janice Cotcher. 





The nth term of a sequence 
20080913 

From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque. 





The height and base of a triangle 
20080912 

From Bailey: The length of the base of a triangle is 1cm less than 5 times the height of the triangle. The area of the triangle is 21 square cm. What is the the height of the triangle and the length of the base of the triangle? Answered by Stephen La Rocque. 





0.151515...=15/99 
20080908 

From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating
decimals and their corresponding fractions.
(ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.)
I was just wondering the reason why this pattern occurs.
Is there a certain element that causes this pattern to occur?
Thanks
Emma Answered by Penny Nom. 





An exclusion zone around a triangle 
20080907 

From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom. 





A security camera 
20080907 

From Rita: A security camera in a neighborhhod carnival is mounted on a wall 9 feet above the floor inside a video gallery. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall? Answered by Stephen La Rocque and Harley Weston. 





The selling price 
20080904 

From Robert: Client wants to sell his property providing he is left with 100000.00$ net.
How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov.
I'm taking the real estate class and this one really got me. Answered by Penny Nom. 





Half a circle 
20080904 

From brandon: what are the area and perimeter and area of half a circle?? Answered by Penny Nom. 





Aboriginal number groupings 
20080904 

From Barbara: Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently? Answered by Harley Weston. 





Four weights 
20080825 

From Darla: A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use? Answered by Penny Nom. 





Eccentricity of an Elliptical Orbit 
20080820 

From Gina: A satellite has an elliptical orbit around the earth with one focus at the earth’s
center, E. The earth’s radius is 4,000 miles. The highest point that the satellite is
from the surface of the earth is 800 miles, and the lowest is 200 miles.
What is the eccentricity of the satellite’s orbit? Answered by Janice Cotcher. 





The intersection of the medians 
20080818 

From Katie: Q: A Triangle is positioned with one side on the xaxis, the coordinates
for the triangle are (a,0), (a,0), (b,c)
a) Find the coordinates of the point of intersection of the perpendicular
bisectors of the sides
b) Find the coordinates of the point of intersection of the medians
c) Find the coordinates of the point of intersection of the altitudes Answered by Penny Nom. 





A 3% increase 
20080818 

From RENEE: I need to know how to do a 3 percent increase for $118,200......x's it by 3% will not work please answer fast Answered by Penny Nom. 





Graphing a piecewise function 
20080812 

From Shanti: how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to 2 and less than 1
2 u if u is greater than or equal to 1 and less than 4 Answered by Penny Nom. 





The base of a triangle 
20080810 

From Mark: What is the formula I need to use to find the base of a triangle sail that is 16 feet high and has an area of 64 square feet. Answered by Stephen La Rocque and Penny Nom. 





Angles in a regular tetrahedron 
20080807 

From Carla: Hi guys,
A regular tetrahedron has all its edges 8cm in length.
Find the angles which an edge makes with the base.
Thanks.
Carla Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





Cost of pencil is rising every year since 7 years ago 
20080806 

From Mari: Cost of pencil is rising every year since 7 years ago. If the cost of
pencil last year was 60 cents which is the sum of the cost from the
last two previous years, what is the cost of the pencil now, the cost
seven years ago. Answered by Penny Nom. 





Demographics 
20080725 

From shahrukh: Each year for 10 years ,the population of a city increased by 5% of its value in the previous year.
If the initial population was 200 000 ,what was the population after 10 years ?? Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20080722 

From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom. 





Taking two math classes 
20080721 

From Bailey: i am going into the 7th grade, but i am going to be taking 9 th grade math.
i was wondering if anyone could help survive doing two different math classes at the same time. Answered by Harley Weston. 





Three consecutive positive integers 
20080720 

From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom. 





Choosing 5 numbers out of 39 numbers 
20080718 

From robert: Please list the way I can choose 5 numbers out of 39 numbers, without repeating them, starting at number 1.
Please send me a list of all 120 combination. Answered by Harley Weston. 





Does the sequence 1 2 4 8 16 32 etc have a name? 
20080717 

From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West. 





1, 2, 4, 8, 16, 32 ... 
20080715 

From eve: I have to find out the fomula for:
1, 2, 4, 8, 16, 32 ... Answered by Penny Nom. 





A reflected line segment 
20080714 

From Peter: Segment AB has endpoints A(1,2) and (3,1). Segment AB is reflected over the yaxis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'? Answered by Janice Cotcher. 





Choosing a number from 1  400 
20080704 

From Peter: The numbers 1400, inclusive, are put into a hat. What is the probability that the first number chosen at random is a multiple of 4 or 17? Express your answer as a common fraction.
How do you do this the question without a calculator? Answered by Leeanne Boehm. 





A series solution of y' = xy 
20080703 

From sasha: I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks Answered by Harley Weston. 





Percentage increase 
20080629 

From Paul: Could you please help me with this question. I was paying $98.00 a month for my health insurance premium, now it is up to $125.83 How much of an increase is that as a percentage increase, and how can I do this on a calculator. I'd like to know how much my increase is as a percentage. Answered by Penny Nom. 





A 7digit odd number 
20080626 

From Godryk: I am the smallest 7digit odd number. my ones digit is the sum of my thousands, and ten thousands digits. What number am I? Answered by Penny Nom. 





Product of Two Integers 
20080625 

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





How do you change bases? 
20080617 

From Peter: How do you change bases eg. 121 from base 3 to base 5? Answered by Penny Nom. 





A piecewise equation 
20080616 

From John: AT&T charges $39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes.
How can I make a piecewise equation of this problem? Answered by Penny Nom. 





An ellipse and circle with the same area 
20080609 

From Michael: The area of the ellipse if equal to the area of a circle with radius=40 ft.
Find the values of a and b using appropriate algebraic techniques, not basic math computations.
A=pi ab and satisfy the constraint a+b=100???? Answered by Penny Nom. 





Geometric sequences 
20080608 

From Rita: A geometric sequence is given. Find the common ratio and write out the first four terms.
(1) {(5)^n}
(2) {(2^n)/(3^(n  1)} Answered by Penny Nom. 





90% of gross leaseable footage 
20080607 

From Rosalind: 90% of gross leaseable footage in the shopping center, being 394,577, excluding that square footage leased by major anchor tenants, being 284,747. Would you deduct the 284,747 from the 394,577, then multiply by the 90%. Or would you multiply the 394,577 by the 90%, then deduct the 284,747? Answered by Penny Nom. 





A recursive formula for 9, 18, 36, 27, ... 
20080605 

From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence.
It does not matter what sort of sequence it is. The confusion remains.
I have not found a textbook or easy math book that explains this process for the average Joe to grasp.
Here are the two questions:
(1) Write a recursive formula for the sequence
9, 18, 36, 72, ...
(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom. 





The path of a baseball 
20080604 

From Tom: How high would a batter have to hit a ball to clear the stadium roof in right field
if the distance to the right field fence is 320 feet from home plate? Is this solvable? Answered by Janice Cotcher. 





Calculating a price based on markup 
20080603 

From Sheldon: I know the most common form for retail businesses of calculating a price based on markup is:
Cost/(1  Markup), but how is this supposed to work for a business that desires a markup of over 100%. Answered by Harley Weston. 





Two consecutive negative even numbers 
20080603 

From Chelsea: The sum of the squares of two consecutive negative even numbers is 100. Find the integers, Answered by Penny Nom. 





Inverse variation 
20080522 

From leria: In Boyle's law, the pressure of gas varies inversely with the volume of the gas. A volume of 11.2 liters of air exerts a pressure of 2.0 atmospheres.
determine the constant of variation and write an equation the models the relationship between the pressure of the gas P and its volume, V. Use the equation to predict the volume of air necessary to exert a presure of 0.25 atmospheres. Answered by Janice Cotcher. 





How much seed do I need per plot? 
20080513 

From Jaye: The plot size is 5 m X 2 m. The seeding rate is 12Kg/ha. How much seed do I need per plot? I have failed to get a proper answer.
Thank you. Answered by Penny Nom. 





Selling price 
20080510 

From Roxane: I'm trying to figure out the formula for the following, I have a product that
I want to receive a certain profit margin, but with this product I also have
to pay a percentage of commission to someone. I need to know how to
calculate my new selling price taking into account the markup percentage, but
I don't want my gross margin to be lowered. I have calculated the markup
percentage to get my new selling price with the commission, but it lowers
my profit margin once I pay the commission and I don't want it to do that. Answered by Penny Nom. 





The area of a sector of a circle 
20080510 

From lupio: a problem asks for the area of a sector in a circle,no central angle,in circle is given only 5cm radius, three answers 1809035
can't find a way to start.Help Answered by Harley Weston. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





The standard form of an ellipse 
20080430 

From Rebecca: I have to write the following equation into standard form of an ellipse:
9(X1)^2 + (Y+1)^2 = 1 Answered by Stephen La Rocque and Harley Weston. 





33+33+3.........up to infinite terms = ? 
20080425 

From Jatin: 33+33+3.........up to infinite terms = ? Answered by Stephen La Rocque. 





Two intersecting circles 
20080417 

From Muhammad: Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart. Answered by Harley Weston. 





Conic sections 
20080414 

From Christine: In my analysis class we are learning about conic sections.
Our project is to create a genral statement of the definition of conic sections.
Truthfully, I have absolutely no clue on how I should write that.
Could you help me? Answered by Walter Whiteley. 





The maximum area of a pizza slice 
20080412 

From charles: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Answered by Harley Weston. 





Two function problems 
20080410 

From keith: find the domain: F(x)= 1/ {ln (x+5)  ln (7x)}
find the inverse: g(t)= sqrt {23 ln (1t)} Answered by Penny Nom. 





cosec [arccos (1/y)] 
20080409 

From Tom: I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is? Answered by Penny Nom. 





1(1P)^75=0.05 
20080405 

From Amy: 1(1P)^75=0.05 Answered by Stephen La Rocque and Penny Nom. 





Two consecutive odd integers 
20080324 

From Jarrod: the sum of two consecutive odd integers is 24. Find the two integers Answered by Stephen La Rocque. 





Circles and semicircles 
20080323 

From sally: Hi i am sally ,
i need to know what is the formula of :
Find perimeter and area of a semicircle ?
Find the area of a circle whose circumference ? Answered by Penny Nom. 





5 9 1 6 10 12 2, where does 3 fit in and why? 
20080322 

From Cassidy: number sequence
5 9 1 6 10 12 2, where does 3 fit in and why? Answered by Claude Tardif. 





4,12,24,40,60,84 
20080318 

From kirsty: Here are the first six terms of a sequence.
4,12,24,40,60,84
Find in terms of n, an expression for the nth term of teh sequence. Answered by Stephen La Rocque. 





Distance seen 
20080318 

From Nev: formule: Distance Seen
S = 1.225 x square root of H
S = Distance seen in Miles
H = Height in Feet
What dose 1.225 Relate To ? Answered by Stephen La Rocque. 





The nth term 
20080316 

From ryan: need help figuring nth term for 1, 2, 5, 14, 41...... could you please help Answered by Penny Nom. 





1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 
20080313 

From Karen: What is the rule for the following pattern, and what would come next?
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ Answered by Penny Nom. 





Inverses of functions 
20080313 

From jess: if g(x)=2x+3 find g^1(g(4))
how do I sovle I cant's figure out what to do with the 4 Answered by Stephen La Rocque. 





Two consecutive odd positive integers 
20080312 

From Sarah: The sum of the squares of two consecutive odd positive integers is 74. What are th integers? Answered by Penny Nom. 





Estimate the cube root of 270 
20080311 

From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the NewtonRaphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. 





Base 5 arithmetic 
20080306 

From Jana: Hello, my name is Jana, i have asked a question here previously about how to count in base5. I am happy now because i can convert any number now and it is very easy for me. The only thing i am having trouble with is understanding how to do a maths sum or times base5 numbers. it is just a bit hard for me. So do you think you could explain how to do a sum in base5 and how to do a multiplication sum. Please help...Thankyou Jana!! Answered by Harley Weston. 





What was the ostrich's speed in miles per hour? 
20080303 

From jacob: If it took an ostrich 2.5 seconds to travel 110 feet and the average speed is 44 feet/ seconds, what was the ostrich's speed in miles per hour? Answered by Penny Nom. 





Convert from base 6 to base 12 
20080302 

From Jade: I am trying to convert 13405 base 6 to a base 12 number. I am not allowed to go into a base 10 number. How will can I base 12 without doing anything with base 10? Thank you kindly. Answered by Stephen La Rocque and Penny Nom. 





The perimeter of a sector of a circle 
20080228 

From erica: What is the perimeter of a sector if the radius is 18 and the middle arc is 150? Answered by Penny Nom. 





3 consecutive odd integers 
20080228 

From Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals 85. Find the 3 consecutive odd integers. Answered by Penny Nom. 





The surface area of an ellipse 
20080225 

From paritosh: how is the surface area of a elliptical dome be calculated when the two diameters are 55 metres and 35 metres and the height of the structure is 13.4 mts? Answered by Harley Weston. 





Counting in base 5 
20080224 

From Jana: my name is Jana, i really need help with a maths question at school. Im confused about how to count up from120 in a base5 format! I'm in year 5 and i really don't get all the complicated stuff. Answered by Stephen La Rocque. 





Actural cost, selling price and commission 
20080221 

From LiSa: I have a question about a few things if anyone can answer...
ex.
actual cost (AC) = $1000
selling price (SP) = $
amount earned for company (C) = 15% of... selling price?
commission 1 (C1) = 2.5%
commission 2 (C2) = 2.5%
How would you calculate how much the company's commission amount would be as well as the amounts for the other 2 that get 2.5%? And what would the selling price be? (the 15% $ + 2.5% $ + 2.5% $ ?)
Is the 2.5% taken from the original amount? I am soooo confused!
If anyone could help, that would be great! Answered by Harley Weston. 





Find the next terms 
20080220 

From Darrin: I was given a number sequence and can't figure out the next terms to this
2,9,20,35,66,91...... Answered by Penny Nom. 





Classifying a triangle 
20080207 

From kevin: scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles Answered by Penny Nom. 





The perimeter of a semicircle 
20080202 

From Lisa: How do you find the perimeter of a semi circle when you are only given
the diameter, say 24 units? 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. 





How do I convert mcg to ml? 
20080127 

From David: How do I convert mcg to ml? Answered by Stephen La Rocque. 





O.T.T.F.F.S.S 
20080125 

From Omar: What is the next letter in the following sequence:
O.T.T.F.F.S.S Answered by Penny Nom. 





Three consecutive odd integers 
20080124 

From daniel: find three consecutive odd integers such that three times the second minus the third is 11 more than the first.
help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while. Answered by Penny Nom. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

From Neil: Find the next two terms in the following number sequence
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128
Find a general rule for the nth term of the sequence Answered by Penny Nom. 





Choosing 6 numbers from 42 
20080119 

From Marcus: If i have 42 numbers to choose from and i could only choose 6 numbers at a time without choosing the same number twice in the same row, how many possibilities are there? Answered by Penny Nom. 





A sector of a circle 
20080117 

From Amandsa: What is the formula for finding the sector of a circle? Answered by Penny Nom. 





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. 





The area of a sector of a circle 
20080111 

From Serenity: A denotes the area of a sector of a circle of radius r formed by the central angle theta.
Find the area A if r=10 meters and theta = 1/2 radians. Answered by Penny Nom. 





Multiplying numbers in bases other than 10 
20080108 

From Imaiya: In class we've been learning about numbers with a base other than ten. For example, base 7, base 5,
and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10.
I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.
Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42
Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78
If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also
if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much,
and once again, thank you for your great site! Answered by Stephen La Rocque. 





Practical applications of sequences 
20080101 

From carl: can you give me examples of different kinds of practical applications of sequences? Answered by Penny Nom. 





Find the lengths, and explain in a 'let statement' 
20071220 

From Cordilla: the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'. Answered by Stephen La Rocque and Harley Weston. 





A 454590 triangle 
20071213 

From Aaditya: explain to me please how to do the 454590 theorem when one of the legs(not the
hypotenuse) is 3. How do you find the remaining two sides? please help me out. Answered by Leeanne Boehm. 





How many houses must they paint? 
20071212 

From Natalie: The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds.
If they work for four months of the summer and their expenses are 152
pounds per a month, how many houses must they paint for each of them
to have one thousand pounds at the end of the summer? Answered by Penny Nom. 





Imprecise measurements 
20071209 

From Sara: Hi!
A water tank, in the shape of a cuboid (length 1.6 m, height 1.2 m, breadth 0.8 m), is full of water.
Water is drained from the tank at a rate of 8 litres per minute. The dimensions of the tank are given to the nearest 10 cm.
The rate at which the water is drained from the tank is given to the nearest 0.5 litres per minute.
(a) Calculate the smallest possible time to drain the tank.
(b) Calculate the greatest possible time to drain the tank.
Many thanks!!! Answered by Stephen La Rocque. 





Three consecutive numbers 
20071208 

From Aris: The product of 3 consecutive numbers is 1716. Find their sum. Answered by Stephen La Rocque. 





A portion of a circle 
20071207 

From Richard: please could you tell me the formula and answer to the following.
I have a circle portion with a radius of 150mm and an angle of 120 deg. If
an arc is drawn from one point to the other as the radii touch the circle
circumference, i need to know the area of the segment and the
formula to carry out the answer.
Many Thanks Answered by Penny Nom. 





A right triangle 
20071206 

From Shubhomoy: The coordinates of a hypotenuse are (1,3) and (4,1). Find the equations of the perpendicular sides. Answered by Harley Weston. 





Representing different bases 
20071205 

From Sudhir: What does a number subscripted to another one denote? (I know that a number superscripted to another denotes the power, but the subscript number is something I have never seen before.) Answered by Stephen La Rocque. 





Percentage increase in profit 
20071204 

From Dee: If I had a certain % increase in profits for the entire year, why can't I add the profits I made for the first 1/2 of the year to the profit I made in the second 1/2 of the year to get the total year end profit percentage? Or how can I compare the increase/decrease for each 1/2 of the year to the total % increase/decrease? Answered by Penny Nom. 





Proving a quadrilateral is a rhombus 
20071203 

From Jeanie: How do you prove that a quadrilateral is a rhombus because the diagonals
of the quadrilateral are perpendicular and bisect each other using the 2column
proof method? Answered by Stephen La Rocque. 





O,T,T,F,F,S,S,?,?,? 
20071128 

From Kim: What are the next 3 letters in this sequence?
O,T,T,F,F,S,S,?,?,? Answered by Stephen La Rocque. 





Direct and inverse variations 
20071127 

From Julie: Please Help I do not understand this question. X varies directly as the square of S and inversely as T. How does X change when S is doubled ? When both S and T are doubled ? I appreciate your help with this problem. Answered by Stephen La Rocque. 





Elimination of mayan prisoners 
20071119 

From Jim: An evil Mayan emperor decides to make an example of 1,000 prisoners. He stands them in a circle with numbers one to a thousand marked on their shirts. He then starts counting: "one in, two, in three out" The third man is immediately executed. This continues round and round and round the circle. While the number in the circle shrinks, every third prisoner is pushed out and executed. And it continues even when there are only two prisoners left alive. What number is on the last prisoner's shirt? Answered by Victoria West. 





Sides and vertices 
20071117 

From derek: What is the correct name for a 2D geometric shape that would look like one slice from a round pizza and how may sides and vertices would it have? I believe you would say it has one vertex and two sides with the curved boundary not resulting in vertices or a side. Your help is much appreciated. Answered by Chris Fisher and Walter Whitelty. 





A matrix equation 
20071116 

From stephanie: Im supposed to solve
( 1 tan =E8/2) ( 1 tan =E8/2)^(1)
(tan =E8/2 1 ) (tan =E8/2 1 )
Matrix AA<(1)=I Answered by Penny Nom. 





Two sequences 
20071114 

From Kim: Pattern........what comes next?
1,4,9,16,25,_____,____
1,4,9,16,27,40,__________,_______ Answered by Penny Nom and Gabe Potter. 





Radial motion 
20071113 

From abdulai: a circular saw with diameter 18.4cm rotates at 2400rpm. What is the angular speed of a point on the edge of the saw blade in radians per second? Answered by Penny Nom. 





What number best completes the series? 
20071112 

From Grace: What number best completes the series?
2 3 7 13 27 ____ Answered by Stephen La Rocque, Penny Nom and Harley Weston. 





The sequence 3,12,26,45.... 
20071112 

From Tra: I can seem to find the realtionship in these sequence of numbers, I am looking for the next three. How can I determine that, I have tried everything??!!!
3,12,26,45.... Answered by Penny Nom. 





Meters per second to miles per hour 
20071108 

From Niecey: If Greg was timed at 0.91 seconds for 10 meters running the 100 meter dash, at that speed, could he pass a car traveling 15 miles per hour in a school zone? Answered by Penny Nom. 





The base and height of a triangle triangle 
20071031 

From mike: How do you find the length of the base or the height of a triangle if the area is 30 square feet? Answered by Penny Nom. 





Subsets of a set 
20071030 

From Snehal: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the
empty set and the set itself.)
a) Show an = 2an1
b) Guess a formula for the value of an and use induction to prove you are
right Answered by Stephen La Rocque. 





Dividing a segment into 3 congruent parts 
20071030 

From Carolyn: I am doing construction. I have a line segment drawn. I need to divide a segment into 3 congruent part. How do I do that? Answered by Penny Nom. 





Variation 
20071029 

From deeqa: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster,
the trip could have been made in 1hr less time. Find the speed
2. The average weekly allowance A of children varies directly as their grade level, G.
If the average allowance of an 8thgrade student is $8.56 per week, what is the average
weekly allowance of a 5thgrade
The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4
working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12
volunteers to complete the job? Answered by Penny Nom. 





Combinations and horse races 
20071028 

From Ian: How do I calculate the number of combinations for:
Horse races,1 horse in each race.I want all combinations covered.
e.g.5 races, 1 horse in each race. R 1&2, R 1&3,R 1&4, R 2,3,4,5, R 1,2,3,4,5 etc etc.I have worked it out manually to 27 combinations
but if I want to cover more than 5 it will be a big excercise to work out the cost manually.
Many Thanks Answered by Victoria West. 





Is there a practical use for radian measure? 
20071026 

From Paula: Is there a practical use for radian measure in any profession? Which professions might us radian as opposed to degree measure? Answered by Harley Weston. 





The perimeter of a circle sector 
20071025 

From sara: Hi!
The area of a sector of a circle is 25 sqcm. The radius of the sector is 6 cm. Calculate the perimeter of the sector.
Many thanks!!! Answered by Penny Nom. 





A sixfold increase 
20071024 

From Fred: If I have $500 and it grew to $3,000, what is the correct description of the increase? Is it a sixfold increase (sextupled), or a fivefold increase (quintupled)?
When I divide $3,000 by $500, the result is six, therefore, a sixfold increase? Answered by Stephen La Rocque. 





Converting bases 
20071024 

From Johanna: Is there an easy way to convert from base to base. For example, base 5 to base 9 or base 2 to base 4 etc Answered by Stephen La Rocque and Penny Nom. 





The nth term 
20071018 

From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom. 





Paying with silver  Part 2 
20071017 

From Shanna: The paying with silver problem. I understand how to do the problem, but could you please explain how you would use base 2 arithmetic to solve it. Answered by Penny Nom. 





the sum of two consecutive integers is 51 
20071017 

From Keira: the sum of two consecutive integers is 51 Answered by Penny Nom. 





0,1,2,3,6,11,20,37,68... 
20071016 

From Pat: Describe the rule for this pattern:
0,1,2,3,6,11,20,37,68...
Thanks Answered by Penny Nom. 





How much water is in a hose? 
20071012 

From Bryan: I need to know how much water (gal) is in a hose thats 100' long by 5" in dia.
Thanks Answered by Stephen La Rocque. 





77,49,36,18,... 
20071011 

From Kim: Find a pattern and predict what comes next in this sequence 77,49,36,18,________________. Answered by Penny Nom. 





Inverses of Quadratic Functions 
20071011 

From Elliot: I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated. Answered by Steve La Rocque and Harley Weston. 





Base 10 to base 5 
20071009 

From Angela: I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a stepbystep instruction on how to do this? Answered by Stephen La Rocque. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





A sequence of numbers 
20070930 

From eleanor: can you find the nth term of the sequence ( n starts at three)
1=?
2=?
3= 4
4= 10
5=20
6 = 35
7= 56
i only hand the 3rd 4th 5th 6th and 7th numbers in the sequence
can you please tell me how to find the nth term and what is it :) Answered by Stephen La Rocque and Victoria West. 





The nth term 
20070929 

From zoe: what is the nth term for the following sequence...
5, 2, 1, 4 Answered by Leeanne Boehm. 





Describe the pattern 
20070929 

From Baffled: Given a rule, extend a pattern and describe it in informal mathematical language:
a) 1, 6, 16, 36, _
b) 2, 6, 14, 30, _
c) 1, 8, 22, 50, _
d) 3, 9, 27, _
e) 2, 7, 17, 37, _ Answered by Stephen La Rocque and Penny Nom. 





Four consecutive integers 
20070928 

From Joshua: We were given a question that involved consecutive integers. I can not seem to solve this question and I am the top student in my class.The question states: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91. How do you solve this question? Thank you very much for your support. Answered by Penny Nom, Stephen la Rocque and Claude Tardif. 





A sector of a circle 
20070926 

From A student: hi im stuck on this question. i have tried to do some, could you please che=
ck it and help me.the answers i have worked out are in red. the question is=
attached. thank you. Answered by Penny Nom. 





The nth term 
20070925 

From Bobby: whats the nth term of 2,12,22,32 ? Answered by Penny Nom. 





A geodesic dome 
20070925 

From Roger: In my ScienceFiction series, I have a Dyson's Sphere tiled with
regular hexagons. The number of hexagons is over 300,000 and the
radius of the Sphere is roughly 80,000,000 miles. The actual size of the
Sphere and hexagons have been left flexible until I can come up with a
definite number of hexagons that would fit. My problem is the pattern of
hexagons which would fit within the sphere without leaving gaps or
overlapping.
My best guess has been to use four equilateral triangles composed of 78606
hexagons, (396 per edge) arranged around the sphere with six 'zippers' to
connect them and four 'caps' at the points, for a total of 316804 hexagons.
Given the fact that each Hex is the same size, does this seem plausible?
Is there some pattern formula I can use to play with these figures? Simple
divsion of areas will not work if the number derived will not fit into the
pattern to leave a perfectly tiled surface. Thank you. Answered by Chris Fisher. 





The sequence 2,4,7,11,16,22 
20070922 

From Simon: I thought i understood how to explain how to work out the nth term on a
sequence of numbers until my son had this sequence to work out 
2,4,7,11,16,22
We have worked out the 2nd differance is +1 but nothing else seems to fit.
Im sure the answer is staring us in the face but cant see the wood for the
trees! Answered by Denis Hanson and Steve La Rocque. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





A fraction sequence 
20070921 

From marissa: i have read the examples you have on fraction sequences, but i am still having
a hard time understanding how to figure this out. for example:
__ 1 2/5 __ 3 __ __ __ __7 Answered by Stephen La Rocque. 





Letter number sequence 
20070921 

From Hope: The challenge problem of the week in 6th grade math is a letter number sequence.
J 1 F 8 M 1 A 0 M 1 J 0 J 1 _ _ _ _ _ _ _ _ _ _
They are to find the next 10 letters and numbers in the line.
They were given a hint : look at the letter sequence by themselves and you should recognize it.
Does it just repeat starting with the F 8 M 1 etc.?
Thank you for your help. Answered by Claude Tardif. 





The hypotenuse 
20070920 

From Kasey: What is the hypotenuse of 96 squared and 108 squared? Answered by Penny Nom. 





What is the inverse function of y=x^3 +x? 
20070919 

From saman: what is the inverse function of y=x^3 +x Answered by Harley Weston. 





Number sentences 
20070915 

From jen: list the addition number sentences that can be written using two sets of cards with the numbers 5 6 and 7. which number sentences have the same addends but show a different order?,,,,,,,,,,,,,,Ithis is for my son in 3rd grade and for the life of us we can't figure it out,,thanks for this elementary help Answered by Harley Weston. 





The nth term 
20070913 

From Rookin: Can you help me find the nth term for this ...
20,17,14,11,8
i'm really confused oh and could you also tell me how you got the answer? Answered by Steve La Rocque, Claude Tardif and Harley Weston. 





The perimeter of a semicircle 
20070911 

From Confused: What is the formula for the perimeter of a semicircle?
Can you please help me out!!!
I need this answer by tomorrow. Answered by Stephen la Rocque. 





What are the next two terms? 
20070911 

From Sassy: I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are. Answered by Stephen la Rocque. 





A sequence of fractions 
20070910 

From mitch: find an expression for T(n), the nth term of the sequence
1/5, 3/8, 5/13, 7/20, 9/29 Answered by Stephen La Rocque. 





Segments on a line 
20070910 

From Cathy: This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments. Answered by Penny Nom. 





The nth term 
20070909 

From Conor: Please can you help me with this question on the subject of the Nth term.
3.5, 5, 6.5, 8, 9.5
5.1, 7.2, 9.3, 11.4... Answered by Penny Nom. 





nth term in this series 
20070907 

From danii: im trying to solve the nth term for this pattern.
1 3 6 10 15 21 28
any help would be appretiated Answered by Stephen la Rocque. 





The next term 
20070907 

From Ariel: Please explain to me why 3^2 is a 9. One calculator give me an answer of positive 9.
WHAT IS THE NEXT TERM IN Each sequence/ What is its term number?
1/2, 2/3, 3/4, 5/6 6/7
1, 1/4, 1/9, 1/16 Answered by Stephen la Rocque. 





A sequence 
20070906 

From aimee: i have the sequence
1,5,14,30,55 and i have been told to use
An squared times Bn times C
and my working should look like this
1 5 14 30 55
4 9 16 25
5 7 9
2 2
But how do i do this Answered by Penny Nom. 





A sequence of fractions 
20070905 

From Arjun: 1/2 3/5 5/8 7/11 need to find the nth term.
I did search the data base & found one for fractions but what I want to know is when calculating nth term for the denominator in the example give in your database how do we get (n1)?
When we deduct the actual term with the one that is in the table give in your example it is more that one. Could you please explain solving the above example? Answered by Penny Nom. 





The first five terms 
20070904 

From JP: Find the first five terms of a sequence with the nth term n^2+2n+1
and 2^n. Answered by Penny Nom. 





Speed of sunrise 
20070904 

From Robert: Facing west in a car, you are watching the sun rise (through the rear view mirror). It peaks the horizon, you take off driving. How fast would you have to drive, to see it rise again? Answered by Stephen La Rocque. 





2,6,7,21,22,66,67 
20070828 

From EDWIN: this doesnt make any sense to me....... i cant find the pattern...
2,6,7,21,22,66,67 Answered by Leeanne Boehm and Stephen La Rocque. 





Applications of sequences and series 
20070827 

From Trish: I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.
I've already used the Fibonacci Sequence and Harmonic Series
and need two more.
The simpler the sequence or series type the better.
I'd also like to know in which nonmathematical areas use sequences and series
and how.
Areas such as engineering or science. Answered by Penny Nom. 





Where do you use trigonometry? 
20070821 

From jenny: where do you use trigonometry besides architecture and engineering? Answered by Stephen La Rocque. 





The tens digit 
20070821 

From Arul: Hi..
Please help me on this question..
Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term? Answered by Penny Nom. 





Common factors 
20070819 

From John: I have problem factorising 2p^3  34p. Please advise me. Answered by Leeanne Boehm, Steve La Rocque and 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. 





Area and perimeter 
20070816 

From sheryl: a 50*70 horse pen is 240 feet and 3500 square feet
a 60*60 horse pen is 240 feet and 3600 square feet
why is there a 100 square feet difference? Answered by Penny Nom. 





Percentage change 
20070813 

From Karen: I need a formula for calculating percentages in Excel. For example, we =
sold 4 units of an item one month, and 105 units the next. I need a =
formula to calculate the percentage increase in sales units. Also, if =
5251 were sold one month and 651 the next, what is the formula for =
calculating the percentage difference? Please help, thank you. Answered by Penny Nom. 





Twenty dining tables 
20070813 

From priya: Utkarsh bought 20 dining tables for Rs 120000 and sold these at a profit equal to the S.P of 4 dining tables.Find the S.P of one dining table.(give the answer in statements) Answered by Stephen La Rocque. 





A right triangle 
20070811 

From Peter: Ok, is it possible to find the height and base of a right triangle when all the information you are given is the length of the hypotenuse?
I also know that the angle between side b and the hypotenuse is 45 degrees. please help. Answered by Walter Whiteley. 





4,18,48,100, __ 
20070807 

From Jeremy: What is the next number in the following sequence?
4,18,48,100, __ Answered by Leeanne Boehm and Stephen La Rocque. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





Angular speed 
20070805 

From Virginia: the engine of a sports car rotates at 5,000 revolutions per minute (rpm). calculate the angular speed of the engine in radians per second. use 2n radians = 1 revolution Answered by Stephen La Rocque. 





A sequence of numbers 
20070727 

From Shamik: Question: A sequence of numbers is defined in the following way.
B(1) = 1
B(n) = B(n1) + {Sum of the digits of B(n1)} for n > 1.
B(1) = 1
B(2) = 2
B(3) = 4
B(4) = 8
B(5) = 16
B(6) = 23
B(7) = 28
B(8) = 38
B(9) = 49
::::::::: and so on ...
Is the number 123456789 a term in the given sequence?
Shamik Answered by Claude Tardif. 





Countable and uncountable sets 
20070724 

From Mac: Hi, i tried to read few webpages related to the countably infinite and uncountable sets.
Even i read few questions from this forum.
But i am not convinced with this explanation. If you have any good book that
explains this in layman term, please redirect me to that.
1) Can you please explain what is the difference between these too ?
2) How could you say set of Natural number and set of even numbers are countably
infinite ?
N={1,2,3,...} and Even= {2,4,6,...}
When an element in the even set is some 2n, we will map it to 'n'.So
now we have a bigger number(2n) right ?
Sorry, i didn't understand that.
...
Can you please help me out to understand that ? Answered by Harley Weston. 





Equality of sets 
20070723 

From Mac: Hi, I learnt set theory recently. My teacher and few of the weblink actually give different
definition for basic set. Can you please solve this ?
My teacher says, {1,2,3} and {1,1,2,3} is also set.
But in this link http://library.thinkquest.org/C0126820/setsubset.html it says,
"A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice."
and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}"
My question is,
1. Whether duplicates allowed in the set or not ?
2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ? Answered by Penny Nom and Harley Weston. 





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. 





Can't find circumference of an ellipse 
20070706 

From Michele: I need to figure the circumference of an oval and I know the height and width. Answered by Penny Nom. 





Log base 2 of log base 2 of x 
20070627 

From alex: y = log base 2 of lag base 2 of x
The slope of the tangent to the given curve at its xintercept is..? Answered by Harley Weston. 





The area of part of a circle 
20070621 

From Sarah: Hi, I need help finding the area of a part of a circle that involves a
chord. I need this answer/help very soon if at all possible. I have
attached a drawing of what I am trying to solve. Thank you for your help!
Sarah! Answered by Penny Nom. 





Finding the center of an ellipse 
20070620 

From Sima: find the center of the ellipse with the equation 3x^2 +4y^2+18x32y5=0 Answered by Penny Nom. 





What is the 100th term? 
20070615 

From George: I have the sequence
50,120,235,406,644
the 1st difference is 70,115,171,238
the 2nd difference is 45,56,67
the 3rd difference is 11,11
i used the a*n^3+b*n^2+c*n+d rule but the a turns out to be a decimal
because 11/6 is 1.833333333 and so i cant find the formula for the 100th term
term. Answered by Penny Nom. 





Percentage increase and decrease 
20070613 

From Anna: I just want to if the following formula is used for the computation of a PERCENTAGE DECREASE:
Old Value  New Value/ Old Value x 100%
My immediate superior is under the impression that the said formula works ONLY for the computation of a percentage INCREASE. He believes that the formula for a percentage DECREASE:
Old Value  New Value/ NEW Value x 100%
On this score, I want to know the correct formula for the computation of percentage decrease. Thank you so much.
Answered by Penny Nom. 





Composition functions 
20070612 

From Gilligan: Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start. Answered by Stephen La Rocque. 





A sequence of circles 
20070611 

From Ann: Please help with solving the following problem!!!
A circle is inscribed in an equilateral triangle with a side of length 2.
Three circles are drawn externally tangent to this circle and internally
tangent to 2 sides of the triangle. 3 more circles are drawn externally
tantgent to these circles and internally tangent to 2 sides of the triangle. if
this process continued forever, what would be the sum of the areas of all the
circle? the answer 1 parent came up with was Pie over 2, but we don't
know how he did it. Can you please show the work or explain the answer to
this problem?
Thank you
Ann
p s my daughter is in 9th grade math. Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





How many terms in this sequence? 
20070611 

From Jesse: How do I find how many terms are in the sequence? 51, 48, 45, ...., 75 Answered by Stephen La Rocque and Penny Nom. 





The intersection of two planes 
20070531 

From Sarim: How to find a intersection of two planes? Answered by Penny Nom. 





Water tank volume 
20070529 

From Cecelia: I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK. Answered by Stephen La Rocque. 





A point on a semicircle 
20070528 

From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom. 





The surface area of a fire hose 
20070526 

From Vanessa: Why do we need to find the surface area of a fire hose (cylinder). Answered by Stephen La Rocque. 





The circumference of an ellipse 
20070525 

From Graham: I have an ellipse that I need to find the circumference of. It is 40ft at its longest point and 25ft at its shortest Answered by Penny Nom. 





Normal distribution 
20070524 

From Paula: Consider a data set that is normally distributed.
The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a
"zvalue" = 2.5. Solve for the standard deviation of
the data set.
b.) Solve for the "zvalue" of 9,900. Answered by Penny Nom. 





Base seven 
20070519 

From Dan: A number X is converted to base 7 and becomes a four digit number. Its leftmost digit is removed and written again as the rightmost digit. The number thus obtained is twice X. Find the decimal representations of all such numbers X. Answered by Penny Nom. 





Parabolas in the real world 
20070518 

From Katherine: Hi, my name is Katherine, and my mean old math teacher just assigned us a test in which
we have to write two examples of how parabolas are used in the real world, each one page
single spaced, size 12!! I know you have already answered some questions like this, but
I still don't understand the whole baseball thing, and any other way parabolas are used.
And how I can write a whole page on it. But that's my problem, not yours, I just need help
with a little explanation on how parabolas are actually used today. I know this might be kind
of confusing for you, but imagine how it is for me!! Answered by Stephen La Rocque. 





Comparing the areas of various shapes 
20070516 

From Kathy: If the perimeters are the same, which has the greater area, a circle, a square, an ellipse, or an octagon? Answered by Stephen La Rocque. 





Maximizing the volume of a cone given the slant length 
20070514 

From Christina: A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Answered by Stephen La Rocque and Kerstin Voigt. 





Finding the hypotenuse without Pythagorus 
20070511 

From Shelbie: How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Answered by Stephen La Rocque. 





Probability of H.I.V. tests 
20070507 

From Danielle: A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.? Answered by Stephen La Rocque. 





A point inside a circle 
20070504 

From edgemitter: There is a point inside a circle (but not in its center) where two perpendicular secants intersect, dividing the circle into four regions with different area. Calculate the area of the four regions Answered by Walter Whiteley. 





Hypotenuse 
20070503 

From ashley: how do you find the hypotenuse Answered by Penny Nom. 





3, 6, 12, 21, 33, 48, 66 
20070502 

From Siew: I need to find the nth term formula for the sequence :
3, 6, 12, 21, 33, 48, 66 Answered by Stephen La Rocque. 





Percentage change 
20070501 

From katie: i no many people have asked about this but im still unsure what is percentage change i have my ks3 tomoro so please reply asap thankz Answered by Penny Nom. 





The sum of two or more consecutive integers 
20070426 

From nana: some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only)
other number (eg. 4) cannot be express in this way.
let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers)
a). list the first few SOALTCI and conjecture the general formula.
b). Prove that any number of the given form(in your answer (a)) is a SOALTCI Answered by Penny Nom. 





A triangle problem 
20070423 

From Dimitri: In the triangle ABC, M is the midpoint of AB and N is the midpoint of AC. Prove that CM and BN cannot bisect.
(I can prove it by contradiction if it is a scalene triangle, but i cant seem to prove it for isosceles) Answered by Chris Fisher. 





Two lines intersect at a right angle 
20070420 

From ellen: The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point
(4,6). Determine the values of a, b & c. Answered by Stephen La Rocque. 





The second derivative 
20070414 

From Gerry: In mathematical context,what do you understand by the term "Second Derivative" Answered by Penny Nom. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





Choosing 6 from a set of 12 
20070412 

From Darren: there are 12 numbers (123456789101112)
how many times can i pick 6 different numbers? Answered by Stephen La Rocque. 





Where will volume 13 go? 
20070412 

From Shawn: A novice librarian shelved a twelvevolume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Stephen La Rocque and Penny Nom. 





Pythagoras was right 
20070411 

From Vineet: in a right angle triangle, hypotenuse side is less than the sum of other two
sides, how the square of hypotenuse is equal to the sum of squares of other two sides? Answered by Stephen La Rocque. 





What are the first 3 terms of this sequence 
20070410 

From kyrie: what are the first 3 terms of this sequence
n2 divided by n squared Answered by Stephen La Rocque. 





4,7,16,43,... 
20070404 

From claire: What is the explicit definition for the sequence 4,7,16,43,...? Answered by Stephen La Rocque and Penny Nom. 





What is the hypotenuse of a right traingle 
20070404 

From debbie: what is the hypotenuse of a right triangle with sides of 38 meters and 24.2 meters. Answered by Stephen La Rocque. 





A set of points in space 
20070404 

From Lenny: What is a set of points in space the same given distance from its center point called? Answered by Stephen La Rocque. 





Algebra 
20070403 

From Emily: 9,365 and 2,242 added to the difference between 255 and half of a number is 11,784. What is the number? Answered by Haley Ess. 





In what base does 25+25=51? 
20070403 

From Jenna: In what base does 25+25=51? Answered by Stephen La Rocque and Penny Nom. 





A geometric series 
20070403 

From jessica: If a geometric series includes 5418+62 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive. Answered by Stephen La Rocque. 





Direct and inverse Variation 
20070403 

From liz: how do you tell if an equation varies Directly or Inversely? ex.
x= 2y or
xy+12=3
i know that if you have three numbers (x. y, z) that it varies jointly but how do you tell if it is Inverse or Direct?
Thanks for the Help!
liz Answered by Stephen La Rocque. 





What does inverse graph represent? 
20070330 

From san: what does inverse graph represent? Answered by Penny Nom. 





Is the inverse of a function always a function? 
20070329 

From San: Is the inverse of a function always a function? Please justify. Thank You! Answered by Penny Nom. 





A beam on a lighthouse 
20070328 

From Lisa: A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P? Answered by Stephen La Rocque. 





The angles in a right triangle 
20070328 

From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom. 





The foci of an ellipse 
20070327 

From Brad: I am trying to figure out how to find the foci of an ellipse x^2/7 + y^2/16 = 1.
Since 16 is the largest denominator I know the major axis is going to be the y axis.
Do I now take 7c^2=16. c^2=167, c^2=9, c=3. So is my foci (0,+3). Answered by Penny Nom. 





An inheritance problem 
20070323 

From Carl: A father of 3 boys, who owns 17 horses dies. He leaves his first son
1/2 of the horses. The sons hate each other. The father leaves the
second son 1/3 of the horses. They are ready to kill each other. He
leaves his youngest son 1/6 of the horses.
Without cutting the horses into pieces how do they split the horses?
I heard this puzzle when I was 12 years old.
1968
The preacher rides up on his horse and said "If I give you my horse will
you quit fighting ? They agree to stop fighting?" Why? Answered by Penny Nom. 





Two consecutive odd numbers 
20070319 

From Alicia: The sum of two consecutive odd numbers is divisible by 4.
Can you make similar statements about the sum of three consecutive odd
numbers and of four consecutive odd numbers?
Generalize your findings.
I tried :
n= smallest odd number
therefore the next = n, n+2 and the second =n+4 and the third = n+6
Now n+ n+2+n+4+n+6/4
Please help I am not sure of this I am just trying Answered by Penny Nom. 





Choosing numbers with no two consecutive 
20070315 

From Meghan: How many combinations are there of 3 numbers chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 but where no 2 of the 3 numbers are consecutive?
Thank you!
Meghan Answered by Penny Nom. 





A truncated cone 
20070310 

From Russell: Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom.
Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service.
Russell Answered by Penny Nom. 





Seven digit account numbers 
20070309 

From Miranda: Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!! Answered by Penny Nom. 





A circle is stretched horizontally by a factor of 2 
20070307 

From bob: I was wondering if you could double check my work?
the question is as follows: The circle X^2+y^22x3= 0 is stretched horizontally by a factor of 2 to obtain an ellipse what is the equation of this ellipse in general form? Answered by Penny Nom. 





Finding the vertical height of a roof 
20070305 

From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque. 





Direct and inverse variation 
20070303 

From Rene: Hi I'm Rene, I'm stuck with some problems in direct and inverse variation.
I know how to solve direct and inverse problems when only one variation is in a question at a time.
EX: p varies inversely as the square root of q, and when p=12, q=36 find p when q=16
12*6 =p*4 72=4p 18=p
But how would you solve a problem like.....
If s varies directly as r and inversely as t, and s=10 when r=5 and t=3, for what value of t will s=3 when r=4 ? Answered by Penny Nom. 





The intersection of two lines 
20070228 

From Tamara: I was told to make a graph to help solve this question. I was given two equations. One was x2y=3 and the other was 2x+y=4. We have to change it to the equation of the line format. Then we graph the line and find the point where they meet. I've been trying to do that, but when i check the answer, It turns out wrong. It's meeting in the wrong spot. I need help please. Answered by Penny Nom. 





Find the nth term 
20070227 

From Dinky: My teacher has set us a project, but i am having trouble finding the nth term for this. the numbers are: 1, 2, 6, 24, 120 could you please help me? thank you dinky113 Answered by Stephen La Rocque and Penny Nom. 





Social security numbers 
20070227 

From Tish: Social Security numbers are in the form #########, where each symbol represents a number 09, how many are possible with this format? Will we ever run out of Social Security numbers?
(This is one question with two parts, I saw some examples but I am still confused because if there are 1 million possibilities then how have we been able to issue out numbers to over 280 US citizens?) (For the second part a yes or no answer is sufficient) Answered by Penny Nom. 





Cutting the top off a circle 
20070225 

From Daniel: If a circle as a diameter of D I cut off a straight part at C from the top What is the formula to find the area of the left over part? Answered by Penny Nom. 





Arithmetic Series 
20070218 

From Krista: Question The sum of the first 4 terms of an arithmetic series is 8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms. Answered by Stephen La Rocque. 





What is the index of the term '119' in the sequence 2, 5, 8, 11? 
20070216 

From joey: What is the index of the term '119' in the sequence 2, 5, 8, 11? Answered by Penny Nom. 





The nth term 
20070213 

From Sarah: I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer? Answered by Stephen La Rocque. 





The sum of a sequence 
20070211 

From joey: find the sum of the first 98 terms of the sequence 3, 5, 1, 3, 5, 1, 3, Answered by Penny Nom. 





Piecewise Functions 
20070209 

From Steph: h(x)={2 if x<0 {x+1 if 0< x <10 {1/2x+16 if x>10 PLEASE HELP Answered by Penny Nom. 





Find the next 3 terms of the sequence 
20070207 

From rose: find the next 3 terms of the sequence 2,3,9,23,48,87 Answered by Penny Nom. 





A triangle inscribed in a semicircle 
20070206 

From Benneth: Consider a triangle inscribed in a semicircle with a radius of R. What are th possible perimeters for the triagle? And the areas? Answered by Penny Nom. 





A 3digit number in base 7 has its digits reversed when expressed in base 9. 
20070128 

From Ashley: A 3digit number in base 7 has its digits reversed when expressed in base 9. Find this number. Answered by Penny Nom. 





The area of a ellipse 
20070125 

From Ranjit: I have a task in which i have to find the area of a ellipse. i find this difficult because i have only been provided with the perimeter, which is 1000m. Answered by Chris Fisher. 





Line segments on dot paper 
20070121 

From Khaori: The three line segments below are drawn on centimeter dot paper.
a. Find the length of each segment to the nearest tenthousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom. 





5,8,11,14,17 
20070118 

From Mairead: the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ? Answered by Paul Betts. 





Points of intersection 
20070118 

From Mark: Find the points of intersection of the given pair of curves. 2x  3y = 8 and 3x  5y = 13 Answered by Steve La Rocque and Haley Ess. 





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. 





What is the percent of the decrease? 
20070110 

From Bill: if the value of xyz company stock drops from $25 per share to $21 per share, what is the percent of the decrease? Answered by Penny Nom. 





Three consecutive odd integers 
20070108 

From Emma: Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third. Answered by Stephen La Rocque. 





Twice the smaller of two consecutive integers is the larger increased by 5. 
20070108 

From Evan: Twice the smaller of two consecutive integers is the larger increased by 5. find the integers. Answered by Stephen La Rocque and Penny Nom. 





13.78g /11.3mL 
20070105 

From Judd: 13.78g /11.3mL Answered by Penny Nom. 





How do I determine the length of an ellipse if the width and area are known? 
20070104 

From Tom: How do I determine the length of an ellipse if the width and area are known? Answered by Steve La Rocque and Karen McIver. 





An octagonal birdhouse 
20061230 

From Verner: I am building a octagon birdhouse,what degree would I cut each side of each piece of wood to assemble the birdhouse? Answered by Penny Nom. 





Percentage increase 
20061221 

From Wang: The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month? Answered by Penny Nom. 





Find the total distance the swing traveled before it stopped. 
20061217 

From Leah: Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped. Answered by Penny Nom. 





1, 3, 6, 10... 
20061215 

From Lisa: What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser. Answered by Stephen La Rocque and Penny Nom. 





The nth term 
20061215 

From Lisa: I have worked out that the nth term for 1, 4, 9, 16 is n squared and 3, 5, 7, 9 is 2n  1, so what is the rule for the sequence 1x3, 4x5, 9x7, 16x9? Answered by Penny Nom. 





The nth term 
20061214 

From Hepzibah: what is the definition of nth term and n? Answered by Penny Nom. 





Base 5 
20061211 

From Shelley: how do you convert decimal numbers to a given base for example 2,875 to base five? Answered by Stephen La Rocque. 





Sectors of a circle 
20061130 

From Maithreyi : A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector? Answered by Stephen La Rocque. 





Percentage increase 
20061129 

From Toya: I have some statistics from year to year based on drug seizures.(units= lbs) e.g. in 2005 123lbs seized in 2006 1518lbs seized. now i worked out the percentage increase as to be in the thousands which from looking at the figures is correct however i don't want to say 1000% increase.
using another formula current previous *100 I got 92%. what exactly does this 92% represent and how can i use this number when presenting my answers instead of using 1000 + % Answered by Stephen La Rocque and Penny Nom. 





An arithmetic series 
20061128 

From Jillian: Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30. Answered by Penny Nom. 





A geometric sequence 
20061128 

From Jillian: Find x so that 2x, x + 5, x  7 are consecutive terms of a geometric sequence. Answered by Stephen La Rocque. 





A problem involving logs 
20061126 

From Beth: any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!!
log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Answered by Stephen La Rocque and Penny Nom. 





Arithmetic with base 2 
20061126 

From Yuva: can we do arithmetic ,base 2. If yes, how and if not, why. Answered by Stephen La Rocque. 





The area of a semicircle 
20061125 

From Melinda: If the radius of a semicircle is 9ft what is the area? Answered by Karen McIver and Penny Nom. 





An Easement 
20061121 

From Ms Porter: I need to acquire a 20 feet easement for a project and I need to know how many square feet are in a 20 feet easement? Answered by Penny Nom. 





The Fibonacci sequence 
20061121 

From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn1 + fn2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n1). Answered by Penny Nom. 





Conic sections 
20061119 

From Joyce: My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Answered by Penny Nom. 





On day 1 on which day will 96 students donate food? 
20061119 

From Veydee: during a canned food drive the number of students who donate food doubles each day. If three students donate food on day 1 on which day will 96 students donate food? we have to find the term rule for this pattern Answered by Penny Nom. 





Induction 
20061116 

From John: Find a formula for 1/(1x3)+1/(2x4)+1/(3x5)...+1/(n(n+2)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result. Answered by Penny Nom. 





Sigma from 0 to infinity of (n^3 / 3^n) 
20061115 

From Cedric: I'm wondering how you would find if this series converges or diverges?
Sigma from 0 to infinity of (n^3 / 3^n)
Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then? Answered by Penny Nom. 





The empty set is a subset of every set 
20061114 

From Narayana: The empty set is a subset of every set Answered by Stephen La Rocque and Penny Nom. 





Some applications of conic sections 
20061113 

From Burt: how are circles, ellipses, and hyperbolas used in everyday life Answered by Penny Nom. 





Piecewise functions 
20061108 

From Kait: We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says: f(x){2x+1, if x <1 f(x){x+4, if x is greater than or equal to 1. Answered by Penny Nom. 





1,4,9,16,25,36..... 
20061106 

From Teje: i cannot find the next number for this sequence 1,4,9,16,25,36..... could u help please Answered by Stephen La Rocque. 





The semester grade 
20061103 

From Caroline: Can you tell me how to calculate a grade based on a percentage formula where 15 assignments account for 40% of the grade and 3 tests account for 60% of the semester grade. Answered by Penny Nom. 





Kilowatts and Horsepower 
20061103 

From Michael: How many Kilowatts=1 Horsepower or Horsepower=1 Kilowatt? Answered by Stephen La Rocque. 





The sum of 2000 consecutive integers is 1000 
20061029 

From Matias: if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is? Answered by Penny Nom. 





Three consecutive integers 
20061029 

From Jimmy: Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6 Answered by Stephen La Rocque. 





The real numbers with decimal representations consisting of all 1s. 
20061029 

From Ivessa: Determine if the following set is countable or uncountable : the real numbers with decimal representations consisting of all 1s. Answered by Steve La Rocque and Walter Whiteley. 





How many sequences are possible? 
20061028 

From Sam: A fair eightfaced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible? Answered by Penny Nom. 





Direct and Inverse variation 
20061027 

From Vishalinee:
i'm not sure how to use the words direct variation and inverse variation to describe thre relationship between: a. speed and distance b.speed and time c. distance and time. and then i need to create equations using the descriptions. i am really messed up with direct and inverse variation. Answered by Karen McIver. 





Three consecutive odd numbers 
20061021 

From Pige: The sum of three consecutive odd numbers is 387. Find the numbers. Answered by Penny Nom. 





A trillion seconds? 
20061016 

From A student: How many years, days, hours, minutes, and seconds in a trillion seconds? Answered by Stephen La Rocque. 





Percentage increase 
20061015 

From Amanpreet: in yr 7, bill was 1.28 m tall, in yr 9 he was 1.67m tall. calculate his percentage increase in height Answered by Stephen La Rocque. 





How many feet tall is the tunnel 
20061014 

From Charles: A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center? Answered by Penny Nom. 





Plotting percentage change 
20061011 

From Beckie: I have worked out a set of percentage differences which are all percentage decrease. Should i express them as a negative percentage as 20%? I also need to plot them on a graph and am not sure whether to just use the percentage difference as it is, in which case i get a positive gradient, or include a negative axis and plot them in this way, in which case i would get a negative gradient. I think the slope of the curve will be the same either way so it might not matter! Answered by Penny. 





Onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5 
20061009 

From Hina: If onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Answered by Steve La Rocque and Claude Tardif. 





The area of an oval 
20061008 

From Bruce: area of an oval: 60" x 120" Answered by Stephen La Rocque. 





How many line segments are necessary? 
20061004 

From Varun: If you place 35 points on a piece of paper so that no three are collinear, how many line segments are necessary to connect each point to all the others? Answered by Stephen La Rocque. 





A number pattern 
20061002 

From Tim:
The patterns that went in 2s, 4s and 5s we got, but we are stuck on the pattern that doubles. We can't come up with the rule or equation that solves it.
With the first number being the term number and the second being the term, this is the pattern:
11
22
34
48
516
632
764
100128
What is the rule for this?
Answered by Stephen La Rocque and Penny Nom. 





The hypotenuse 
20061002 

From Ashley: How do you find the hypotenuse of a right triangle? I don't understand how to find c. Answered by Stephen La Rocque. 





The focus of a parabola 
20061001 

From Lily: I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me? Answered by Penny Nom. 





2 5 11 17 23 31 ? 
20060928 

From Bernice: How do you determine the next number in the following sequence: 2 5 11 17 23 31 ? Answered by Penny Nom. 





Piecewise functions 
20060924 

From Claudia: hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it.
my problem is
g(x){x+2 if x <2}
g(x){2x  1 if x> or = 2} Answered by Penny Nom. 





Find the nth term 
20060913 

From Shakira:
my question is  Find an expression for the nth term of each sequence.
a. 6,15, 28, 45, 66
b, 1/5, 3/8, 5/13, 7/20, 6/29  these are fractions
Answered by Penny Nom. 





5, 3, 2, 1, 1, 0, __, __ 
20060912 

From Sherrie: next two terms in the sequence:
5, 3, 2, 1, 1, 0, __, __ Answered by Stephen La Rocque. 





Brackets and more brackets 
20060829 

From Michelle: Feeling stupid asking but it's been awhile ... {{{2}}} ...what is this really saying ....are the outer brackets = null? Answered by Stephen La Rocque. 





Points of intersection 
20060820 

From Gianella:
Find the points of intersection by solving this problem analytically.
y= x cubed
y= x
Answered by Stephen La Rocque. 





Find the points of intersection 
20060818 

From Ingrid:
The question says find the points of intersection of the graphs of the equation, and check your results analytically.
x squared + y squared=25
2x+ y=10
Answered by Stephen La Rocque. 





A concrete semicircle 
20060815 

From John: I have to figure out how many yards of concrete I need for a semicircle. I have a radius of 21 feet and the concrete is 4" thick. I took 3.14 x (21)^2 then divided by 40 to get how many yards of concrete but that doesn't seem right. Answered by Penny Nom. 





Marking out a circle 
20060628 

From Peter: given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius. Answered by Stephen La Rocque and Penny Nom. 





The area of a house 
20060628 

From Michael: I would like to know how to measure the area of a house? Answered by Penny Nom. 





The area of a sector and a triangle 
20060623 

From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom. 





As close to 841 as possible 
20060621 

From Alan: using these numbers by either add subtract division multiply come up with the answer as close to 841
100 25 10 7 6 3 Answered by Paul Betts. 





13 57 91 11 31 51 ?? 
20060615 

From Chastity: im trying to determine the missing number in the sequence
13 57 91 11 31 51 ?? Answered by Claude Tardif, Steve La Rocque and Natasha Glydon. 





The perimeter of a pool 
20060605 

From Troy: How many Linear feet would a pool be if the pool was 18 by 38 foot oval Answered by Penny Nom. 





What is the value of csc (2pi/3)? 
20060604 

From Kishor: What is the value of csc (2pi/3)? Answered by Stephen La Rocque. 





What is the sum of the first 100 whole numbers? 
20060531 

From Jo: what is the sum of the first 100 whole numbers? Answered by Natasha Glydon, Paul Betts and Penny Nom. 





The area of part of a circle 
20060529 

From Larry: need to find area of a circle between a given line (cord) to the circumference of the circle (see attachment). I often review blue prints of homes and many times have to know the area the home. Answered by Stephen La Rocque and Penny Nom. 





The nth term of a sequence 
20060524 

From A student: please could you give me a formula for the following numbers for my teacher
3 8 15 24 35 Answered by Chris Fisher. 





Three purses 
20060522 

From Marcee: If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If $60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if $40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold? Answered by Penny Nom. 





We are 2 pairs of consecutive 2 digit numbers ... 
20060513 

From A perent: We are 2 pairs of consecutive 2 digit numbers that are factors of the number of feet in a mile. Who are we? Answered by Claude Tardif. 





A person is given 3 true or false questions 
20060511 

From Larry: A person is given 3 true or false questions. They have no idea of the answers. What is the probability of the person getting them all correct? Could you show me a tree for this. Answered by Penny Nom. 





Small pipes and large pipes 
20060509 

From geece: A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.
How long will 5 small pipes, on their own, take to drain the reservoir? Answered by Penny Nom. 





Adding consecutive numbers 
20060426 

From Lisa: When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Answered by Stephen La Rocque. 





Geometric sequence and basic functions (graphs) 
20060420 

From Marlene: Which of the basic functions is related to the geometric sequence:
Linear, Quadratic, Rational, or Exponential?
Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque. 





Arithmetic and Geometric Sequences 
20060419 

From Skye: If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence. Answered by Stephen La Rocque. 





Reverse percentage 
20060419 

From Mike: How would I calculate a reverse percentage?
Let me give you an example. I have two values that calculate to a success rate of 93.32. Total=1546051 Failures=103302. (1546051103302)/1546051=93.32% success.
Now how much would I need to increase the total value to get the success up to 95%? Answered by Stephen La Rocque. 





Overlapping area of two circles 
20060415 

From Jade: Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
Answered by Stephen La Rocque. 





What is the cost price? 
20060414 

From Purushotham: If the selling price is 120 and the profit is 20%, what is the cost price? Answered by Stephen La Rocque. 





The product of successive terms in sequences 
20060413 

From Forrest: 1) Find three successive terms in an arithmetic sequence such that their sum is 24 and their product is 440
2) Find three successive terms in a geometric sequence such that their sum is 21 and their product is 216 Answered by Penny Nom. 





Finding the inverse of a function 
20060412 

From Sam: If g(x) = 2x+3/5 then how do I find the inverse? Answered by Walter Whiteley. 





Arithmetic Sums 
20060412 

From Angel: (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28.
(b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Answered by Stephen La Rocque. 





Sum of a Geometric Sequence 
20060411 

From Andre: In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque. 





A plant increases its height by 1/2 the first day,... 
20060330 

From Andy: A plant increases its height by 1/2 the first day, 1/3 the second day, 1/4 the third day and so on. How many days did it take to grow to 100 times its height? Answered by Stephen La Rocque. 





Can an equilateral triangle have an obtuse angle? 
20060326 

From Chris: Can an equilateral triangle have an obtuse angle?
I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?
Answered by Stephen La Rocque. 





The cartesian product of a countably infinite collection of countably infinite sets 
20060325 

From Geetha: Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Answered by Penny Nom. 





How much fabric do I need? 
20060325 

From Michelle:
I AM DECORATING A STAGE FOR A BOARD OF DIRECTORS MEETING AND I NEED TO BUY FABRIC AND I DON’T WANT TO WASTE $$ BY BUYING TOO MUCH FABRIC OR NOT ENOUGH FABRIC.
THE AREA THAT I’M NEEDING MATERIAL FOR IS, 12ft HIGH BY 34ft WIDE.
THE FABRIC COMES IN ROLLS OF 60” (inches) x 100 yards.
SO HOW MUCH FABRIC SHOULD I NEED TO FOR THE AREA I’M WANTING TO COVER?
Answered by Stephen La Rocque and Penny Nom. 





Piecewise functions 
20060321 

From Kris: First Problem:
Southeast Electric charges .09 cents per kilowatthour for the first 200 kWh.The company charges .11 cents per kilowatthour for all electrical usage in excess of 200 kWh. How many kilowatthours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?
Second Problem:
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs overtime worked. Again I don't know how to set up the equation to come up with the answer.
I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful. Answered by Penny Nom. 





How far from Earth is Neptune? 
20060321 

From Scott: A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune? Answered by Penny. 





The square footage of an area in my backyard 
20060317 

From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom. 





Divide the product of three consecutive positive integers by their mean 
20060312 

From Sandy: When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers? Answered by Stephen La Rocque. 





Two consecutive even integers 
20060311 

From Cheryl: Find two consecutive even integers that have a sum of 450
Answered by Stephen La Rocque. 





How many of these cubes have no wax of them? 
20060310 

From Iban: cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm.
How many of these cubes have no wax of them? Answered by Stephen La Rocque. 





8,_,4,9,1,_,10,3,_,0 
20060308 

From Rachel: I cant figure out this sequence if someone could help me
8,_,4,9,1,_,10,3,_,0 Answered by Claude Tardif. 





A nine digit number 
20060306 

From Ryan: What is the total number of possible combinations of a nine digit number (ie., social security number) including repeating numbers? Answered by Stephen La Rocque and Penny Nom. 





2,4,9,6,5,6,____,____,____,... 
20060306 

From Mike: I am having problems figuring out the following sequence:
2,4,9,6,5,6,____,____,____,...
We were able to guess that the pattern simply started to reverse itself,
but I was wondering if there were other possibilities.
Answered by Claude Tardif. 





The nth term 
20060305 

From Umar: my question is what is the nth term for a house of cards 4 stories high if you use the following numbers:
2 7 15 26 Answered by Penny Nom. 





A 5900% increase 
20060303 

From Pat: I want to find out the % of production increase from 250 dolls a month to 15,000 dolls a month. i think it is 5900% but that seems too high. Answered by Penny Nom. 





A cone with an oval as base 
20060301 

From Richard: I am trying to find the volume of a cone that is not round but oval. Answered by Penn Nom. 





Luke and Slim have only one horse. 
20060226 

From Emily: Luke and Slim have only one horse. Luke rides for the agreed on distance and then ties up the horse for Slim, who has been walking. Meanwhile, Luke walks on ahead. They alternate walking and riding. If they walk 4 miles per hour, and ride 12 miles per hour, what part of the time is the horse resting? Answered by Penny Nom. 





The nth term of a sequence 
20060221 

From Mike: I'm having trouble finding the nth term in an equation, can you help me? Answered by Stephen La Rocque. 





Percent gain 
20060214 

From Bill: If a stock is bought at $3.50 and sold at $5.80, what percent was the gain? Answered by Penny Nom. 





Base pi 
20060213 

From Joe: How would you convert the number 10 from the decimal system of numeration (base 10) into a system of numeration of base pi.
Answered by Stephen La Rocque. 





Find two consecutive integers whose product is 182 
20060209 

From Anthony: Find two consecutive integers whose product is 182 Answered by Steve La Rocque. 





The intersection of a line and a circle 
20060202 

From Bernice: if i am given an equation of a circle and 2 points in a line how do i know if the line intersects the circle and how do i determine the points of intersection Answered by Chris Fisher. 





Arithmetic progressions 
20060131 

From A student: 1)the sum to n terms of a particular series is given by S_{n}=17n3n^{2}
a)find an expression for the n term of the series
b)show that the series is an arithmetic progression
2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference
Answered by Penny Nom. 





An array problem 
20060131 

From Cynthia:
Write a number sentence for this array........
It's a rectangle box 3 down and 4 wide.
Answered by Penny Nom. 





Percentage increase in sound intensity 
20060129 

From David: I am doing some emotion response mapping.
Being a composer I know how to push the heart beat tempo by a % increase of BPM in my music. I want to know how to calculate an increase in intensity of sound. Now I have 60 decibels. I want an increase of intensity by a factor n% with out going over 156 decibels.
Answered by Penny Nom. 





how can i find the height of a triangle if i have the base and the hypotenuse 
20060127 

From Kelsey: how can i find the height of a triangle if i have the base and the hypotenuse Answered by Penny Nom. 





Sectors and arcs 
20060125 

From Wael: How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom. 





Finding the nth term in fractions 
20060123 

From Zarina: Each term in this sequence is made by increasing the numerator by 1 and the denominator by 3. here are the first five terms:
1/4, 2/7, 3/10, 4/13, 5/16, ...
(a) write an expression for the nth term: Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





Percentage change when you start from zero 
20060102 

From Joseph: I am not sure if my meaning for calculation for a percent change (CP/P)x100) is correct. In this case, C=10, P=0, does this mean 100 percent increase from previous period? Answered by Harley Weston. 





The area of a sector of a circle 
20060102 

From Natashia: How do you find the area of a shaded sector of a circle? Answered by Penny Nom. 





Joey had 8 drinking glasses, all of different sizes. 
20051229 

From Danielle: Joey had 8 drinking glasses, all of different sizes. he has lined them up from smallest to largest and numbered them #1 (smallest) to #8 (largest). he knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold!
He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Her are his results: Answered by Penny Nom. 





Percent change 
20051217 

From Marie: What is the percentage change when 1500 becomes 2000? Answered by Penny Nom. 





Percentage increase 
20051215 

From Luiz: I would like to know how much net income in % we have increased from 2005 to a 2006(projection).
2005 Net Income Actual: $1,599,887
2006 Net Income Budgeted: $2,067,339 Answered by Penny Nom. 





Find the nth term 
20051214 

From Kevin: How do i find the nth term of 1 4 9 16 25 36 Answered by Penny Nom. 





The stair problem 
20051206 

From Arnold:
My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?
1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations
Answered by Harley Weston. 





An Arithmetic sequence 
20051201 

From Aana:
The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.
Here's what I did to find d
a+2d=19; 25+2d= 19 ;1925=2d d=6/2=3
This is where I'm stuck. Can you please provide me with some guidance.
Answered by Penny Nom. 





The sum of n consecutive integers 
20051127 

From Craig:
If 875 is expressed as the sum of n consecutive integers (n > 1), then the number
of possible values of n is?
Possible Answers:
A) 15
B) 8
C) 7
D) 16
E) 4
Answered by Penny Nom. 





Notation for the second derivative 
20051108 

From Mussawar: my question is ^{d}/_{dx}( ^{dy}/_{dx}) = ^{d2y}/_{dx2}. why it is not equal to ^{d2y}/_{d2x}. Answered by Penny Nom. 





How many passengers boarded the plane in Phoenix? 
20051103 

From Vish: Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix? Answered by Penny Nom. 





A tangent to a parabola 
20051102 

From A student: Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Answered by Penny Nom. 





2, 6, 12, 20, 30, ... 
20051101 

From Rebecca: I have a sequence of I have a sequence of 2, 6, 12, 20, 30, and have no idea how to figure out the nth term please help! Answered by Claude Tardif. 





The area of an irregular semicircle 
20051014 

From Bob: Is there a way to compute the area of an irregular semicircle i.e. one in which the arc length is not determined by the diameter; and is therefore not technically any part circular  yet still possessing an arched side? Answered by Penny Nom. 





Calculer la clé 
20050929 

From Un eleve: Chaque individu a un numéro INSEE de 13 chiffres auquels est adjointe une clé de deux chiffres.
voici comment est calculée cette clé : Answered by Claude Tardif. 





Open dots and closed dots 
20050929 

From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny. 





Find the next 5 terms 
20050924 

From Grant: n+7, 2n0.5, 4n. Find the next 5 terms of each one and explain the sequence in words Answered by Penny Nom. 





Converting from base ten to base five 
20050921 

From Julie: My sister is home schooled and we are trying to convert from base 10 to base 5. We are trying to teach and we have never had this in school. If we could have some examples of some problems and how to do them we would appreciate this. Answered by Penny Nom. 





Percentage increase 
20050919 

From Dory: Last year sales was 120,000 $ and this year sales is 280,000 $, there was an increase in sales. what I would like to know is the percentage increase between the years with the formula. Answered by Penny Nom. 





A 3dimensional pie shape 
20050917 

From Bill: Your site appeared in my search for the name of a 3dimensional pie shape. 2d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it? Answered by Chris Fisher. 





Find the first five terms of this sequence? 
20050917 

From Jade: my homework says can you find the first five terms of this sequence?
5n6 i can`t figure it out. Answered by Penny Nom. 





Elliptic trigonometry 
20050915 

From Krystal: I'm currently searching for a science project topic and i have the idea of deriving elliptic trigonometry analogous to circular trigonometry. My questions are:
Is this project "possible" to do? Answered by Chris Fisher and Harley Weston. 





A piecewise function 
20050915 

From Duncan: A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Answered by Penny Nom. 





Finding the nth term 
20050912 

From Paul:
Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences.
1/3 1/2 3/5 2/3
and
1 3 6 10
Answered by Penny Nom. 





The sum of a series 
20050831 

From Aamod: Find the sum of the given series till n terms:
(1^{4}\1*3) + (2^{4}\3*5) + (3^{4}\5*7)............... till n terms Answered by Chri Fisher. 





1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 
20050830 

From Liz: Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. Answered by Penny Nom. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





y = log(x) + x. Solve for x. 
20050826 

From Alain:
I have the following equation:
y = ln(x) + x
How do I solve for x?
Answered by Penny Nom. 





Is this percentage change or percentage increase? 
20050815 

From Betty: When calculating a percentage, if the formula is
A(new)  B(old)/A(new)
Is this percentage change or percentage increase? Answered by Penny Nom. 





The Maclaurin series generated by f(x)=x^ cosx + 1 
20050810 

From Latto: f(x)=x^{3}·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
Answered by Penny Nom. 





The equation of an ellipse 
20050717 

From Allan: I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given. No other points on the ellipse are given. Again, the only "givens" are:
Length of latus rectum = 12
Location of directrix is x = 16
If I could determine the eccentricity, I could proceed from there by taking the ratio of the distance from a focus to the latus rectum point to the distance of the point from the directrix, but I lack the x coordinate of c. I've searched the text, and feel I've "missed something" somewhere! I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be. Please indicate where I'm going wrong. Answered by Chris Fisher. 





A lighthouse is located on a small island,... 
20050714 

From Brittnee: A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom. 





Percent change 
20050701 

From Betty: Can you tell me the difference between Percentage Change, Percentage Increase, Percentage Difference and please give an example of each, I am very visual. Answered by Penny Nom. 





A geometric sequence 
20050621 

From A student:
The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q. Answered by Penny Nom. 





The circumference of an oval pool 
20050518 

From John: I have an oval pool of which I am trying to find the circumference. it is 38 feet long and 19 feet wide Answered by Penny Nom. 





Angle of incline 
20050515 

From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom. 





Adding consecutive integers 
20050513 

From Yas: i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5 Answered by Penny Nom. 





A 5% increase 
20050427 

From Debra: How can I determine the increased percentage of a dollar amount? I.e.: One dollar amount is $202 and another is $150, how can I determine the 5% increase from last year on the $202 dollar amount? Answered by Claude Tardif. 





The least integer of a set of consecutive integers 
20050419 

From Lucia: The least integer of a set of consecutive integers is 25. If the sum of these integers is 26, how many integers are in the set? Answered by Penny Nom. 





Percentage increase 
20050419 

From Tom: What is the percentage increase from (negative $9262.00) to (positive $3840.00)? Answered by Penny Nom. 





A Taylor series for ln(x) 
20050416 

From Anood: i have to represent ln(x) as a power series about 2
i`m not getting the final answer which is ln 2+ sigma (((1)^{(n+1)}/
(n*2^{n}))*(x2)^{n}). i don`t get the ln 2 part
i show you my trial
f(x)= ln x.
f(x)=(1/x) .
f(x)= (1/x^{2})*1/2!
f(x)= (2/x^{3})*1/3!
f(x)= (6/x^{4})* 1/4!
so the pattern shows me that f(n)= ((1)^{(n+1)})/x^{n} *n)
so f(2)= sigma ((1)^{(n+1)})/2^{n} *n) *(x2)^{n}
so as you see i don`t get ln 2
Answered by Penny Nom. 





Two overlapping circles 
20050320 

From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom. 





Dimensions of a roof 
20050318 

From A roofer?: A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle. Answered by Penny Nom. 





Biodiesel 
20050308 

From William: My son is doing an demonstration for science class about how to make biodiesel. we are having problems with the conversion. for instance we think there are approx 190 liters in 50 gallons. Is this correct? Also if you needed 3.5 grams of lye per liter, would that be 662g of lye. Answered by Penny Nom. 





Spraying roses 
20050303 

From A student: A litre and a half of water has 0.045 grams of herbicide added for spraying roses. How many grams of herbicide per litre is this? Answered by Penny Nom. 





Reverse pecentage 
20050301 

From Nathan: Question for you. If I have spent $10.00, what is the mathamatical equation to
figure out what the G.S.T (7%) was?
Also if I were to spend $80.00 on a hotel, and I would like to know how much
G.S.T (7%) and how much provincial tax (6%) I spent how would I go about this.
Answered by Penny Nom. 





A countably infinite collection of countably infinite sets 
20050226 

From Feroz: Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set? Answered by Penny Nom. 





Each interior angle of a particular polygon is an obtuse angle... 
20050222 

From Victoria: Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have? Answered by Walter Whiteley. 





arcsech x 
20050210 

From Monica: Prove that arcsech x = ln[(1 + (1x^{2})^{(1/2)}) / x ] Answered by Penny Nom. 





A seating arrangement 
20050203 

From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom. 





A line segment connecting two vertices of a polygon 
20050202 

From James: What is a line segment (not a side) connecting two vertices of a polygon called? Answered by Penny Nom. 





Sum to n terms of the series i.(2^(ni)) 
20050128 

From Satya: Sum to n terms of the series i.(2^{ni}) Answered by Penny Nom. 





Quadratics 
20050105 

From Usman: Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and emailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject. Answered by Harley Weston. 





An elliptical table 
20050103 

From Roger: Want to make an elliptical table, say the long (major) axis is 4 feet, and the short (minor) axis is 3 feet. I can construct this figure, but I'm trying to figure out what the exact dimension of a rectangle within this ellipse will be if I make the table a drop leaf type where the drop dimensions are equal for each end of both the long and short axes. Intuitively, it looks like there is one and only one solution. Answered by Penny Nom. 





A line from the center of the patch to the periphery 
20050101 

From Sandrine: I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Answered by Denis Hanson and Harley Weston. 





An arithmetic progression 
20041224 

From A student: the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50 Answered by Penny Nom. 





Irrigation and a sector of a circle 
20041223 

From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





Two intersecting lines 
20041218 

From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston. 





A sequence 
20041211 

From Amanda: Find the nth term of the following sequence
4, 10, 28, 82 Answered by Penny Nom. 





Geometric sequence 
20041204 

From Lesa: Find a formula for the geometric sequence: (√3  √2), (4  √6), (6√3  2√2), … Answered by Penny Nom. 





Cost before the markup 
20041123 

From Norman: the sum of eg $130 includes the markup of 30%.
However I need to calculate the percentage to apply to the $130 to assess the cost ie $100. Answered by Penny Nom. 





Proof by induction 
20041120 

From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:
a(1) = 3 and a(k+1) = 2a(k) for k > 1.
Note: Quantities in brackets are subscripts
> means 'equal to or greater than'.
Using the recursive formula, the first 4 terms are;
a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24
The nth term a(n) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





A sequence 
20041119 

From Liucy: Find the Nth term:
10 40 90 160 250 Answered by Penny Nom. 





A 40% reduction 
20041110 

From Cathy: I'm having trouble figuring out how to figure a percentage??? it's easy to find what 40% of any given number is, but how would i accurately figure out what is the final number is when i know the number after the 40% has been removed? when i add 40% to this number it obviously is lower than it should
be. the best i could figure is;
x=?40% > x?=40% i'm all confused???? Answered by Penny Nom. 





The points of intersection of two graphs 
20041105 

From Benjamin: How do I find the points of intersection of the two functions:
1) y = 2  ex
2) y = 1 + x2 Answered by Harley Weston. 





A 40% increase in garage space 
20041020 

From Dianna: A bus company recently expanded and no longer has enough room in its garage for all of its buses. Twelve of the buses have to be stored outside. If the company decides to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company own? Answered by Penny Nom. 





The third derivative 
20041015 

From Holly: Why would you ever take the third derivative? Answered by Harley Weston. 





Direct and inverse variation 
20041005 

From Abraham: Given that y varies inversely as x and x varies directly as z.If z is doubled then y is halved.Why is that true.Please explain.I'm having trouble understanding the different types of variation Answered by Penny Nom. 





1,3,6,11,18,29,__ 
20040921 

From Guillermo: How do you get to the answer of this sequence
1,3,6,11,18,29,__ Answered by Claude Tardif. 





f(x) = x4 if x<2 
20040921 

From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Answered by Penny Nom. 





B={A,{A}} 
20040920 

From Muhammad: Let A be a set and let B = {A,{A}}.
(a) Explain the elements of set B (with some example)
(b) Prove that A is not a subset of B. Answered by Penny. 





The hypotenuse of a right triangle 
20040920 

From Shannon: I am trying to find the hypotenuse of a right triangle with only the length of the opposite side. What is the formula as I don't have the length of the adjacent side? Can I compute it without knowing what the other two angles are? Answered by Penny Nom. 





Perimeter and area of a semi_circle 
20040918 

From A student: I want to know how to find the perimeter and area of a semicircle and a quartercircle. Answered by Penny Nom. 





A challenge 
20040917 

From Lasse: xy
xx
xyx
xxx
xyxx
"x" and "y" each represents a number.
Find out the system to make the next line Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





1+3+5+...+(2n+1) 
20040910 

From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)^{2} Answered by Penny Nom. 





An inverse 
20040909 

From Hillary: I cannot figure out the inverse of this function.
f(x)= 1/2x 1 Answered by Penny Nom. 





The nth term 
20040908 

From Alex: What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?... Answered by Penny Nom. 





d varies inversely with g 
20040907 

From Ashlyn: d varies inversely with g when d=8 and g=2
a. write d as a function of g using function
notation.
b. find d(10). Answered by Penny Nom. 





The intersection of planes 
20040907 

From Joshua: I was wondering about the intersection of planes. Can planes intersect? Answered by Penny Nom. 





Nine minutes 
20040902 

From A student: You have two hour glassesone measures 7 minutes and one measures 4 minutes.How can you time 9 minutes? Answered by Penny Nom. 





The radius of a circle 
20040824 

From Peter: If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius? Answered by Penny Nom. 





The series from i=1 to n :ai 
20040818 

From Ken: a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj
b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj Answered by Penny Nom. 





The intersection of two graphs 
20040728 

From JJ: Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Answered by Penny Nom. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





The inverse of a quintic function 
20040722 

From A student: I'm really having trouble finding out the inverse of this quintic equation. F(X)= X^{5}+3X^{3}+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out. Answered by Penny Nom. 





The number of blocks in a mile 
20040718 

From Valerie: I don't know if you can help me but I was wondering how many blocks are in a mile in Ocean City, New Jersey? Answered by Penny Nom. 





Two puzzles 
20040713 

From Fred: A young man's car developed a flat tire while he was driving along a deserted street. He pulled over to the curb and did all the usual things; removed the hub cap; unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them rolled down a nearby grate. Peering through the bars of the grate the man thought he could see the lugs about 6 feet below in a shallow water puddle. He had a problem, how do you think he solved it?
It is noon, your lunch hour, but you can not go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine the sun will be shining in 36 hours? Justify your answer. Answered by Penny Nom. 





An Octagonal playhouse 
20040713 

From Levi: I'm building an octagon playhouse for my son that is 8 feet wide.
what would be the measurements of each of the eight sides. Answered by Harley Weston. 





Choosing 5 numbers from 1,...,36 
20040630 

From A lottery player?: how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five Answered by Penny Nom. 





Jack's social security number 
20040608 

From A student: Jack's social security number contains each of the nonzero digits exactly once. By examining the digits from left to right, he also found that 1 divides the first digit evenly, 2 divides the sum of the first two digirs evenly, 3 divides the sum of the first three digits evenly, and so on, until 9 divides the sum of all the digits evenly. What is Jack's social security number? Answered by Penny Nom. 





The base of a triangle 
20040525 

From Ralph: With a 30 degree angle at the top of a triangle and a height of 15 what is the base? Answered by Penny Nom. 





Programming without trig functions 
20040525 

From Derek: I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston. 





Setting up an equation 
20040430 

From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)
and that
xy = 22
Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom. 





The sum of 4,0,4..., 156 
20040428 

From Christina: find the requested sum of the arithmetic sequence
4,0,4..., 156 Answered by Penny Nom. 





Related rates and baseball 
20040426 

From Bethany: A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing? Answered by Penny Nom. 





A geometric sequence 
20040413 

From Michael: In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Answered by Penny Nom. 





What is the nth term 
20040407 

From Jason: 1 4 10 20 35 56 84
what is the nth term Answered by Claude Tardif. 





Trisecting an arbitrary angle 
20040406 

From Joe: Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S Answered by Chris Fisher. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) Answered by Penny Nom. 





The degree sequence of a graph 
20040331 

From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom. 





Sections, area and acres 
20040323 

From Tony: An acre , it can be any size right . so when they
refer to a section of a township which is 640 acres,
also 1 square mile does this mean that 1 sections
length if sqaure and there is 5,280 ft in 1 mile does
it meanthat if you took 1 side of the square of of 4 sides
the lenth would be 5,280 feet long and by multiplying
5,280 x 5,280 it would give you the square mile in
square feet. i guess what I 'm asking is what is the
perimeter of 1 acre if it was shape like a square.
sorry to make this confusing but if you can help I
would appreciate it. Answered by Penny Nom. 





What's the next term? 
20040322 

From Garrett:
A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please...
What's the next number in this series...
5, 12, 17, 29, 46, ?
And this series...
12, 19, 28, 39, 52, 67, ?
and these...
ocoa, boco, oboc, dobo, odob, ?
Answered by Claude Tardif. 





Baseball games 
20040314 

From Fabian: Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Answered by Penny Nom. 





Equivalent sets 
20040306 

From A student: If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Answered by Penny Nom. 





Cosine of 35 degrees 
20040303 

From Jason: How do you find the exact solution to cosine 35 degrees. Answered by Chris Fisher. 





An elliptic cone 
20040224 

From Ben:
I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this.
The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in.
So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out.
Answered by Penny Nom. 





A worm crawling home 
20040218 

From Cindy: A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time? Answered by Penny Nom. 





Geometric sequences 
20040203 

From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





Sets 
20040127 

From Susan: My child has the following problems to solve, and we are puzzled.
1. Compare the subset symbols to the inequality symbols of less than or greater than.
2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C? Answered by Penny Nom. 





A problem with sets 
20040120 

From Jason:
Given that the universal set S is the set of all sports fans, and
F={xx is a football fan}
B={xx is a basketball fan}
H={xx is a hockey fan}
a)Describe (F^B)' (f intersect b)' in words
b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans.
Answered by Penny Nom. 





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. 





Two consecutive negative integers 
20040117 

From Amanda: Find two consecutive negative intergers whose product is 182. Answered by Penny Nom. 





37 with four 4'2 
20040103 

From Myra: Using four fours and only four fours to get an answer of 37. Answered by Claude Tardif. 





Percent increase 
20031224 

From Frank: How does one figure the percent of increase or decrease in the cost of an item? Answered by Penny Nom. 





An elliptical race track 
20031216 

From Judy: the inner rail of a race track is a perfect ellipse. the track is a standard width all the way around. how can i prove that the outer rail is a ellipse? Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





A point and a line 
20031119 

From Meenakshi:
Given a line segment L(x_{1},y_{1})
to (x_{2},y_{2}) and a Point P(x_{3},y_{3}).
I need the formula to find a point on the line L that is closest to
the point (x_{3},y_{3}). Answered by Penny Nom. 





The 4th difference 
20031117 

From Jack: If i had a sequence which was the same at the 4th difference, aka difference
to the 4th, like:
1 5 14 30 56 96
(sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1
then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an^{4}+bn^{3}+cn^{2}+dn+e Answered by Penny Nom. 





Divisibility by 7 
20031114 

From A student: how do you test a number to see if it is divisible by 7 or not? Answered by Penny Nom. 





root24 = 2 root6 
20031113 

From Burke: I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6 Answered by Penny Nom. 





Chisenbop 
20031106 

From Jaclyn: Hi there i was wondering if you would have any information on "counting on your fingers" or " Chisabop". Answered by Penny Nom. 





Knitting gauge and felting 
20031027 

From Sara:
I wish to create a pattern to knit an item that will then be felted, thus, shrink as a result. In order to determine the proper gauge to use in creating the item, I produced a gauge swatch, noted the original properties and then the postfelting properties. They are as follow: Before Felting: 20 stitches(width) x 20 rows(height)yielded: Gauge: 3.2 stitches(width) and 4 rows(height) = 1" Dimensions: 6.25"(width) x 5.25"(height) After Felting: 20 stitches(width) x 20 rows(height) Dimensions: 4"(width) x 3"(height) How do I calculate the percentage change in size to accurately determine the number of stitches and rows needed to produce the desired dimensions for the finished (felted) item? Answered by Penny Nom. 





Maine and Nevada 
20031024 

From Jimmy:
From 1989 to 1990, the population of Nevada increased b y 157,000, and that of Maine increased by 30,000. In 1990, the population of Nevada was 1,206,152, and that of Maine was 1,233,223. If the populations of the two states continue to increase at the same rates, when will the populations of Nevada and Maine be the same? Write a verbal model for this problem Write an equation for the model Solve the equation and answer the question. Answered by Penny Nom. 





Arithmetic in bases other than 10 
20031022 

From Kim: how do you add, subtract, multiply and devide in base 3, base 5, etc? Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





1 + 1 = 10 
20030917 

From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





Converting from base 10 to base 5 
20030910 

From Susy:
My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5. His first question of: 24(10) he has calculated to be 4x5 + 4x1 = 44 (5) The next question however is the tricky one.Ý We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it. 25 (10) = _________________ 100 (5) Can you help us figure out how we reach the answer. Answered by Claude Tardif and Penny Nom. 





Consecutive integers 
20030907 

From Amy: I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5? Answered by Penny Nom. 





Can 2 vertical planes intersect? 
20030906 

From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom. 





One million seconds 
20030904 

From Vince: If you can write a number each second for one million seconds, how many hours would it take? Answered by Penny Nom. 





Grooming the king's horses 
20030904 

From Janelle: the stable boy had 90% of the kings horses groomed.the next day the king acquired 25% more horses. Now there was 105 horses not prepared for the kings men. How many horses did the king originally have? Answered by Penny Nom. 





Converting to base 10 
20030828 

From Karen: My son is in 5th grade.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý Can you explain it to me in the simplest terms? Answered by Penny Nom. 





Graphing a piecewise function 
20030824 

From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom. 





39 consecutive natural numbers 
20030819 

From A student: Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Answered by Penny Nom. 





Percentage decrease in sales 
20030731 

From Linda: If I had sales in January of 2002 that were $42,493.73 and sales that were $37,281.59.Ý The difference is $5374.50.Ý What is the percentage of decrease in sales? Answered by Penny Nom. 





Is 3/5 CLOSEST to 0, 1/2 or 1? 
20030709 

From A student: I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2. Answered by Penny Nom. 





Setting up a word problem 
20030630 

From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom. 





Sesame Street on Stage 
20030625 

From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom. 





A 40% markup 
20030612 

From Nick: I am attempting to determine the Retail price of an item that costs me 11.00. Our company wants to sell it at a markup of 40%. I calculated this two ways, first the way I thought it should be done. Second, the way the calculator does it (and my accountant).
 Cost + Cost*(percentmarkup/100)= retail price 11.00 + 11.00*.40 = retail price 11.00 + 4.40 = 15.40 retail price
 Using the calculators Mark Up key the answer is 18.33. Or 7.33 more than the cost or 67%.
I am confused by this Mark Up key and how it calculates. I used a cost of $10.00 and marked it up 50%. I thought it should equal $15.00 but the calculator says $20.00? This seems to be 100% markup, yes? Can you explain the difference between the way I did it and the way a Business calculator does it? Answered by Penny Nom. 





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. 





Teaching second grade 
20030610 

From A teacher: I am going to be teaching second grade next year. How can I differentiate instruction in mathematics to meet the needs of all of my students, from those who need intervention to those who need challenges? What are some techniques I can try for this grade level? Answered by Diane Hanson. 





$1/week for week 1 and then double each week 
20030528 

From A student: I AM DOING A PROJECT FOR MATH I AM TRYING TO CREATE A SEQUENCE BASED ON: MAKING A SALARY OF $1/WK FOR THE FIRST WEEK WITH IT DOUBLING EVERY WEEK FOR 52 WEEKS, SO MY SEQUENCE LOOKS LIKE THIS: 1,2,4,8,16,32,64,128,256,512,1024 ETC. THERE WOULD BE 52#'s TOTAL IN MY SEQUENCE.I BELIEVE IT IS CALLED A FINITE SEQUENCE. MY QUESTION IS HOW DO I CREATE A FORMULA/RULE FOR THIS PARTICULAR SEQUENCE? MY GOAL BEING TO FIND THE 52nd TERM IN THE SEQUENCE. Answered by Penny Nom. 





Two sequences that agree in the first 4 terms 
20030526 

From A student: Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest? 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. 





A trig identity 
20030520 

From Patty: Please help with the following
1/ tanx + cotx = sinxcosx Answered by Penny Nom. 





R= 5.3lnx + x. 
20030511 

From A student: Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition? Answered by Harley Weston. 





positive multiples of 10 that are the sum of four consecutive integers 
20030501 

From Taurus: How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers? Answered by Penny Nom. 





Profit for a dance studio 
20030428 

From Craig: A dance studio charges $80 per student for a series of 2 hour lessons. The studio's costs are $30 per hour for the instructor, $15 per lesson for the room rental, and $3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class. 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. 





One one 
20030422 

From Brad: find the next two rows of numbers?
1
1 1
2 1
1 1 1 2
3 1 1 2
1 1 1 2 1 3
Answered by Leeanne Boehm. 





Chopping trees 
20030419 

From Tamara:
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom. 





How many hits? 
20030406 

From Jack:
My name is Jack. I'm a uncle. Student is in the 5th grade email is above. If a baseball player at sping training had a good season with the following: one seventh of his hits were doubles. 12.5% of his hits were home runs. But didn't have any triples. How many hits did he have? Can you give me an explanation of you solved the problem. Answered by Penny Nom. 





Uses of conic sections 
20030401 

From William: My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful. Answered by Leeanne Boehm. 





Friends and enemies 
20030324 

From Becky:
Consider a room that contains six people. Any two people are either friends of each other, or they are enemies. A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies
B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite. Answered by Penny Nom. 





A sequence that converges to e 
20030316 

From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





A section of land 
20030225 

From Bev: How many acres in a section of land? How many square miles is in a secion of land? Answered by Penny Nom. 





Percentage decrease 
20030220 

From Hope: What number decreased by 33^{1}/_{3}% is 30? Answered by Penny Nom. 





Numbers in base 5 
20030216 

From Lori: I'm trying to help my 6th grader with converting numbers like 82 to base 5 and 182 to base 12. We saw your examples on 613, but still are confused. Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





Three consecutive positive intergers 
20030209 

From Yew: Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.
ex. (7)(8)(9) = 504 = 6 (84) Answered by Penny Nom. 





The sum of the first 1000 even integers 
20030206 

From Jill: What is the sum of the first 1000 even integers? Answered by Paul Betts. 





Arithmitic sequence 
20030201 

From A student: I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Answered by Claude Tardif. 





1+2+3+...+500 
20030131 

From Brian: What is the sum of the numbers from 1 to 500 inclusive? Answered by Paul Betts. 





25% more 
20030116 

From Charlie: If I buy something for $10 and want to sell for 25% more, do I multiply by 1.25 or divide by .75? Or another way  why do I get $13.33 when dividing by .75 ? Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





What is larger than infinity? 
20030112 

From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston. 





A rectangular prism 
20030109 

From Julie: How many faces on a rectangular prism and how many bases? Can the base also be a face and can a face also be a base? Answered by Diane Hanson. 





Repeating decimals 
20030108 

From A student: If k=.9repeating, and 10k=9.9repeating then 10kk=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify? Answered by Penny Nom. 





Constructions of polygons 
20030103 

From Garrett: Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon? Answered by Chris Fisher. 





The intersection of conics 
20021219 

From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston. 





A bouncing ball 
20021214 

From Eman:
Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.  Find the maximum height to which the ball rises after two bounces.
 Find the total distance that the ball has traveled when it hits the floor for the tenth time.
 Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.
Answered by Penny Nom. 





A geometric sequence 
20021202 

From Wanda: the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence. Answered by Penny Nom. 





Combinations of 1,2,3,...,10 
20021127 

From Gord: If I had the numbers from 110 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom. 





Making 7 
20021126 

From Bill: At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, , /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer. Answered by Claude Tardif. 





A two stage rocket 
20021126 

From Hoda: a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex). Answered by Claude Tardif. 





Differentiating inverses 
20021120 

From Amy: f(x)= x^{3}+x+1, a=1 find g'(a) (g = f^{ 1}). I am having trouble finding g(a). Answered by Penny Nom. 





The horse race 
20021119 

From Pat: The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed? Answered by Penny Nom. 
