







A penny is thrown from the top of a building 
20180316 

From Zoraida: A penny is thrown from the top of a 26.7meter building and hits the ground 3.39 seconds after it was thrown. The penny reached its maximum height above the ground 0.89 seconds after it was thrown.
a. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.
b. What is the maximum height of the penny above the ground? Answered by Penny Nom. 





Aspect ratio 
20180301 

From brad: can you help me find the width if I know the length and aspect ratio of a object?
length = 78
aspect ratio = 1.42
width=?
length = 107
aspect radio= 2.02
width= ?
thank you Answered by Penny Nom. 





Parents, grandparents, great grandparents, ... 
20180228 

From jessica: every person has 2 birth parents, 4 birth grandparents, and so on. These people are known as ancestors. How many ancestors does a person have in each generation? write in exponential form. 3ed generation, greatgrandparents? 4th generation? 10th generation? Answered by Penny Nom. 





Dividing a region in half 
20180224 

From mandy: There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the xaxis into two regions with equal area. What is the slope of that line? Answered by Penny Nom. 





The decimal form of a fraction 
20180112 

From Tom: Prove that the decimal representation of the quotient of 2 integers must repeat (if it does not terminate). Answered by Penny Nom. 





The square root of 6 is irrational 
20171002 

From John: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational? Answered by Penny Nom. 





Ratios and proportions 
20170801 

From khurram: what is ratio and proportion? please give a detailed note on this topic, i am really panic of these calculations Answered by Penny Nom. 





Five rational numbers between 2 and 1 
20170531 

From Prince: Five rational numbers between 2 and 1 Answered by Penny Nom. 





Rational numbers between 2 and 3 
20170408 

From Medha: Find 12 rational numbers between2 and 3 Answered by Penny Nom. 





Is the square root of 2 plus the square root of 2 irrational? 
20170329 

From haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number? Answered by Penny Nom. 





The ratio of two ages 
20170315 

From Angel: The sum of Keith's age and Alan's age is 36. Four years ago, the ratio of Keith's age to Alan's age was 4:3. Find the ratio of their present age Answered by Penny Nom. 





The ratio of students to teachers 
20170120 

From Dylan: The ratio of students to teachers at a school is 19:1. How many students are there in each total number of people? Answered by Penny Nom. 





A rational number between 4 and 5 
20170103 

From Anshika: Write rational number between 4 and 5 Answered by Penny Nom. 





20+30*0+1=? 
20161226 

From Mr: 20+30*0+1=? Answered by Penny Nom. 





Why are equivalent fractions equal? Part 2. 
20161122 

From Anandmay: Hi!
I saw one of your answered questions:Why are equivalent fractions equal?
The same question I had for why i searched and ended up entering this wonderful site.
The answer was so much experimental based.I mean,for example,it was explained how
3/4 was equal to 6/8 by dividing a unit into 4 equal parts and taking four of the parts,and then dividing the
same unit into 8 equal parts and then taking 6 of them.The result was that both the taken parts were equal.
(That is,3 out of 4 equal parts were equal to 6 of the 8 equal parts.)
But,this was very much nongeneralized and experimentalbased result(proof).
And we all know that in mathematics,we confirm some particular thing for all the numbers iff we generalize
it.
So,can you explain more clearly 'HOW' the 3 parts of the 4 equal parts and the 6 of the 8 equal parts of the unit
equal(that is the same)?I don't want experimental proof.I want clear proof,and thus please give a generalized
proof for all fractions and their equivalents.
Thanks! Answered by Penny Nom. 





Integrate (x^2  4x + 4) ^4/3 
20160915 

From Ifah: Hi i have questions please answer
Integral 2 sampai 3 dari (x²  4x + 4) ^4/3 dx Answered by Penny Nom. 





A ratio of boys to girls 
20160612 

From Jasper: There are 600 pupils in a school. The ratio of the boys to girls in the school is 3:5 how many girls and how many boys are in the school Answered by Penny Nom. 





4 carpenters can build 8 houses in 10 days. 
20160405 

From Kenneth: Hello:
Here is my question:
4 carpenters can build 8 houses in 10 days. 2 carpenters can build how many houses in 15 days?
Here is one solution:
The number of houses built is jointly proportional to the number of carpenters and the number of days. So h = kcd where k is a constant. Substituting the given: 8 = k*40, so k = 1/5. Our formula is then h = cd/5. I'm not sure how to determine whether or not one unit is jointly proportional to any other unit.
However, if 2 carpenters are unknown as in 4 carpenters can build 8 houses in 10 days. How many carpenters can build 6 houses in 15 days? What is the solution using this method? And likewise, if days are unknown, as in 4 carpenters can build 8 houses in 10 days. 2 carpenters can build 6 houses in how many days?
I thank you for your assistance. Answered by Penny Nom. 





The integral of a sum 
20160310 

From Rahul: How to solve definite integral of a sum. The specific problem is as follows,
Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx.
The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral
of first term. But integral of the sum I do not understand at all. Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





Integration of dx/(x^2+1)^3 
20160107 

From Ishank: Integration of dx/(x^2+1)^3 Answered by Penny Nom. 





A ratio word problem 
20160106 

From Nina: The length and the width of the rectangle is in the ration 5:3. Its area is 375m2. Find its perimeter. Answered by Penny Nom. 





The dimensions of a rectangle given its area and aspect ratio 
20151213 

From colum: Can you work out the length and width of a rectangle where you know only the area and aspect ratio Answered by Penny Nom. 





Dealing with surds 
20151114 

From Agnes: simplify (1√3)(1÷3+√3) Answered by Penny Nom. 





An example of an irrational number 
20151022 

From Allison: It ask me to find an example of an irrational number less than 5 and I don't
understand what the difference from a rational number and an irrational
number besides the fact that a rational number can be repeated and shown in
a simple fraction and an irrational number can't be written in a simple
fraction.
Can you help me? Answered by Penny Nom. 





2.236... 
20151013 

From Ann: 2.236...
What is the most specific category of numbers does this fall into? Rational or Irrational? Does the .... mean that it repeats? Answered by Harley Weston. 





Square roots 
20150921 

From mariana: I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks) Answered by Penny Nom. 





Order of operations 
20150912 

From Tanisha: I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the same...so does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!
Thank you for your help!! Answered by Penny Nom. 





The length of a shadow 
20150801 

From maaz: Hello
I am having trouble with this question:
Lizzie, who is 6 feet tall, stands in her driveway at night, exactly
24 feet from the base of a spotlight, and casts a shadow that is 12
feet long if her friend Hannah who is 5 feet tall decides to stand
next to lizzie how long will her shadow be? Answered by Penny Nom. 





Is 22/7 is an irrational number? 
20150607 

From Sayak: Is 22/7 is an irrational number Answered by Penny Nom. 





Folding a rectangle to preserve the aspect ratio 
20150509 

From Anna: If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles? Answered by Penny Nom. 





Sharing $600 in the ratio of 2 to 3 
20150411 

From Kenneth: Hello:
If two people share $600.00 in a ratio of 2 to 3, which calculations are correct: 2/3 X $600.00 & 1/3 X $600.00 or 2/5 X $600.00 & 3/5 X $600.00?
The denominator 5 is determined by adding 2 and 3 from the ratio.
I thank you for your reply. Answered by Penny Nom. 





3 over "x" plus 5 
20150223 

From Kenny: 3 over "x" plus 5. I don't know this is either a polynomial and if so how would you define it. Answered by Harley Weston. 





Ratio of gas to oil 
20150202 

From Chris: I would like to find the gas oil ratio for a 2 cycle engine.
I have the gallons of gas and the ounces of oil used by
the engine, but I want to find what the ratio is. For example
I used 5.675 gallons of gas and 5 ounces oil what is the ratio?
Please explain step by step, and I understand there are 128oz in
a gallon. Answered by Harley Weston. 





How do you change a decimal to a ratio? 
20141129 

From Esmeralda: How do you change a decimal to a ratio? Express the decimal 0.2 as a ratio. Answered by Penny Nom. 





What is 20 and 3/5 of 10? 
20141126 

From Jeannine: What is 20 and 3/5 of 10? Question is written exactly this way.
Is this 20 3/5 times 10 (103/5 times 10), or is it 20 and (3/5 times 10)? Answered by Penny Nom. 





Ratios ond percents 
20140813 

From aswathi: if the ratio of cost price and selling price of an article is be as 10:11,the percentage of profit is Answered by Tyler Wood. 





Dealing cards in the ratio of 4:3:6 
20140731 

From aneeqa: Maria, Sofia and Diana shared some cards in the ratio of 4 : 3 : 6. Diana received 14 more cards than Maria. How many cards did Sofia receive? Answered by Penny Nom. 





Sharing in the ratio of of 2:3:5 
20140711 

From Muzdalfah: Amount of Tsh 12,000 is to be shared among John,Hidaya and sabrina in the ratio of
of 2:3:5 respectivly.How will each get? Answered by Penny Nom. 





50+913 multiplied by 2= 
20140625 

From Adrian: 50+913 multiplied by 2= Answered by Penny Nom. 





The ratio of 1:1:2 
20140620 

From FREDERICK: 3 girls shared some hair ribbons in the ratio of 1:1:2 what is the total number of hair ribbons if the third girl got 14 ribbons. Answered by prnny. 





1÷[1√2(order of surd is 4)] 
20140502 

From Anoushka: if t=1÷[1√2(order of surd is 4)] , then t=? Answered by Penny Nom. 





Ratios 
20140418 

From Kenneth: Should ratios contain only whole numbers and not any fractional numbers?
For example, 8:1, 2:5 have whole numbers. The ratios 2.5:10 and 1:4.5 do not have just whole numbers entirely.
If it is incorrect to express a ratio with fractional numbers, why are complex fractions correct?
I thank you for your reply. Answered by Harley Weston. 





Ratios 
20140418 

From Kenneth: Should ratios contain only whole numbers and not any fractional numbers?
For example, 8:1, 2:5 have whole numbers. The ratios 2.5:10 and 1:4.5 do not have just whole numbers entirely.
If it is incorrect to express a ratio with fractional numbers, why are complex fractions correct?
I thank you for your reply. Answered by Harley Weston. 





The area bounded by the Xaxis and y=x^(2)4 from 5 to 0 
20140415 

From Lexie: Determine the area that is bounded by the following curve and the xaxis on the interval below. (Round your answer to three decimal places)
y=x^(2)4, 5 ≤ x ≤ 0
The answer is 32.333 but I have no idea how to get there. Answered by Penny Nom. 





The ratio of boys to girls is 5:3 
20140310 

From jane: The ratio of the number of boys to the number of girls in the concert hall is 5:3. After additional 28 boys entered the concert hall, the ratio of the number of boys to the number of girls become 3:1 How many girls are their in the concert hall? Answered by Penny Nom. 





Order of operations 
20140204 

From Alex: Hi there,i got problem with order of operation.Can you please help to find a solution for this?
Thank u beforehand
63(7+2)+(2+4)/34. Answered by Penny Nom. 





Mixing water and wine 
20140119 

From manish: a man mixes three part of water to one part of wine.When he consumes
one part of mixture he realise that the drink is too dilute and hence adds one part of
wine to the remaining quantity what is the ratio of water to wine in the new mixture. Answered by Penny Nom. 





The ratio of two shares 
20140117 

From Kenneth: Hello:
Two people share $100.00 as follows: $25.00 and $75.00.
The two share the $100.00 in a ratio of 1 to 3.
I want to think that the two people share the $100.00 in a ratio of 1 to 4.
Can you explain why 1 to 3 is correct and 1 to 4 is not?
I thank you for your reply. Answered by Penny Nom. 





Is this operation associative? 
20140114 

From patrick: Associative test: Can you explain the following to me?
Is the following operation associative?: x*y=x+y+1
1) x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2
2) (x*y)*z=(x+y+1)*z=(x+y+1)+z+1=x+y+z+2
The answer is yes as 1) = 2)
My specific questions are:
1) How x*(y*z)=x*(y+z+1)=x+(y+z+1)+1 ?
2) How (x+y+1)*z=(x+y+1)+z+1?
Thank you!! Answered by Penny Nom. 





A ratio problem 
20131031 

From indu: students of a school have been into 2 groups in the ratio 6:11, if the group has 870 students, how many students are there in all the school? Answered by Penny Nom. 





Proportional rates 
20131010 

From Varsha: A province's Ministry of Social services has found that both the number of people needing social assistance and the province's total expenditures on social assistance are proportional to the rate of unemployment. Last August when the provincial unemployment rate was 8.4 %, the province provided assistance to 89,300 individuals at a total cost of 4107.4 million. The forecast unemployment rate for next August is 7.9%. How many people can the province expect to need social assistance next August? What amount should the province budget for social assistance in August? Answered by Penny Nom. 





The ratio of salt to water 
20131006 

From varsha: My name is Varsha. I am a student and below is my question:
1. The brine used in an industrial process is 12.5% salt by weight. What i=
s the ratio (by weights) of salt to water to the brine?
Thank you
Varsha Answered by Penny Nom. 





A sequence of operations, in order 
20130920 

From jen: multiply 46x23
add 342
divide by 70
subtract 5
I not sure what the answer is..i need to know the answer..thanks.. Answered by Penny Nom. 





Golden Ratio 
20130826 

From Mark: Please Help. I'm trying to help my Child and I have no clue on this math question.
Rectangular shapes with a length to width ratio of approximately 5 to 3 are pleasing to the eye.
The ratio is know as the golden ratio. A designer can us the expression 1/3(5w) to find the
length of such a rectangle with width 6 inches. Answered by Robert Dawson and Penny Nom. 





Distance as a function of acceleration 
20130710 

From Tom: If you start at a stoplight and your acceleration is 16t  t^2, how far have you gone after 8 seconds? Answered by Penny Nom. 





Sharing in a car rental 
20130409 

From Marilyn: 8 persons are planning to share equally the cost of a rental car.
If 1 person withdraws from the arrangement and the others share
equally the entire cost of the car, then the share of each of the
remaining persons is increased by? Answered by Penny Nom. 





The dimensions of a rectangle are in the ratio 5:3 
20130308 

From SM: 4. The dimensions of a rectangle are in the ratio 5:3. If the longer side is 18 cm,
a) What is the length of the shorter side?
b) What is the area of the rectangle? Answered by Penny Nom. 





A messy arithmetic expression 
20130224 

From niiaryee: (((((5^2*4^3)1/5+9^3/3)+(25+(4*5)/15)^210)/10/2)3))))) Answered by Penny Nom. 





4*4+4*4+44*4=??? 
20130206 

From Jacky: 4*4+4*4+44*4=??? Answered by Penny Nom. 





Integration from 0 to 2pi of 1/(3cos x + 2) dx 
20130204 

From ankit: Integration from 0 to 2pi of 1/(3cos x + 2) dx Answered by Harley Weston. 





A railroad embankment 
20130122 

From clint: the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft.. find the amount of the earth removed, if the top level of the bank remained unchanged. Answered by Penny Nom. 





3x6)+(12divided by2)8= ? 
20121217 

From christina: hi my question that's been bothering me is what's
(3x6)+(12divided by2)8= ????? Answered by Penny Nom. 





An integral 
20121216 

From Slavena: integration of (lnx)^2 / x dx Answered by Penny Nom. 





4+4x5+4= ? 
20121031 

From Bob: 4+4x5+4= ? Answered by Harley Weston. 





Two cubes 
20120904 

From alexis: a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes Answered by Penny Nom. 





5 + 5 + 5  5 + 5 + 5  5 + 5 x 0 = 
20120729 

From Tom: 5 + 5 + 5  5 + 5 + 5  5 + 5 x 0 = Answered by Harley Weston. 





93(2+6)/62*5 
20120608 

From Sammi: Hi there,
I am doing a practice test for my admittance into a college accounting program
and I am really confused by this equation.
The answer I got was way off what the test answer sheet says it should be.
The question is
93(2+6)/62*5
If you could explain how the answer beccomes 35 that would be greatly apprciated!!
Thank you! Answered by Robert Dawson. 





Sharing the profit 
20120514 

From Mafiza: A and B started a business by investing $6000 and $8000 respectively. At the end of the year, a profit of $2100 is made. How much amount will A get as his share of profit? Answered by Penny Nom. 





Three metallic cubes 
20120513 

From Pragun: Three metallic cubes whose edges are in the ratio 3:4:5 are melt to form a single cube whose diagonal is 12*square root of 3. What are lengths of the edges(in cm) of the three cubes Answered by Penny Nom. 





Ratios 
20120420 

From olawale: if 3 boys share y mangoes among themselves in the ratio x : 2x : 3x. if the largest share was 30, find the value of y. Answered by Paul Betts. 





Integral 1/(25x^2)^3/2 
20120222 

From John: Integral 1/(25x^2)^3/2 Answered by Harley Weston. 





A 3 to 1 ratio of girls to boys 
20120212 

From amanda: At a recent school dance it was observed that there was a 3 to 1 ratio of girls to boys. If 204 students attended the dance, how many boys, and how many girls were there? Answered by Penny Nom. 





A volume of revolution 
20120111 

From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the xaxis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom. 





Uniform acceleration 
20111206 

From Android: At a certain instant, two cars A and B are 2000 ft apart. At this instant, car A is traveling at 15 miles/hr. and accelerating at 3 ft/s^2 while B is moving towards A at 30 miles/hr. and an acceleration of 2 ft/s^2.
Find the ff:
a.) The possible time of their collusion in minutes.
b.) The distance in ft. each has traveled before collusion. Answered by Penny Nom. 





Ratios 
20111017 

From Kenneth: Can you think of a ratio that has units that have not canceled out?
Do not use a rate as an example, for example miles per hour.
Would the following make sense? What is the book to student ratio in
a classroom with 20 students and 15 books? Student to book ratio of
20 students to 15 books or (4 students):(3 books). Answered by Penny Nom. 





 16 x 6 / 2 
20110909 

From Nadiyah: i dont understand how to answer this question ;
 16 x 6 / 2
i still dont understand it with bedmas
/ = divison
please help! Answered by Penny Nom. 





A ratio as a fraction in lowest terms 
20110812 

From jonecia: write this ratio as a fraction in lowest terms 707days of 112days? Answered by Melanie Tyrer. 





A rational number 
20110517 

From owais: according to definition of irrational number "a number which cannot be
expressed in p/q form is called irrational number"
square root of 2 is a irrational number but if i round off the digit correct
to two decimal places so it becomes 1.41 and we can easily convert
into p/q form so it is a rational number ??? Answered by Penny Nom. 





Dividing the profits 
20110419 

From Tracy: I need to know how to come up with the answers to the following problems. I need to be able to show my work. So can you help me on how to come up with the answers to questions like these. Thanks.
Three individuals form a partnership and agree to divide the profits equally. X invests
$9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less
does x receive compared to having the profits divided in proportion to the amounts
invested by X, Y, and Z?
In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the
larger type, a printed page contains 1,800 words. Using a smaller type, a page contains
2,400 words. The article is allotted 21 full pages in a magazine. How many pages must be
in smaller type? ___________
thank you Answered by Penny Nom. 





An antiderivative of the square root of (8t + 3) 
20110419 

From Caitlyn: I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem.
What's the antiderivative of the square root of (8t + 3)
~Caitlyn= Answered by Penny Nom. 





PEDMAS 
20110410 

From Ross: 48 ÷ 2 (9+3)
Is the answer 2 or 288? Answered by Harley Weston. 





Administration costs and profit 
20110405 

From brian: Hi , If I have direct job costs of $100. and my administration is 20 % and I want to make a 15 % profit , how would I calculate the administration and profit and what would be the total of each be and also the final total?
Thanks,
Brian Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





Integrating ln^3x/x 
20110114 

From ken: y=ln^3x/x from x=1 to x=11 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 railway cut 
20101212 

From jade: the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft.. find the amount of the earth removed, if the top level of the bank remained unchanged. Answered by Penny Nom. 





The integral of (x^2*exp(x)/(exp(x)1)^2 
20100809 

From sujoy: please find this integral for me
int(x^2*exp(x)/(exp(x)1)^2 Answered by Robert Dawson. 





Ratios 
20100806 

From Ashleigh: Hi, I am dealing with ratios of me and 9 other students. I was wondering how you turn an arm span and height into a ratio? for example if a person has a height of 62 and an arm span of 63 what would the ratio be for that? Answered by Penny Nom. 





A rational equation 
20100802 

From Bailey: 3/x
+
x/x+2
______
2/x+2 Answered by Penny Nom. 





1.2731568 
20100616 

From angel: is 1.2731568 a natural number a whole number a irrational number or a inter Answered by Robert Dawson. 





Who is more extravagant? 
20100601 

From likhitha: kunal and ramit have Rs.40 and Rs.50 respectively. Kunal spends
Rs.18 and ramit spends Rs.21.Who is more extravagant ? Answered by Penny Nom. 





Integration of sin^3 (2x) 
20100529 

From ascher: how do you integrate this equation
∫ sin^3 (2x) dx Answered by Robert Dawson and Penny Nom. 





Ratios and proportions with mixed units 
20100513 

From Kenneth: Is it incorrect to have a proportion with numbers containing units that are not the same on both sides of the equal sign?
Here is an example: $0.07/$1.00 = ?/$0.89 is okay, but if I add a different unit (20 ounces) to one side of the equal sign but not the same unit to the other, is the proportion incorrect?
$0.07/$1.00 = ?/$0.89/20 ounces.
In order to determine the missing amount, the calculation becomes ($0.07/$1.00)/$0.89/20 ounces = $?, but is this proportion correct with the units as they are?
Two dollarunits cancel leaving dollar/ounces equals $?/ounces, but is this correct? Answered by Robert Dawson. 





A circle inscribed in a square inscribed in a circle 
20100428 

From jouniella: A square is inscribe to the first circle, then another circle is inscribe to the square. Find the ratio of the 2 circles. Answered by Penny Nom. 





Rational root theorem 
20100414 

From deciree: How could i get the value of x with this equation:
1/13x^3+12x/13=1/2
Thank you! Answered by Harley Weston. 





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. 





Integrate the ((4th root of x^3)+1) dx 
20100412 

From Bridget: integrate the ((4th root of x^3)+1) dx Answered by Tyler Wood. 





A rectangle problem 
20100412 

From Charlene: The ratio of the width to the length of a certain rectangle is equal to the ratio of its length to the difference between its length and twice its width. If the area of the rectangle is 25cm^2, then what are its dimensions? Present a non algebraic solution? Answered by Tyler Wood. 





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. 





A ratios problem 
20100401 

From Jules: 1a) If 2/3 of the boys and 3/4 of the girls at a party are dancing, what is the
ratio of boys to girls, if all the dancing couples consist of a boy
and girl?
b) If the total number of the boys and girls of the party is 153, how
many boys are at the party? Answered by Penny Nom. 





The integral of X^3/the square root of 1x^2 dx 
20100307 

From William: The integral of X^3/the square root of 1x^2 dx. Answered by Harley Weston. 





If 2 is to 55, then 6 is to ? 
20100304 

From patty: Example,
If 2 is to 55, then 6 is to ? How do I begin to figure this out, is is an algebra formula? Answered by Penny Nom. 





A ratio 
20100222 

From manoj: in a dept there are 350 employees and in the other there are 158 find ratio Answered by Penny Nom. 





A geometric sequence 
20100222 

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





Fahrenheit and celcius 
20100219 

From Carol: Zack is packing for a trip to Scotland. He read that the average temperature in the Summer is 18degrees C during the day, and 7 degrees during the night. What is the difference between the high and low temperatures in degrees Fahrenheit? (F=9/5C=32) Answered by Lorraine Dame. 





Integration of cos (x^2+y^2) dx dy 
20100212 

From anna: How do you evaluate the integration of integration of cos (x^2+y^2) dx dy? Answered by Tyler Wood. 





Order of operations 
20100207 

From addie: (3+10) x 10  8 x 4 = Answered by Penny Nom. 





An integral 
20100129 

From amr: find the value of the following integral:
(1+x)power (1/2) dx Answered by Robert Dawson. 





(24x3)+(7x8)(20/5)+(4x7) 
20091201 

From Marilyn: (24x3)+(7x8)(20/5)+(4x7)
Thought I had the answer but the form says no. Could you solve it for me please. Answered by Penny Nom. 





The base and height of a triangle are in the ratio of 3:2 
20091118 

From Mike: Find the base and height of a triangle using the ratio 3:2 and an area of 108 inches square. Is there a formula we need to use?
Thanks
Mike Answered by Penny Nom. 





Rationals 
20091030 

From Jawsh: I don't quite understand the whole idea of rationals.
If you have 3Squareroot 49. Is that equal to 3Squareroot 7^2?
Can you break it down with an example for me please. Answered by Robert Dawson. 





Proof that the root of 27 is irrational 
20091018 

From Scarlet: How do you prove that the square root of 27 is irrational? Answered by Victoria West. 





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

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





Integration of cos (x^2) dx 
20091012 

From Venkat: How do you evaluate the integration of cos (x^2) dx ? Answered by Harley Weston. 





4 squared and (4) squared 
20090929 

From Andrea: Is 4 squared the same as (4) squared? I am thinking the first is 16 and the second is +16. I am trying to clarify for my students. Answered by Penny Nom. 





Evaluating x^2 + (yz  3)^2 
20090928 

From Kathy: My daughter and I are having trouble solving this equation:
x²+ (yz – 3)²
if x=4,y=2 and z=0
We are having difficulty with the x² part of the equation. Thanks Answered by Penny Nom. 





Order of operations 
20090924 

From aman: my question is regarding the fact
i have a formula which looks like this :
(ratio 1 + ratio 2 divided by 2)
so my question is do i add first then divide by 2 or do it all together Answered by Penny Nom. 





5 x 8 + 6 divided 6  12 x 2 
20090924 

From Susan: 5 x 8 + 6 divided 6  12 x 2. I am not sure of the rules of operation for this type of question Answered by Penny Nom. 





A calculation from a ratio 
20090921 

From Rob: How do I calculate the height of a rectangle that has is 16:9 from only the width?
For example a rectangle is 1000 wide, what is it's height if it is a 16:9 ratio? What is the formula? Answered by Harley Weston. 





solve integral of ( x^2+x+1)^5 
20090918 

From jaka: solve integral of ( x^2+x+1)^5 Answered by Robert Dawson. 





Investing in four accounts 
20090829 

From Kenneth: Hello:
An investor wants to divide $1000.00 into four amounts or accounts  one account earning 2%, the second account earning 5%, the third earning 9%, and the fourth earning 12%. He wants the overall total return to equal 5%.
What are some of the monetary amounts that can be invested into these four accounts to earn him the 5% total return, 5% of $1,000.00? Answered by Penny Nom. 





The ratio of girls to boys in class is 4:3 
20090824 

From Linda: The ratio of girls to boys in class is 4:3. Total of 35 students, how many more girls than boys? Answered by Penny Nom. 





An antiderivative problem 
20090813 

From Indrajit: ∫4e^x + 6e^x/(9e^x + 4e^x)dx = Ax + Bloge(9e2x  4) + C
then A=?......B=?.....C=?
plz solve it...."^" stands for "to the power of".... Answered by Harley Weston. 





root 2 is irrational 
20090731 

From prateet: prove that root2 is an irrational number. Answered by Robert Dawson. 





The integral of x^x 
20090618 

From ANGIKAR: what would be the integration of (X^Xdx)?
give answer in details. Answered by Robert Dawson and Harley Weston. 





Number & Operation Puzzle 
20090612 

From Francine: How can I get the number 26 using 1,2,3,4,&5 and using addition, subtraction, multiplication and division. Each operator and digit must be used exactly once. My son presented me this question and I can't determine if it's even possible. Answered by Janice Cotcher. 





Properties of Inequality 
20090605 

From Nazrul: We know that if a>b then (1/a)<(1/b)
But why 5> 2 implies (1/5)>(1/2) .
Thank you in advance for your help. Answered by Robert J. Dawson. 





Equivalent fractions 
20090522 

From Jocelyn: give two other ratios that are equal to each
example: 6/9 Answered by Penny Nom. 





The ratio 3 to 4 to 5 
20090519 

From Josey: The perimeter of a right triangle is 42 inches. If the lengths of the sides of the triangle are in the ratio 3 to 4 to 5, what are their lengths in inches? Answered by Penny Nom. 





Hens and roosters 
20090516 

From Rogerson: In a certain poultry farm, the ratio of the number of hens to roosters is 3:5. If 15 new roosters are added, a third of the farm will be compose of hens. Find the original number of chickens. Answered by Stephen La Rocque. 





A geometric progression 
20090516 

From sweta: find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90. Answered by Penny Nom. 





The integral of a to power x squared 
20090428 

From JIM: WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO
WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE
SOLVED : a to power x squared . is this still true ?
CURIOUS , JIM Answered by Robert Dawson. 





Two similar rectangles 
20090419 

From Alyssa: The ratio of the lengths of corresponding sides of two similar rectangles is 3:5. the small rectangle has an area of 36 square centimeters. What is the are of the large rectangle? Answered by Penny Nom. 





The integral of the square root of the sine function 
20090407 

From Indrajit: how to integrate this derivative???
∫√sinx Answered by Harley Weston. 





Depth to height ratio 
20090326 

From Janet: Is there a formula to determine how deep something (a cabinet) should be based on how tall it is? Answered by Robert Dawson. 





A 1.5:1 rectangle 
20090323 

From melody: I have an origami model that says to use a 1.5:1 rectangle. I don't understand how to calculate the size of paper I need to use. Surely there is a formula to calculate this ratio? Thanks for your help. Answered by Penny Nom. 





The ratio of the volumes of two cylinders 
20090318 

From jdkaj: cylinder a has radius 1m and height 4m. cylinder b has radius 2m and height 4m. find the ratio of the volue of cylinder a to the volume of b Answered by Penny Nom. 





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. 





Augmented matrix: independent, dependent, or inconsistent? 
20090223 

From Anna: Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.
x + y + z = 11
x  y + 3z = 5
2x + 2y + 2z = 15 Answered by Harley Weston. 





The area between the xaxis and a curve 
20090218 

From Lauren: This is from a homework question I can't figure out.
Let R be the region in the fourth quadrant enclosed by the xaxis
and the curve y= x^2  2kx, where k > 0. If the area of the region R is 36
then what is the value of k? Answered by Robert Dawson. 





A goat in a square paddock 
20090210 

From lachlan: A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.
a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?
b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be? Answered by Penny Nom. 





A falling object 
20090201 

From Tamara: We drop an object from rest (i.e. its initial spped is zero. It is falling freely toward the ground. What will be its speed after 5 seconds of falling? Answered by Penny Nom. 





What will be its speed after 10s? 
20090201 

From Tamara: An object has an initial speed of 5 m/s and is accelerating with 2 m/s2 (m/s squared) acceleration. What will be its speed after 10s? Answered by Penny Nom. 





The Golden Ratio 
20090120 

From Vincent: hello, my name is Vince,
I am wondering how the Golden ratio was used by early mathematicians.
What formula did they use to find it? open for anything... thank You! Answered by Robert Dawson. 





The integral of f(x)dx and the integral of f(x4)dx 
20090102 

From Katie: Calculus:
If the definite integral from 2 to 6 of f(x)dx=10 and the definite integral from 2 to 6 of f(x)dx=3, then the definite integral from 2 to 6 of f(x4)dx= ?
I don't understand how to solve definite integrals when the function has something more than just x inside the parenthesis such as f(4x). Answered by Robert Dawson. 





Solution Concentration 
20081206 

From Manjola: I mixed 100 ml of 28% Ammonium nitrate, with 100 mL of 68% nitric acid. What is the concentration of the resulting solution?
Thank you Answered by Janice Cotcher. 





Graphing Rational Functions 
20081205 

From Bahra: The question in my homework is: Find all vertical, horizontal, and slant
asymptotes, x and yintercepts, and symetries, and then graph each
function. Check your work with a graphing calculator.
y=3/x+3 meanng: ( y= 3 over x+3) Answered by Janice Cotcher. 





Evaporation of waste water 
20081121 

From Alexandra: Engineers know that the amount of water lost due to evaporation
is directly proportional to the surface area of the holding tanks and
that the local climate causes water to evaporate at the rate of about
gallon of water per hour for each square foot of water exposed to
the air. About how many total gallons of waste water may enter the
three tanks each day to maintain full capacity?
I know that the answer is 50x10^3 but i don't know why. Answered by Penny Nom. 





A ratio to a decimal 
20081114 

From manny: Express 22 : 5 as a decimal. Round to the nearest hundredth Answered by Penny Nom. 





Antiderivative of 1/(x(1  x)) 
20081022 

From Matt: derivative of dx/(x(1x))
From what I've seen I should break apart the equation as such
derivative of dx/x  dx/(1x)
and then get the 2 corresponding log functions.
If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative. Answered by Harley Weston. 





Scaling a logo 
20081020 

From Carl: Hello!
I hope that you can help me out here. I've been trying to figure this out for awhile now and can't come up with the answer logically.
I am a graphic designer by trade and need to figure out how large my client's logo should be.
The logo will need to be sized proportionally with the surface area of the page.
The logo will always be sized at 1.2938(w) x .75(h) on a letter size page (8.5 x 11).
My question is...
When you increase the size of the page (not always proportionally sized  dimensionally) how do figure out the NEW size of the logo.
I could have a page 20" x 40" or 30' x 4'... or ANY size really.
I believe I have the new surface area of the logo but can't find the new dimensions. Answered by Harley Weston. 





The ratio of two chemicals 
20081020 

From Nathan: if there is a chemical mixture of 5:2 and the total amount of the entire solution is 1400 gallons, how many gallons make up the stronger side of the solution? I believe the answer is 1,000 but I figured it out in a nontraditional way so I wanted to understand the basic formula used to determine these types of questions.
thank you Answered by Penny Nom. 





A ratio problem with cookies 
20081018 

From nadha: SAMANDHA,AMANDHA AND NICOLE sold some cookies in the ratio 3:4:7
how many more cookies did AMANDA and NICOLE sell than SAMANTHA if NICOLE had sold 91 cookies? Answered by Penny Nom. 





Using the augmented matrix 
20081017 

From Karlena: I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically
x+y+2z=30
2x+3y+2z=53
x+2y+3z=47 Answered by Harley Weston. 





Integration 
20081017 

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





Algebraic fractions 
20081006 

From Kayla: (x^29)/x times (x^34x)/(x^2+5x+6) Answered by Harley Weston. 





Three equal ratios 
20080926 

From Jodi: For the ratio given, find three equal ratios: 2 miles/8 minutes Answered by Penny Nom. 





Art and Integers 
20080917 

From pamela: how do artists use integers? Answered by Janice Cotcher. 





An associative binary operation 
20080908 

From Skye: Suppose that * is an associative binary operation on a set S. Show that the set H={a E S such that a*x=x*a for all x E S} is closed under *. (We think of H as consisting of all elements of S that commute with every element in S.)
Thanks! Answered by Harley Weston. 





Is this operation associative? 
20080906 

From Francesca: Determine whether the binary operation * defined is commutative and whether * is associative
* defined on Z by a*b = ab\
I understand how to figure out if it's commutative, but I thought for a binary operation to be associative, it had to have at least three elements, so I don't know how to tell if this associative or not. Answered by Penny Nom and Victoria West. 





The lengths of the sides of a rectangle are in ratio 5:3 
20080829 

From todd: the lengths of the sides of a rectangle are in ratio 5:3 the perimeter of the rectangle is 32 cm find the length of each side Answered by Stephen La Rocque. 





A water acid mixture 
20080819 

From Sulagna: A chemical solution is made by mixing an acid with water in the ratio 1:24.
This solution is then taken and mixed with water in the ratio 1:3. How much acid
would be there in 200ml of this final solution? Answered by Penny Nom. 





BEDMAS 
20080812 

From Rebecca: I have 3 questions.
1) I don't really understand BEDMAS.Im going in to the 6th grade and im
kind of nervis about it.?
2)When you're doing BEDMAS what does the small 3 or 2 above the
other numerals mean?
3)How would you answer this:5+2 x 9  9 x 12= ?? Answered by Janice Cotcher. 





Nonterminating, nonrepeating decimals 
20080803 

From Peter: How do you take a random, nonterminating, nonrepeating decimal into a fraction? Answered by Stephen La Rocque. 





Integral of X^2 
20080728 

From Hemanshu: Integral of X^2 Answered by Janice Cotcher. 





Time with NonUniform Motion 
20080721 

From jenina: An unmarked police car, travelling a constant 95km/h, is passed by a speeder travelling 145km/h. precisely 1.00s after the speed passes, the policeman steps on the accelerator. If the police car’s acceleration is 2.00m/s², how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)? Answered by Janice Cotcher. 





Rational numbers 
20080716 

From hinal: list 12 rational numbers which lie between
a) 1 and 0
b) 3 and 3 Answered by Penny Nom. 





Fish in a pond 
20080628 

From Peter: At the beginning of a study 24 fish are caught, tagged, and released back into a large pond containing fish. A few days later, 19 fish are caught from the pond and three of them have tags. Using this ratio, how many total fish would you expect to be living in the pond?
The answer is 152. Why is that? Answered by Leeanne Boehm. 





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. 





The volume of a solid 
20080604 

From Tom: The base of a certain solid is a circle of radius 2 while cross sections perpendicular to the
base are isosceles triangles of height 1. What is the volume of the solid? Answered by Harley Weston. 





Throwing a ball on the moon 
20080521 

From leria: equation for motion of moon is h=2.67t^2 + vt + s
equation for earth h=16t + vt + s
Suppose you are on an outpost on the moon and Jan is back on Earth. Both people toss a ball from a height of 96 feet with an initial velocity of 16 feet per second. How much longer will your ball stay in motion on the moon than Jan's on the earth?
Math Central,
I'm having a difficult time understanding which numbers to plug into the formula. Answered by Stephen La Rocque. 





The weight of a concrete column 
20080511 

From russell: a cylindrical form is filled with a slow curing concrete. The base of the form
is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity
causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a
density of 50 lb/ft^3 at the top. Assume that the density varies linearly
from the top to the bottom, and compute the total weight of the resulting
concrete column Answered by Harley Weston. 





How can the distance between two points be irrational? 
20080507 

From Dawn: Yesterday my advanced 7th grade prealgebra students were finding the distance between two points on a coordinate grid using the distance formula. A student asked me how come we or math I guess is able to represent a finite distance with an irrational number. I found this to be a very interesting question. I and the 7 other math teachers on my staff had discussed this and we have a variety of thing to say to the kid, but nothing that amounts to an actual answer. The students have studied what it means for a number to be irrational, and they cannot understand how that can "measure" a line that obviously stops. Got any suggestions? Answered by Stephen La Rocque, Penny Nom, Claude Tardif and Victoria West. 





1/35/6=1/x, solve for x 
20080501 

From Lavada: 1/35/6=1/x How do I solve this problem. Answered by Penny Nom. 





The ratio of their perimeters to two regular hexagons 
20080429 

From td: Two regular hexagons have areas of 54 square root of 3 and 150 square root of 3, what is the ratio of their perimeters? Answered by Stephen La Rocque. 





Adding rational functions 
20080429 

From Jonathon: 1/(x+3) + 1/(x^2+5x+6) = Answered by Penny Nom. 





A circle inscribed in a triangle 
20080426 

From Amar: I have been given a circle inscribed in a triangle and have been told to prove that the ratio of the perimeter of the triangle to the circumference of the circle is the same as the ratio of the area of the triangle to the area of the circle. How would this be done? Answered by Stephen La Rocque and Walter Whiteley. 





At what value of t is the maximum acceleration? 
20080425 

From Mary: Velocity of a function (which is the first derivative of its position) is defined over the interval 0 to 12 using the following piecewise function: v(t)=1 from 0 to 4, v(t)=x5 from (4 to 8 and v(t)=x+11 from (8 to 12. At what value of t is the maximum acceleration? Answered by Stephen La Rocque. 





Why does 2^2 = 4 when 2 * 2 = 4? 
20080422 

From blaine: Why does 2^2 = 4 when 2 * 2 = 4? Answered by Penny Nom. 





Ratios and fractions 
20080420 

From Alissa: What is the formula for writing the ration of two numbers as a fraction? Answered by Leeanne Boehm. 





Simplify 5x^5/8 / 15x^2/12 
20080418 

From Kyler: 5x^5/8 / 15x^2/12 Divide the rational expressions. Simplify the results. Answered by Penny Nom. 





Integrate 2x(x^21)^5 dx 
20080417 

From joey: pls help me to integrate
2x(x^21)^5 dx using the substitution u=x^21 Answered by Harley Weston. 





2500mL of Phosphoric acid 
20080409 

From Trina: If I have 2500mL of Phosphoric acid that has a fluoride concentration of 0.91% and need to increase it to 1.40% how much 49% HF do I need to add? Answered by Harley Weston. 





The integral of dx / (4x^2  25)^3/2 
20080401 

From Meghan: I have a question from the trigonometric substitution of my calculus course.
integral of dx / (4x^2  25)^3/2 Answered by Harley Weston. 





Is this an irrational number? 
20080322 

From Tom: Is it possible to build an irrational number with numbers that are just 1's and 2's where only finitely many 2's appear? If so, how do we build it and how do we know it is irrational? Answered by Penny Nom. 





How would I graph: x  2 divided by x^2  4? 
20080319 

From Sean: How would I graph: x  2 divided by x^2  4 using a method in extreme values of
functions or completing the square
x  2/ x^24 Answered by Stephen La Rocque. 





A widthtolength ratio of 2 : 3 
20080311 

From Stephanie: The national flag of France has a widthtolength ratio of 2 : 3. What is the width of an 18inch long French flag? Answered by Penny Nom. 





Two points moving on a straight line 
20080306 

From laura: Particle A travels at constant speed of 1.0ms1 in straight line, passing particle B, at which time particle B beings traveling with constant acceleration of 0.2ms2 until reaching Particle A.
What equations represent the displacement of particle A and particle B measure from the point they first pass?
How long does it take for particle B to catch up with particle A?
What is the speed of particle B when reaching particle A?
What distance have both particles traveled from where they first pass to where they meet again?
Calculate the displacement of both particle A and B at 2 second intervals between t=0s and t=12s? Answered by Stephen La Rocque and Penny Nom. 





Integrate (4+x^2) / (x (2+x)^2) 
20080225 

From Russell: integrate (4+x^2) / (x (2+x)^2)
I really need to know the steps involved in doing this integral, I already have
the answer through wolfram integrator but for some reason can not
get to the answer given. Please help Answered by Harley Weston. 





cos(2x)=(cos x)^2 (sin x)^2 
20080225 

From azarnia: comment démontrer que : cos(2x)=(cos x)²_(sin x)² Answered by Maxime Fortier Bourque. 





10  3 + 2 
20080221 

From Amrit: what 103+2
is it 5 or 9 Answered by Penny Nom. 





Two regions with equal area 
20080213 

From James: There is a line through the origin that divides the region bounded by the parabola y=3x5x^2 and the xaxis into two regions with equal area. What is the slope of that line? Answered by Harley Weston. 





For the Canadian flag, the ratio of width to length is 1:2. 
20080212 

From Kelly: For the Canadian flag, the ratio of width to length is 1:2.
What is the perimeter of a Canadian flag that is 12 ft. long?
Are all Canadian flags similar shapes? Explain with a diagram. Answered by Penny Nom. 





How much tax does Zoe have to pay? 
20080211 

From Kelly: Rahsad pays $6.30 tax for a pair of shoes that is priced at $45.
His friend Zoe purchases another pair of shoes on sale for $25 in the same store.
How much tax does Zoe have to pay?
Solve the problem in two ways. Show your work.
What assumptions did you make? Answered by Penny Nom. 





Numbers and Operations 
20080202 

From Charlotte: On the TABE (Test for Adult Basic Education) test, one of the categories
is number operation. I would like to know what consist of number operation. Answered by Penny Nom. 





Integration by parts 
20080130 

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





How far from the corner will the police catch the car? 
20080127 

From Joel: A car is going down the road at a speed of 90km/h in a 50km/h zone.
As the car passes a corner, a police cruiser sitting there notices it. Five
seconds later the cruiser begins accelerating at 5.0m/s squared.
Assuming that he is able to maintain this acceleration, how far from the
corner will the police catch the car? How fast will the cruiser be going? 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. 





The integral of Sqrt(sin x) 
20080124 

From tariq: find integration
Sqrt(sinx) dx , from x=bi/4 to 3bi/4 Answered by Harley Weston. 





An integral 
20080124 

From Meghan: Evaluate the indefinite integral of (x^3 +1)^(1/3) * x^5 * dx. Answered by Brennan Yaremko. 





Integration 
20080123 

From Russell: how to integrate
1/x ln^2 [x] dx Answered by Harley Weston. 





Simplify 63:77 
20071212 

From Selah: Simplify 63:77 Answered by Penny Nom. 





The rational root theorem 
20071209 

From Josh: Prove the rational root theorem (where, in a polynomial equation, all
factors of the constant divided by all factors of the leading coefficient
are possible rational roots of the equation). Answered by Penny Nom. 





What would be the cost of a 10 in * 15 in canvas? 
20071201 

From Jasmine: a 40in *60 in canvas is sold for $60.00 if the price is determined by the cost of the material what would be the cost of a 10 in * 15 in canvas Answered by Stephen La Rocque. 





The scale of a picture 
20071130 

From Sylvia: 1. A artist draws a picture of a house with a rose brush in front. In his picture the rose brush is 1.5 cm high and the house is 7.5 cm high. In reality the rose brush is 0.75 m high. How tall is the house in reality (in meters)? Explain
2. There are six short pieces of link chain. Each having four links. It takes 10 sec to cut a link and 25 sec to weld it back together. What is the shortest possible time to make the longest chain? Explain Answered by Penny Nom. 





An augmented matrix 
20071129 

From Beth: I am having troubles fiinding this augnmented matrix. I know how to do it
but everytime i do it it get a different answer and its not the right answer.
Could you help me to make sure I do it right?
Here is the problem:
4x  3y = 5
2x +9y = 6 Answered by Harley Weston. 





(322 x 5) divided by 2 + 8 
20071128 

From Kim: Solve
(322 x 5) divided by 2 + 8 Answered by Leeanne Boehm. 





Two integrals 
20071109 

From Akilan: how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2.
Please send me how to do this question. Having exams on Monday. Please help. Answered by Harley Weston. 





Ratios 
20071107 

From Barbara: There 100 cars in lot A and 20 in lot B, after the attendant moved 20 cars from lot A into lot B. what was the ratio number of cars in A to the number of cars in lot B? Answered by Penny Nom. 





What is a rational number between 5.9 and 6? 
20071106 

From cathy: What is the rational number between 5.9 and 6? Answered by Penny Nom. 





An irrational number 
20071029 

From Clara: Find an irrational number between 0.53 (with 53 as repeating)
and 0.54 (with 54 repeating)
I changed each to 53/99 and 54/99 with 1/99 being the difference.
Please help me. Answered by Stephen La Rocque, Penny Nom and Harley Weston. 





Constantly accelerated motion 
20071029 

From Priyanka: A, B and C are three points lying in that order on a straight line. A body is
projected from B towards A with speed 3 m/s. The body experiences an
acceleration of 1 m/s^2 towards C. If BC =20 m, find the time taken to reach C and
the distance travelled by the body from the moment of projection until it reaches C. Answered by Stephen La Rocque. 





Order of operations 
20071017 

From Devon: What function precedes the other? ie; 18  4 x2 = Answered by Penny Nom. 





15 divided by 5a 
20071012 

From Susan: Is "5a" considered an expression to be solved first, or do you simply go in PEMDAS order with the 15 divided by 5 in the following problem: Evaluate when a = 2 15 divided by 5a Answered by Penny Nom. 





Simplifying algebraic expressions 
20071009 

From Sakeena: (2^2*3)^x+1/2^2x*3x Answered by Stephen La Rocque. 





Simplifying rational expressions 
20071009 

From Bama: x(x2)+1 divided by x^23x+2 Answered by Stephen La Rocque. 





Subtracting rational expressions 
20071009 

From Pamela: Subtract:
6p – w __ 4c + p
w – 4 w – 4
Answered by Stephen La Rocque. 





Solving arithmetic problems in the right order (BEDMAS) 
20071005 

From Kim: 3+4x2(10 divided by 5)= what? Answered by Penny Nom. 





Gas and oil at a 50:1 ratio 
20071003 

From Cindy: How much gas and oil do you put in a 1.7 litre jug at a 50:1 ratio? Answered by Stephen La Rocque. 





Irrational functions 
20071001 

From alicia: i have a question about irrationals functions.
i have been using them quite some time now, but i wonder where they can be found in daily life?
i hope you can help me, Answered by Harley Weston. 





A fraction that cannot be simplified 
20070917 

From Kevin: Make a fraction that cannot be simplified and has 24 as its denominator? Answered by Stephen La Rocque and Chris Langdon. 





The ratio of arm span to height 
20070917 

From Chandler: I am doing ratios and I was wondering if... well let me explain first. I have data on the arm span and heights of 10 students including myself now i have my measurements of me are 66inches arm span. and 66 inches height. my second piece of data is 71 inches arm span and 67 inches height now my ratio is 71:67 right? i thought i would need to simplify. but i cant really simplify this ratio and these numbers. what do I do? Answered by Stephen La Rocque. 





Fractions, ratios and percentages all mixed together 
20070829 

From Charon: Example: x : 1/4% :: 9 3/5 : 1/200 Answered by Stephen La Rocque. 





The irrationality of PI 
20070807 

From Matthew: I have what I like to think of as a rather interesting question that I can't explain confidently for the life of me.
If we take a circle with a radius of 1 and we calculate the circumference, we can use 2 pi R.
Doing this calculation results in a circumference of 6.28318530717~ which goes on forever.
However, if you were to take a that same circle in the real world, say with radius 1cm and wrap a string around
it, and then measure the string, you don't get 6.28~, you get something like 6.2, a much more finite distance. The length
of the string is not an irrational number, like the math claims it to be. Answered by Claude Tardiff and Stephen La Rocque. 





A binary operation 
20070731 

From sofia: Prove that if * is associative and commutative binary operation on a set S, then
(a*b)*(c*d) = [(d*c)*a]*b
for all a,b,c,d element in S. Assume the associative Law only for triples as in the definition that is, assume only
(x*y)*z = x*(y*z)
for all x,y,z element in S. Answered by Penny Nom. 





Binary operations 
20070730 

From jim: prove or disprove:
Every binary operation on a set consisting of a single element is both commutative and associative.
Answered by Penny Nom. 





Three pipes of varying diameters 
20070629 

From JYOTI: three pipes of varying diameters can fill the vessels of 1,2,and 3 L in 4,18,and 48 min respectively. what is the ratio of their diameters?(assume that speed of the flow is same in all the cases) Answered by Sue Dunham. 





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





Simplifying a quartic rational expression using long division 
20070614 

From Megan: x+2/12x^4+17x^3+0x^2+8x40= Answered by Stephen La Rocque and Penny Nom. 





Circumscribing a golden cuboid with a sphere: surface areas 
20070614 

From Ainslie: A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi. Answered by Stephen La Rocque. 





Rational polynomial expressions 
20070609 

From a student: I have a question that continues to lead me to the answer x/(x  1) but according to my math book, the answer should be 1/(x  1).
Who is right? Who is wrong?
Here is the question:
(x^2  6x  27)/(x^2  11x + 18) DIVIDED by (x^3 + 2x^2  3x)/(x^2  2x) Answered by Stephen La Rocque. 





Repeating decimals and rational numbers 
20070531 

From lil: Why are repeating decimals considered rational numbers? Answered by Penny Nom and Gabriel Potter. 





The limit of a rational function 
20070528 

From Imad: 3 _______ 3 _______
lim \/ 1 + x  \/ 1  x
x>0  
x Answered by Penny Nom. 





Positive rational numbers 
20070522 

From Rebecca: What is the definition of positive rationals/positive rational numbers? Answered by Stephen La Rocque. 





Simplifying a rational expression 
20070429 

From Tamika: X^2 + 10X + 24
______________
X + 6
SIMPLIFY EACH RATIONAL EXPRESSION (IF YOU CAN'T SIMPLIFY IT, WRITE ALREADY SIMPLIFIED) Answered by Stephen La Rocque. 





Producing chocolate bars 
20070426 

From anne: If you have to produce an average of 114 bars of chocolate over 7.5 hours how many do you have to produce over 9.5 hours. Answered by Penny Nom. 





The speed at which the conveyor moves 
20070417 

From Sheila: I am trying to figure out the speed (ft/min) of a conveyor.
It has a 1HP, 1200 RPM motor with a reducer that has a ratio of 60:1.
My reducer sprocket pitch diameter is 7.027 and my drive sprocket pitch diameter is 11.474.
How do I use this information to find the speed at which the conveyor moves? Answered by Stephen La Rocque. 





Lowest terms 
20070417 

From Dawn: For some reason, I have a hard time with Ratio and/or rate problems.
My problem is as follow: Write each rate or ratio as a fraction in lowest
terms. 6 days to 39 hours Answered by Stephen La Rocque. 





Write each rate or ratio as a fraction in lowest terms 
20070417 

From Dawn: Write each rate or ratio as a fraction in lowest terms.
$59.00 for 231 minutes 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. 





The sum of two rational numbers 
20070404 

From Fathia: Hi,
Could please help me with this question?
Prove that if a and b are rational numbers then a + b is a rational number.
Thank you, Answered by Stephen La Rocque. 





Adding and Subtracting Rational Expressions 
20070321 

From Pricilla: Pricilla
I do not know how to do this problem. Don't know where to start.
[(5)/(2x8)]+[(3x^2+15)/(x^34x^2+5x20)] Answered by Stephen La Rocque. 





How long does she have to get out of the way? 
20070223 

From Sharon: How do I solve this? The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s  16t^2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 6 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Answered by Penny Nom. 





The size of a TV screen 
20070222 

From katie: The ratio of height to width for a tv screen is 9 to 16. How high is a screen that is 30 in. wide? I don't know how to work this, we have to show our work. Answered by Gabriel Potter and Penny Nom. 





Acceleration 
20070220 

From thomas: Don't know if this service still exists. ACCELERATION CALCULATION initial vel 0km/hr final vel 24km/hr time 3s Answered by Stephen La Rocque. 





Grams/milliliters 
20070219 

From Keshia: If there are 27 grams of sugar in 240 mililiters, How many grams are in 100 mililiters? I have been trying to figure this question out for about an hour and I cannot seem to get it. Thank you for your help. Answered by Chris Fisher and Haley Ess. 





A person jumps from the roof of a house 
20070213 

From Jessie: A person jumps from the roof of a house 3.9m high. When he strikes the ground below, he bends his knees so that the torso decelerates over an approximate distance of 0.70m. If the mass of his torso (excluding legs) is 42kg, find a) his velocity just before his feet strike the ground , and b) the average force exerted on his torso by his legs during deceleration.
Please provide calculations and answers for comparison. Answered by Stephen La Rocque. 





Integration 
20070202 

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





Freefalling objects 
20070125 

From Patricia: How long will it take a stone dropped from atop a 1000meter tall building to reach the ground? Answered by Stephen La Rocque. 





Is 2^2 = 4 or 4? 
20070123 

From Joan: Is 2 squared, when written without parentheses around the 2, 4 or could this correctly be solved by squaring 2 (2 x 2) for an answer of 4? Or, to correctly get an answer of 4, would the problem have to read (2) squared? Answered by Stephen La Rocque. 





Ratios 
20070122 

From Evan: David's company has 300 employees. The ratio of men to women is 4 : 6 . After hiring 60 new people with a 4 : 1 men to women ratio, what is men to women ratio in David's company now? Answered by Stephen La Rocque. 





Answer to skill testing question 
20070118 

From Mike: This question was on a ballot. Is the right answer 36 or 1? 5+21X6= Answered by Stephen La Rocque. 





how do i find ratio of 1,000mm to 5m 
20070118 

From Harry: how do i find ratio of 1,000mm to 5m Answered by Paul Betts. 





Two consecutive angles of a parallelogram 
20070117 

From Veronica: The measures of two consecutive angles of a parallelogram are in the ratio 9:11. Find the measure of each angle. Answered by Penny Nom. 





The volume of a frustum of a pyramid 
20070117 

From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom. 





How much lemon oil do you need to make 10.15L of polish? 
20070116 

From Sajad: to make an environmentally safe furniture polish, you can combine lemon oil and mineral oil in the ratio 3:200, by volume. How much lemon oil do you need to make 10.15L of polish? Answered by Penny Nom. 





Throwing a stone downwards 
20070112 

From Momo: a stone is thrown vertically downward with an initial speed of 14m/s from a height of 65 m above the ground. A) how far does the stone travel in the first 2.0 s? B) what is the stone velocity just before it hits the ground? Answered by Stephen La Rocque. 





Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 
20070109 

From James: How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Answered by Penny Nom. 





13.78g /11.3mL 
20070105 

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





Prove that square root of 3 is irrational. 
20061221 

From Humera: Prove that square root of 3 is irrational. Answered by Stephen La Rocque. 





Equal ratios 
20061213 

From Velkis: 5:18=20:? Answered by Penny Nom. 





Fill in the signs 
20061207 

From Ujwala: 4$4$4$4=20 Fill in the signs in the place of dollor symbol. Answered by Stephen La Rocque. 





Ratios 
20061120 

From Debbie: Business mileage:7,200 Private Mileage 10,800 What is the ratio of his business mileage to his private mileage Answered by Penny Nom. 





Composition of functions 
20061119 

From RJ: Let f0(x) = 2/2x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque. 





Scale factors and ratios 
20061119 

From Maggie: I have a BIG math test coming up, and it's about scale factors and ratios, but i don't understand them at all. How can you tell the difference between scale factors and ratios? and How are they used in the everyday world? Answered by Penny Nom. 





What percent of the people oppose putting in curbs? 
20061117 

From DeeDee: The ratio of people who support putting in curbs to those who oppose it is 2 to 5. what percent of the people oppose putting in curbs? Answered by Stephen La Rocque. 





Find the distance function s(t) given the acceleration function a(t) 
20061116 

From David: Find the distance function s(t) of the acceleration function: a(t)= sin(0.1t)/ cos^3(0.1t) Answered by Penny Nom. 





The name of an equation 
20061113 

From Lee: I am struggling to find the name of the following equation. I remember watching a TV programme introduced by Arthur C Clarke. The programme focused on an equation that gave a wonderful pattern that went on into infinity. Two maths professors discussed this equation.It was described as 'Gods equation' as it was compared to the shape of trees and other shapes in nature. It was named after the inventor/discoverer. If you have any ideas i would be most grateful. Answered by Penny Nom. 





Ratios, proportions and medicine 
20061025 

From Steven: I don't understand why we need to learn about ratios and proportions because i want to become a doctor and i don't know if i'll ever use this type of math. Answered by Penny Nom, Claude Tardif and Walter Whiteley. 





Stairs for the front of a new community center 
20061024 

From Tia: 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. Are these stairs within carpenters guidelines,which state that the ratio of rise to run should be between 0.45 and 0.60 Answered by Penny Nom. 





(2324/4)525+214 
20061015 

From Sherin: (2324/4)525+214 Answered by Penny Nom. 





Two gears 
20061012 

From A student: gear a on the left has 18 teeth and gear b on the left has 8 teeth.
suppose gear b makes one complete rotation in the counterclockwise direction. give the angle of rotation and direction for the rotation of gear a. Answered by Stephen La Rocque and Penny Nom. 





BEDMAS 
20060924 

From Partick: if you have a question like this (4)(4)+(4)+4 how do you solve it step by step Answered by Penny Nom. 





Help me prove that the square root of 6 is irrational 
20060923 

From Sylvia: Could you please help me prove that the square root of 6 is irrational ? Answered by Stephen La Rocque. 





what is 8+(2)(5)/4(1)4(2+3) 
20060908 

From Jordan: what is 8+(2)(5)/4(1)4(2+3) Answered by Paul Betts. 





16X27+32÷426 
20060820 

From Amanda: The question was 16X27+32÷426. Answered by Stephen La Rocque. 





An Integral 
20060730 

From Aniket:
I am Aniket studing in 12 th standard At Mumbai
I have following integration problem please give me a solution
integral of 1/under root of (5x^{2}  2x) dx
Answered by Penny Nom. 





I want to calibrate a glucose meter 
20060727 

From John: If I have 3 glucose control solutions having:
Low  50 mg/dl
Normal  100 mg/dl
High  330 mg/dl
I want to calibrate a glucose meter but I need more than these 3 data points. How can I mix these up to get different concentrations in between 50 and 100, 100 and 330. I would like to mix up different concentrations and put them in test tubes or whatever to do some calibration work. Like 70 mg/dl, 90 mg/dl, etc. More data points should be in between say 50 and 100 since this is normal, 90 mg/dl is considered close to normal.
Answered by Stephen La Rocque. 





Order of operations 
20060629 

From Jaden:
(1) A triangle has vertices at (3,3) (7,3) and (2,5). What is the area of the triangle?
Is there a way of doing this so that you dont have to graph it? If the x axis is horizontal can i say it is the base and the yaxis is horizontal meaning the height. Would I be able to do this...3 to 7>9 spaces, 3 to 5>7 spaces9(7)63/2=31.5
(2) A cube has a surface area of 54 square centimeters. What is the volume of the cube in cubic centimeters?
Answered by Stephen La Rocque. 





Order of Operations 
20060629 

From Marcy: I have been having problems with this skill testing question. I know the rules of operation but I don't understand why they would put it in brackets. Can you help me. I have two answers but I would like to know which one is right. Im having a disagreement with a friend over this matter. Thank you so much
[ (20 + 82  6) ÷ 16 ] x 14 Answered by Steve La Rocque and Paul Betts. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





Ordre des opérations 
20060407 

From Chantal: 1435/5x2364= j'aimerais savoir la reponse et que veux dire la barre / Answered by Claude Tardif. 





BEDMAS 
20060321 

From Andie: It's been a long time since I've used bedmas. I'm still confused as to what the answer to this question would be.
30  (2 x 9) + (15/3)= Answered by Penny Nom. 





An equilateral triangle and a regular hexagon 
20060228 

From Trevor: An equilateral triangle and a regular hexagon have equal length perimeters. What is the ratio of their areas? Answered by Penny Nom and Stephen La Rocque. 





Equal fractions 
20060210 

From Dylan: write three equal ratios
3/4 _________________________
Answered by Penny Nom. 





BEDMAS 
20060131 

From Janielle: What Do All the Letters In BEDMAS Stand for? Answered by Penny. 





What is the ratio of 3 cups to 3 quarts? 
20060125 

From Virjeannia: What is the ratio of 3 cups to 3 quarts? Answered by RoverDaddy. 





The circumference of a larger circle is twice the circumference of a smaller circle. 
20060120 

From Amanda: The circumference of a larger circle is twice the circumference of a smaller circle. What is the ratio of the radius of the smaller circle to the diameter of the larger circle? Answered by Penny Nom. 





BEDMAS 
20051124 

From Judy: My name is Judy and I am a grade 6 teacher.
We have just started our lessons on the order of operations and my students have asked me why we have BEDMAS and what is the logic to it.
Is there a reason that that we do math in this particular order?
Who invented this rule or how was it decided on and when? Answered by Walter Whiteley. 





Rational expressions 
20051115 

From Zach: I can solve easy problems such as (x/2)+3=2+(3x/4). That is easy because the Lowest Common Denominator is 4. But what really gets me stuck is a problem like this one.
(6/x2) = ( 21/(x2)(x+2) )+ 1. Answered by Penny Nom. 





Velocity and acceleration 
20051027 

From Candace: When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared where do the units go when you make it an equation? How can a function be an area? Answered by Harley Weston. 





2x/x^29  6/x^2+x12 
20050927 

From Emily Ann: 2x/x^{2}9  6/x^{2}+x12 Answered by Penny Nom. 





A rational arithmetic expression 
20050914 

From Vijay: How to simplify following Grade 9 math problem:
(4/9) X (21/32) X (3/14) Answered by Penny Nom. 





BEDMAS 
20050901 

From A student: I am a student and am wondering about the answer to this question.
56/2(31)
is the answer 7?
Answered by Harley Weston. 





Converting rational numbers 
20050807 

From Joe:
I am helping my son with his converting rational
numbers in the form of A/B where A and B are integers and
B not equal to zero
I think I am doing this right but I am not sure so
below are the problems and our answers are beside
them, please let me know if these answerers are correct
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. 





Jobs relating to the topics of ratios and proportions 
20050517 

From Alexa: What are some jobs relating to the topics of ratios and proportions other than architects and map makers? Answered by Walter Whiteley. 





The limit as x approaches 3 of (sqrt(x+1)2)/(x3) 
20050414 

From Abraham: What is the limit as x approaches 3 of
(sqrt(x+1)2)/(x3) Answered by Penny. 





Rational functions 
20050405 

From Nicole: My name is Nicole and I am a teacher at Weyburn Comprehensive School. I am currently teaching both Math B30 and Calculus 30 at the school and I have a question about rational functions. I know that if a rational function (by definition) has common factors in the numerator and the denominator then it is not a rational function (math b30) however in calculus this common factor creates a hole in our graph. Can you explain to me why a common factor or constant does not give us a rational function? Answered by Penny Nom and Leeanne Boehm. 





The integral of tan^4x 
20050331 

From Nicole: college student. need help with tough integral.
the integral of 2tan^{4}xdx
Answered by Penny Nom. 





The ratios of Business, Accounting and Engineering majors are: 7:8:10. 
20050311 

From John: There are 500 students in a collage class. The ratios of Business, Accounting and Engineering majors are: 7:8:10.
How many Engineering majors are there in the class?
Answered by Penny Nom. 





Strategies for teaching operations with positive and negative decimal numbers 
20050202 

From Erin: I am wondering if you can suggest any strategies for teaching operations with positive and negative decimal numbers that do not rely on rules that must be memorized? Answered by Diane Hanson. 





Approximating an integral 
20050127 

From A student: i used excel to find the area under a graph instead of integrating the function the analytical way. These are the different answers i got with different width of the xvalues, the smaller the xincrement gets the more precise the area is when compared to the answer obtained the numerical way. I have trouble seeing why the answers i get is getting bigger and bigger and not smaller can someone plz explain? Answered by Penny Nom. 





The golden ratio 
20041231 

From Cristina: let x represent the longer segment. to find the golden ratio, write a proportion such that the longer of the two segments is the geometric mean between the shorter segment and the entire segment.Use the quadratic Formula to solve the proportion for X. Find the value in both radical and decimal form. Answered by Penny Nom. 





A regular hexagon is inscribed in a circle. 
20041208 

From Abraham: A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.
Answered by Walter Whiteley. 





Order of operations 
20041110 

From Andrew: I'm trying to solve this question, and I can't seem to remember the rules back from my high school days.
(40 x 8 ) / 2 + 55  15 =
Can you help me with the answer? Answered by Harley Weston. 





Bedmas 
20041109 

From Fariha: i have a single line question and am not sure of the method
it would be appreciated if u could send me a method and a solution Q : 1 + 9 / 2 + 5 * 1000
would this be solved by BEDMAS? if not, why? Answered by Penny Nom. 





Bedmas 
20041030 

From Gina: I am just curious whether Bedmas would be used in the following question as it is not in the typical Bedmas format.
Multiply 12 x 24
Add 26
Divide by 2
Subtract 7
Would we go about doing it in the sequence it is given or in Bedmas ? Answered by Penny Nom. 





Ratios and rates 
20041027 

From Kenneth: What is the difference between a ratio and a rate? Answered by Penny Nom. 





Accelerating to the speed of light 
20040930 

From Lars: How long time would it take to accelerate up to the speed of light with an acceleration speed similar to 0100 seconds in 5 seconds? Answered by Penny Nom. 





Rational expressions 
20040924 

From A student: In general, I understand rational expressions except when it comes to solving problems such as:
x+y/2xy  2x/y2x or m4/3m4 + 3m+2/43m
I am confounded by the issue of having to find a common denominator. For example, if I tried to solve these problems by multiplying both denominators they would still be uncommon. Answered by Claude Tardif. 





Order of operations 
20040904 

From Leanne: 6 + 3  2 x 3 = Answered by Claude Tardif. 





Combined operations 
20040826 

From Louise: Question 2 1/4 x 1/8 / 1 3/4 x 12 4/9 x 3 = Answered by Penny Nom. 





50/5x  y 
20040822 

From Rick: Niece has a question that was marked wrong but we are unable to determine how the teacher calculated and arrived at the answer? The problem was as follows:
50 / 5x  y =
x=5
y=1 Answered by Harley Weston and Leeanne Boehm. 





Integrating e^sin(x) 
20040804 

From A student: I need to know that how to solve the integral " e^sin x", Answered by Harley Weston. 





An equation with rational terms 
20040617 

From Louise: simplify the expression
(a^{2}+n^{2})/2n = a^{2} + (a^{2}n2)/2n Answered by Penny Nom. 





Rational expressions 
20040406 

From Shivani: I am in 11th grade Honors Algebra II. We are currently learning about adding and subtracting rational expressions. I looked at the other questions that were similar to that of mine, but they weren't quite answering my question. I have been working on many problems to practice and see if I can come up with the correct answer, but I can't, I got like 2 out of every 7 right on my school homework. I get the easy ones, where when you have to find the LCD, it's just the other denominator. But, on others you have to really think about it. Those are hard. Here are some of the problems that I cannot get at all: (x2  3x + 1)/(x2  4)  (x2 + 2x +4)/(2  x)  (x  4) /(x  2)
The correct answer is:
(x3 + 4x2 + 7x + 17)/(x2  4) Answered by Penny Nom. 





Ratios 
20040405 

From Tim: The ratio of W to H was 7 to 9. The ratio of H to I was 9 to 5. If the sum of the W and H exceeded twice the number of I by 12, how many were W, how were H and how many were I? Answered by Penny Nom. 





(3x50)+20/5=? 
20040403 

From A student: what is the answer to:
(3x50)+20/5=? Answered by Penny Nom. 





Ratio and proportion 
20040402 

From Kenneth: The terms of a ratio in a proportion are often expressed as a is to b as c is to d.
Example: 2/4 = 6/12 this proportion represents that 2 is to 4 as 6 is to 12.
What does the "a is to b as c is to d" really represent or indicate in ratios? Answered by Claude Tardif. 





BEDMAS 
20040320 

From Brad: I am in grade 7. My teacher tells me brackets always first, well i know that but, 5 (4) x 2
Does the (4) count as a bracket or is it just telling you not to minus 4 from 5 but to multiply 5 x 4 ? Am i correct? Answered by Penny Nom. 





Some ratio problems 
20040313 

From Hossen:
1) After James spent 2/5 of his pocket money on magazines, and 1/4 of his pocket money at a football match, he had £1.75 left. How much pcket money did he have in the beginning?
2) A joint of Lamb costs £5.95 per/kg. The price per kilogram is reduced. A joint weighing 1.2kg is reduced by 50p.
A) What is the reduced price per kilogram?
c Answered by Penny Nom. 





Order of operations 
20040128 

From John:
I am trying to find out any information concerning the development of the order of operations. for example, when (why/how) did it become the case that 2 + 3 x 5 =17, rather than 25.
any insight is appreciated. Thank you.
Answered by Penny Nom. 





Polynomials 
20040125 

From Bruce:
A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = a_{n}x^{n} + a_{n1}x^{n1} + ... + a_{1}x + a_{0}
The value of n must be an nonnegative integer. That is, it must be
whole number; it is equal to zero or a positive integer.
The coefficients, as they are called, are a_{n}, a_{n1},
..., a_{1}, a_{0}. These
are real numbers.
Questions:
 why must n be positive?
 what are some historical facts
about the evolution of the definition?
Answered by Harley Weston. 





g on Mars 
20040122 

From RC: To measure the acceleration on Mars an object is dropped from a height of 160m. It takes 10s for this object to hit the ground. What is the value for g on Mars?g Answered by Penny Nom. 





BEDMAS 
20040121 

From Jessica and her mom:
my mom and I were wondering 2 things.
1. what is the reason for having bedmas.
2. 5+54+[6x3(6+13x2) 5+9]
Answered by Penny Nom. 





Ratios and proportions 
20031231 

From Frank: I would like to know how you use 'ratios and proportions' in everyday life. Answered by Penny Nom. 





AB/AP=AP/PB 
20031120 

From James: My name is James McBride. I'm having a difficult time with a pre calculus problem, which goes as follows: "show that AB/AP=AP/PB is equal to (1+5^1/2)/2 (one plus the sqaure root of five with the sum divided by two. I can't do the square root sign, sorry.) I have tried to solve for PB in terms of the other varialbles and then work the quadratic equation. THAT DOES NOT WORK!!!! I am befuddled. Please help me. I am a student of secondary level. Answered by Penny Nom. 





Equal ratios 
20031107 

From A student: In the ratio 3:8=17__, can__be a whole number? Answered by Penny Nom. 





The golden ratio 
20030923 

From Phillip: The Golden Section can be made from an equilatereral triangle inscribed within a circle. The Golden Section is achieved by joining the mid points of two arms of the triangle to the circumference. I can prove this by erecting a perpendicular to the line outside the circle, but am interested to see how it can be proved from within the circle. Answered by Chris Fisher. 





Order of operations 
20030907 

From Brian:
It has to do with the 4 rules of operations, Parentheses first before operations outside/evaluate all exponential expressions/all multiplication and divisions/then all additions and subtractions. Who made these rules and when did they make them,,, I know its somewhat of an unorthadox question but I must know. I would really appreciate it. Answered by Penny Nom. 





A helicopter rises vertically 
20030902 

From Kate: A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)^{2} How far above the ground will the helicopter be after 3 seconds? Answered by Penny Nom. 





Odd powers of sine and cosine 
20030625 

From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the powerreducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston. 





43(m+1)=(38) 
20030625 

From Jamie:
I have a problem, like most of your mailers, I do remember BEDMAS but maybe I'm missing the finer points! It's been a while, he goes 43(m+1)=(38) Answered by Penny Nom. 





BEDMAS 
20030531 

From Kristie: (3x50)+20/5=?
I know bedmas but i forget how to do it. Answered by Penny Nom. 





Subtracting rational expressions 
20030510 

From Simone: hi, i'm totally lost. i understand that you need to find a lowest common denominator to subtract two fractions (rational expressions) with different denominators. but what if the denominators are "x1" and "x". is x the common denominator? if so what happens to the "1"? do you know of any live online help i can get with the following: 3/(x1)  (12x)/x i've looked through my notes and have no examples that quite match that i can follow to get through it. please help! Answered by Penny Nom. 





Integrating e^x sin(x) 
20030503 

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





38 minus 10 plus 12 divided by 4 times 16 
20030423 

From James: please help me work this math problem 38 minus 10 plus 12 divided by 4 times 16 Answered by Harley Weston. 





Excluded values 
20030222 

From Josh: Why do you think it is necessary to include the "excluded values" when you write your answers to rational expressions? Answered by Penny Nom. 





Order of operations 
20030216 

From A student: How is the order of operation used in everyday life other than in a math class or at school? Also .... Can you give me a list of all the mathematician that are still living that uses the order of operation? Answered by Claude Tardif. 





Order of operations 
20030215 

From Debbie: Question: 20(9+4)x7=? Possible answer 71 or 49? Answered by Penny Nom. 





BEDMAS 
20030209 

From Stefanie: I do remember the rules of BEDMAS, but for some reason this question puzzles me. 6 X 9  3 + 44 I started with the Multiplication 54  3 + 44 But then I got stuck, do I proceed with adding the 44 and subtracting the 3 or figure out what 3 + 44 is, but then how would that work with 54?
Answered by Penny Nom. 





Rational expressions 
20030122 

From A student:
// = the main fraction line 1.) a+1/a1 + a1/a+1 // a+1/a1  a1/a+1 2.) 2/a(squared)3a+2 + 2/a(squared)a2 // 2/a(squared)1 + 2/ a(squared)+4a+3 Answered by Penny Nom. 





Integration of 1/(2+cos(x)) 
20030107 

From A student: integral from pi to 0 of dx/(2+cos x) i used the substitution t=tan(x/2) and i ended up with integral from +infinity to 0 of 2dt/(t^{2}+3) which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please. Answered by Penny Nom. 





Two numbers have a ratio of 5:3 
20030101 

From Patricia: Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? Answered by Penny Nom. 





Augmented matrix 
20021231 

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





Gears and ratios 
20021117 

From Matt: if gear A has 12teeth and Gear B has 16teeth and gear C has 10teeth and gear A turns 40 times how many times will gear C turn Answered by Penny Nom. 





Rational expressions 
20021003 

From Ashley: 1/x(squared) + 5/xy Answered by Penny Nom. 





Number play 
20020924 

From Julie: Organize these numbers and the operations so that each equation is correct. Use each coice only once per equation.
36 18 12 6  + ( ) /
_________________________ = 22
_________________________ = 41 Answered by Claude Tardif. 





3810+12divided by4multiplied by 16 
20020830 

From Brenda: my math question is as follows: 3810+12divided by4multiplied by 16=? Answered by Penny Nom. 





Student to teacher ratio 
20020828 

From A student: central middle school has 2470 students and the ratio of students to teachers is 26:1 how many new teachers are needed to reduce this to 19:1? Answered by Penny Nom. 





Mixing gas and oil 
20020827 

From Sherry: how do I calculate the correct fuel ratio for a boat motor? 50:1 the oil containers only say how many ounces to add to 5 gallons of fuel to make a 50:1 ratio.(13 ounces to 5 gallons of fuel) I have a 20 gallon tank so what if I add 11.6 gallons of fuel, what formula would I apply to get the correct measurement of oil to add? Answered by Penny Nom. 





Order of operations 
20020718 

From Danna: I would like to know how to solve this type of problem; I already have the answer. Problem: 2 [5 (4 + 6)  2] = 96 Also, what do you call this type of problem? Thanks a lot. Answered by Penny Nom. 





Integrating x^x 
20020618 

From Jeremy: I am a student at the University of Kansas and I am wondering if there is a general antiderivative for x^{ x} (i.e. the integral of x^{ x} dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question. Answered by Claude Tardif. 





A good rule of thumb when driving 
20020613 

From Lisa: A good rule of thumb when driving is that you should be about one car length away from the car in front of you for every 10 miles per hour that you are travelling. Suppose you follow this rule perfectly (so you are exactly the correct distance away). You are waiting at a stop light with your front bumper just touching the car in front of you. The light turns green and the car in front accelerates at a constant rate "r". Calculate how you should accelerate in order to follow the rule. Answered by Penny Nom. 





Ratios and weights on Neptune 
20020603 

From Janice: The ratio of an object's weight on earth to it's weight on Neptune is 5:7. How much would a person who weighs 150 pounds on earth weigh on Neptune. Answered by Penny Nom. 





8/13*26/27 
20020501 

From Arias: 8/13*26/27= Answered by Penny Nom. 





An augmented matrix 
20020420 

From A student: Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is a+2b+c=0 2a+5b+4c=1 ab9c=5 Answered by Penny Nom. 





Arc length 
20020417 

From Vix: Find the point on the curve r(t)=(12sint)i(12cost)j+5tk at a distance 13pi units along the curve from the point (0,12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston. 





Ratios 
20020417 

From A student:
 Medication is givin at 1cc. per 20 pounds of body weight. A dog weighs 16 pounds how many ccs. of medication does the dog get?
 Dr. Lee wants you to prepare 1000 ml. of a 10% dextrose solution in lactaed ringers for diuresis or a patient you have a 1 L bag of lactated ringers and 500 ml of 50% dextrose for injection. How would you prpare the solution?
Answered by Penny Nom. 





Two triangles 
20020403 

From Scott: Consider 2 triangles: Triangle PMB and Triangle PLA. Triangle PLA is contained within Triangle PMB. Side LA is parallel to Side MB. Point L is located on Side PM. Point A is located on Side PB. If the ratio PL:LM = 5, then what is PB:PA ?? Answered by harley Weston. 





Meg's biscuits 
20020329 

From Tami: Meg's biscuits recipe calls for 4 cups of flour for every 1.5 cups of milk. If Meg uses 6 cups of flour, how many cups of milk will she need? Answered by Penny Nom. 





The square root of 2 
20020305 

From Roger: Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root? Answered by Penny Nom. 





Fractions to decimals and percents 
20011231 

From A student: 2/5 , 4/8 , 4/10 , 3/5 , 6/8 , 7/7 (what is the decimal and percent for each)
1/5 , 1/10 , 1/8 , 1/1 (what is the decimal for each)
100 PERCENT, WHAT IS THE DECIMAL?
The ratio of boys to girls in a class is 1:4. What percent of the class are girls? Answered by Penny Nom. 





The probability that the area of a triangle is smaller that 1/8 
20011221 

From Hoda: Given unit square pick two points on adjacent sides of the square , what is the probability that the area of the resulting triangle is smaller that 1/8? I tried to tackle the problem by first sketching a square with the four vertices at (0,0), (1,1), (0,1) and (1,1). The answer seems to be the area under the curve y=0.25/x between 1 and 0, but how can you integrate such a function when ln0 is undefined? any help would be highly appreciated. Answered by Andrei Volodin. 





Ratios and proportions 
20011126 

From Adam: I am doing a project where I come to this website and ask a math expert about a certain topic. My topic is ratios and proportions. Can you please tell me what your job is and how you use ratio's and proportions in your job. Can you also please explain what ratios and proportions are. Answered by Harley Weston. 





Ratios 
20011121 

From Mike: Simplify these ratios. 7 1/4 inches to 2 feet. $0.02 per $1.75 Answered by Peny Nom. 





Ratio and proportion 
20011010 

From Steve: Where would you use a proportion and/or a ratio in a real life job or problem. Answered by Leeanne Boehm and Walter Whiteley. 





1:5 
20010927 

From Sandy: A colleague and I have a disagreement about dilutions. I seem to remember that I was taught (although it was a long time ago) that a RATIO was written thusly: 1:5 , and read " one part to five parts", for a total of 6 parts. On the other hand, a fraction is written: 1/5 and is read" one part in five" for a total of 5 parts. My colleague says that the ratio reads "one part in five" and is essentially the same as a fraction. Which is right? Have I been doing dilutions wrong all this time? I teach Animal Nursing and need to know where I can find a consise answer to such questions for making up medicated fluids, etc. Answered by Penny Nom. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





Area between curves 
20010613 

From Phil:
question 1 find the area bound by the curves y = x^{2} + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x^{2} + y^{2} = 9 about the xaxis Answered by Harley Weston. 





SPRT 
20010524 

From A researcher: I have a medicalpharmaceutical study that says: SPRT (something to do with Secuential and Truncated). Do You know what it means S.P.R.T. and what it is? Answered by Ejaz Ahmed and Penny Nom. 





National consumption function 
20010509 

From Brian: If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Answered by Harley Weston. 





Dividing fractions 
20010509 

From Rina: I just wanted to ask if you could help me in math. See I'm having a test soon and its on Dividing Fractions and I just don't get it. My math teacher says that I'll be just fine but I failed my math quiz. I went to ask eric but they could help me so they told me to go to you. So here I am asking you if you could help me. Answered by Penny Nom. 





The average value of a continuous function 
20010508 

From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston. 





Adding and subtracting rational expressions 
20010503 

From Donna: Adding and subtracting Rational expressions. I am in grade 10 and I am a student here is an example of the questions: 1/(x+1)  1/(x1) = ? Answered by Penny Nom. 





Logs for the fire 
20010502 

From Tom: Three girls named Amanda, Beatrice, and Cleo visit a summer cottage. Amanda brings 5 logs for the fire, Beatrice brings 3 logs and Cleo contributes 80 cents. How should the money be divided among the other two girls so that each of the three is felt to have contributed equally to the cost of the fire. Answered by Penny Nom. 





Oil revenue 
20010421 

From Brian: Suppose that t months from now an oil well will be producing crude oil at the rate of r(t), not a constant, barrels per month and that the price of crude oil will be p(t), not a constant, dollars per barrel. Assume that the oil is sold as soon as it is extracted from the ground.  Find an expression for the total revenue from the oil well, R(t).
 A certain oil well that currently yields 400 barrels of crude oil a month will run dry in 2 years. The price of crude oil is currently $18 per barrel and is expected to rise at a constant rate of 3 cents per barrel per month. What will be the total revenue from this well? {Hint: Model the degraded production rate with the equation:
r(t) = (ABt)e^{0.04t}} Answered by Harley Weston. 





Integration by parts 
20010409 

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





Two integrals 
20010403 

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





66:1 
20010326 

From A student: I need to know how to convert the ratio 66:1 to a percentage. I can not find an answer any where online when the second number is a 1. Answered by Penny Nom. 





Cube roots on a calculator 
20010324 

From Will: Hi my name is Will.I have a question about the calculator TI83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that? Answered by Judi McDonald. 





A jogger 
20010312 

From Bill: At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes. a) write an expression for the velocity of the jogger at time t. b) what is the total distance traveled by the jogger in that 10minute interval. Answered by Harley Weston. 





The nth place of pi 
20010227 

From Andrew: I have always wondered; is it possible to find the value of an irrational number, such as (phi) at it's nth decimal place??? You would plug the decimal place into the formula and the value would be given at the specified decimal place. When we look at the expression { (sqr 5 + 1)/2 } we are in a sense visualising the number in it's entirety, so the formula may include elements of the above expression in some form. Answered by Claude Tardif. 





Ratios 
20010220 

From Louise: there are 3 people and they decide to share their tips (working in a restaurant) ann gets £180 tony £130 peter £90 total amount is £36 what share should they get. Answered by Penny Nom. 





Books and cars 
20010213 

From Aquilya:
 A pile of books is 96.08cm. If each book is 0.8cm thick. How many books are in th pile?
 2. A car travels 9.84km on 0.6 litres of petrol. How far will the car travel on 3.7 litres of petrol?
Answered by Penny Nom. 





What is wrong with these probelms? 
20010209 

From Cindy: Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Error in patterns: 13/35=1/5; 27/73=2/3; 16/64=1/4 4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11 2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10 Answered by Leeanne Boehm and Penny Nom. 





More repeating decimals 
20010117 

From Alan: I am neither a math teacher nor a student, but I hope you will consider my question anyway. I recently was discussing repeated decimals with a friend, and went on the web to find out more about a pattern was looking for years ago. In doing so I came upon your correspondence on repeating decimals. . . . Answered by Chris Fisher and Penny Nom. 





Repeating decimal notation 
20001231 

From Clarende Duby: I have seen single repeating decimals for ex. 1/3 = 0.3 with the dot above the 3 to represent the repeating decimal. Then, there is the more common form of the bar over the top of the repeating number or group of numbers (called the period?). Which notation is correct? Answered by Penny Nom. 





Solving x  sin(x) = constant 
20001229 

From Keith Roble: If x is in radians, how do you solve for x, where: xsin(x) = constant? Answered by Harley Weston. 





How do you integrate secant(theta)? 
20001222 

From Robert Williamson: How do you integrate secant(theta)? I know the answer is ln [sec(theta) + tan(theta)] but how do you get there? Answered by Claude tardif. 





When did the man go out? 
20001214 

From Rajesh: A man goes out in time between 5 and 6 and when he comes back he observes that two hands have interchanged position. Find when the man did go out? Answered by Penny Nom. 





Three problems 
20001214 

From Sarah: Hi, my name is Sarah, and I'm asking this question on behalf of niece who is in secondary two. Thank you. Q1. What is the angle formed by the hour hand and the minute hand of a 12 hour clock at 5.50pm. . . . Answered by Penny Nom. 





Direct and inverse variation 
20001212 

From Ashley: I'm stuck on this unit of direct and inverse variation..please and my problems and show me how to do each PLEASE!!! Assume that y varies directly as x If y= 4 when x = 2, find y when x= 6 Assume that y varies inversely as x If y =4 when x=2, find y when x =6 Answered by Penny Nom. 





The aspect ratio of a rectangle 
20001204 

From Ron Delavigne: The aspect ratio of this rectangle is 4:3. That is A to B is 3. And B to C is 4. If I know the lenght of A to C is 19 inches, how can I find the length of A to B, and B to C. Answered by Penny Nom. 





A nonintegrable function 
20001203 

From Mark Spilker: I have a proof that I cannot do here it goes. Let F(x)= 1 if x is a rational number 0 if x is an irrational number Prove the function is not intregrable on the interval (0,1). Hint: Show that no matter how small the norm of the partition, the Riemann Sum for the SigmaNotation F(w_{i}) Delta_{i}X is not unique. Answered by Harley Weston. 





An integration problem 
20001130 

From A student: If a>0 and the integral from b to 0 of 1/(1+x) equals 1/2 the integral from a to 0 of 1/(1+x), express "b" in terms of "a" Answered by Claude tardif. 





Order of operations 
20001126 

From Margaret Pratt: My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+15= She arrives at 8 as the answer and has been told this is incorrect. Any help you can give would be appreciated. Answered by Penny Nom. 





Comparing an integral and a sum 
20001121 

From Douglas Norberg: A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 2^{30} which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston. 





Cutting the lawn 
20001026 

From Kacie: Ellen can mow a lawn in 2 hours. Mary can mow the same lawn in 1.5 hours. How long would it take them to mow the lawn together? Answered by Penny Nom. 





Working together on a job 
20001023 

From Nicole: WORKING TOGETHER ON A JOB: Patrice, by himself can paint 4 rooms in 10 hours. If he hires April to help they can do the same job together in 6 hours. If he lets April work alone , how long will it take her to paint 4 rooms? Answered by Claude Tardif. 





The scale on a map 
20001021 

From Caroline: On a map scale of 1:15000 the distance between two buildings is 31.4cm what is the actual distance in km. Answered by Penny Nom. 





Sunflower seeds 
20001009 

From A parent: Find the number of 3/4 pound of sunflower seeds that can be filled with 225 pounds of sunflower seeds Answered by Penny Nom. 





Repeating decimals 
20001006 

From Mary O'Sullivan: I understand that with repeating decimals (those with a pattern), the number of digits repeated is put into fraction form with the same number of 9's ex. 0.4444 = 4/9 0.145145145 = 145/999 How can I explain why this is so? Some inquisitive 8th graders are anxious to find out! Answered by Penny Nom and Walter Whiteley. 





Dividing a region in half 
20000921 

From Kerry: There is a line through the origin that divides the region bounded by the parabola y=xx^{2} and the xaxis into two regions with equal area. What is the slope of the line? Answered by Penny Nom. 





Order of operations 
20000919 

From Nicole: the problem is, 4x818 divided by 6= do you solve this by doing 4x8=32 then by dividing 18by 6= 3, then subtracting 3 from 32 = 29? If not what is the order of operation? Answered by Penny Nom. 





Rational Numbers 
20000914 

From Josh Kuhar: How can you tell a number is rational? Answered by Harley Weston. 





Gravity 
20000906 

From Robert Broomfield: If they dropped a 1lb object from 40,000 feet in the air, at what speed would it it the ground? Answered by Harley Weston. 





Making milkshakes 
20000904 

From Linda: To make a chocolate milkshake, 3 parts chocolate syrup are mixed with 2 parts malt. To make a vanilla milkshake, 2 parts vanilla syrup are mixed with 1 part malt. If equal parts chocolate and vanilla milkshakes are mixed, what is the proportion of malt to milkshake? Answered by Penny Nom. 





Six typists 
20000819 

From Paula Duncan: If it takes a typist 4.5 hours to type 860 words, how many hours would it take 6 typist to do 16800 words? Answered by Penny Nom. 





Numerator and denominator 
20000618 

From Maureen Beard: What is the origin of the terms numerator and denominater? Answered by Penny Nom. 





Calculus Research Questions 
20000522 

From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston. 





Two calculus problems 
20000501 

From Kaushal Shah: How Do WE Integrate the following Functions,  Integral xtanx dx
 How was natural base "e" discovered and why e=2.7.......
Answered by Claude Tardif. 





The area of a triangle using calculus 
20000415 

From Todd Bowie: Hi, I am not a student but am reviewing calculus for an upcoming interview. I would like to know how to derive the area of a triangle using calculus. Thanks! Answered by Patrick Maidorn. 





The square root of 3 
20000404 

From Mr. William: Prove that root 3 is irrational Answered by Harley Weston. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





Rationals, irrationals and integers 
20000314 

From Erin McKeon: Why does the letter J represent the set of integers, the letter Q represent a set of rational numbers and the letter P represent a set of irrational numbers? What do each of these letters stand for? Answered by Harley Weston. 





Eligibility in a contest 
20000314 

From Ken Rabley: Hi, hoping you can help. Dispute among coworkers. Tell me, what is the correct answer to the following question: 1936 + (2406/4812) x (4756  3256) + 1250 Seems this is the question for eligibility in a contest...We have come up with various solutions, all which may be correct. Answered by Penny Nom. 





Order of operations 
20000227 

From Mildred Saulsbery: Find the value of the expression. 6(5+1)  9(1+1) _____________ 5(8  6) 2^{3} Answered by Harley Weston. 





Some integration problems 
20000223 

From Tim Valentine: I am having a great deal of difficulty with the following integrals, can you help? I think they need the use of trig substitution or integration by parts but I cannot figure out how to begin. Thanks! The integral of 1/(2+3x^{2}) dx. and The integral of x * square root of (4x+5) dx. Answered by Harley Weston. 





Party favors 
20000222 

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





Pi 
20000222 

From Shelley Collier: Numbers that can be written in the form p/q where p and q are integers, (q not 0), are known as rational numbers. What you are missing is that p and q must be integers. The fact that Pi is irrational means that you can't have a circle with both the circumference and diameter being integers. In fact you can't even have the circumference and diameter both rational since the quotient of two rationals is again a rational. Answered by Claude Tardif and Penny Nom. 





Irrational algebraic functions 
20000221 

From Bucky Cadena: Here is the multipart problem: Given f(x) = x3* squareroot of x + 4 What does the f(x) intercept equal Find the two values for which f(x) = 5 Find the one value for which f(x) = 3 Answered by Harley Weston. 





Mixing oil and gas 
20000125 

From Karen: My hubby is ready to use his snow blower and is supposed to use 50:1 measurement....50 parts gas to 1 part oil......how does he do this if he has 1 gallon of gas? How much oil do we use...need info asap.....hopefully you are there! Answered by Harley Weston. 





Order of operations 
20000116 

From Dorothy: I was wondering if you could tell me where I can get some info. on how to solve the following problem. I was given the answer but I don't know how it is solved. 4+2x(6x2)5=23 Answered by Penny Nom. 





Ratios 
20000111 

From Cyndi:
My name is Cyndi and i am in middle school in the 8th grade. The questions i am about to ask come from my book. My return address is PR_Angel1@yahoo.com The directions on a can of lemonade mix say to use 8 tablespoons of mix to make 2 quarts of lemonade. Heathcliff wants to make 7 quarts of lemonade. How many tablespoons of mix should he use? and In a recent year, the ratio of men to women in the United States armed forces were about 9 to 1  if there are 90 men in a random group of military personnel, how many women would you expect to find in the group?
 in a group of 90 military personnel, how many of them would you expect to be women?
 what percent of armed forces personnel were women in that year?
Answered by Penny Nom. 





Fibonacci Numbers 
19991215 

From Gary Nelb: I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different. Answered by Denis Hanson. 





Two calculus problems 
19991213 

From Alan: I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Answered by Harley Weston.






Ratios and proportions 
19991119 

From Rebecca: I'm not that good of a student and I was woundering if there is a shortcut to ratios and proportion. My 6th grade teach tought all we needed to know. I was just wounder if there was an easier way. Answered by Claude Tardif and Harley Weston. 





Order of operations 
19991025 

From Garrett: 99*(57+76)*91085/9 Answered by Penny Nom. 





(5)^2, 5^2 and (5)^2 
19991013 

From Jennifer Brown: What is the difference between the following problems: (5)^{2}, 5^{2} and (5)^{2} Our text book (Beginning Algebra, fourth edition, published by McGraw Hill, by Streeter, Huthison and Hoetzle) says the second and third problem are exactly the same. I don't see how that can be. Is there a mathematical rule that explains this? Answered by Penny Nom. 





8*(5a)=15 
19990922 

From Shelby: 8*(5a)=15 i cannot get this question!! please help me!! Answered by Harley Weston. 





How many went to the game? 
19990909 

From Lisa Schmidt: If 3/4 more students went to the game than actually did go to the game, 25% of all students in the entire school would have gone. What fraction of students in the entire school went to the game? Answered by Harley Weston. 





The Binomial Theorem for rational exponents 
19990415 

From Angela Evans: The full question is this: Isaac Newton generalized the Binomial Theorem to rational exponents. That is, he derived series of expansions for such expressions as (x+y)^{3} (x+y)^{2/3} (x+y)^{5/6} What did Newton find? What are the first four terms of the series expansions of binomials above? How can this extended Binomial Thrm. be used to aid in calculations? Answered by Penny Nom. 





Linear programming and optimization 
19990409 

From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





Simplifying Radicals 
19990126 

From Mary: I would like to know how to simplify this question:
4 __________________ squareroot7 + squareroot3
I know the answer is (sqrt7  sqrt3) but i would really love to know how to get that answer!! Thanks. Answered by Jack LeSage and Penny Nom. 





Root 17 is Irrational 
19990121 

From John Murdock: If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational. Answered by Harley Weston. 





Turning Fractions into Decimals 
19990116 

From Lynn: How do you do it step by step Answered by Jack LeSage. 





6.99999... = ? 
19981205 

From Tom: I have had a rather heated arguement with my students. Please settle this for me. Solve <,>, = 6.99999... __ 7 Thank you. Answered by Penny Nom. 





Terminating decimals 
19981116 

From Debra Karr: A college student studying elementary education asked me a question that I could not think of the correct answer. How can you look at a fraction and tell if is a terminating or non terminating decimal? Answered by Jack LeSage and Penny Nom. 





Adding Fractions 
19981015 

From Lindsay: please help me!!!! Answered by Harley Weston. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 





Repeating Decimals 
19981001 

From Chris Norton: Could you PLEASE give the formula to find out the number of digits in a repeating decimal before it repeats. I have been trying to get it for weeks from Math sites on the Internet. Can you please, please help me ? Chris Norton Answered by Chris Fisher and Penny Nom. 





Rational and Irrational Numbers 
19980919 

From Ri: I am trying to explain rational & irrational numbers to my niece who is grade 7 and am having difficulties. Could you please explain the difference between rational & irrational numbers. Thank you Ri Answered by Penny Nom. 





Rational Numbers 
19980905 

From Kristin Mckenzie: Iam a secondary student with a math question I don't know how to do. This is the question: Explain whether each decimal number represents a rational number. (a) 0.16 (b) 0.12 (c) 3.125 (d) 0.27 (e) 0,212 112 111 2 .... (f) 0. 457 92 If it wouldn't be a problem i would really appreciate it if you sent back the instructions on how to do the question. My name is Kristin Mckenzie and my return email is lexus1999@hotmail.com Thankyou for you time Answered by Jack LeSage and Harley Weston. 





The area and the circumference of a circle. 
19980827 

From Jason Wright: I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Answered by Walter Whiteley. 





Calculus problems 
19980713 

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





A Calculus Problem 
19980628 

From Lorraine: I'm a postsecondary student taking calculus by correspondence. I'm stuck on the following question (and similar ones) Can you help? Evaluate the following indefinite integral: d(theta)  1 + sin (theta) (It says to multiply both numerator and denominator by: 1  sin(theta) Thanks Lorraine Answered by Harley Weston. 





(2)^x 
19971212 

From Ken Bokinac: During our math class last week we came accross an equation that we could not graph we were wondering if you could help us try and graph it. The question is: y=(2)^x Answered by Harley Weston. 





Ratios. 
19971126 

From Jennifer Kim: I am a grade 12 math student who would like to know if there is an easy way to solve In a school the ratio of the number of Grade 11 students to the number of grade 12 students is 4:3. If there were 5 fewer students in grade 11 and 3 more students in grade 12, the ratio would be 7:6. How many students in each grade? Answered by Penny Nom. 





Division by a fraction. 
19971121 

From Roger Marchegiano: I am interested in a solution to the following extra credit problem for my son in Geometry. We have been unable to produce a satisfactory response: Show a geometric representation of the division of fractions algorithm, (When you divide fractions you multiply the numerator by the reciprocal of the denominator). Answered by Penny Nom. 





A Question About Pi. 
19970708 

From Mike Chan: I have read the section Repeating Decimals in your data base. It mention that 1/17 has at most only 16 repeating digits. But, why does "pi" have an infinite number of digits (and not repeating ). Answered by Penny Nom. 





A proof that e is Irrational. 
19970430 

From Peter Hall and Jenny: We have a little mathematical problem... we need some help proving e is an irrational number! We don't feel very confident in our formulas, so if You have the time to give us a little explanation we would be very grateful!!! Answered by Doug Farenick and Penny Nom. 





Repeating Decimals 
19970124 

From Grant Reed: Is there a way to tell that the repeating decimal for 1/17 has no more than 16 repeating digits? Answered by Penny Nom. 





Priority of operations 
19961104 

From Wallace: What is the answer to this problem? Let x=2 and y=3. Evaluate 12x / 2y (if the old division sign is used). Answered by Chris Fisher. 





What is the golden section? 
19950917 

From Cindy: What is the golden section of a line? Answered by Denis Hanson. 





Ordre des opérations 
20060515 

From Chantal: 2324/4153+619= je sais pas comment calculer merci Answered by Claude Tardif. 





Nombre d'or 
20031031 

From Claude:
Comment démontrer que si a/b est égal au nombre d'or alors a+b/a est égal aussi au nombre d'or Comment faut t il choisir a et b pour que le puzzle de lewis caroll soit réalisable? on sait déjà que les nombres 8 et 5 ainsi que 6 et 3 ne sont pas valables. Answered by Claude Tardif. 





Opérations de base 
20030705 

From AnneMarie: Je m'appelle AnneMarie et je suis enseignante de 5e année à l'école Domaine des copains de Balmoral au NouveauBrunswick. Récemment, j'ai participé à un concours intitulé: Budweiser King Pack Nascar Hat Promo. Afin de réclamer le prix, qui est une casquette, je devais répondre à une question réglementaire. Il s'agissait d'une phrase mathématique qui se présentait comme suit: 4 x 26  24 / 8 = qui se lit: 4 fois 26 moins 24 divisé par 8 Answered by Claude Tardif. 





Fractions 
20030510 

From Jacques: Voici la question qu'il pose: 2 x (1/2+1/4) + 3 + 2 x (1/31/4). La reponse est 4 2/3. Pourriez m'expliquer etapes par etapes ce que je dois faire. Answered by Claude Tardif et Diane Hanson. 





Ses points de discontinuités est les irrationnelles 
20020108 

From Un eleve: Je voudrait montrer qu'il n'existe pas de fonction de R>R tels que ses points de discontinuités est les irrationnelles, en utilisant la methode de "baire". Answered by Claude Tardif. 





Fraction rationnelle 
20011211 

From Audrey: réduire en une seule fraction et simplifier.
(42x+x^{2})/(2+x)  (x+2) Answered by Claude Tardif. 





Recherhce sur pi et exponentielle 
20010317 

From Cyril: étudiant a la fac de sciences de montpellier je cherche des informations concernant la demonstration suivante: "comment prouver que pi et exponentielle sont irrationnels?" Answered by Claude Tardif. 





le nombre d'or 
20000614 

From Belhaj Saad: quel est le nombre d'or? Answered by Claude Tardif. 

