







More on millions and billions 
20100311 

From julio: shouldn't the thousands of millions, tens of thousands of millions, and hundreds of thousands of millions be called what they are? technically they are not billions because billions come after 999,999,999,999 . It would sound better to call the numbers by their real name when economists talk about the national deficit besides mathematics is a very precise science that doesn't admit mistakes. Or am I wrong? I know that in other countries is expressed different than here. I have this question to different people and nobody has a "logical" explanation to it. " that's the way is here in the US" does not explain any thing Answered by Penny Nom. 





Foiled by foil 
20090720 

From RAY: how u do the foil ?
the question (x+4)(x+5) Answered by Robert Dawson. 





16 golfers 
20090318 

From Bill: We have 16 golfers. We golf for 5 days, in foursomes. It should work out that each player plays with each other player 1 time exactly.
I just can't figure it out.
Thank you in advance!
Bill Answered by Claude Tardif and Victoria West. 





A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





Calculating the area (acreage) of a four sided lot 
20070718 

From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque. 





Lot size / acreage (more than three sides) 
20070511 

From Martha: What is the lot size of the following dimensions equivalent to acre.
141.85 x 52.55 x 217.63 x 38.89 x 68.08 Answered by Penny Nom and Stephen La Rocque. 





Finding the area of a regular polygon 
20070504 

From Dana: We are trying to figure the square footage of a tetradecagon....sort of a round house with 14 sides that are 8 ft' in length. It has a height of 9 ft. How do we figure the square footage of this? Answered by Stephen La Rocque. 





Calculating volume of concrete, dirt, sand, anything. 
20061117 

From Debbie: [This article contains a special calculator to help you find the volume (for example, the cubic yards) of material required to fill (or empty) a space if you know the length, width and depth.]
We are wanting to pour a 24'x30' slab that is 5" deep. How many cubic yards of cement do we need? Answered by Penny Nom. 





Billions and more! and even more! 
20040301 

From Steph: What comes after undecillion? Answered by Penny Nom. 





Billions and more! 
19970915 

From Mahabir B. Gupta: I would like to know how you americans write the number 1 billion. Do you say "One thousand million"..can you answer by giving me examples? 1,000,000> 1 million 1,000,000,000>1 billion Why is it that in spanish it is different? Answered by Penny Nom. 





Why is lbs the abbreviation for pounds? 
19961003 

From Nancy Mutdosch: What does lbs stand for? Why is it the abbreviation for pounds? Answered by Chris Fisher. 





A normal distribution problem 
20140419 

From Melanie: This is the question:
The lifetime of a certain type of car tire are normally distributed. The mean lifetime of a car tire is 40,000 miles with a standard deviation of 5,000 miles. Consider a sample of 10,000 tires. A) How many tires would you expect to last between 35,000 and 45,000 miles? b) How many tires would you expect to last between 30,000 and 40,000 miles? c) How many tires would you expect to last less than 40,000 miles? d)How many tires would you expect to last more than 50,000 miles? e) How many tires would you expect to last less then 25,000 miles? f) What tires would you want on your car and explain your reasoning
Not at all sure that we've done any of this correctly and not sure how to determine how many tires will last less than 25,000 miles.
Any help is appreciated. Answered by Penny Nom. 





An input output table 
20140419 

From Stephanie: I have an input output table with x/y filled out except one x and one y. I need help. How do I find X? Answered by Penny Nom. 





Simultaneous equations with fractions 
20140419 

From Maryam: I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:
x/8  y = 5/2
3x + y/3 = 13 Answered by Penny Nom. 





Robyn and Shaun swim 
20140418 

From kajinthan: robyn swims four 35m lengths.shaun swims eight 15m widths. how much further does robyn swim?solve this maths Answered by Penny Nom. 





A frustum of a pyramid with a square base 
20140418 

From tuba: a pyramid has a base of 10 m and is 15 m high.what is the volume? if 6m is removed from top what is the volume of the remaining frustum? Answered by Penny Nom. 





A circle is divided into three sectors 
20140417 

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





Barrels of oil 
20140416 

From daryl: Looking for an accurate number to use when calculating barrels per inch in a a tank with the following dimensions:
Nominal diameter  15'6", nominal height  16ft, nominal capacity  500 barrels. These are commonly referred to as 500x16 tanks.
Currently we are using 2.6 barrels per inch. We need 180 barrels for a full load so I'm trying to figure out how many total inches I need to load 180 bbl. This has been a matter of debate for some time. Thanks for your help. 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. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





A conditional probability problem 
20140413 

From Chiluya: Two fair dice are rolled. what is the probability that the number on the first die was at least as large as 4 given that the sum of the two dice was 8? Answered by Penny Nom. 





The cost before the sales tax 
20140413 

From Juanda: Hello,
I know the customer cost with tax and I know the sales tax.
How do I find out the customer cost prior to the added sales tax?
Thank you Answered by Penny Nom. 





A sand trench around a pool 
20140413 

From steve: How sand is needed to back fill a trench around a 24ft dia. pool that is 26" deep by 2ft wide. Making the outside dia. 26ft.
Thank You Answered by Penny Nom. 





Manipulating an equation 
20140412 

From Paul: S=4wl+2wh and solve for h Answered by Penny Nom. 





A slab of wet clay 
20140412 

From Karen: How many square feet ( at 1/4 inch thickness) are in 100 lbs. of wet clay? Answered by Penny Nom. 





A golf league with 20 players over 17 weeks 
20140412 

From Chris: I have a golf league 20 players and 17 weeks. We don't have teams so I just want to have everyone to play with each other the about same number of time and, hopefully, randomly distributed throughout the season. We have had situations in the past where two people play together for three weeks in a row and then not anymore for the rest of the season. From other posts, I see how to schedule the first 5 weeks without repeats but I can’t figure out an algorithm to for the rest of the season. Thanks! Answered by Victoria West. 





Decimals,fractions and percentages 
20140411 

From Frances: Ask an expert to find out their real life usage of your topic... that is the question.
meaning what is your real life usage of using decimals,fractions and percentages.
This is all part of my math assignment to ask an expert real life usage... so please
reply back as soon as possible Answered by Penny Nom. 





A golf league consisting of 14 two man teams 
20140410 

From Kevin: Hello,
I need to make a schedule for a golf league consisting of 14 two man teams playing over the course of 20 weeks. I understand that each team will play at least once and I believe 7 teams will play each other twice over the course of the season. How would I generate this schedule. Thank you,
Kevin Perry Answered by Victoria West. 





How fast did Jessica grow? 
20140410 

From jasmine: when she was 14 jessica was 5 feet, 4inches tall . at 18 she is now 6 feet, 2inches tall .how fast did jessica grow during this time Answered by Robert Dawson. 





The surface area of a circular dome 
20140410 

From Shafiqah: Is this a dome's surface area formula??
{{2 × π r × h square units}}
Is the surface area of the floor for the dome is calculate too in this formula?
Thanks for answering. =) Answered by Robert Dawson and Penny Nom. 





Two rectangular prisms 
20140410 

From hannah: two rectangular prisms have a combined volume of 432 cubic feet Prism A has half the volume prism b has what are the volumes of prism a and prism Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





Two circles that touch each other externally 
20140408 

From Ameya: Two circles of radii a and b (a > b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST^2 is equal to Answered by Chris Fisher. 





The surface area of a rectangular prism 
20140408 

From Manraj: Find the surface area of a rectangular prism with dimensions 4, 5, and 7 units. Answered by Penny Nom. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





Cutting a hexagon from a disk 
20140405 

From Paul: I am a machinist and sometimes need to make a hex from
round material.
If I know the distance of the flat sides opposite one another
of my hex, how can I calculate the size of material I need to turn
to give me the right diameter to finish the part with six sides? Answered by Penny Nom. 





A 4 digit number 
20140404 

From LIM: "A" is a 4 digit number formed by all the numbers from 1 to 4. When "A" is divided by 9, the remainder is the biggest possible value. What is the biggest value of A? Answered by Chris Fisher. 





The locus of a point 
20140404 

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





3/4lbs of nails fills a container 2/3 full 
20140404 

From Tyler: If 3/4lbs of nails fills a container 2/3 full, then how many lbs of nails will fill the container? Answered by Penny Nom. 





Golf for 8 playing 7 rounds 
20140403 

From Evan: We are going on a golf trip to Scotland and are trying to work out the pairings. There are 8 of us playing 7 rounds. We would like to be partnered up in 2's with everyone once and have evenly split up foursomes. Thanks for the help Answered by Victoria West. 





Evaluate x(3x+5) if x=2 
20140403 

From Destiny: I wanted to know the value of x(3x+5) if x=2 Answered by Penny Nom. 





Shadows of a father and son 
20140402 

From esada: the father and son cast a shadow of 11 feet and 8 feet,respectively if the son is 4'8'' in height,how tall is the father? Answered by Penny Nom. 





Is this a right triangle? 
20140401 

From amina: decide whether or not the following points are the vertices of right triangle (9,2),(1,2),(9,11) Answered by Penny Nom. 





A schedule for an 8 man golf team playing 4 each week 
20140401 

From Harold: We have an 8 man golf team and wish to schedule only 4 to play each week and to have each member play with one of the other 7 at least once.
What is the simplest method. Number of weeks could be up to 18 or so. Answered by Victoria West. 





A cubical tank 
20140401 

From renzo: A cubical tank contains 2048 cubic ft of water when HALFFULL. Find the total area of the tank and the length of its diagonal Answered by Penny Nom. 





Reducing the size of a poster by a scale factor of 1/3 
20140401 

From deeshon: eric is making a smaller copy of a poster that measures 20.4 cm wide by 34.2 cm long.he reduces the original by a scale factor of 1/3.what are the dimensions of the copy Answered by Penny Nom. 





Golf with 20 players and one compulsory bye 
20140331 

From Wayne: I'm trying to run an event with 20 players, I would like if at all possible to limit amount of people playing repetitively together. (Mix it up and play with different people). Here's the conditions. I want groups of 4 over 5 rounds. On each round I want 4 players to drop out and have a bye (to help run the game) but I dont want them helping a group they've played in if I can help it. Is this possible ? Answered by Victoria West. 





A schedule for 6 people 
20140329 

From John: How do I set up a schedule where six people are here for ten of twenty days.
Arranged in rotating groups of three, so everyone works with everyone else.
Everyone works with everyone else at least once and everyone works ten days. Answered by Victoria West. 





A cyclic quadrilateral 
20140328 

From Carly: Suppose ABCD is a cyclic quadrilateral, i.e A, B, C, and D are the points on a circle,
given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre
of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint.
Thank you. Answered by Chris Fisher. 





Percentage increase of the population of a town 
20140328 

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





12 golfers, 6 rounds 
20140327 

From Bill: I have a group of 12 golfers playing 6 rounds of golf. I am
looking for a pairings schedule that allows each golfer to play
at least one round in a foursome with each of the other eleven
players.
Can you provide me with a solution? Answered by Victoria West. 





A table of values 
20140327 

From Marisol: A table value X 0,1,2,3,4,5,6 and Y 3,7,11,15,19,23,27 . what relationship of X to Y is represent by which equation? A . y= 4x. B y =x+3 . C y =4x+3 or . D y =4x3 Answered by Penny Nom. 





12 golfers, 24 weeks 
20140327 

From George: I have 12 golfers and want to set up a season schedule that will avoid duplication of playing partners as much as possible. The saeson is 24 weeks long. Do you have a formula? Answered by Victoria West. 





An inequality 
20140327 

From James: a step on a stairway is at least 8 inches high. write and solve an inequality to represent the maximum number of steps between floors that are 10 feet apart Answered by Penny Nom. 





13 golfers in groupings of 4, 3, 3 and 3 
20140326 

From Lennart: How can I organise 13 players playing in groupings of 4,3,3,3 for 3 rounds of golf in a way that all play with all others but a minimum of times with the same players(?)If possible, nobody should play in the 4 ball more than once. I would be grateful for an answer/proposal! Thank you, LR Answered by Victoria West. 





A word problem with fractions 
20140326 

From lois: a man has a stack of boards, he cuts 3/5 off each board, after he cuts the boards he finds he has enough pieces left to make 4 boards the length of the original boards. how many boards did he start with. Answered by Penny Nom. 





Justin and his father went fishing 
20140326 

From Confused: Justin and his father went fishing and together caught 12 fish.
Three times the number of fish that Justin caught exceeds 12 by
as much as 5 times the number that his father caught exceeds 8.
How many fish did each catch? Answered by Harley Weston. 





The faces of a triangle 
20140324 

From Westun: Your answer says that a triangle has 0 faces but isn't
the part of the shape you see the face!? Because i am having trouble
with that so could you help me!
thanks! :) Answered by Penny Nom. 





9 golfers in groups of 3 
20140322 

From Andrew: We are a group of 9 golfers.
We play 4 rounds in 3 groups of 3.
What would be the most equitable where everyone plays with another at least 1 time...?.
Thank you. Answered by Victoria West. 





Riding on a Ferris wheel 
20140321 

From Claire: A Ferris wheel has a radius of 72 feet and its center is 85 feet above the ground. At the top of the Ferris wheel, Sam is in the topmost car. If the Ferris wheel makes two complete revolutions per minute, how high above the ground will Sam be after 10 seconds? Answered by Penny Nom. 





Three digit padlock combinations 
20140320 

From Edwin: Would appreciate if you can provide me with the list of different combinations that can be obtained from a three digits number. I lost the access code of a three digits number padlock (and need to open it order to get important documents Answered by Penny Nom. 





Ms. Werenich's nickels, dimes and quarters 
20140319 

From London: Ms. Werenich has twice as many dimes as nickels and 4 more quarters than nickels. If she has $4.50, how many of each coin does she have? What would the let statements be of this problem and can you solve it? Answered by Penny Nom. 





Find two numbers with a sum of 8 and a difference of 4 
20140319 

From Elisabeth: Find two numbers with a sum of 8 and a difference of 4. Let x be the greater number and y be the lesser number. Answered by Penny Nom. 





A formula for determining concrete volume in cu. yd. 
20140319 

From Steven: I know a couple of formulas for determining concrete volume in cu.yd. the one I use most frequently is length in feet x width in feet x thickness in inch. Divided by 324. It works every time. Where does the number 324 come from. Answered by Penny Nom. 





14 teams divided into two equal divisions 
20140318 

From C: We have 14 teams divided into two equal divisions. We want each team to play each team in their division one time and four teams from the other division one time. What is the schedule Answered by Victoria West. 





A circle inscribed in a right triangle 
20140316 

From akshaya: A circle with centre O and radius r is inscribed in a right angled triangle ABC. If AB=5 cm, BC=12 cm and < B=90*, then find the value of r. Answered by Penny Nom. 





2 rectangular prisms are similar by a scale of 0.75 
20140316 

From gina: 2 rectangular prisms are similar by a scale of 0.75. The volume of the smaller prism is 27cm3 (cubed). How many cubic centimeters is the volume of the larger prism? Answered by Penny Nom. 





Two overlapping arcs in a square 
20140315 

From Jean: I have a square with side 4 cm. There are two overlapping arcs going from vertex to diagonal vertex. The other two vertices are the center of the arcs, which are shaded. How do I find the area of the shaded arcs? The overlapping arcs when shaded resemble a long thin football
Thank you for your help. Answered by Penny Nom and Walter Whiteley. 





The area of a 5 sided lot 
20140315 

From Michael: Question from michael:
This lot is in feet. 59x154x109x188x137 per the plot plan Answered by Harley Weston. 





Three consecutive whole numbers 
20140313 

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





A chord length of 2 cm 
20140313 

From prema: I am having only chord length as 2cm. how to find arc length and degree Answered by Penny Nom. 





A cable around the Earth 
20140313 

From fikile: By how much must an equatorial cable be extended in order that it runs 1meter above the ground? Answered by Penny Nom. 





A parabolic suspension bridge 
20140311 

From jeffrey: the towers of a parabolic suspension bridges 200 meter long are 40 meter high and the lowest point of the cable is 10 meter above the roadway.Find the vertical distance from the roadway to the cable at 50 meter from the center. Answered by Penny Nom. 





8 golfers for 7 rounds 
20140311 

From Brian: We have 8 guys playing 7 rounds of golf.
We want to play with each player as a partner only once, sounds simple but i can not come up with the match ups beyond the first 4 matches.
I believe the numbers should work perfectly where each player can play with another as a partner only once each throughout the week.
Please help. Answered by Robert Dawson. 





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. 





24 golfers playing 3 rounds 
20140310 

From Jim: How can I rotate 24 golfers playing 3 rounds of golf so that none of them play with the same person twice. Answered by Victoria West. 





A circle which is tangent to two perpendicular lines 
20140309 

From MJ: I'm a College Student taking up Bachelor of Secondary Education on Math Subject.
And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:
"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"
But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle.
Thanks in advance! :) Answered by Penny Nom. 





A word problem 
20140309 

From Joanne: Ashley weighs 5kgs more than Joyce. Their total weight is 41 kgs. What is the weight of Ashley? Answered by Penny Nom. 





A schedule for 6 teams over 12 weeks 
20140309 

From Paul: So I have a question. I noticed you came up with ways to create schedules and we are having a really hard time making our lineup correctly. Basically we have 6 teams that will play over a 12 week period every Monday night. The time slots are 1 hr each playing at 6, 7 and 8. We would like each team to play 3 games at each time slot over the 12 weeks. Is this something that can actually be accomplished?
Thanks so much for your help! Answered by Eric Venables. 





Eleven golfers 
20140308 

From Leon: I have a group of 11 golfers wanting to play 10 rounds of golf in grouping of 4,4,3 .What is the best solution so that everyone plays each other as many times as possible Answered by Victoria West. 





Simple interest 
20140308 

From lynn: I need to find what the interest will be for: 5000.00 @ 16.5%
annual rate, and the same for 10.8 % for 5000.00 annual rate all one question
thank you for your aid Answered by Penny Nom. 





The volume of scale in a pipe 
20140308 

From Sid: What is the estimated volume of scale (Liters) if you have a 12 inch ID pipe,300 feet long with scale 1/2 inch thick. Please show me the method and formula. Thank you for your assistance. Answered by Penny Nom. 





The angle of depression 
20140308 

From Ranger_minor: A woman of height 1.4 metres standing
on the top of a building 34.6 metres high
views a tree some distance away.
she observes that the angle of depression of the bottom of the tree
is 35 degrees and the angle of depression of the top of the tree
is 29 degrees.
assume that the building and the tree are on level ground :
1). calculate the distance of the woman
from the top of the tree measured along her line of sight. Answered by Penny Nom. 





Determine the selling price 
20140308 

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





The equation of a circle 
20140307 

From Balraj: I have to draw a circle x^2+y^2 =8x . please tell me how to understand these coordinates ? please elaborate , on how to understand these types of equations. Answered by Penny Nom. 





What are the possible lengths of the hypotenuse? 
20140307 

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





Mixing oil and gas 
20140307 

From Geoff: What amount of oil would I need to mix on 501 basis for a4litre tank (13.57ozs) capacity tank. Thank you Answered by Penny Nom. 





The inverse of y = 5^x 
20140307 

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





Parallel chords 
20140306 

From Raj: AB andCD are two chords which are in the same side of the circle.The length of AB=12 and CD= 24.if the distance between them is 4 then find their radius. Pls help me I just believe on you guys I am having my exam after 3 days Answered by p. 





A circle graph 
20140306 

From Caitlyn: I need to find the measure of the central angle that represents the amount of time spent on each activity.
My question includes a circle graph with the following: Sleep 31%, Other 15%, Entertainment 18%, Errands 7%,
Work 20%, and Food 9%. Answered by Penny Nom. 





A speed word problem 
20140224 

From kiss: Hank bicycles 5 km/h slower than Kelly. In the time that it takes Hank to bicycle 42 km, Kelly can bicycle 57 km. How fast does each bicyclist travel? Answered by Penny Nom. 





A word problem 
20140223 

From Anh: The Texas State Legislature is comprised of state senators and state representatives. The sum of the number of senators and representatives is 181. There are 119 more representatives than senators. How many senators and how many representatives make up the Texas Legislature? Answered by Penny Nom. 





A word problem with fractions 
20140223 

From alex: In a certain fraction the number by n the denominator is greater than the number by3.If 2 is added to both the numerator and denominator ,the fraction is increased by 6/35..Find the fraction. Answered by Penny Nom. 





x^3+(1/x^3)=18√3 
20140223 

From Asiv: if x^3+(1/x^3)=18√3; then what is the value of x? Answered by Penny Nom. 





9 golfers divided into 3 teams 
20140222 

From Steve: We have 9 golfers, divided into 3 teams each day. Play is over 6 days. Can you devise a schedule to ensure pairings allow for all golfers to play at least once with all participants?
Also, that the pairings have one player from another team. Answered by Victoria West. 





A circle through three points 
20140222 

From Mohammad: Find the equation of circle passing through the origin and the points (a,b) and (b,a).
Find the length of chords that it cuts off from the axes. Answered by Chris Fisher. 





Finding the retail price 
20140222 

From Judy: An item is currently on sale at 37% off the retail price. The item now sells for $350.
My Question:
What is the retail price and what is the formula or steps to figuring that out? Answered by Penny Nom. 





A limit with trig functions 
20140222 

From pearl: (what is the value of limit of x as it approaches 0 of sin8x divided by cos6x) Answered by Penny Nom. 





8 team schedule over 7 days 
20140221 

From Andrea: I need to organize 8 teams.
Each team has to go through 8 games against another team, but not against the same as before. Answered by Victoria West. 





2.3% of $17.3 trillion 
20140221 

From C: What is the annual interest on $17.3 trillion at a rate of 2.3%. Thank you Answered by Penny Nom. 





Gradient 
20140221 

From Nancy: calculate the gradient of the line AB when the line AB is passing through the points A (2,1,) and B ( 4, 3).) Answered by Penny Nom. 





A 7 person golf schedule 
20140221 

From Claude: Golf Holiday: 7 guys, play a 4some and a 3some each day for 10 days.
Want to have the best balance of each player playing with every other player
the same number of times and each player playing in an equal number of
4somes and 3somes. Answered by Victoria West. 





A fountain surrounded by a walk 
20140218 

From Maddie: A square Water Fountain is Surrounded by a walk 2 yards wide.
If the Area of the Fountain is 2/3 of the total area of the Fountain and the Walk.
What are the Outside Dimensions of the Walk Answered by Penny Nom. 





The graph of y=2x+4 
20140218 

From tyler: y=2x+4 graph Answered by Penny Nom. 





Paul is making banana bread 
20140217 

From John: Paul is making banana bread. The number of cups of bananas he uses is proportional to the number of loaves of bread. Paul uses 11 1/4 cups of bananas to make 5 loaves of bread. Which equation represents the relationship between c, the number of cups of bananas, and b, the number of loaves of bread?
A) C=4/9 b
B) C=2b
C) C= 2 1/4 b
D) C=5b Answered by Penny Nom. 





Selecting a card 
20140216 

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





The growth of a tree 
20140216 

From Emily: If a tree is 10 ft tall after 2 years and 25 ft tall after 5 yrs , find the rate of change of growth
Of the tree if y is the height in ft and x is the number of years. Answered by Penny Nom. 





What is the exponential form of 1/square root of 6v? 
20140216 

From Prince: What is the exponential form of 1/square root of 6v Answered by Penny Nom. 





Simultaneous fractional equations 
20140215 

From benjamin: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic
here is the question:
using substitution method, solve the simultaneous equation.
(x+1)/(y+2)=0.5
(x2)/(y1)=1/3 Answered by Penny Nom. 





The grade of a road as a percent 
20140214 

From Emily: What is the grade of the road shown below expressed as a percent rounded to one decimal place?
Rise is 40feet
Run is 380 feet Answered by Penny Nom. 





Rolls of window film 
20140214 

From Travis: This question is probably close to the same question as "roll of paper"
We have Rolls of Window Film that we are trying to figure out an equation for a spreadsheet that we can use to "inventory" our window film.
We use a caliper tool to measure the thickness of the roll in millimeters.
the core thickness = 1.90mm
Full Roll thickness(including core) = 9.08mm to 9.12mm
Film thickness = 0.06
Full Roll of Film is supposed to average 1200" of film
What equation could we use to get the approximate inches left remaining on the roll if we measured the roll including the core with the Caliper tool in Millimeters? Answered by Harley Weston. 





Some mixed nuts 
20140212 

From Andrew: How many kg of mixed nuts that contain 30% peanuts must Paul add to 6kg of mixed nuts that contain 38% peanuts to make a mixture that contains 33% peanuts? Answered by Penny Nom. 





A word problem 
20140211 

From cyril: In a rectangle,the length is 1.5 times the breadth.if the length is shortened by 3 m and the breadth is lengthened by 3 m, the rectangle will be a square. Calculate the dimensions of the rectangle. Answered by Penny Nom. 





Water in a conical funnel 
20140211 

From Marcus: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Penny Nom. 





A ball in a box 
20140209 

From kenneth: I have 2 questions.What is the radius of the largest ball that will fit into a box that has the inside dimensions of 6feet by 8 feet by 10feet. and the second question is how many cubic feet of concrete will you need to complete a patio that is 20 feet long by 15 feet wide by 5 inches in hight. Answered by Penny Nom. 





8 golfers, 11 rounds 
20140209 

From Clare: I am leading a group of 8 golfers who will be playing 11 rounds each
at the end of next month and have been tasked with coming up with
a schedule that allows, as close as possible, that has everyone playing
an equal number of rounds with each other. Do you have any suggestions? Answered by Penny Nom. 





The volume of a cone 
20140208 

From hibba: why is the volume of right circular cone divided by 3? Answered by Penny Nom. 





Can a cylinder be considered a circular prism? 
20140208 

From Davina: Can a cylinder be considered a circular prism? Answered by Penny Nom. 





Pizza for 24 
20140207 

From Delaney: if 8 people eat 2/3 of a honey chicken pizza how many pizzas are need to feed 24?
How is this problem solved. Thank you! Answered by Penny Nom. 





A number with all the digits different 
20140207 

From Jon: I'm not a mathematician but just curious. Is there a name for a number of up to ten digits where each digit is different,
i.e the equivalent of an isogram in linguistics? My online banking gives me a random 8digit number each time I log on
and it is rare to get one of the type I refer to. There must be calculable odds, but I'm only allowed one question!
Thanks in advance
Jon Answered by Harley Weston. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





Walking up and down a hill 
20140206 

From flo: michelle walks 4 km to the top of a hill at 3 km/h then immediately walks back down at an average speed of 5 km/h what is her average speed for the 8km walk Answered by Penny Nom. 





A triangle has angels in the extended ratio of 2:5:8 
20140206 

From Rubina: a triangle has angels in the extended ratio of 2:5:8. find the measure of
all three angles? Answered by Penny Nom. 





The volume of a frustum 
20140202 

From mike: volume of frustum R23", r 18", h 16" Answered by Penny Nom. 





Conics 
20140201 

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





The dimensions of a room 
20140201 

From jenna: The length of a rectangular room is 2m more than the width. Find the dimensions if the perimeter of the room is 34m Answered by Penny Nom. 





Related rates 
20140130 

From Veronica: A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of 2.00 inches/second. Find the rate at which the water is being drained. Answered by Penny Nom. 





A man and a kite 
20140129 

From Veronica: A man flies a kite at a height of 120 meters. The wind carries the kite horizontally away from him at a rate of 8 meters/second. How fast is the distance between the man and the kite changing when the kite is 130 meters away from him? Answered by Penny Nom. 





A bizarre percentage problem 
20140129 

From matthew: by what percent was the child's sodium level beneath the normal range?
the child's sodium level was 107 where the normal is 136145 Answered by Harley Weston. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 Answered by Penny Nom. 





An inequality 
20140125 

From LANELL: this is a problem to solve: 1/3 + 2/7 >=x/21  part of the answer is (oo)
not exactly that similarit is on a calculator as a symbol sure you know what it is I am talking about the x will be a number Answered by Penny Nom. 





Problem solving 
20140124 

From ngozi: There are 4 children in the Owens family. Jamie 1 1/2 times as all as Kelly and he is 6 inches taller than Olivia. Sammy is 56 inches tall, which is 2 inches taller than Olivia. Find Jamie's height Answered by Penny Nom. 





Kate, Tess and Nina 
20140123 

From Sam: Kate is 16 yrs. younger then Tess. Nina is 8 yrs.older then Kate. The sum of their ages is 189. How old is each? Answered by Penny Nom. 





The fourth side of a quadrilateral 
20140123 

From joanna: left vertical measurement 2560mm
right vertical measurement 1850mm
base horizontal measurement 1750mm
question  what will the 4th measurement be please.
using a scale drawing I make it approx 1900mm but require an accurate measurement
regards
Joanna Answered by Penny Nom. 





A word problem involving fractions 
20140123 

From Pamela: John put 1/4 of his flowers in a vase
He gave 1/2 to of the flower to his wife
He gave 1/5 of the flowers to his daughter
He has 8 flowers left
How many flowers did John start with Answered by Penny Nom. 





Reducing the area of a parking lot 
20140119 

From Robin: The school is reducing the area of its 20yd by 50yd parking lot by removing a strip at one end of the parking lot and another strip of the same width from one side. The new area of the parking lot is 504 said yes. Find the width of the removed strip 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. 





Mark's books 
20140118 

From Jason: Mark has 312 books in his bookcases he has 11 times as many fiction books as nonfiction books how many fiction books does mark have?
26 212 286 301 Answered by Penny Nom. 





A rectangular shaped property 
20140117 

From Donna: If I I have property that is rectangle shaped. I I know the ends are 100 feet how many feet would the sides be to make 5.4 acres Answered by Penny Nom. 





An inequality 
20140117 

From Rosie: 4x/x2<3
four x divided by x2 is less than or equal to 3 Answered by Penny Nom. 





$9.50 in coins 
20140115 

From dana: you have $9.50 in coins. it has twice as many nickels as quarters and three times as many dimes as nickels. how many of each coin do you have? Answered by Penny Nom. 





Five cubes 
20140115 

From Bob: Rick has five cubes. When he arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 2 cm. The largest cube is as high as a tower built from the two smallest cubes. How high is a tower built from all five cubes? Answered by Penny Nom. 





Watching a bouncing ball through a window 
20140115 

From Bob: A ball falls from the roof, at a height of 10m. After each impact on the ground it bounces back up to 4/5 of its previous height. How many times will the ball appear in front of a rectangular window whose bottom edge is at a height of 5m, and whose top edge at a height of 6m? 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 7% solution 
20140114 

From imran: what amount of H2SO4 should be added to make 5mL of 0.7% H2SO4 solution Answered by Penny Nom. 





The train fares are proportional to the square root of distance traveled 
20140111 

From manish: train fares are proportional to the sq .root of distance traveled. the train fare is Rs. 24.4 for a distance of 140 kms. by how much % does the total fare increase if the same distance is covered by breaking the journey after every 35 kms. Answered by Penny Nom. 





On what day of the week was July 4, 1904? 
20140111 

From Madi: Hi guys,
I have a question. July 4, 1903, was a Tuesday. On what day of the
week was July 4, 1904? If you could give me an equation that would
work for any question like this, that would be GREAT!
Your fellow math scholar (in training),
Madi Answered by Penny Nom. 





A rectangle inscribed in a circle 
20140110 

From Marian: A 16 cm by 12 cm rectangle is inscribed in a circle. Find the radius of the circle. Answered by Penny Nom. 





4x^37x^22x 
20140110 

From Alvi: 4x^37x^22x Answered by Penny Nom. 





Radio direction finders 
20140109 

From Nathan: Radio direction finders set up two points A and B, which are 2.5 miles
apart on an eastwest line. From A, it is found that the bearing of a
signal from a radio transmitter is N36.33 degress E, while from B the
bearing of the same signal is N53.67 degrees W. Find the distance of
the transmitter from B. Answered by Penny Nom. 





A boxandwhisker plot with one whisker 
20140109 

From Susan:
Question from Susan, a teacher:
I read your answer to the question about could a box & whisker have NO whiskers.
It made sense to me. However I am preparing for my advanced class and I have a sample graph comparing box plots of data.
Several of the box have only 1 whisker. There is no explanation for this. Can you help me out. I cannot think of a data set that would produce this. Thanks! Answered by Penny Nom. 





Two tuna boats 
20140109 

From amanda: Two tuna boats start from the same port at the same time, but they head in opposite directions. The faster boat travels 10 knots per hour faster than the slower boat. At the end of 8 hours, they were 272 nautical miles had each boat traveled by the end of the 8 hour period? Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

From Natasha: Would one flip the inequality symbol in this equation: (explain why)
(9a)/(9) > 81
And please explain in what circumstances one would flip the inequality sign
THANKS! Answered by Penny Nom. 





A tire rolls 100 feet in a straight line 
20140107 

From Alanna: A tire has a diameter of 26 inches. If it goes 100 feet in a straight line, how many complete revolutions did it make? Answered by Penny Nom. 





A scalene triangle 
20140107 

From cherry: Hi
I have been given a scalene triangle of sides 
8m, 6m, and 10m ..
Please help me to find out the area and help me to find out the height .. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20140106 

From Anonymous: An equilateral triangle with sides 6 inches is inscribed in a circle. What is the diameter of the circle? Answered by Penny Nom. 





Units digit 
20140103 

From gracie: 9^23 units digit Answered by Penny Nom. 





4 children 
20131231 

From hope: 4 children; Peter is 7 years old & is 4 years younger than Dave. Dave is 9 years older than Paul. Paul is 11 years younger than Frances. Please list the children in order from oldest to youngest?!
thank you and anxiously await your answer, Hope Answered by Penny Nom. 





The slope of the line y=2x+5 
20131229 

From victoria: what is the slope of the line with the equation y=2x+5 Answered by Penny Nom. 





Distance from a point to a line 
20131228 

From Sue: I need to find the distances from the west line on 1st Take Point and 2nd
Take Point.
Thanks,
Sue Answered by Penny Nom. 





ug/l and ppb 
20131227 

From Wally: convert 40.5 ug/l to ppb? Answered by Penny Nom. 





A linear equation 
20131226 

From khushboo: A farmer sowed wheat and paddy in two fields of total area 5000 sq.m. Write a linear equation and draw a graph to represent the same? Answered by Penny Nom. 





The area of a quadrilateral 
20131221 

From khushboo: Find the area of quadrilateral pqrs in which
angle QPS=90°,PQ=12cm, PS=9cm, QR=8cm and SR=17cm.
(Hint: PQRS has two parts) Answered by Penny Nom. 





Analytic Geometry 
20131218 

From fRitz: if (x,4) is equidistant from (5,2) and (3,4), find x. Answered by Penny Nom. 





Schedule for a 4 team basketball league 
20131208 

From Sommer: I need a schedule for my kids basketball league. There are 4 teams.
We will play every Saturday for 4 weeks with 4 games per Saturday.
Week 5 will be the playoffs where 1st will play 4th and 2nd will play 3rd.
Week 6 will be winners of week 5. Please help!! Answered by Victoria West. 





A circle insubscribed in an isosceles trapezoid 
20131208 

From Bob: A circle is insubscribed in an isosceles trapezoid, with
parallel lengths of 8cm and 18cm.
What is the lengths of sloping edges and why? Answered by Robert Dawson. 





A word problem 
20131208 

From Malissa: I am attempting to help my son with his math word problem, please help thank you .
Kylie and Ethan kept scrapbooks of their grandfather's stories from world war II. Kylie has 6 more than half the number of pages Ethan has. If Kylie has 21 pages in her scrapbook, how many pages are in Ethan's scrapbook? Answered by Penny Nom. 





conical lamp stand/staved wood 
20131207 

From Henry: need to make lamp stand that is wooden staved; need it to be 25 inches at bottom and 10 inches at top; need to know angles for staves to be cut; the lamp stand will be rounded on a lathe and will be 40 inches tall John Lucas built one and it is pictured on his web page. thank you for any help/direction; I checked out the answered for cone shaped objects on your page but didn't find what I could use. thanks again. Henrywoodturner, parent teacher student . . . . . Answered by Harley Weston. 





How do I graph y=2x1? 
20131207 

From cindy: How do I graph y=2x1? Answered by Penny Nom. 





f(x)= a+b*lnx 
20131204 

From Kevin: How do I find the curve, algebraically on paper, for f(x)= a+b*lnx with data points
(6,1303) (9,1639). I can do it with LnReg on a calculator but I want to know how
to get the same results or close to the same results by working it out on paper.
When I run it through the LnReg on the calculator I get, f(x)=181.792+828.678 Ln x.
How did it achieve this solution? Answered by Penny Nom. 





Problem solving with fractions 
20131203 

From Jennie: Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim.
If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul? Answered by Penny Nom. 





Exponential form 
20131201 

From Alina: My question says to express each number in exponent form in as many different ways as I can; 16, 81 and 64. How do I do this? Answered by Penny Nom. 





Factor 
20131201 

From Rosa: How do you factor 9x^2  12y^2? Answered by Penny Nom. 





What is the slope of this line? 
20131201 

From Charlene: What is the slope of this line? Answered by Penny Nom. 





0.35 as a fraction 
20131128 

From Laura: How do you write 0.35 as a fraction or mixed number?
Laura Answered by Penny Nom. 





People on a bus 
20131128 

From jeric: 3/10 of the passenger in a bus were men, 2/7 of the remainder were women and the rest were children, if there were 50 passengers in the bus, how many more children than women were there? Answered by Penny Nom. 





The area of a parallelogram 
20131128 

From shivam: a parallelogram has sides 34 cm and 20 cm .one of its diagonal is 42 cm. calculate its area Answered by Harley Weston. 





A sale price for a TV 
20131128 

From tom: a TV can be purchased for $278 normally is $328. what is the percent of the present cost of this TV will you be saving? Answered by Penny Nom. 





Base 5 arithmetic 
20131127 

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





2 concentric circles 
20131127 

From Dimaris: The radius of the outer circle of 2 concentric circles is x. An
equilateral triangle inscribed in the outer circle also circumscribes the
inner circle. What is the radius of the inner circle in terms of x? Answered by Penny Nom. 





Problem solving 
20131126 

From Moira: Amy has £5 more than Ben. Ben has twice as much as Chris. In total they have £20 how much do they each have Answered by Penny Nom. 





Three roommates share the rent 
20131123 

From Cortlin: Because of different bedroom sizes, three roommates decide to split the rent this way:
Roommate A pays 75% as much as B does, and C pays 40% as much as B does.
What fractional part and percent of the rent does each roommate pay? Answered by Penny Nom. 





A schedule for 32 golfers 
20131122 

From Scott: I would like a schedule for 32 guys playing in 8 foursomes for 13 week. I would like it so that no one plays in the same foursome more than once or twice. Is this possible to do??? Can you let me know at bogeysm@yahoo.com if you can do it and if you will do it. Answered by Victoria West. 





Admiring handblown glass ornaments 
20131121 

From Ruby: We are admiring hand blown glass ornaments 5% are
unmarketable due to defects what is the probability the 3rd
ornament is the first defective one Answered by Penny Nom. 





Why can't we add or subtract speed? 
20131121 

From kashish: why we cannot add or subtract "speed" / directly in any given distance , speed , time questions? Answered by Chris Fisher. 





Scheduling 10 people for 5 rounds 
20131120 

From Keith: Using golf as an example, I would like to schedule 10 people for 5 rounds with 2 groups of 4 and 1 twosome each round. I would like to minimze the number of times any one player plays with another. Can you provide an optimal schedule? Thank you for your help. Answered by Victoria West. 





The area of an irregular octagon 
20131118 

From zafar: if i have a rectangular octagon then how i can find its area
1. The length of rectangle is 42 and the width is 21 and and the base length is 4212 =30 i mean the
length of base =30 Answered by Penny Nom. 





Evaluate log3 14 
20131117 

From Tash: Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms.
log3 14 Answered by Penny Nom. 





Solve 0=2(x5)^2+4 
20131117 

From Leila: How do you find the solution to 0=2(x5)^2+4 Answered by Penny Nom. 





Inflection Point 
20131115 

From Z.: I was wondering if the function F(x)= x/ln(x) had an inflection point?
If yes, why it's not visible on the graph of the function?
Thanks. Answered by Penny Nom. 





n log n = 36 * 10 ^ 12 
20131112 

From shihab: How to find value of n in this equation :
n log n = 36 * 10 ^ 12 Answered by Penny Nom. 





One train overtaking another 
20131111 

From kiran: two trains of equal length are running in parallel tracks in the same direction with the speed of 60km/hr and 90km/hr respectively the latter completely crosses the former in 30 seconds the length of each train is in mtr Answered by Penny Nom. 





Matrices 
20131110 

From Ricky: Why must we have brackets around matrices. Why don't we just neatly write an array of entries crosswise and up and down to indicate a particular matrix? Answered by Chris Fisher. 





A lever 
20131109 

From Durgesh: A farmer uses a 2 m long lever to lift large rocks from the ground of his field . He places a fulcrum 20cm from the rock end of the lever and then stands on the other end, levering out the rock. If the farmer weighs 100 kg , what is the heaviest mass of the ro ck that he can lift using this method? (how to solve) Answered by Penny Nom. 





The popcorn box problem 
20131107 

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





Substitution type simultaneous equations 
20131103 

From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^23x+4 and 3x2y=1
I have rearranged 3x2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you. Answered by Penny Nom. 





Water flowing out of a tank 
20131103 

From Carolyn: The flow of water out of a hole in a tank is known to be proportional to the square root of the height of water above the hole.
That is,
dV/dt (proportional to) sq root (h)
The tank has a constant crosssectional area A, show that the height of water in the tank is given by
h = ((kt+C)/2)^2
If the tank is 9 metres high, and it takes 5 hours for it to drain from full to half full,
how much longer will we have to wait until it is completely empty? Answered by Penny Nom. 





The depth of a lot 
20131102 

From Gini: what is the depth of a lot with 45 feet frontage containing 1080 sq yards 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. 





An extension using concrete blocks 
20131030 

From david: hi how many concrete blocks would i need for an extension 50 ft long ,20 ft wide and 12ft height Answered by Penny Nom. 





A sloped concrete wall 
20131030 

From Brad: We are planning on pouring concrete in a wall form that is sloped. One end is 73 inches tall, and it tapers to 24 inches tall over a distance of 348 inches. It is flat on bottom and sides and is 12 inches thick. Thanks. Answered by Penny Nom. 





Is5/11 a positive rational number? 
20131030 

From tazneem: Is5/11 a positive rational number Answered by Penny Nom. 





A plane 
20131027 

From Thomas: Why is this 3d plane flat?
if m ≠ n
arcsin(sin(m*arctan(x/y))), arcsin(cos(n*arctan(x/y))),
Piarcsin(sin(m*arctan(x/y)))arcsin(cos(n*arctan(x/y)))
This is using radians.
These are angles of a triangle, when m and n are the same it is a right triangle. All three inputs are not equal to each other. The last input is pi minus the first two inputs, which makes a complete triangle.
I was kind of hoping to find more lissajous curves. It doesn't make sense to me that this is a flat plane, a diagonal one at that.
I'm not a student or anything. I'm just wasting time. Answered by Chris Fisher. 





The perimeter of a rectangle 
20131024 

From sana: if the length is given 70 m and the breadth is given as 40 m find the perimeter of the rectangle Answered by Penny Nom. 





A stem and leaf plot 
20131024 

From mary: Hi
I'm trying to answer my child's question on stem and leaf plot. For grade 4, the question is where do you put 57 in this list
6 0
5 4 8 8 9 4 6 4 Answered by Penny Nom. 





Tim is standing in a hole 
20131023 

From Marvel: Tim is standing in a hole that is 4 feet deep.
Ben asks him how much deeper is he going to dig the hole.
Tim replies he will dig to the level that is 4 feet 2 inches deeper
and that then the top of his head will be the same distance below
ground level that it is now above. How tall is Tim? Answered by Penny Nom. 





Extraneous solutions 
20131022 

From tom: i need an equation where x=2 is the correct answer and x=3 is an extraneous solution. can you provide me with such an equation?? Answered by Harley Weston. 





Together, Tom and Max have 72 football cards 
20131021 

From Maureen: Together, Tom and Max have 72 football cards. Tom has 2 more than 4 times as many cards as Max has. How many football cards does Tom Have? Answered by Penny Nom. 





Peter bought pizza and drinks 
20131019 

From sd: Peter spent $30 on pizza and 3/4 of the remainder on drinks. He has 2/9 of the original amount left. How much had he at first? Answered by Penny Nom. 





A string wrapped around three circles 
20131019 

From Jim: A recent puzzle ' find the length of a string around 3 touching
1 meter diameter circles ' gave this answer : the string
touches 120° (or pi/3 meters) of each circle. Then
3(1+pi/3) = 3+pi meters is the required length. I do not see how
it was determined that the string touches 120° or pi/3 meters?
Please explain . Thankyou , Jim Answered by Penny Nom. 





What the dog weighs 
20131017 

From linda: Sam has a dog and rabbit together they weigh 104 lbs the dog weighs 12 times more then the rabbit what is the dogs weight Answered by Penny Nom. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





Four tangent circles 
20131009 

From Nilesh: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know. Answered by Robert Dawson. 





Maximize the volume of a cone 
20131009 

From Conlan: Hi I am dong calculus at school and I'm stumped by this question:
A cone has a slant length of 30cm. Calculate the height, h, of the cone
if the volume is to be a maximum.
If anyone can help me it would be greatly appreciated.
thanks. Answered by Penny Nom. 





A line through (5, 1) 
20131008 

From allison: find an equation in standard form for line passing through point (5,1) and perpendicular to line x=4 Answered by Penny Nom. 





Two bikers race on a circular track 
20131003 

From bryan: two bikers race on a circular track. biker a can circle the track in 8 minutes, and biker b can circle the track in 6 minutes. From the start of the race, how many minutes will it be before biker b overtakes biker a. Answered by Chris Fisher. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places Answered by Penny Nom. 





Problem solving 
20131002 

From naomi: My son having trouble a math problem please help with this question a bag of cough drops contains 36 drops. the fraction of each flavor is shown in the table strawberry 5/12 honey 1/12 cherry 1/6 mint1/9 and lemon 1/4 which flavor is the greast in the bag Answered by Penny Nom. 





Group the addends so that you can add mentally 
20131001 

From monica: the questions in the homework says change the order or group the addends so that you can add mentally ,find the sum and tell which property you used
120+37+280 and 25+25+30 Answered by Penny Nom. 





Two teams of 4 playing 4 rounds of golf 
20130929 

From Tom: We would like to play a ryder cup format with two teams of 4 playing 4 rounds of golf. Three of the rounds would be pairs playing each other and one round would be singles. How can we set up the foursomes so we balance the number of times we play with every other golfer. Answered by Victoria West. 





Cubic centimeters, milliliters and grams 
20130926 

From Laura: How do I find the volume of a cube with dimensions of .78 cm, .3 cm and .22 cm? Then find the volume in ML and the mass if filled with water? Answered by Penny Nom. 





12 golfers for 7 rounds 
20130925 

From Dennis: I have 12 golfers playing a round of golf for seven days. How can I setup teams so that everyone plays with everyone at least once in those seven days. Thanks! Answered by Victoria West. 





A schedule for 2, 7 team divisions 
20130924 

From Sampson: I'm looking to set up a weekly schedule within a 22 week segment of 2 7 team divisions where every team plays every other team in their divison 3 times and have 4 cross over games with 4 of the other 7 teams in the other division. I've yet to figure this out.
Thanks for your time. Answered by Victoria West. 





6 golfers in threesomes over 7 rounds 
20130924 

From David: I have 6 golfers, (2 threesomes) who will be playing 7 rounds of golf. What is the best way to pair the 6 players so they play with as many different players over the 7 rounds? Answered by Victoria West. 





A pool, a school, a park and home 
20130924 

From Selena: The distance from the park to the pool is the same distance as the distance from your house to school. The school is between the pool and your house. Prove that the distance from the park to the school is the same distance from the pool to your house. Answered by Robert Dawson. 





25 people are attending a 5 day meeting. 
20130920 

From Lisa: 25 people are attending a 5 day meeting. There are 5 tables, with each table seating 5 (or 6). I want each person to sit at a different table every day with completely different people.
Is this possible. Can do I figure this out?
I have each of the people a letter designation from A to Y. Each table
have a number from 1 to 5.
Thank you! Answered by Victoria West. 





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. 





A rectangular hyperbola 
20130919 

From Soumya: Is the graph of an inverse variation a RECTANGULAR HYPERBOLA? If it is, then how can be the equation of a rectangular hyperbola be xy=constant , whereas in the books it is written that the graph of a rectangular hyperbola is x^2y^2=a^2? Answered by Chris Fisher. 





The number of cords on a pile of wood 
20130918 

From Gary: a cord of wood is 4 feet by 4 feet by 8 feet, how much wood is a row that is 16 in by 5 foot by 32 feet? Answered by Penny Nom. 





If the earth was made of a ball of string 
20130918 

From Tammy: My 9 year old son asked me a question and I have no idea how to work it out! Please can you help?
If the earth was made of a ball of string and you unravelled the string how long would it be? Assuming the string is 5mm thick. Answered by Penny Nom. 





The volume of an attic 
20130918 

From David: I have small equipment hut that has a small attic space that I want
to blow insulation into it.
The attic size is shaped like a triangle that is about
8 feet by 10 feet by 7 inches at the highest point.
I need to estimate the volume in square feet or cubic feet to
know how many bags of insulation to blow into the space.
Thanks Answered by Penny Nom. 





A concrete walk around a pool 
20130918 

From poornima: circular Swimming pool is surrounded by a concrete walk 4 feet wide, if the area of the walk is 11/25 of the area of the pool, then the radius of the pool in feet is Answered by Penny Nom. 





Covering a styrofoam ball with fabric 
20130911 

From Alice: I am trying to create a pattern in order to cover a styrofoam ball with fabric. The pattern needs to be done in such a way as to have only a center seam, rather than several vertical lines as in slicing a melon. Answered by Chris Fisher. 





Intersection points and diagonals 
20130911 

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





Miles per minute to miles per hour 
20130908 

From Adam: Convert 250 miles per min to miles per hour Answered by Penny Nom. 





A contest with 31 people 
20130906 

From Kevin: There is a contest with 31 people and only one winner each week.
We play for 17 weeks.
What are the odds of winning at least one week?
The chances of winning each week are independent from previous weeks. Answered by Robert Dawson. 





A garden path 
20130906 

From mary: garden path has 8 white slabs, four of the slabs are one third grey, what area of the path is grey Answered by Penny Nom. 





A word problem 
20130905 

From Thomas: I'm trying to help my 9th grade child with their homework. The problem is the
Length of a rectangle is twice as long as it is wide. The perimeter is 68m. Find
It's length and width Answered by Penny Nom. 





2^x . 5^3 = x^4 
20130905 

From Zuhdina: Hi, I got a question, 2^x . 5^3 = x^4
I want to know the value of x without using calculator, I've already done some questions in logarithm and I always stuck in the same model equationI think if someone shows me the way, I can do the other 'stuck equations' Answered by Penny Nom. 





6 golfers in threesomes 
20130904 

From Gregg: We have 6 golfers playing in threesomes for three rounds of golf. I would like each golfer to play equally with the other 5. How can this be done. Answered by Victoria West. 





A Holeinone on all four par 3's 
20130904 

From Robert: There are four (4) par 3's at a specific 18 hole course.
One member has the honor of making a Holeinone on all four par 3's.
It has taken him 8 years to do it!
How does one go about computing the odds of this TREMENDOUS accomplishment?
Respectfully,
Robert laffal Answered by Victoria West. 





7 golfers, a threesome and a foursome 
20130904 

From Scott: I'm leading a golf trip with 7 guys, and we're playing 5 rounds of golf together with a threesome and a foursome at each course..
I want to set up a schedule where each person plays at least two rounds with each of the other 6 guys.
Is that possible? I can't seem to find the right combinations.
Thanks for your help! Answered by Victoria West. 





14 golfers in two person teams 
20130904 

From Stewart: How to rotate 14 golfers in two person teams without duplication until all have been paired at least once. Play is once per week. Answered by Victoria West. 





A two digit number 
20130904 

From JEFFERSON: The sum of the digits is 6. When the digits are interchange, the new number represented is 3 time the 10 digit of the original number. Find the original number? Answered by Penny Nom. 





How many nickles do you have? 
20130904 

From Monica: You have 15 more dimes than nickels. If you have $2.55, how many nickels do you have? Answered by Penny Nom. 





Ordering crushed stone 
20130903 

From Prakash: Dear Sirs,
I am working in a Soft Landscaping contracting company. If I need to purchase crushed stone with the size 5070mm for $53,429 m^2$ area, how many 20feet containers should I need to order to my suppliers? The 20foot container has internal dimensions 5,897 mm by 2,348 mm by 2,285 mm and the $53,429 m^2$ area is to be covered by 10 cm of stone. Answered by Harley Weston. 





A schedule for 18 golfers 
20130829 

From Brian: After searching the data base which helped me solve at least 3 other issues I have one more un answered question. I have 18 golfers split into 6 threesomes for 4 days of golf. What is my best option for a schedule mixing them all up as much as possible over the course of the 4 days Answered by Victoria West. 





An algebraic equation 
20130828 

From walter: i'm a parent helping my daughter can you do a step by step on this equation been out of school for years thanks (4w28)+(11w+13)=180 thanks Answered by Penny Nom. 





More than half of the people said... 
20130826 

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





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. 





More on the scheduling of 16 golfers in 4 rounds 
20130826 

From Peter: I see your formula for 16 players 4 rounds.
Is it possible to get the players into different groups each day.
E.G Player 1 in group 1 the first day,
Group 2 the second day,
Group 3 the third day,
Group 4 the fourth day.
Then so on through the players. Answered by Victoria West. 





Tesseract 
20130822 

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





Constructing a triangle 
20130822 

From Nazrul: The base, the difference of the angles adjoining the base and the sum of the other
two sides are given. How can I draw the triangle?
Please help me. Answered by Chris Fisher. 





Euclid's Parallel Postulate 
20130820 

From Justin: Hello there,
I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable?
Thank you so much for any help you can provide! Answered by Robert Dawson. 





Similar rectangles 
20130817 

From Mattie: The dimensions of a rectangularshaped picture frame are 14 inches long and four inches wide. Which dimensions below represent another frame that i geometrically similar>
a. l=49 in. and w=14in.
b. l=7in and w=3in
c. l=21in and w=8in
d. l=24in and w=14in
thanks Answered by Penny Nom. 





Equal ordinate and abscissa 
20130815 

From sonit: the slope of tangent to the curve y=(4x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Answered by Penny Nom. 





Two perpendicular lines 
20130815 

From Hanna: The problem says, "Write the equation in standard form for the line that is perpendicular to the graph of y=5x+1 with a yintercept of 4." I have no clue how to do this. Please help me! Answered by Penny Nom. 





Golf for 11 
20130814 

From Don: 2 foursomes and 1 threesome for 6 rounds of golf Answered by Victoria West and Harley Weston. 





The volume of a pond 
20130814 

From Kelly: I have a pond that measures 335 feet wide, 385 feet long and 18 feet deep with a 4:1 slope on all four side. How do I figure out how many gallons of water this pond will hold? Answered by Harley Weston. 





Using trig to find the height of a hill 
20130814 

From Anna: From the top of a hill, the angles of depression of two successive milestones on a level road, which leads straight away from the hill, are 5degrees and 15degrees respectively. Fine the height of the hill.
Suggestion: BE is drawn perpendicular to AD. Find BE, then BD, finally CD.
Thanks :) Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





A mixture problem 
20130811 

From MJ: How many liters of pure acetic acid must be mixed with 3 liters of a 30% acetic acid to obtain a mixture of 65%? Answered by Penny Nom. 





If I know only the tax amount, how do I figure out total cost? 
20130811 

From Patric: If I know only the tax amount, how do I figure out total cost? Answered by Penny Nom. 





Differentiate x^x  2^sinx 
20130809 

From tarun: derivative of x^x  2^sinx Answered by Penny Nom. 





Four equations 
20130808 

From may: HI how to solve this 4 equations?
A+C = 0
4A+B8C+D=1
3A+16C8D=29
12A+3B+16D=5 Answered by Robert Dawson. 





Practical uses of trigonometry 
20130806 

From tharindu: use of trigonometry Answered by Penny Nom. 





Slicing through a cone to form an ellipse 
20130806 

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





A golf tournament for 12 people 
20130801 

From Brad: I've looked all over the web for a solution to this (including searching the archives here) to no avail.
We're doing a golf tournament with twelve people. Each person has a "handicap" that demonstrates their skill level. We have these numbers for each of the 12 players. We are trying to figure out how to schedule two rounds of golf with the most balance possible.
 We are playing two "real" rounds of golf (18 holes). There are four people per group.
 We want to split each round into two 9 hole games, which gives us a total of 4 games
 Halfway through (after 9 holes), you switch partners within the foursome that you're playing in.
 We want everyone to play with 4 unique different teammates
So say you start the first 18 hole round as a group of Players 1, 2, 3, and 4. Players 1 and 2 are a team, and players 3 and 4 are a team. After 9 holes, Player 1 would either be paired up with Player 3 or 4, and the other two players would pair up as well. Then the next day we will mix up the foursomes and do the same thing.
In terms of just pure scheduling this is simple. But I'm trying to figure out how to best balance the handicaps (simple average of each team's two handicaps works here). Assuming I'll need some sort of program or spreadsheet.
Any help or even a push in the right direction would be a tremendous help. Thanks in advance to anyone who wants to give this a shot. Answered by Victoria West. 





Golf for 16 
20130731 

From Graylin: I am going on a golf trip and we have 16 players and need to know a formula that will allow us to all play together at some point in the 4 rounds we are playing. If not possible please provide best case.
Thanks. Answered by Victoria West. 





16 golfers 
20130731 

From Pat: 16 golfers...3 nine hole rounds a day...for 4 days.
what are the best pairings for the fewest repeats of partners? Answered by Victoria West. 





Dilution of concentrated acid 
20130731 

From Adom: I have 500mls of 90% conc. of an acid. Now I need to prepare 20% concentration from this (say 100mls of this). How much of the stock solution do I take and how much water to add? Thanks! Answered by Penny Nom. 





Two parallel chords of a circle 
20130730 

From Don: two parallel chords of a circle AB and CD on the same side from the center measure 6cm and 11 cm respectively. The distance between the 2 chords is 3 cm. Find the radius Answered by Penny Nom. 





A mixture problem 
20130729 

From Lucy: Hi,
For the following question:
Ten pounds of mixed nuts contain 50 percent peanuts. How many pounds of peanuts must be added so that the final mixture has 60 percent peanuts?(A) 2.5 (B) 5 (C) 6 (D) 10 (E) 12.5,
my math book gives my the following explanation: Try choice (C): 6 pounds of peanuts. The original 10pound mixture contained 50 percent peanuts, or 5 pounds. Now you have 11 pounds of peanuts in a 16pound mixture, more than 60 percent. This result automatically eliminates choices (D) and (E) as well.Why would this result automatically rule out D and E? How can you tell?
Thank you for taking the time to answer my question. Answered by Robert Dawson and Penny Nom. 





A word problem 
20130729 

From Gontsejalo: Your firm held a dance competition. 900 people attended the dance competion.The cost of admission was 20rand per person and 30,50rand per couple.Twice as mant 20rand tickets as 30,50rand tickets were sold.find the amount of money obtained from the tickets sales Answered by Penny Nom. 





The area of a semicircle 
20130728 

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





A triangle construction 
20130727 

From Nazrul: Two angles and the difference of the lengths of their opposite sides of a
triangle are given. How can I draw the triangle.
Please help me. Answered by Chris Fisher. 





Ann has a bag of marbles. 
20130725 

From Carmen: Ann has a bag of marbles. she gave one half to her friend Tina and then one third to her friend Tom. Now left with 15. How many did she had originally? Answered by Robert Dawson and Penny Nom. 





GST and PST 
20130722 

From Bev: Total sales revenues are 116391.38 this amount includes 5% GST and 80% of this amount includes a 7% provincial tax. The other 20% is PST exempt. GST is included in all. How do I figure the PST I owe? Answered by Penny Nom. 





What is the value of 2((i)^(1/2))? 
20130722 

From Delilah: What is the value of 2((i)^(1/2)) ?
i.e. absolute value of 2 multiplied by square root of i. Answered by Penny Nom. 





What is the smallest number? (i.e. the closest number to zero) 
20130722 

From Charlie: What is the smallest number? (i.e. the closest number to zero) Answered by Harley Weston. 





18/y=30/25 what number does y represent 
20130720 

From celeste: 18/y=30/25 what number does y represent Answered by Penny Nom. 





Solve x = ln(x) 
20130719 

From Udayan: Sir/Madam,
How to find the solutions of the equation,
x = ln(x) Answered by Penny Nom. 





10 guys playing 89 hole rounds 
20130719 

From Jason: I have 10 guys playing 8 9 hole matchplay rounds. I need to have everybody play the other 9 men, but need to limit them to only a 9 hole match between them. If we need to go 334 or 244 for a better solution, that may be possible. Answered by Victoria West. 





1,990 cubic yards in gallons 
20130716 

From Tayler: You have 1,990 cubic yards of concrete to pour.
If the average swimming pool holds 25,000 gallons, how many pools can
Be poured with the 1,990 cubic yards of concrete.
1 cubic yard= 27 cubic feet Answered by Penny Nom. 





A quadratic with no real roots 
20130715 

From Pranav: If ax^2+bx5=0 has no real roots. Then d sign of 1) a+b5
2) (25a5b5)(4a+2b5) will be what ?? Answered by Penny Nom. 





150 litres has been drawn from a tank 
20130714 

From henry: When 150 litres has been drawn from a tank, it is 3/8 full, how many litres will the tank hold? Answered by Penny Nom. 





Dirt to fill a pool 
20130713 

From Neil: I had a 24 foot diameter pool. The perimeter of it was at ground
level. The pool sloped 1 foot deeper to the middle. In other
words "a 1 ft. dish. How many cubic yards of dirt do I need to
fill this hole? Answered by Penny Nom. 





Simultaneous equations 
20130710 

From Warren: solve this simultaneous equation: xy=4
2x+3y=14 Answered by 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. 





Scheduling a 12 person fishing 
20130709 

From Don: Greetings Math Central!
I searched the index, but could not find a similar quandary.
Here's my predicament:
I am seeking help in scheduling a 12 person fishing outing.
We have four boats.
I would like to schedule three fishermen to a boat.
We fish 2 1/2 days, split into morning and afternoon sessions.
Thursday afternoon, Friday morning, Friday afternoon, Saturday morning, and
Saturday afternoon
We switch boats after lunch, with each fisherman moving to a different boat,
with different partners.
I would like to have each fisherman fish with as many others in the group as
possible, with a minimum of partner duplication.
I would like to have each fisherman fish in all of the four different boats
over the course of the trip at least once.
Would you please suggest a boat / fishing partner schedule that fits my
parameters as closely as possible.
Thank you!
Don Answered by Victoria West. 





Diego and his dog 
20130709 

From William: john went hunting and walked at a speed of 4 km/h. one hour later, Diego and his dog went to meet john with a speed of 6 km/h and the dog was running between john and diego until they meet up with a speed of 18 km/h. After Diego meets john, how much distance did the dog run? Answered by Penny Nom. 





4 couples golfing 
20130706 

From Brian: We have 4 couples going on a 4 day golf vacation playing 4 rounds of golf.
I have spent hours trying to set up a schedule that allows the 4 spouse to play together,
and then each spouse to play with one of the other spouses (men with women) for the]
other 3 rounds.
I would like the foursomes to be different as possible. Also, noone should RIDE in a cart with the
same person more than once.
I am not a math guy so I try to do this by working it out on paper, over
and over again. It ain't working!!
If you can help, I am very thankful.
Brian Answered by Victoria West. 





The angle of elevation of the sun 
20130703 

From Maurice: A vertical pole with a length of 7m cast a shadow with a length of 5m. Calculate the angle of elevation of the sun and include a diagram. Answered by Penny Nom. 





8 golfers playing 8 games 
20130703 

From Johan: We have 8 golfers playing 8 games, and we want to schedule them so that they play together equal amount of times, or as close as you can get to that.
They will be playing in two four balls each day.
Anyone sorted this one out yet, I will really appreciate a solution?
Thanks
Johan Answered by Victoria West. 





13 golfers playing 5 rounds 
20130703 

From Alan: i have 13 golfers playing 5 rounds. want everyone to play together at least once. Answered by Victoria West. 





13 golfers 
20130702 

From James: 13 golfers playing in 4 groups [4,3,3,3 per group] for four rounds.
Can it be scheduled so that no two people play together more than twice? Answered by Victoria West. 





A league schedule for 6 hockey team 
20130702 

From Giovanni: Hello, I try to make a league schedule for 6 hockey team. Each team will play 36 games during the regular season.
I cannot find a proper schedule generator. Can you help me please?
Thank you Answered by Victoria West. 





Fantasy football league 
20130618 

From Chris: Hello,
I am the commissioner of a fantasy football league. In this week, we play all 17 weeks of the season. It's a 12 team league, and we play each team twice. To do that, we have 5 "double header" weeks, which means you play 2 different teams. I am struggling to come up with a schedule to make this work. Does anyone have a solution? Answered by Victoria West. 





A 3 acre plot 
20130617 

From Chad: I have 3 acres 100ft at the top and bottom what is the length of each side to make up the 3 acres Answered by Penny Nom. 





{(1+x)^1/31/3X(1+x)^2/3}/(1+x)^2/3 
20130617 

From STEPHEN: {(1+x)^1/31/3X(1+x)^2/3}/(1+x)^2/3 Answered by Penny Nom. 





An isosceles tiangle 
20130616 

From Izzy: what's the height of an isosceles triangle which has a base of 50 m, and both of the other sides are 25 m? Answered by Penny Nom. 





16 golfers in 2 groups of 8 
20130615 

From Derek: we are 16 golfers.2 groups of 8."A" group & "B" group.We are playing 4 rounds,4 players at a time,2 from each group.We don't want to play with or against the same person twice.IE we want to play with 7 different people each day.Is it possible ?thanksDerek Answered by Victoria West. 





4=(1+.08)^x 
20130615 

From Samantha: I can't seem to understand how to solve for x when it is in power form, here is the equation:
4=(1+.08)^x Answered by Penny Nom. 





Surrounding a pipe with concrete 
20130611 

From jeanne: I need 2 inches of cement around a 20 inch pipe that is 20 feet long. Thank you. Answered by Penny Nom. 





Two numbers whose difference is 16 
20130608 

From Johan: Two numbers whose difference is 16 and whose sum is 120 Answered by Penny Nom. 





A kennel for a beagle 
20130603 

From david: Hi, I'm building some beagle kennels and I am in need of help with an angle problem. I need to place a roof on my kennel with a drop of 2inches across 3ft 10inches. the posts on the right side will be 5ft and the post on the left will be 4ft 10in. the posts are 4x4 and the space to be covered is 3ft 10in from the outside of the 4x4. Please help, thanks. Answered by Penny Nom. 





Four circles 
20130529 

From varsha: four circular cardboard pieces each of radius 7cm are placed in such a way that each piece touches two other pieces. find the area enclosed by the four pieces. Answered by Penny Nom. 





21 golfers 
20130527 

From Linda: A database search for a question on how to schedule 20 golfers in groups of 4 was very helpful ( Mona's answer referred to by C. Fisher 932008) I'm very glad I found this sight.
Our problem is we will have 21 golfers in the second half of the season. Is it possible to figure out that schedule? I assume we will have to include byes, but I'm not sure how to go about doing that.
Thank you. Answered by Victoria West. 





Simson line 
20130523 

From Nazrul: From any point p lying on the circumcircle of the triangle perpendiculars
PD , PE are drawn on BC,CA respectively. The line segment ED intersects at
the point 0 ; prove that PO ⊥ AB ( PO is perpendicular to AB ). Answered by Chris Fisher. 





Two overlapping circles 
20130522 

From Alexandra: There are two overlapping circles. The two nonoverlapping regions have areas A and B.
As the area of overlap changes, the values of A and B also change.
Prove that no matter how big and small the overlap is, the difference between
A and B is always the same. Answered by Penny Nom. 





The square footage of a 17 inch by 17 inch tile 
20130518 

From Leroy: How do I calculate the square footage of a 17inch by 17 inch tile Answered by Penny Nom. 





r=10cos(t) in cylindrical coordinates 
20130518 

From r.m: question from calculus exam: what is the figure obtained having eqn.r=10cos(t) in cylinderical coordinates?
i know it is a cylinder with center (5,0) ,but can't the equation represent two cylinders ,one with center
(5,0) and the other with center (5,0).
thanks for any help. Answered by Penny Nom. 





The percentage of fat in a container of yogurt 
20130517 

From Katy: There is a question that I' having trouble with. It says: "A container of yogurt
contains 228 g of water, 54 g of carbohydrates, 12 g of protein and
6 g of fat, what percentage of the yogurt is fat?" How do you convert 6 g
into percentage? Answered by Penny Nom. 





Cutting three sections of pipe 
20130516 

From Michael: A plumber cuts three sections of pipe from a 12’ length of ABS pipe, the lengths of the sections
are 33 3/8”, 56 5/8” and 39 7/8”. What is left over from the full length, if the saw cut is 1/8”
wide? Answered by Penny Nom. 





8 3/4 as a decimal 
20130515 

From Luisa: How to make 8 3/4 into a decimal Answered by Penny Nom. 





HCF and LCM 
20130515 

From Kelly: If HCF and LCM of two numbers is 7 and 20 respectively, then the number/s is/are…. Answered by Penny Nom. 





A circle and a chord 
20130514 

From yashvardhan: A circle which radius 13cm. Find the length of the chord which is 5 cm away from center Answered by Penny Nom. 





An equation in two variables 
20130514 

From Steve: Verify solutions to an equation in two variables. 4x2y=8 (3, 2) Answered by Penny Nom. 





Dice 
20130514 

From Julia: What is the probability of rolling(as many times as necessary) a die and getting a total number(sum) when all the rolls are added together of 11? Answered by Lorraine Dame. 





A 2digit number 
20130513 

From A teacher: Find a “2digit number” where the sum of the 1st digit (on the Left)
and the square of the 2nd digit equal the same number. Answered by Lorraine Dame, Harley Weston. 





Compound interest 
20130510 

From Kyla: I am doing correspondents and cannot figure out how to explain the solution to this question, I do not understand how they came to this answer and need it explained step by step so I can complete the following questions in this unit, please help!!!
Calculating compound Interest
Johnny invest $800 that pays 8% compounded quarterly for 5 years. How much is the investment worth at the end of the 5th year? Answered by Penny Nom. 





Water use in a rectangular flush tank 
20130510 

From milo: A rectangular flush tank 22" by 71/4 contains water to depth of 17" how many gallons of water will be saved if a conservation device reduces the capacity to 3/5 of this amount? And reduced to the nearest tenth Answered by Penny Nom. 





20 golfers over 5 days 
20130509 

From Russ: we have 20 golfers over 5 days, with 4 people per foursome which makes 5 groups each day. I would like to each person to play with everyone at least once if possible. Do you have a formula for this? Answered by Victoria West. 





siin (A) and sin (A/2) 
20130509 

From shanaia: given that sin A=4/5 and A is obtuse.find sin (A/2) Answered by Penny Nom. 





A triangle and an incircle 
20130509 

From Max: On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Answered by Chris Fisher. 





The surface of a solid 
20130507 

From mustafa: I am doing a research paper on solid surface applications . Part of the project is to find four at least in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where solid surface are used in our world today and I really can't find anything.. Thanking you in advance, mustafa Answered by Penny Nom. 





Drawing a pentagon 
20130506 

From jacob: hello. i am trying to draw a template for a project. but i don't have a
protractor. i'm trying to draw a normal pentagon with 2cm sides. what
i'm trying to figure out is the distance in centimeters from point a, to c,
in a straight line. this is needed so that i can measure and create the
shape without a protractor, and keep the angles and sides correct.
if you can help me with the measurement, or help me another way,
any help would be greatly appreciated. thank you. Answered by Penny Nom. 





A silver figurine 
20130503 

From Renee: I have a silver figurine, the density of silver is 10.5g/cm3. if the figurine weighed 149 g. to determine the volume, he dropped it into a cylindrical glas of water. the diameter of the glass is 6 cm and the figurine was pure silver, by how much should the water level in the glass rise? Answered by Penny Nom. 





A word problem 
20130503 

From Shaneaya: Keikio spent the day bird watching and counted 34 more birds in the morning than in the afternoon. If she counted a total of 76 birds, how many birds did she count in the afternoon? Answered by Penny Nom. 





The rings of a bull's eye 
20130428 

From Math: The bull’s eye of a target is a circle 20 cm in diameter. It is surrounded by four rings, each 15 cm wide. Find the area of each ring. Answered by Penny Nom. 





What is the original price? 
20130425 

From Dylan: shirts on sale for 25% off, the sale price is 12.75. What is the original price? Answered by Penny Nom. 





How do i reverse this formula? 
20130420 

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





A circle, a chord and an arc 
20130416 

From Tim: Morning,
I was told the chord is 3000mm and the depth of chord is 300mm, I can
find the radius,(1500 squared + 300 Squared) Divided by (300 + 300)
but don't know how to calculate the length of the circle defined by the chord.
Regards
Tim
Answered by Penny Nom. 





A cyclic rhombus 
20130416 

From Marisa: I know that the only rhombus that can be inscribed in a circle is a square, but why is that? I've been racking my brain and the internet for solutions, but have found no logical explainations in relation to the arc degrees and angles. Please help. Answered by Chris Fisher. 





8 golfers, 3 rounds 
20130415 

From justin: I have 8 golfers going on a trip. We have 3 rounds to play.
We would like to play with everyone (with or against.) Is this
possible? If so could you send me the formula please and thank you! Answered by Robert Dawson. 





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

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





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





The area of a right triangle 
20130410 

From derek: The legs of a right triangle measure 4 and 6 inches. The area of the triangle is 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. 





10 golfers playing four rounds 
20130409 

From Terry: I've searched "golf" and "golf 10" but don't see 10 golfers playing four rounds (each round having one foursome plus two threesomes, and no "flights" as in one earlier answer); each player playing at least once with a maximum number of the other nine over the four rounds? Answered by Victoria West. 





The equation of a line 
20130404 

From Miranda: My coordinates provided are (6, 6) and (8, 9) and i need to put this into ax=bx=c format. I remember the equation to find the slope of y2y1/x2x1 to get the slope. However when i put that back into the y=mx+b format it still leaves me with a lot of variables. Please help :) Answered by Penny Nom. 





A gravel pile in the shape of a triangular pyramid 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Question 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





16 golfers over 15 days 
20130402 

From Mark: 16 golfers, each plays the other 15 golfers once each over 15 days.
played in four foursomes each day.
What is schedule that allows each golfer to play with other golfers an equal number of times? Answered by Victoria West. 





Every vertex of a cube is assigned a number +1 or 1 
20130401 

From Shankar: Every vertex of a cube is assigned a number +1 or 1 . Every face has a number that is the product of all the numbers in its corners. Then the 14 numbers are summed up ( all the vertices and faces ). Can the sum be 0? Answered by Chris Fisher. 





The distance between 2 lines in 4D 
20130401 

From samane: how can i measure the distance between 2 lines in 4D?? Answered by Chris Fisher. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





Simultaneous equations with fractions 
20130331 

From Terence: 5/x6/y=1
17/x+30/y=16
I been spending whole day to solve this question. Would be very grateful if you can help I try
The denominator value is a equations term which make is simultaneous equations so hard. Answered by Penny Nom. 





The area of an isosceles right triangle 
20130330 

From Michelle: We have a triangle it is a right isosceles. The sides touching the right angle are 10 cm. They hypotenuse is 14.1 (the base) we are trying to find the height of this so we can figure out the area of a shaded sector of a circle. Answered by Chris Fisher. 





A shortest distance problem 
20130328 

From LYNDELL: I have a right triangle and know the length of all sides. How do I calculate the shortest distance from the vertex of the 90 degree angle to the hypotenuse? Answered by Penny Nom. 





Tangents to the curve y = x^3 
20130324 

From Ethan: How many tangent lines to the curve y = x^33 pass through the
point (2, 4)? For each such line, and the exact coordinates of the point of
tangency on the curve. Answered by Penny Nom. 





Trigonometry 
20130323 

From Tizoc: I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance! Answered by Penny Nom. 





Cumulative Frequency Math Question 
20130320 

From Primadonna:
Hi,
Please help me solve this question.
Thank you so much.
The cumulative frequency table below shows the length of time that 30 students spent text messaging on a weekend.
Minutes Used 
Cumulative Frequency 
3140 
2 
3150 
5 
3160 
10 
3170 
19 
3180 
30 
Which 10minute interval contains the first quartile?
(1) 31–40
(2) 41–50
(3) 51–60
(4) 61–70 Answered by Penny Nom. 





Five players in a 4player partnership game 
20130319 

From Dee: I have 5 players who are playing in a 4player partnership game & want to rotate the 5th person in in such a way that each person is each other person's partner for a game. How can such a rotation be done? Answered by Penny Nom. 





The dimensions of a rectangle 
20130319 

From stephanie: the length of a rectangle is 5m more than twice its width, and the area of the rectangle is 88m^2 find the demensions of the rectangle Answered by Penny Nom. 





Sixdigit passwords 
20130319 

From Judy: Hello:
Can you please explain why the answer to the following question is 10^6?
What is the number of possible sixdigit passwords when using the digits 0 through 9, with repetition allowed.
Thank you. Answered by Penny Nom. 





Tiling a floor 
20130318 

From whitley: Question from Whitley, a student:
How many square feet of tile do you need to cover the floor of a room that is 20ft, 25ft, 15ft, 20ft, 5ft, and 5ft
I made a replica of the floor Answered by Penny Nom. 





An algebraic exercise 
20130318 

From autumn: given: f(x)=x/(x^2+2) determine: [f(xh)f(x)]/h Answered by Penny Nom. 





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

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





Row echelon form 
20130315 

From Shawn: Please help me put matrix in row echelon form:
1 9 8 0
5 8 1 35
1 4 1 17 Answered by Penny Nom. 





Driving a rental car 
20130313 

From teresa: Driving a rental car x miles cost y= 0.25x + 25 dollars.
(a) How much would it cost to rent the car but not drive it?
(b) How much does it cost to drive the car 1 additional mile?
(c) What is the yintercept of y= 0.25x + 25? What does it represent?
(d) What is the slope of y= 0.25x + 25? What does it represent? Answered by Penny Nom. 





A 3 digit number puzzle 
20130311 

From Bonnie: My number has 3 digits. My number is not a multiple of 100. My number is a multiple of 50. My number is a factor of 1000. What is my number? Answered by Penny Nom. 





A chart for y=mx+b 
20130311 

From jacinda: how to make a chart for y=mx+b Answered by Penny Nom. 





Fencing a parcel of land 
20130311 

From Koleen: How much fencing do I need for an 56,850 parcel of land for a 15 stable horse barn Answered by Penny Nom. 





6 miles in 28 minutes what's my average speed? 
20130305 

From lynda: 6 miles in 28 minutes what's my average speed? Answered by Penny Nom. 





f(x) + f ''''(x)=0 
20130305 

From Andreea: Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something. Answered by Brennan Yaremko. 





What is the subtotal & GST? 
20130304 

From REBECCA: Hi, I have a total of $300.
What is the subtotal & GST?
How do I work backwards? Answered by Penny Nom. 





Markup and discount to get a sale price 
20130302 

From Warren:
If you are an ardent shopper you will be aware of the discount (% decrease) marketing strategy to produce the sale price. I began to wonder just how much markup (% increase) was added initially to an item in order to deliver the discounted sale price.
It was simple to construct a formula to convert one to the other.
For example a 30% (mark down) decrease in price required a 42.86% (mark up) to increase the price initially to Tag price. However when I started apply the formulae to a number of circumstances I noticed some very interesting circumstances associated with this relationship
For example a 99.999999% decrease is numerically equal to a 9,999,999,925% increase (huge ratio difference) while conversely a 0.1% decrease is numerically equal to a 0.10010010% increase (Infinitesimally small ratio difference) so the patterns appears logarithmic not linear.
However what really caught my attention was this pattern
See http://www.ozsmart.com/doc/percentage.htm
My questions is why does the decline in the ratio of increases in required mark up (%) price peak at 50 and 51% precisely and then expand again as the percentage move higher
Any explanation would be appreciated Answered by Harley Weston. 





A linear programming problem 
20130227 

From Kelley: A manufacturer of skis produces two types: downhill and crosscountry. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing is increased to 48 hours.

Downhill 
Crosscountry 
time available 
manufacturing time per ski 
2 hrs 
1 hr 
40 hr 
finishing time per ski 
1 hr 
1 hr 
32 hr 
profit per ski 
$70 
$50 

Answered by Penny Nom. 





100 animals 
20130225 

From Jessica: You have exactly $100.00 to spend. You must get 100 animals.
The chicks cost $0.10 each.
The pigs cost $2.00 each.
The sheep cost $5.00 each.
You must get some of each animal.
How many of each animal can you get? Answered by Penny Nom. 





The tangent to a circle at a point on the circle 
20130222 

From Andrew: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Answered by Penny Nom. 





Fractions over fractions 
20130222 

From Kenssa: Question from Kenssa, a parent:
Simplify: 3(7/x)(6/x^2) / (3/x^2)+(5/x)2 Answered by Harley Weston. 





Your profit should be 20% of your cost 
20130221 

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





Solve sin 3x = 0.1254 with x between o and 360 degrees 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Solve sin 3x = 0.1254 with 0 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Solve 8 logx > x 
20130219 

From Fulvio: Hi, could you solve this equation in algebraic form:
8logx>x Answered by Harley Weston. 





A trig word problem 
20130218 

From Amy: Susan notices an unusual rock formation at an angle of 30 degrees to the right of her direction of travel as she is white water rafting. as she continues in a relatively straight path for 20 m, the rock formation appears to be at 45 degrees to the right. she cotninues until the rock formation is directly to her right. how far is she fromt he rock formation? Answered by Penny Nom. 





Extraneous solutions 
20130218 

From Eileen: (5x+4)^1/23x=0 Answered by Penny Nom. 





Related rates 
20130217 

From Ishaak: A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^21/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute. Answered by Penny Nom. 





Swimming upstream and downstream 
20130215 

From Kimberly: a beaver swims down to its lodge 4 times faster than it swims upstream. how many times faster is its speed in still water than the speed of the stream? Answered by Penny Nom. 





Chocolate bars and puzzles 
20130215 

From sandy: Alan bought a box of puzzle and two bar of chocolate for $28.
Jan bought 3 boxes of puzzle and a bar of chocolate similar to
Alan for $69.
a) Find the cost of a box of puzzle
b) Find the cost of a bar of chocolate Answered by Penny Nom. 





An electron in a TV tube 
20130215 

From anu: an electron in a TV tube is beamed horizontally at a speed of (50^6) m/sec. towards the face of a tube 40 cm away
about how far will the electron drop before it hits? no information has been provided of initial height from where it is beamed. Answered by Robert Dawson. 





A word problem involving toys 
20130214 

From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls? Answered by Penny Nom. 





A curve in 3space 
20130214 

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





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





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

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





The height of an aerial 
20130212 

From ASIT: A vertical aerial stands on a horizontal ground. A surveyor positioned due east of the aerial measures the elevation of the Top as 48 degree. He moves due south 30metre and measure the elevation as 44 degree. determine the height of the aerial Answered by Penny Nom. 





A cubical shipping container 
20130212 

From Chantel: The length, width and height of a cubical shipping container are all
decreased by 1.0 ft, thereby decreasing the volume of the cube by
37 ft3(feetcubed) What was the volume of the original container?
(recall: volume of cube with a side length x=x3) Define the variable,
write a quadratic equation and solve by factoring. Answered by Penny Nom. 





The equation of a circle 
20130211 

From mhd: Complete the equation of the circle centered at(0,4) with radius 3 Answered by Penny Nom. 





Simultaneous equations 
20130210 

From Michael: 2P + 1/3V =8
3P  2/V=5 Answered by Penny Nom. 





The height of a sheet metal cone 
20130209 

From Charles: Sheet metal cone.
I need a cone with a finished base of 38.19719 diameter
The cone is to be from a 48 diameter round with the wedge cut out.
The best calculation I have is the arc is 286.479. (correct?)
Could you verify this arc angle but more so what is the cone height? Answered by Harley Weston. 





Brian is x years old 
20130206 

From Sabrina: Brian is x years old.
Peter is 4 years older than Brian.
Amy is 2 years younger than Brian.
The total of their ages is 26 years.
Work out the value of x. Answered by Penny Nom. 





What is the domain of f(x)=sin(ln(x))/ln(x)? 
20130206 

From Behrooz: Hi, the following problem may be interesting:
What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.
Best regards
Behrooz Answered by Penny Nom. 





Exponential form 
20130205 

From Sandra: What is 37,008 in exponential form? Help me please!!! Answered by Penny Nom. 





We have 10 golfers and four rounds of golf in two days 
20130205 

From Steve: We are having a golf tournament. We have 10 golfers and four rounds of golf in two days. We are going to break the group of 10 into two flights. Flight A and Flight B. We would like all members in Flight A to play one nine hole match against each other. All players in Flight B to play one nine hole match against each other. Could we play in groups of 4,3 and 3? What is the best way to make the pairings work? Answered by Robert Dawson. 





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 relation on a collection of sets 
20130204 

From raji: suppose R be a non empty relation on a collection of sets defined by ARB if and only if A intersection B is nullset.then.....the correct answer is R is symmetric and not transitive...my doubt is how it is symmetric Answered by Penny Nom. 





7x1/41/3[2x 1x/2]=19/3 
20130203 

From M: 7x1/41/3[2x 1x/2]=19/3 Answered by Penny Nom. 





Multiplication in base two 
20130201 

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





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom. 





The multiplication table for the different bases 
20130201 

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





The area of a rectangle 
20130129 

From Bali: if the length of the
rectangular field is decreased by 5m,
its area is decreased by 70 sqm. if the
width is increased by 6m, the area is
increased by 180 sqm. determine the
length and width of the rectangular
field? Answered by Penny Nom. 





w varies jointly with the square of u and the cube of d 
20130126 

From Desiree: i don't understand how to answer this 'w varies jointly with the square of u and the cube of d' Answered by Penny Nom. 





We have 2 teams of 6 couples each that play 6 games 
20130125 

From Denise: We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each. Answered by Chris Fisher. 





Use 9,10,6,8, and 4 to make 10 
20130125 

From Able: How do you calculate using BEDMAS 9,10,6,8,4 to equal 10 Answered by Penny Nom. 





A geometry word problem 
20130124 

From Matthew: "G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"
How would you solve this? Answered by Penny Nom. 





Golf for 17 
20130123 

From Richard: I have looked through the examples on your site but can't find one that suits. I am fiddling with one to see if I can get a result; but not confident.
I have 17 players playing 6 rounds in 3 groups of 4 and 1 group of 5. Two players will not be included in any 5 ball group. Can you help me please. Answered by Victoria West. 





Golf for 18 for 18 weeks 
20130122 

From Al: We have 18 two man golf teams and we play once a week for 18
weeks. We need a formula to schedule these teams so that they play
each other one time only. Answered by Victoria West. 





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. 





Plotting y=f(x)+2 
20130121 

From Gavin: how would you plot y=f(x)+2 Answered by Penny Nom. 





How many students have neither brown hair or hazel eyes? 
20130120 

From Julie: There are 28 students in a class. 15 have brown hair, 17 have hazel eyes, and 10 have both. How many students have neither brown hair or hazel eyes? Answered by Penny Nom. 





Maximize profit 
20130119 

From Chris: A firm has the following total revenue and total cost function.
TR=100x2x^2
TC=1/3x^35x^2+30x
Where x=output
Find the output level to minimize profit and the level of profit achieved at this output. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20130117 

From Nicole: How do you find the shaded region of a circle if an unshaded equilateral triangle in inscribed in it. The only other things I know about the problem are that the side lengths of the equilateral triangle are 14 inches. Answered by Penny Nom. 





The weight of a pipe full of water 
20130116 

From joe: how do you figure out the weight of a pipe full of water Answered by Harley Weston. 





A balance puzzle 
20130114 

From Emily: I'm stuck on this problem and feel that it can't work! The problem is: there is a door with a balance scale on it. In order to open the door, you have to use the 5 weights to balance the scale. On the left side you have 2 boxes to place the weights and on the right side you have 3. You're 5 weights are as follows: 1lbs, 2lbs, 3lbs, 4lbs, 5lbs. How do you place the weights so that the scale is balanced? Answered by Penny Nom. 





Percent as a fractional relationship 
20130114 

From Kenneth: What does the following indicate?
"A percent is another way of expressing the ratio or fractional relationship
of two numbers."
I know what a ratio is, but the term "fractional relationship" confuses me.
I thank you for your reply. Answered by Penny Nom. 





A large ditch 
20130111 

From steve: hi
i have a large ditch to make a road entrance accross, the ditch is a green field on one side
and a highway on the other side
the ditch depth is 1.8m on the field side and 3.2 on the highway side
the culvert pipe is 1,2m in diameter
are you with me so far?
the entrance from the highway will be 26m wide tapering in to 6m  ,20 m in from the highway
there will be a concrete slab of 150mm over the top
the fall from highway to field must not exceed 1/8
any ideas how much stone it will need Answered by Harley Weston. 





The side lengths of a triangle 
20130107 

From Katie: How do I find the side lengths of a triangle knowing the base and its height?
Thank you, Answered by Penny Nom. 





A trig identity 
20130104 

From Tehmas: Prove sinC+sinD=2sin(C+D/2)cos(CD/2) Answered by Harley Weston. 





The quadratic formula 
20130103 

From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion 2x^2+3x+2=0 Answered by Penny Nom. 





Mod versus Rem in Turing 
20130101 

From Eric: I am a teacher teaching computer science using Turing. I am having
difficulty understanding why one would use the mod operator versus the rem
remainder operator.
Mod seems to make the resulting sign depend on the sign of the divisor,
whereas rem makes the resulting sign depend on the dividend.
Examples:
11 mod 5 = 1 and 11 rem 5 =1
11 mod 5 = 4 and 11 rem 5 = 1
11 mod 5 = 4 and 11 rem 5 =1
11 mod 5 = 1 and 11 rem 5 = 1
What I can't understand is why this would matter. For example, 11 / 5 =
2.2 and 11 / 5 = 2.2 get the same result.
So how is a remainder dependent on the sign of one of the parts?
What benefit would using one over the other have?
Any insight would be most helpful!
Eric Answered by Harley Weston. 





A triangular island 
20121229 

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





Solve 2x^4+x^337x>26x^2+12 using a graphical approach. 
20121229 

From Tehmas: Solve 2x^4+x^337x>26x^2+12 using a graphical approach.
I don't know how to find the xintercepts or yintercepts in this form. Answered by Penny Nom. 





A 12 acre parcel of land 
20121228 

From John: What are the dimensions of a 12acre parcel if it is 3 square acres deep and 4 square acres wide? Answered by Penny Nom. 





Increasing the size of a gift box 
20121227 

From Tehmas: The dimensions of a gift box are consective positive integers such that the height is the lowest integer and the length is the greatest integer. If the height is increased by 1cm, the width increased by 2 cm, and the length increased by 3 cm, then a larger box is constructed and the volume is increased by 456 cm^3. Determine the dimensions of each box. Answered by Harley Weston. 





Two polynomials are divisible by x  2 
20121226 

From Tehmas: Determine the values of m and n so that the polynomials 2x^3+mx^2+nx3 and x^33mx^2+2nx+4 are both divisible by x2. Answered by Penny Nom. 





A 4 digit phone lock using the digits 4, 2, 3 and 0 
20121224 

From Ragu: I would like to know formula for searching a combination of 4 digit. eg.
I knew my Phone Lock combination is my car plate number 4230. But
this time, i used another way around instead of 4230.
But I am sure, there is only this 4 digits only. 4 & 2 & 3 & 0 Answered by Penny Nom. 





The last 4 digits of a cell phone number 
20121222 

From Jacob: If the last 4 digits of a cell phone number, XXXXXXABCD, are restricted where: A cannot be 0 or 1 and B cannot be 0 / how many possible 4 digit combinations are left? 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. 





Milling round stock to square stock 
20121217 

From Bryan: Question from Bryan:
I want to know what the smallest diameter round is that will make a 31/4" square? Is there a formula for that? I am milling round stock into square.
Thank you. Answered by Harley Weston. 





An integral 
20121216 

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





An area bounded by lines 
20121216 

From sidra: find area bounded by functions:
y=x
y=2x
and y=5x Answered by Penny Nom. 





A max/min problem 
20121214 

From bailey: A right angled triangle OPQ is drawn as shown where O is at (0,0).
P is a point on the parabola y = ax – x^2
and Q is on the xaxis.
Show that the maximum possible area for the triangle OPQ is (2a^3)/(27) Answered by Penny Nom. 





The perimeter of an equilateral triangle 
20121214 

From shreyaarora: if the area of on equilateral triangle is 24/3cm,then what is its perimeter Answered by Penny Nom. 





A project on reclaiming water 
20121211 

From shannon: I'm doing a report to reclaim water off of our campus facility to store in a cistern to use to flush toilets.
In Southeast Wisconsin and average of 82 inches of rain and snow fall annually.
I want to collect that off of the roof of our school building.
The roof is 37128 square feet.
how many gallons annually could I collect? Answered by Penny Nom. 





A parabolic bridge 
20121209 

From Elizabeth: 1) The figure below shows a bridge across a river. The arch of the bridge is a parabola and the six vertical cables that help support the road are equally spaced at 4m intervals. Figure B shows the parabolic arch in an xy coordinate system, with the leftend of the arch at the origin. As indicated in Figure B, the length of the leftmost cable is 3.072 m.
I'm suppose to find the (xh)^2=4a(yk) equation for this word problem and I really do not know where to begin.
Afterwards, I need to find the lengths of the other cables and the maximum height of the arch of the road as well which I am very confused about Answered by Penny Nom. 





Mark has 312 books 
20121207 

From paul: Mark has 312 books. He has 11 times as many fiction books as non fiction books. How many fiction books does he have? Answered by Penny Nom. 





An arrow is shot straight up in the air 
20121206 

From heather: The skywalk is a glass bottomed platform that hangs over the edge of the Grand Canyon and is suspended 4000 feet above the floor of the canyon. If a tourist shot an arrow straight up in the air from the observation platform, the arrow's height could be modeled by H(t) =16^2 + 240 + 4000 where H(t) is the height of the arrow above the canyon floor in feet t seconds after being shot, t>0.
(a) Find H(5) and explain its meaning Answered by Penny Nom. 





The angles of elevation and depression 
20121203 

From Chelsey: a person on a balcony of one building looks towards a second building. if the angle of elevation to the top of the second building is 25 degrees, the angle of depression to the bottom of the second building is 17 degrees, and the balcony of the first building is 22 feet above the ground, what is the height of the second building? Answered by Penny Nom. 





Transposition error 
20121203 

From Carol: What is the correct term for when a child writes 61 instead of 16, or 83 for 38when they switch the place values of a number? Answered by Chris Fisher. 





A circle inscribed in a triangle 
20121128 

From Angie: Circle O is inscribed in triangle ABC. Angle A = 50 and angle B = 60. Find arc XY in dgrees Answered by Penny Nom. 





Sinx=logx+x^2 
20121128 

From yasmin: Sinx=logx+x^2 Answered by Harley Weston. 





The area of a triangle given its vertices 
20121127 

From elizabeth: how to calculate the area of a triangle using points ABC a (2,5) b ( 4,3) c ( 6, 1) Answered by Penny Nom. 





Two sides of a triangle 
20121125 

From Nazrul: In the triangle ABC, AB>AC and the bisector AD of angle BAC intersects BC at D. How can I prove that angle ADB is an obtuse angle. Answered by Penny Nom. 





What is the probability that the sixth draw will be a red ball? 
20121123 

From Patty: The probability of drawing a red ball out of a bag containing one red ball and one black ball is 1/2. An experiment is conducted where these two balls are placed in a bag before drawing a ball out. A ball is drawn 5 times from the bag containing the two balls. Each of the first five times the red ball was drawn out. what is the probability that the sixth draw will be a red ball? Answered by Penny Nom. 





Golf for 2 groups of 4 for six rounds 
20121121 

From Andy: You have very kindly responded to a couple of questions I asked previously and I have tried to find the answer to my current query on the various links etc. My question: There are 8 of us going on a Golf Tour and we will be playing 2 groups of 4 for six rounds of golf. Is there a suitable schedule that works to ensure everyone plays with each other the same number of times (or as close as possible). Many thanks again for your help. Answered by Victoria West. 





A function problem 
20121118 

From nahla: f: IN > IN
n > f(n)
for every n that belongs the IN : fof(x) = 4n  3
and for every n that belongs to IN f(2^n) = 2^(n+1) 1
Calculate f(993) Answered by Penny Nom. 





The square of any odd number, decreased by 1, is divisible by 8 
20121116 

From bailey: Prove that the square of any odd number, decreased by 1, is divisible by 8 Answered by Penny Nom. 





A path around a pond 
20121116 

From bailey: hi there,
A circular pond is surrounded by a path 1 metre wide.
The area of the path is 1/4 of the area of the pond.
Find the radius of the pond.
Thanks Answered by Penny Nom. 





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

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





How much should I price the earrings? 
20121113 

From Sharon: I want to sell some earrings and make a $12.00 profit on them I have to pay a
35% commission on them. How much should I price the earrings? Answered by Penny Nom. 





5<2x+1<1 
20121111 

From Rahul: How does 5<2x+1<1 changes to 1<2x+1<5. What is the rule?
Can we apply absolute value function throughout the first inequality i.e. can we say 5<2x+1<1. But then it becomes 5<2x+1<1 which is impossible because 5 is not less than 1. Answered by Penny Nom. 





What's your secret? 
20121111 

From ryan: Tuscan school has a fair. At the fair, Pia plays "what's your secret?
The game starts with 3 players who are told the same secret.
Each of those 3 players tells another 3 player, and so on.
At the end of the 3rd round, everyone who knows the secret
will compare what they have heard. What number in exponent form
represents the number of people who know the secret after 3 rounds?
How many people is that?
Thank you very much.
P.S. I got 3 cube. which is 27
But when i map it out I end up with 39. Answered by Penny Nom. 





Practical uses of trigonometry 
20121111 

From Michael: Where can I find books or information on real life function of sine and cosine? Answered by Penny Nom. 





A mathematical expression with the answer 7 
20121110 

From emily: hey um i need to find and problem that fallows bedmas that has one division one multiplication and one sub and one add and one brackets and one exponents that has the answer of number 7 Answered by Penny Nom. 





Converting a mixed number to a decimal 
20121110 

From Mahaveer: Convert mixed fraction to decimals: 4 2/6 Answered by Penny Nom. 





The derivative of y = sin (30º + x) 
20121107 

From Saskia: derivative of y = sin (30º + x) Answered by Harley Weston. 





Joe and Chris each bought a six pack of cola 
20121101 

From Loulou: Joe and Chris each bought a six pack of cola. Joe gave 2/3 of his away and Chris gave half as many as Joe. how many more colas did Chris have than Joe Answered by Penny Nom. 





Filling a box with wood chips 
20121031 

From leeAnne: Each bag of wood chippings will fill 4m3 how bags would be needed?
Volume of box is 572 cm3
L=11CM
W= 6.5CM
H=8CM Answered by Penny Nom. 





Frosting a three layer cake 
20121030 

From johnathan: Each layer of a 3 layer cake is a cylinder with height 7.5 cm. The bottom layer has diamegter 25 cm. The middle layer has dimegter 22.5 cm. The top layer has diameter 20 cm. The surface of the cke is frosted. What area of the cake is frosted. I get 1695.56 but the answer in the book is 2081.3 Answered by Penny Nom. 





The sum of a number p and twentyone 
20121030 

From mayra: the sum of a number p and twentyone Answered by Penny Nom. 





Introductory algebra 
20121030 

From kevon: if x = 7 is used in the expression 2x + 5 what is the output Answered by Penny Nom. 





birdhouse in the shape of a rectangular prism 
20121029 

From Tiffany: Hello, I am Tiff M. from NYC.
I was solving a math problem about adding,subtracting,multiplying
or dividing fractions and mixed numbers. I am not getting this
question below.
* Laura is building a birdhouse in the shape of a rectangular prism.
The base of the birdhouse has an area of 5 square inches. The
height of the birdhouse is 2 7/12 inches. Laura calculated the
volume of the bird house to be 10 7/12in. Is she correct?
If not, what did she do wrong? Answered by Robert Dawson. 





Forming an algebraic expression 
20121027 

From ashley: A sidewalk has a constant width W and comprises several short sections having lengths
12, 14,and 10 feet. How do I find the simplified expression that gives the number of square feet of sidewalk? Answered by Penny Nom. 





An implicit differentiation problem 
20121026 

From Katie: find y' of x^2y2y^3=3x+2y Answered by Harley Weston. 





How fast is the distance between the aircraft and the car increasing? 
20121024 

From Steven: At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car? Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





Differentiation rules 
20121023 

From Morgan: Use the derivative rules to differentiate each of the following:
1. f(x)=1/x1 2. f(x)= sqrt(x) Answered by Penny Nom. 





Some 6 digit numbers 
20121023 

From Mason: How many different 6 digit numbers can you make using the digits 1 ,2 5, 6, 7, and 9? How many of these sixdigit numbers are divisible by 6? Answered by Penny Nom. 





A 2 acre plot 
20121022 

From bob: If a plot of land on the south side is 290.16 feet wide, how many feet on the west and east side to the north to make a 2 acre plot?
Thank You Bob Answered by Penny Nom. 





Solving for a/b 
20121021 

From Jenny: If a + 3b is equal to 175% of 6b, what is the value of a/b? Answered by Penny Nom. 





Converting a fraction to a decimal 
20121020 

From A Teacher: My students want an easy way to convert a fraction to a decimal, can I get one from you? Answered by Penny Nom. 





Two congruent circles in a rectangle 
20121020 

From Alexander: Have you ever solved a problem, in which you have a rectangle, from which you need to cut the largest two circles of equivalent diameter? I bisected a rectangle diagonally, but the circles, while tangent to two of the sides, are not tangent to eachother. Can you devise a method for two equivalent circles, that are tangent to two sides, are also to eachother?
Take for example a piece of paper, Each if the two largest circles has a diameter that is greater than the distance to the midpoint of the diagonal bisector of the rectangle. Answered by Chris Fisher. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





Whites and Sulphurs butterflies 
20121019 

From Arlene: The Whites and Sulphurs are one major family of butterflies. There are about 720 varieties. Eleven times more Whites and Sulphurs live outside North America, mostly tropical Asia and Africa, than live inside North America. How many of this family of butterflies live in North America? How many live in the rest of the world? Answered by Penny Nom. 





The nth term of a sequence 
20121019 

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





Revolutions per second 
20121018 

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





Passing out graph paper 
20121018 

From Andrea: mr karnowski has a stack of 125 sheets of graph paper.He is passing out g sheets to each of his students. What is the expression for the number of sheets he will pass out to the first 5 students? Answered by Penny Nom. 





Percentiles 
20121017 

From Kenneth: Question from Kenneth:
Hello:
What is a common calculation used to determine percentiles?
For example, five employees have the following salaries:
Office worker 1  $25,000
Office worker 2  $27,000
Office worker 3  $30,000
Office worker 4  $32,000
Office worker 5  $35,000
What is the percentile rank of office worker 3 who earns $30,000?
Here's what I know: Add the number of salaries. Total: 5
Add the smallest number of salaries less than $30,000. There are two.
Now, divide 2 by 5 and multiply by 100. 2/5 * 100 = 40
I think the office worker making $30,000 is in the 40th percentile.
and I'm not sure what this ranking indicates.
I thank you for any helpful reply and or different calculation. Answered by Harley Weston. 





The degree measure of the central arc of a circle 
20121017 

From Crystal: On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc? Answered by Penny Nom. 





The height of a triangle 
20121017 

From Brian: the base of my triangle is 12 metres and the two sides are 8.45 metres
can you help me find the height of the triangle Answered by Penny Nom. 





Walking home from school 
20121015 

From margie: My sister can walk from school to home in 40 minutes. I can walk from school to home in 30 minutes. Today I stayed for some extra help, and my sister was already 2/5 of the way home when I started. If I walk at my usual speed, can I catch my sister before she gets home? If yes exactly what fraction of the trip have we covered when I catch her? If no exactly what fraction of the trip have I covered when my sister gets home? Answered by Penny Nom. 





A question about a parallelogram 
20121014 

From Renu: Question from renu, a parent:
ABCD is a parallelogram. BP and DQ are two parallel lines cutting AC at P and Q respectively. prove that BPDQ is a parallelogram Answered by Harley Weston. 





A tank with an inner walled compartment 
20121012 

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





A word problem involving a fraction 
20121012 

From Derrick: If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do? Answered by Penny Nom. 





GST in New Zealand 
20121010 

From Colleen: I work out my claimable gst each month but need to know the total sales or purchases amounts for filling in my six monthly paper work. How do I do that. I tried doing the opposite of calculating the gst i.e. x3 and /23 but it is slightly different to my total. Answered by Penny Nom. 





A four digit number 
20121009 

From cyndi: find this 4 digit number: the tens digit is 1/3 of the hundreds digit; the 2 digit number formed by the tens and ones digits i the largest prime number smaller than 40; the sum of all 4 digits is the same as the number of face on an icosahedron ? what is the number? Answered by Penny Nom. 





Three piles of top soil 
20121007 

From Steve: I need your help please, I am looking to purchase some top soil and keep getting conflicting answers.
There are 3 piles and here are the sizes;
Pile #1: 203 feet around and 21.29 feet high.
Pile #2: 195 feet around and 18.75 feet high.
Pile #3: 150 feet around and 17.98 feet high.
I look forward to hearing back from you asap.
Thank You!
Steve Answered by Harley Weston. 





A problem that yields a linear equation 
20121007 

From Eshraj: one fourth of a whole number is three more than one fifth of the next whole number.find the whole number Answered by Penny Nom. 





How many oranges? 
20121006 

From Rodger:
Question from Rodger, a teacher:
How Many Oranges?
Marjorie, Colleen, and Bob picked oranges together. They were tired after picking a large number of oranges and so fell asleep. Marjorie woke first and decided to take her third of the oranges and head home. She counted the oranges, and found that the number was divisible by 3 if she took one of the oranges first. Marjorie took one orange and then took onethird of the remaining oranges. She left quietly.
Bob awoke a short time later, noticed that Colleen was sleeping, and presumed Marjorie had gone for a walk. He decided to head home because he wasn't feeling well. Not realizing that anyone had left, he counted the oranges and found that the number of oranges was two more than a number that could be easily divided by 3. So he took the two extra oranges and then onethird of what was left. He left without waking Colleen and without waiting for Marjorie to return.
Colleen finally awoke and wondered where her friends had gone. She assumed they were both busy somewhere nearby. Before she left, she counted the oranges and was surprised at how small the number was. She found that the number of oranges was one more than a multiple of three, so she took the extra orange and one third of those remaining.
1. What was the total number of oranges the friends picked?
2. How many oranges were left behind when Colleen departed?
3. Is more than one answer possible for the total number of oranges? If so, what other numbers are possible? Explain.
4. Based on the values you found in problem 3, determine a reasonable solution to the problem. Explain your answer.
5. Is it possible that five oranges remained after Colleen took her share? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern
5. Is it possible that five oranges remained after Colleen took her “share”? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern Answered by Penny Nom. 





Two circle problems 
20121005 

From shahad: question 1
find an equation for the circle through the point (0,0) and (6,0) that a tangent to the line y=1
question 2
find an equation for the circle through the point (0,0) and (17,7) whose center lies on the line 12x5y=0 Answered by Penny Nom. 





Painting 400 drums 
20121005 

From Jordan: This cylinder is given:
Cylinder with a height of 84 cm and a diameter of 54 cm.
Question: The exterior of the drum (cylinder), except the base, is to be painted blue. calculate how many litres of paint will be needed to paint 400 drums if one litre of paint covers 8.8meters Squared.
Answer to nearest tenth of a litre. Answered by Harley Weston. 





\mbox 
20121005 

From Jordan: This cylinder is given:
Cylinder with a height of 84 cm and a diameter of 54 cm.
Question: The exterior of the drum (cylinder), except the base, is to be painted blue. calculate how many litres of paint will be needed to paint 400 drums if one litre of paint covers 8.8meters Squared.
Answer to nearest tenth of a litre. Answered by Harley Weston. 





Four tangent circles 
20121004 

From renu: inside of a circle K of radius length measure R,three circular discs A,Band C each of radius r are placed so that each touches the other two and K . express R in terms of r. in the space between K, A and B , another circular disc D is placed which just touches K, A and B. if the radius is s, show that (6+root3)s=(2+root3)r Answered by Penny Nom. 





Find an algebraic expression 
20121003 

From Karen:
Question from Karen, a parent:
Find an algebraic expression relating the input and output.
input 
output 


3 
1 
9 
3 
15 
5 
21 
7 
27 
9 
Answered by Penny Nom. 





Solve 8tr=12t for t 
20120929 

From Monejah: I need help solving 8tr=12t for t Answered by Penny Nom. 





A problem involving simple interest 
20120927 

From Tash: The amount of money in a single year of an investment after P dollars were initially invested is A = P + Prt, where r is the rate of simple interest. What expression describes P? How much money was initially invested if the account has $1000 one year after the initial investment and the interest rate was 5%? Answered by Penny Nom. 





More on marbles in a jar 
20120927 

From josh:
Question from josh, a student:
Suppose you have a jar containing 100 red marbles and 100 white marbles. A) If you draw 5 marbles in a row, throwing each marble across the room as you draw it, what is the probability that at least one of them was red? B) If you draw 101 marbles in a row, throwing each one across the room as you draw it, now what is the probability that at least one of them was red?
I saw that this answer was already answered but "The probability that at least one is red is 1 minus the probability that they are all white." makes no sense to me can you please explain i thought that each time a marble is taken out the amount left is different can you please explain better Answered by Robert Dawson. 





The perimeter of a rectangle 
20120919 

From aretha: calculate the perimeter of a rectangle with the long side 462ft x 9inches and the short side 50% less. Answered by Penny Nom. 





Changing the sign of an inequality 
20120919 

From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom. 





Equivalent sets 
20120913 

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





Equivalent fractions 
20120913 

From lily: if i had 1/3 and i had to find the problem an they gave me 20 what will be the denominator Answered by Penny Nom. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





The dimensions of a rectangle 
20120912 

From Becky: A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle. Answered by Penny Nom. 





An equilateral triangle and a regular hexagon in a circle 
20120911 

From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom. 





The units digit 
20120911 

From Shaunice: Simplify each of the following expressions and determine what the last
digit would be.
a. (24^15) 4 Answered by Penny Nom. 





Golf for 12 
20120910 

From John: To have 12 players in groups of 4 playing in 4 games with different people each day Answered by Victoria West. 





The height of a building 
20120908 

From Lin: How do surveyors determine a height of a building 150 feet away with an observation angle at 40 degrees?
What is the elevation of that top floor? Answered by Penny Nom. 





A profit of 35% 
20120907 

From Jack: If a product cost me $10.00 and I want a profit of 35% what is my sell price? How do I figure the sale price to make a 35% profit on the sale? Answered by Penny Nom. 





The volume of fluid in a tank 
20120906 

From Dave: I have vertical round flat bottom tanks of various dimensions. It is easy to find total volume but I would like to know how to figure out the coversion factor to go from how many centimeters of liquid is in the tank to the number of total cubic meters of volume. So if my float gauge on the tank says there is 50 cm of fluid in the tank, how many cubic meter of total volume is there? Answered by Harley Weston. 





The hypotenuse 
20120906 

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





(2y+1)/3=(1y1)/2 
20120906 

From jenna: (2y+1)/3=(1y1)/2 Answered by Penny Nom. 





A container of split peas 
20120906 

From Laurie: I have a container that is 471 square inches (length*width) and is 2.3 inches high. I want to cover the bottom with 1/2 inch of split peas, in order to anchor escort cards (place cards) for a wedding. How many pounds of split peas do I need to cover the area to a height of 1/2 inch? Thanks Answered by Penny Nom. 





Row echelon form 
20120905 

From Jennifer: Hello, my name is Jennifer. I am a 12th grader in PreCalculus and I was wondering if you may help me with Row Echelon Form.
x + 2y  3z = 5
2x  4y  6z = 10
3x + 7y  2z = 13 Answered by Penny Nom. 





Angular velocity 
20120905 

From Kyra: A belt connects a pulley of radius 8cm to a pulley of radius 6cm. Each point on the belt is travelling at 24 cm/sec. Find the angular velocity of each pulley. Answered by Penny Nom. 





A tangent to f(x) = 1/x 
20120904 

From Steven: Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Answered by Penny Nom. 





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. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





The number of solutions of sinx = x^2 + x +1 
20120901 

From anamika: number of solutions of
sinx = x^2 + x +1
graphically? Answered by Penny Nom. 





The area of a rectangle 
20120831 

From mario: The area of a triangle when on side is x and the other is x+6 Answered by Harley Weston. 





Exponntial form 
20120830 

From Robin: My math teacher has asked the question:
"Write mmmxxjmyy2 in exponential form"
How would you solve this problem? Answered by Penny Nom. 





Golf for 20, two teams of 10 
20120830 

From Mark: Hi
I have to teams of 10 people playing Ryder cup format(against each other)
Can I have all 20 people playing with someone different over 3rounds of golf while remaining on there respective team I.e. players 1 to 10 must team up with a player of that group against a pair for players 11 to 20
I hope you can solve this for me
Thanks a bunch Mark Answered by Victoria West. 





12 golfers, 4 rounds 
20120829 

From Paul: We have 12 golfers who will play four rounds of golf  how can we organize the foursomes so that each player has the most exposure to the other 11 players? Answered by Victoria West. 





A schedule for 6 teams and 37 games 
20120829 

From Giovanni: Hello, i try to prepare a schedules for 6 teams, and every teams will play 37 games before the playoff. How to make a schedules? thanks Answered by Victoria West. 





Minutes and seconds 
20120829 

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





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





Expected value 
20120825 

From melanie: The probabilities are 0.24 , 0.35 , 0.29 , and 0.12 that a speculator will be able to sell a subdivision lot within a year at a profit of P120, 500 , at a profit of P80,000 , at a profit of P40,000 , or at a lost of P60,000 respectively . What is his expected profit ? Answered by Penny Nom. 





Probability 
20120823 

From Christine: In a study of alcoholics, it was found out that 40% had alcoholic fathers and 6% had alcoholic mother. Fourtytwo percent had at least one alcoholic parent. What is the probability that a randomly selected alcoholic will ... Answered by Penny Nom. 





A 2digit number 
20120823 

From patty: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is Answered by Penny Nom. 





The difference of the numbers on two dice 
20120819 

From dilys: Two fair dice are thrown. Find the probability that the difference of the two numbers is divisible by 4? Answered by Chris Fisher and Lorraine Dame. 





The volume of a sphere 
20120818 

From Rohit: why isn't volume of a sphere = Area of a semicircle x the circumference.
i.e. if we revolve a semicircle around its axis we get a sphere Answered by Penny Nom. 





Kirkman schoolgirl problem 
20120818 

From Anthony: need to have the number from 115 in 6 rounds of 3 numbers without the numbers be repeating in the same row . eg round 1
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
2nd round
1 4 7
10 13 2
5 8 11
14 3 6
9 12 15 Answered by Chris Fisher. 





A rotating schedule 
20120816 

From Dusty: Ok, Im trying to create a rotating schedule. There are four jobs and four people but, one of four people cant preform one job. How can I figure out a rotating schedule for this issue? Answered by Victoria West. 





Golf for 16 in 7 rounds 
20120816 

From Elizabeth: Hello,
I am trying to sort out golfing for 16 guys for 7 rounds. However the twist is that the teams are broken down into 8 old boys vs. 8 young boys. Ideally, each of the players would only play each other once within their own team and then twice within all of the matches. Is that possible? Thanks for your help, my brain is hurting! Answered by Victoria West. 





The length and depth of a chord 
20120816 

From Tim: Can I find the radius of a circle, if I have a chord of 2400mm, and a depth
between the center of the chord and the perimeter of the circle of 150mm ?
Thanks
Tim Answered by Penny Nom. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





A tapestry rod on a curved wall 
20120814 

From Marlyn: I have a curved wall with a radius of 6'. I am trying to have a 36" rod made to hang a tapestry and need to figure out the degree measure of the arc.
Can you help me please? Answered by Penny Nom. 





The exponential function form f(x)=a^x 
20120813 

From Lucy: Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative? Answered by Penny Nom. 





Two altitudes of a scalene triangle 
20120813 

From grace: Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is also an integer, what is the biggest that it can be? Justify all of your conclusions. Answered by Chris Fisher. 





The intersection of normal subgroups 
20120813 

From nokks: let (G,*) BE A Group and prove that the intresection of normal subgroups of G is itself a normal subgroup of G Answered by Penny Nom. 





The volume of half an ellipsoid 
20120810 

From Darcy: Hi,
I need to calculate the volume of half an ellipsoid, split horizontally along the long axis. In effect, an oval shaped mound of soil. So the bottom would be an ellipse. I have the length, width and height measurements but not the formula. Thanks! Answered by Robert Dawson and Walter Whiteley. 





A 4 digit number 
20120809 

From May: The number is given as ABCD. The first digit is a quarter of the last digit. The second digit is one less than the first digit.
When the number ABCD is multiplied by four its digits appear in the reverse order. None of the digits are the same. What is the number. Pleas help because my child need help and I can not do this. Thank you. Answered by Penny Nom. 





The difference between two numbers is 7. 
20120809 

From May: The difference between two numbers is 7. When the two numbers are multiplied the answer is 60. How do I work out the two numbers,I tried solving for one unknown and substitution and can not do it. Pleas show me how to do this. Answered by Penny Nom. 





A garden in the back yard 
20120804 

From Lucy: Your boss says that his wife has put an 18 × 51 foot garden in along the whole back end of their back yard. He says that this has reduced the backyard lawn area by 24%. What are the total dimensions of his back yard? What are the dimensions of the remaining lawn area? I found this question on purplemath(http://www.purplemath.com/modules/percntof3.htm). I still don't understand how to solve it. Can you walk me through the process please?
Thank you in advance for taking the time to answer my question. Answered by Penny Nom. 





A plane travelling with the wind and against the wind 
20120803 

From Gwen: The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed? 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. 





Three right triangles 
20120726 

From Jora: I am having a lot of difficulties with this question.
Name: Jora
Subject: Math
Who are you: Student Answered by Chris Fisher. 





The distance between overlapping circles 
20120726 

From Jeff: I have two circles of different size that overlap one another:
Circle #1 has an area(A) of 731,475, so I can calculate its radius as 482.6.
Circle #2 has an area(A) of 502,517, so I can calculate its radius as 400.
If I know that the area where they overlap is 179,271, how can I calculate the distance between the midpoints of these two circles? Answered by Chris Fisher. 





John's electronic store 
20120725 

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





A regular hexagon inscribed in a circle 
20120725 

From jim: A regular hexagon with an area of 24√3 is inscribed in a circle. What is the area of the circle? Answered by Penny Nom. 





The area of a rectangle 
20120724 

From michael: the dimension of the rectangle are (x+5) and (x3) find its area Answered by Penny Nom. 





A pile of topsoil 
20120723 

From Perry: I have a pile of topsoil that is 42ft long and 16ft tall shaped like a cone how many yards of topsoil do I have. Answered by Penny Nom. 





Fence post holes 
20120719 

From Gerry: Hello, I'm digging 30 8" dia holes, 5 ft deep for fence posts that are 4"x 4" Can you please help me figure out how much stone dust I should order for all 30 holes. Thanks Answered by Penny Nom. 





A truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





2 threesomes for golf over 4 days 
20120716 

From Jim: How to arrange for 2 threesomes for golf over 4 days equitably. Answered by Victoria West. 





Probability and curling rings 
20120716 

From Fatima: In the olympic event of curling, the scoring area consists of four concentric circles on the ice with radii of 6 inches,
3 feet, 4 feet, and 6 feet
If a team member lands a (43 pound) stone randomly within the scoring area, find the probability that it ends up centred on
a.red b.white c.blue
I am explaining the figure also in words
The smallest Circle is of White color then a blue colour circle then again a White colour circle then the last big circle of red color
The answer for a bit is 5/9
I tried it with many ways but I am not getting the answer
Please clearly tell me what is n(S)and what is n(E). Answered by Penny Nom. 





A volume of revolution 
20120715 

From Tewodros: Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the yaxis and determine the volume using the shell method. Answered by Harley Weston. 





The angular elevation of the sun 
20120714 

From VINEET: WHAT IS ANGULAR ELEVATION OF THE SUM Answered by Penny Nom. 





A sand box with 14 sides 
20120710 

From Tom: Want to build a sand box for a pool that is fourteen foot round wanted to make it in fourteen pieces of wood what angle would each piece be and how long would each piece be Answered by Harley Weston. 





The height of an isosceles triangle 
20120710 

From ken: I am trying to determine the various heights of an isosceles triangle, if each has the same base dimension and varies in the degree of the base (equal) angles. What is the method to do this?
As an example, of the base is 10, and the two equal angles are each 45 degrees, what is the height? With the same base (10), but with the two equal angles at 60 degrees, what is the height? And with the same base (10) and the two equal angles at 75 degrees, what would be the height?
I know how to calculate the degrees of the third angle (add the degrees of the known angles, and subtract from 180); but am unsure if that is needed for figuring the overall height.
And to be clear; I am not looking for the length of the sides of the triangle, but the height from the base to the top point.
Thank you! Answered by Chris Fisher. 





2x+underroot2=3x43underroot2 
20120709 

From Eshraj: 2x+underroot2=3x43underroot2 Answered by Penny Nom. 





Six people divided into three groups of two 
20120709 

From Fatima: Six people call them A,B,C,D,E,F are randomly divided into three groups of two,find the probability of the below event(do not impose unwanted ordering among groups)
E andF are in the same group
I solved it but I have a doubt that it is wrong .
My answer is 576
Please help to solve this problem. Answered by Lorraine Dame and Penny Nom. 





Finite probability 
20120708 

From Fatima: Tamika selects two different numbers at random from the set{8,9,10}and adds them.Carlos takes two different numbers
at random from the set {3,5,6}and multiplies them.What is the probability that Tamika's result is greater than Carlo's result Answered by Penny Nom. 





A cubical tank 
20120707 

From jake: a storage tank is in the form of a cube. when it is full of water,the volume of water is 15.625 m cube. if the present depth of water is 1.3m, find the volume of water already used from tank Answered by Penny Nom. 





An octagonal sandbox around a pool 
20120612 

From Linda: My pool is 15 feet across and it is round.
How do I measure to cut wood to build a sandbox around it? was thinking it will look like an octagon.
Thanks Answered by Harley Weston. 





Two equations involving fractions 
20120612 

From Fatima: Hi ,teacher gave two question to my daughter as follows
Solve 2/x+3=(1/xx9)(1/x3)and
Solve (4/x2)(x/x+2)=16/xx4
Please help me
Thanks & regards fatima Answered by Penny Nom. 





Expanded exponential form? 
20120612 

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





Scheduling an academic competition 
20120612 

From Mike: I need to schedule 18 high school teams to play each other in a "Jeopardy!"like academic competition. Teams compete against each other 6 at a time (simultaneously) in 3 different rooms. What will the minimum amount of matches (I believe 6 ?) we would have to play to ensure that each team plays every other team exactly twice?
And more importantly: what would that schedule look like?
The best I've come up with is having most teams playing twice, but with 2 pairs of teams having to play either only once or sometimes 3 times.
Thanks in advance for any help you can give! :)
Mike Answered by Chris Fisher. 





The position of an aircraft relative to the airport 
20120608 

From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing. Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north. What are the x,y, and z components (in meters) of the position vector. The xaxis is east, the yaxis is north and the zaxis is vertical. Answered by Penny Nom. 





A multinomial theorem 
20120608 

From Anuj: if (1+x+xsquare) whole raise to 20 is a0 + a1x + ........ + a20xraise to 40, then find a0 + a2 + a4 + .......... + a38.
How do you solve this??????? Answered by Robert Dawson. 





Long division 
20120607 

From Emily: Simplify the expression using long division (9x^241x6)/(x4) Answered by Penny Nom. 





A reel of cotton thread 
20120605 

From Grace: 91 meters of cotton goes round the cotton reel. About how many times does the cotton go round the reel?
Give your answer to the nearest ten.
(The Diameter of the cylinder is 3cm) Answered by Penny Nom. 





29 golfers 
20120604 

From robert: i have 29 golfers and have to make 8 teams for a golf scramble there will be 5 teams of 4 and 3 teams of 3 what is the fairest way to make up the teams? Answered by Victoria West. 





16 golfers, 4 rounds 
20120604 

From Gerry: 16 golfers, 4 rounds  best pairings so that everyone plays with each other at least once. Answered by Harley Weston. 





A cyclist a jogger and a fly 
20120604 

From Emd: A cyclist & a jogger are 20 miles apart.
Cyclist goes 20 mph & jogger 7mph towards each other.
A fly starts on nose of cyclist & flies at 20 mph from cyclist to jogger &
back & forth until they meet.
How far has the fly travelled? Answered by Penny Nom. 





A parabola 
20120604 

From Madeline: In a parabola, I need to know what "a" b and c determine. I think that a determines the width of the parabola, but I am not exactly sure what b, and c do. Answered by Robert Dawson. 





Translation of a graph 
20120602 

From Sean: the information is thus:
$f(x)=3(x+1)^22$
I wish to translate up 2 units and move 2 units right. Answered by Penny Nom. 





An octagonal home 
20120529 

From Jan: Lot size is 30' by 30' will a 1,165sq ft. Octagon home fit on lot? I don't know the wall size's only the total size of building? Thank You for have this?
If this won't fit what size in sq ft will fit? Answered by Penny Nom. 





Golf 16 
20120529 

From marknp: 16 players only want tp play with one player each one time Answered by Victoria West. 





The volume of a wedge 
20120528 

From olwethu: volume of wedge that have side 3,3 cm and 6,2 cm and 20 cm long? Answered by Penny Nom. 





The area of a semicircle 
20120528 

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





Multiples 
20120528 

From Kenneth: If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc.
Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.?
Or do fractions have no multiples? Answered by Penny Nom. 





Division in base eleven 
20120527 

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





Finding the circumcentre 
20120524 

From Glen: Hi,
I'm having trouble finding the circumcentre of these 3 coordinates A(1,1) B(10.5,1) and C(6,6).
I understand what circumcentre is but I cannot work out where it is.
Thanks very Much,
Glen Answered by Chris Fisher. 





A 10 inch circle using 2x4s 
20120519 

From Ralph: I want to form a 10" circle with 4"high pieces of 2 x4's. If each 2x4 piece sit next to each other,What degree would I have to cut
each side of the 2x4's, and how many would I need to form a 10 inch circle. I know there is a formula for this out there somewhere. Answered by Harley Weston. 





How fast am i driving? 
20120518 

From bozenga: How fast am I driving if I cover 40 feet in .1 seconds (1/10th of a second)? Answered by Penny Nom. 





Romeo and Juliet live 40 miles apart 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Math, time and rate 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Three tennis balls 
20120517 

From eiman: Three tennis balls are placed inside a container . the tennis balls are tangent to the top, bottom,and sides of the container . find the volume of air inside the container surrounding the tennis balls if the diameter of the tennis balls is 6 inches Answered by Chris Fisher. 





16 golfers 
20120517 

From Nohemi: Can 16 golfers each play in foursomes for 6 days?
I found the answer for 5 days, but is it possible to do it for 6. Answered by Robert Dawson. 





The area of a triangle 
20120517 

From Emilee: hi. How do i find the area of a triangle if the vertices are (3,0) (2,2) and (3,0). I graphed it and it came out a triangle. How do I find the area of it in an easy way? Answered by Penny Nom. 





Slope 
20120516 

From Kodie: What is the easiest way to find slope? Answered by Penny Nom. 





A lamp shade 
20120515 

From Fleur: I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre
Please could you give the pattern (cut out) dimensions for final cut. Answered by Penny Nom. 





Multiplying binomials 
20120514 

From Jordan: How do I solve the equation:
3(x+4)(x6) Answered by Penny Nom. 





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. 





A normal distribution problem 
20120513 

From Alysia: The scores on a test taken by 1000 students are normally distributed with a mean of 66 and standard of deviation of 12. If the college wishes only the top 8% of people to get an A, what would the cutoff score be for the A's? Answered by Penny Nom. 





Solve for x 
20120512 

From Desiree: 3x 5^2=8 Answered by Penny Nom. 





Water in a hemispherical bowl 
20120512 

From Jimmy: A bowl of water, being a hemisphere has a radius of 36cm.
Water is filled in the bowl and has depth of 18 cm.
Find the surface area of the water? Answered by Penny Nom. 





Golf for 6 
20120512 

From Steve: We have six golfers playing in two threesomes for six rounds of golf. Can you help solve this so that everyone plays with everyone else the same amount of times or close to it? Thanks! Answered by Victoria West. 





Drawing an isosceles triangle 
20120510 

From Nazrul: How can I draw an isosceles triangle whose each angle adjacent to the base is twice the vertex angle? Answered by Chris Fisher. 





Cycling and running 
20120507 

From liz: a biathlete travels 20 miles in 2.25 hours. She cycles part of the way at 12 mph and runs the rest at 5 mph. How far did she run? Answered by Penny Nom. 





A 25% sulfuric acid solution 
20120503 

From Scott: In order to make a 25% solution with 96% Sulfuric Acid, how much of the Sulfuric do I add to DI water to make up 2000ml?? Answered by Penny Nom. 





Golf: 8 players over 4 days in 4balls 
20120503 

From JimB: I cannot seem to get this to work. Previous answers cover 2balls, but we are 4balls.
What we really want is for each player to play with each other, at least once and no more than twice.
Ideally, each would also play equally in the first and the second 4ball of the day. Answered by Victoria West. 





The maximum distance from the vertex of a triangle 
20120502 

From David: There are three towns A,B,and C, equidistant apart.
A car is 3 miles from town A, and 4 miles from town B.
(ie, somehwere outside of the triangle which the three towns form)
What is the maximum distance that the car can be from town A?
This was asked as quiz question in my local pub last Sunday.
The answer is 7. How do I prove it?
Best regards. David in Denton. Answered by Robert Dawson and Chris Fisher. 





The dimensions of a rectangle 
20120430 

From Nikki: Name the dimensions of a rectangle that has the same area as this triangle?
I found the area of the triangle, which is 30. What do I have to do in order to complete this math problem? Answered by Penny Nom. 





Third side of a irregular triangle. 
20120427 

From Darya.: How to find third side of irregular triangle if c = 17m, b = 28m and area S = 210m^2. Answered by Penny Nom. 





The parameterization of a parabola 
20120427 

From Shawna: I am having problems finding the parameterization of a parabola. The question I was given is: Find the work done if a particle moves from the points (2,4) to (1,1) along the parabola y=x^2, while subject to the vector force of F=(x^3y,xy). So how would I start with finding the parameterization of a parabola? Answered by Penny Nom. 





A circle inscribed in a triangle inscribed in a circle 
20120426 

From Maty: How do i find the area of a triangle inscribed a circle while another smaller circle is circumscribed by the same triangle and the radius is 8. Answered by Chris Fisher. 





The exponential form of log8=P 
20120425 

From Kristina: what is the exponential form of log8=P Answered by Penny Nom. 





The circumcentre and orthocentre of a triangle 
20120425 

From Nazrul: The circumcentre and orthocentre of a triangle is given. A point on a side of the triangle
given. A vertex of the triangle on the circumcircle is also given.
How can I draw the triangle?
Please Help me.
Thank you for answering my previous questions. Answered by Chris Fisher. 





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

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





A puzzle with a triangle and 57 
20120425 

From sharon:
Question from sharon, a parent:
We have been battling with this for days and cant find any solution 
Using each of the following numbers once, fill all the spaces in the triangles so that each side of the triangle adds up to 57
numbers are 11,12,13,14,15,16,17,18,19
diagram is 
Any ideas ? this has to be in in just over 24 hrs ......help! Answered by Chris Fisher. 





A sloped yard 
20120424 

From William: Trying to calculate fill dirt for leveling a sloped yard to place a slab. Slab is 30'x40', yard slopes from corner #1 south 40' to Corner #4 drop is 11". From corner #1 east 30' to corner #2, drop is 11 1/4". From corner #1 southeast at a 45 degrees, 50' to corner #3, drop is 19 3/4". Corners numbered in a clockwise direction. Answered by Penny Nom. 





A parabolic bridge 
20120424 

From Adiba: A bridge constructed over a bayou has a supporting arch in the shape of a parabola .Find the equation of the parabolic arch if the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.
I did the problem but not sure is it correct .
I did like this f(0)=0we get c=40 if we took quadratic equation in x for a down ward parabola then how to find b and a please show me the answer of either a or b .Or I should use the standard form of parabola y=a(xh)^2+k then how to find a,h,k please help me Answered by Penny Nom. 





2x^2+5x+2 
20120423 

From eddie: 2x^2+5x+2 Answered by Penny Nom. 





A common chord to two circles 
20120422 

From Nicole: What is a common chord between two circles and how is it found in the problem: Two circles intersect and have a common chord, the radii of the circles are 13 and 15, the distance between the circle's centers is 14, find the common chord. Answered by Penny Nom. 





Gray siding and stone chimneys 
20120422 

From lupita: Fifty houses are on the north side of a river. The 2nd house has gray siding, and every 5th house after that also has gray siding. The 11th house has a stone chimney; every 3rd house after that also has a stone chimney. How many of the 50 houses have stone chimneys but do not have gray siding? Answered by Penny Nom. 





The sarsen circle 
20120421 

From Firdous: I found the circumference but after what to do I am not getting the question is.The diameter of the sarsen circle is 33 meters,since there were originally 30 sarsen stones located on the circumference, how far apart wold the centres of the stones have been?Round to the nearest tenth of a meter. Answered by Penny Nom. 





The area of a quadrilateral 
20120421 

From Rajat: calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''. Answered by Penny Nom. 





Golf for 12 
20120420 

From glenn: need to schedule 12 players for a 20 week season Answered by Victoria West. 





Golf for 12 
20120420 

From Bram: We are heading on a golf trip with 12 guys, playing 6 rounds. Can you please provide the formula whcih which have the least duplication.
Thanks in advance,
Bram Answered by Victoria West. 





Liters and gallons 
20120420 

From ann: the fuel tank of jacks car hold 72 litres when full jack uses half a tank of fuel he travels240 miles how many miles does he cover for each gallon of fuel Answered by Penny Nom. 





16 golfers 
20120420 

From steve: i have 16 golfers, 4 in "A" flight , 4 in "B" flight , 4 in "C" and 4 in "D"
We are playing 4 rounds (4 teams of 4) and every group must have a player from the A B C an D
flight, and in no round may 2 people have already played together! Answered by Victoria West. 





What was the class average? 
20120420 

From olwale: a class which consist of 15 boys and 10 girls sit for a test. the average score of the boys is 20 and the girls' is 25. find the average score of the class. Answered by Penny Nom. 





5 machine make 5 gadgets in 5 minutes 
20120420 

From Charles: 5 machine make 5 gadgets in 5 minutes,
so how long does it take for 100 machines make 100 gadgets? Answered by Penny Nom. 





Golf for 12 
20120418 

From Brent: I have a golf group that is set up as follows: 12 players, broken into
2 teams of 6. I am looking for a formula to have one player from team A
play against one player for team B each round, not repeat the match, and
ride with as little duplication as possible. I know that it is not statistically
possible with these numbers and will have at least one round that has
duplication. Answered by Robert Dawson. 





Golf for 10 
20120418 

From Bob: Question from Bob:
Hi,
I am trying to set up pairings for 4 rounds of golf with only 10 golfers (2 foursomes and 1 twosome) and trying to minimize duplications. Any formulas or help? Answered by Victoria West and Harley Weston. 





An equation of the form y=mx 
20120417 

From Samiya: what would be an equation of the form y=mx with the points (2, 6) and (1, 3) for the line? Answered by Penny Nom. 





A pyramid on a regular hexagon 
20120414 

From deepak: There is pyramid on a base which is a regular hexagon of side 2a cm.
If every slant edge of this pyramid
is of length 5a/2 cm, than what will be the volume of this pyramid Answered by Penny Nom. 





A tangent line to a circle 
20120414 

From Novelyn: find an equation of the line tangent to a circle with equation x^2+y^2+6x8y27=0 at the point P(1,2) Answered by Penny Nom. 





A 14 man golf league 
20120412 

From Paul: 14 man golf league. Need to have alternating 2 man teams for 18 weeks. Need to rotate foursomes so no one is stuck in twosome more than once. Can you help? Answered by Robert Dawson and Victoria West. 





A golf league with 2 man teams 
20120411 

From Cosmo: wanting to set up a golf league with 2 man teams. There are 14 A players and 14 B players.We want each A player to team with each B player once and each A player to play against each other A player once.Is this possible Answered by Victoria West. 





Two cars approach a rightangled intersection 
20120410 

From Michael: Two cars approach a rightangled intersection, one traveling south a 40km/h and the other west at 70km/h.
When the faster car is 4km from the intersection and the other case if 3km from the intersection,
how fast is the distance between the car cars changing? Answered by Penny Nom. 





The height of a cylindrical container 
20120410 

From Rodney: a cylindrical container has a radius of 6cm. the container is holding 255 cm3 of water. rounded to the nearest quarter inch, what is the minimum height of the container? Answered by Penny Nom. 





Golf for 28 
20120410 

From EARL: HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR
5 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF
4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO
PLAY WITH ONE ANOTHER ONCE AND NOT PLAY
WITH EACH MORE THAN ONCE IF POSSIBLE OR LIMIT
THE TIMES A GOLFER PLAYS WITH ANOTHER TO A
MINIMUM IF POSSIBLE. (PLEASE SEND AN EXAMPLE
OF THE SCHEDULING OF THE GROUPS FOR THE TEE
OFF ORDER)
THANKS FOR ANY SOLUTIONS YOU CAN PROVIDE.
EARL Answered by Robert Dawson. 





A semicircular roof gutter 
20120409 

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





A maximization problem 
20120409 

From Nancy: After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^0.02t  e^0.42t. Determine the time when the maximum concentration of drug occurs. Answered by Penny Nom. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





A number puzzle 
20120407 

From Kenya: my number is less than 25
my number of tiles will make only one rectangle
my number is odd
my number is a factor of 36 Answered by Penny Nom. 





Water is flowing from tank A to tank B 
20120406 

From Noel: At First, Tank A was completely filled with water. The tap from Tank A was then turned on and water flowed out at a constant rate. The water which flowed out was collected into Tank B. At the end of 6 minutes, Tank A was 2/3 full. After a further 8 minutes, Tank A had 2.4 liters of water left while Tank B was completely filled with water. Find the capacity of Tank B. Answered by Penny Nom. 





A 12 foot long board 
20120405 

From Lesley: If I have a board 12 feet long and am building shelves 2 1/4 feet in
length, how many inches are left? Answered by Jaymi Peterson and Penny Nom. 





A rectangular prism 
20120405 

From Tori: How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft. Answered by Penny Nom. 





The area of a right triangle 
20120403 

From Shelli: How do you find the area of a right triangle if you only know that the hypotenuse is 10 and that the base and height are unknown but are equal? Answered by Penny Nom. 





Radioactive decay 
20120402 

From Christy: Hello, how do I go about answering this question?
Should I be using the formula Ce^(kt)?
Given that the decay constant for Radium is .000428/year, how long, to the nearest year, does it take a sample to decay to 15% of its present mass? Answered by Penny Nom. 





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

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





A circle drawn around a equilateral triangle 
20120401 

From BIMAL: what is the diameter of a circle drawn around a equilateral triangle of size 6 cm Answered by Penny Nom. 





A lot with a slope 
20120330 

From Carlos: I have a lot with a slope. On the right I need to bring it up 2', From that point to the left is 112' which at this point I need to bring it up 5' for it to be level . The distance front to back is 80'. What is the cubic yards of this area that I need to fill in. Answered by Harley Weston. 





Golf for 17 
20120329 

From Richard: Hi Guys,
I have a scheduling problem which I don't think you have covered before.
Apologies if you have!
I have 17 golfers due to play 4 rounds of golf.
Each round will consist of 3 threeballs and 2 fourballs (ie. 17 golfers in 5 groups)!
Is it possible to come up with a schedule where each golfer plays
with different partners in each round? Answered by Robert Dawson. 





The period T of a pendulum 
20120327 

From Ashley: The period T of a pendulum is given in terms of its length, l, by T=2pi sqrt(l/g) where g is the acceleration due to gravity(a constant)
a. find dT/dl
b. what is the sign of dT/dl
c. what does the sign of dT/dl tell you about the period of the pendulums? Answered by Penny Nom. 





A uniform probability density function 
20120326 

From Noeline: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





The equation of a line 
20120326 

From Danielle: Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (2,0) and (0,3)?
Thank You! Answered by Penny Nom. 





Painting a pool 
20120325 

From Salai: A swimming pool measures 8m long, 6m wide and 1.5 m deep. The special paint for the pool cost $6per square metre.
How much will it cost to paint the interior surfaces of the pool ? Answered by Penny Nom. 





A cubic inequality 
20120325 

From Victoria: The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 Answered by Penny Nom. 





Angle measures 
20120321 

From jogiboy: how can i get the sine theta if the given is 3.14/3 Answered by Penny Nom. 





How long will it take lee to catch up with jodie? 
20120321 

From kirsten: for example, if jodie is on the bus travelling at 10 m.p.h and lee is walking at 4 m.p.h how long will it take lee to catch up with jodie?? what is this mathematical name for this Answered by Harley Weston. 





A steamroller with a 3 foot diameter and a 6 foot width makes 20 revolutions 
20120321 

From Robert: A steamroller with a 3 foot diameter and a 6 foot width makes 20 revolutions. How much ground area does it pave? Answered by Penny Nom. 





Gravel, sand, cement and an equilateral triangle 
20120321 

From saheed: how many tonnes of gravel and sand,bags of cements will be required to concrete 5feet depth/deep of 4feet equilateral triangle? Answered by Harley Weston. 





Two overlapping circles 
20120321 

From Monty: If you have a 3.75" radius circle overlapping a 5" radius circle with their centers 3" apart what would be the area of the nonoverlapped portion of the small circle? Answered by Penny Nom. 





The area of an irregular hexagon 
20120320 

From Jacob: I am having trouble finding the area of an irregular hexagon with 5 right angles.
It has 5 given sides, with the lengths as follows:
8.2 ft.
6 ft.
4.5 ft.
2.2 ft.
6 and one third ft. Answered by Chris Fisher. 





Remainders 
20120318 

From Leslie: Question: Janice has some marbles. When she divides them into groups of 4, she has 2 marbles left over. If she divides them into groups of 5, she will also have 2 left over. What is the least number of marbles she can have? Answered by Penny Nom. 





The length is inversely proportional to the width 
20120318 

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





A vertical line passing through (10,4) 
20120316 

From Isabelle: Hi! My question is this:
Write the equation of each line described:
A vertical line passing through (10,4)
I would really appreciate your help!
Thanks,
Isabelle Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

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





Probability 
20120314 

From tom: Let A and B be events with p(A ∪ B)= 7/8, p(A ∩ B)= 1/4, p(A' )= 5/8
Find:
a. p(A)
b. p(B)
c. P(A ∩ B')
...problem for me is that if p(A') = 5/8 then P(A) should be 1/4...so that the p(A' ∪ A) = p(A ∪ B) = 7/8...however, the book says the answer for p(A) is 3/8...does that mean, my interpretation is wrong (because if it is, then all my answers would be crap)...or is it just another typographical error? Answered by Penny Nom. 





The dimensions of a rectangle 
20120313 

From irvyn: if you are only given the area and the perimeter how do you find the dimension? Answered by Penny Nom. 





A trapezoidal prism filled with sand 
20120312 

From Maria: could a Trapezoid that is 80 inches high with a 54 inch width top and a 89 inch width bottom and a 80 inch depth hold 58 cubic yards of sand? Answered by Robert Dawson. 





Circles 
20120311 

From Deniz: Two circles are externally tangent and the lengths of their diameters are 4 and 6. Find the length of the segment joining the centers of the circles. Answered by Penny Nom. 





Buying school supplies 
20120309 

From Jada: Hi, my daughter is having difficulties with a problem she is in the 5th grade, and insisted that it was a guess and check problem, but she really doesn't understand, and I don't either. Can you help us out?
Danielle is buying school supplies. She
has $7.25 to spend.
Notebook: $0.75
Pencils: $1.95
Pens: $2.50
Planner: $5.00
Please help by explaining the guess and check strategy for a problem like this. Thank you. Answered by Penny Nom. 





A clock takes 3 seconds to strick the hour of 3 o'clock 
20120309 

From saptarshi: [ A clock takes 3 seconds to strick the hour of 3 o'clock. How many seconds will it take to strick 9 o'clock?] Answered by Robert Dawson. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





A lost combination 
20120306 

From pam: I lost the combination for my luggage that I haven't used for many years. It is a 3 digit combination. I'm pretty sure only these numbers could have been used: 0,1,2,3,7,8,9. Can you give me a calculated list of all these combinations? Answered by Penny Nom. 





The dimensions of a conical tent 
20120304 

From yash: a conical tent is to accommodate 11 people.Each person must have 4m square of space on the ground and 20m cube at air to breathe.Find the height and radius of the conical tent.26202 Answered by Penny Nom. 





Tina is older than Catherine by 1 year and 7 months 
20120303 

From jennifer: Tina is older than Catherine by 1 year and 7 months. Karen is
younger than Tina by 2 years and 11 months. If Karen is 7 years and
2 months old, find out Catherine's age. Answered by Penny Nom. 





Percentage of water in a soil sample 
20120301 

From avi: what i need is the formula in getting the percentage from gram.
situation:
i need to know how many percent will i declare in getting the moisture of a soil sample
i weighed 2,000 grams of soil before i dried it out in the oven, after few hours the recovery
of the dried out soil is 1,700 grams. How many percent will be the water content?
kindly send me a formula in computing this.
thank u very much! Answered by Penny Nom. 





The area and perimeter of a rectangle 
20120301 

From RAJIB: PEREMETER OF A RECTANGLE IS 24. FIND THE AREA ? Answered by Penny Nom. 





The height of an equilateral triangle 
20120229 

From Carley: Hi my name is Carley. I am an 8th garder. What us the height of an equilateral triangle si the sides are 18 cm? Answered by Penny Nom. 





Mr. Schneider's mass 
20120229 

From Khiya: Mr. Schneider's mass is 2 digits. The first digit is 3 times the second digit. Both digits are odd numbers, and his mass is greater than 35 kg. What is Mr. Schneider's mass? Answered by Penny Nom. 





Measuring the liquid in a horizontal tank 
20120228 

From Philip: I have a steel gas tank that is 3' dia X 5' length. The total volume is 1000 litres.
But how much is left when I use a stick and measure 6" from the bottom or 12" or 24" ??
Is there a formula to use for this task?
Thanks. Answered by Harley Weston. 





The weight of a steel plate 
20120227 

From david: what is the weight of a steel plate that is 1/2" thick, 20" wide, and 45"long if the steel weigh .28 lb per cubic inch. Answered by Penny Nom. 





Tiling a floor 
20120227 

From jamie: how many 16in by 16in blocks would it take to cover a 16ft by 16ft floor? Answered by Penny Nom. 





Parametric equations 2 
20120225 

From Kathy: If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you! Answered by Harley Weston. 





Expected value 
20120224 

From Lara: A life insurance company sells a $250,000 1year term life insurance policy to a 20yearold male for $350. According to the National Vital Statistics Report the probability that the male survives the year is 0.998734. Compute and interpret the expected value of this policy to the insurance company.
I'm very confused on how to do this. I assume x is the profit the insurance company makes in the year of $350 but beyond that I don't know what to do. Thanks. Answered by Penny Nom. 





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

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





The volume of an irregular tetrahedron 
20120222 

From Brittany: If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(4,3,5), B(2,1,2), C(0,5,0), and D(2,0,0) can you shown me the working and formular to find the volume? Answered by Robert Dawson. 





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

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





A 23 acre airport runway 
20120221 

From Ron: I have a 23 acre plot. If it were in a straight line, would it be enough distance for a plane to take off and land if the plane needed 1 mile? Answered by Robert Dawson and Penny Nom. 





The 10000th day of her life 
20120221 

From derrick: Ella was born early in the morning on a Friday.She got married on the 10000th day of her life. What day of the week was it? Answered by Penny Nom. 





Tim sells 6 times as many oranges as apples 
20120220 

From Bronwen: Tim sells 6 times as many oranges as apples. If he sell 490 in total one morning, how many of each type were sold? Answered by Penny Nom. 





A circle inscribed in a quarter circle 
20120220 

From sonam: ABC is a quarter circle and a circle is inscribed in it and if AB=1cm than find radius of a small circle. Answered by Penny Nom. 





Demarkus is paving a new driveway 
20120219 

From Anita: Demarkus is paving a new driveway for a local YMCA volunteer club. The driveway is 90 yards long and 6 yards wide. If the concrete cost $2.50 per square foot, how much will it cost Demarkus to cover the driveway? Answered by Penny Nom. 





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

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





Fractions and proportions 
20120216 

From Kenneth: Hello:
I read the following in an old textbook:
Display the numbers 27, 18, 26, and 39 so as to form a proportion.
Which set of equal fractions is correct?
18/27 = 26/39
18/26 = 27/39
I thank you for your reply. Answered by Penny Nom. 





Margie threw a ball 
20120216 

From mary: at 9:45 Margie threw a ball upwards while standing on a platform 35ft above the ground. The height after t seconds follows the equation:
h(t)= 0.6t^2 +72t+35
a) what will be the maximum height of the ball?
b)how long will it take the ball reach its maximum height?? Answered by Harley Weston. 





Figures with dots 
20120215 

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





A word problem 
20120215 

From Bo: Jane guessed a number. Tom guessed a number that was double the sum of 1 more than twice the number guessed by Jane. Sum of the numbers guessed by both were 27, what are the numbers? Answered by Penny Nom. 





36 golfers 
20120215 

From Steve: We will have 36 golfers playing 4 rounds of golf and would like to have different foursomes each round. In other words, no player will play with another more than once. Answered by Harley Weston. 





A cylindrical container 
20120214 

From KRIS: YOU ARE PaCKAGING 4 EQUAL SIZED PAINT CANS WITH A RADIUS 8CM AND A HEIGHT OF 20CM, IN A CIRCULAR CONTAINER.What is the surface area of the packing container? Answered by Penny Nom. 





Jack and Kate set off in their cars ... 
20120213 

From akiri: Jack and Kate set off in their cars from the same point to travel the same journey. Jack has a start of eight minutes before Katie sets off. If Jack travels at 50mph and Katie travels at 75mph, how many miles will be travelled when the two cars are level? Answered by Penny Nom. 





A storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. Answered by Penny Nom. 





Simplify the expression 
20120212 

From Christy: Hi guys, ok so I'm having problems with solving this equation since it's been so long I've done precal.
I have to find critical points so I have to find the derivative first. This is what I've done so far
s(t)= (t6)^4 * (t+1)^2
t'= 4(t6)^3*(1)*(t+1)^2+ 2(t+1)(1)*(t6)^4
so this is where I got stuck, which is the algebra part. How can I simplify this to get the answer to figure out the critical points. Answered by Penny Nom. 





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 circle and a chord 
20120211 

From Sophia: The diagram shows a circle with a chord that is 10cm long. The middle of the chord is 12cm from the centre of the circle. Calculate the radius.
Chord length is 10cm.
The distance from the centre to chord is 12 cm. Answered by Penny Nom. 





Can the result of the calculation be 2? 
20120209 

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





Litres in a box 
20120209 

From vicky: how much litre water can be filled in a box of 12 inches *24 inches *12inches Answered by Penny Nom. 





Two circles 
20120208 

From crisfe: find the point where the common cord of the circles x2+y2=25, x2+y212x6y+35=0 process there line centers. what point they intercepts? Answered by Penny Nom. 





Wallpapering a room 
20120208 

From jimmy: Ms. Frank is going to
wallpaper a living room with dimensions
24 feet long, 18 feet wide, and 8 feet
high. What surface area does Ms. Frank
plan to wallpaper? Answered by Penny Nom. 





The curvature of the earth 
20120208 

From sean: Question from sean, a student:
Two people 1.8 metres tall walk directly away from each other until they can no longer see each other (due to the curvature of the earth, which has a radius of about 6378 km).
A) Find a function relating the height of two identical objects with the distance between them using the scenario above as an example.
B) Sketch this function (you may use Graphmatica if you wish). Over what domain and range does the function exist?
C) Describe this relation in practical terms. Answered by Harley Weston. 





A road around a garden 
20120207 

From Manu: Inside a square garden of side 158m, a road 4m wide is built all around. What is the area of the remaining part of the garden? Answered by Penny Nom. 





The volume of a round tube 
20120207 

From I.C: I need to find out how long a 10" round tube needs to be in order for there to be .95 cubic feet of air space Answered by Harley Weston. 





Expressing 0.5% 
20120206 

From Kenneth: Hello:
It is correct to express 0.5% as 5 tenths of one percent.
Is it also correct to express 0.5% as 5 tenths of onehundred percentage points or 5 tenths of one percentage point?
I think it would be 5 tenths of one percentage point because 5 tenths of onehundred percentage points would be 50 percentage points, but I'm not sure.
I thank you for your reply. Answered by Penny Nom. 





Notation for the second derivative 
20120206 

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





A quartic polynomial that is a perfect square 
20120205 

From archit: If P(x)=x^4+ax^3+bx^28x+1 is a perfect square then (a+b)=? Answered by Penny Nom. 





A rectangular block and a sphere 
20120202 

From snehal: a solid rectangular block of metal 49 cm. by 44cm. 18cm. is melted and formed into a solid sphere, find the radius of the sphere[22/7] Answered by Penny Nom. 





There is a police officer in pursuit of suspect 
20120201 

From Jay: There is a police officer in pursuit of suspect. They suspect is driving on a straight road traveling at 79 mph, the officer is 233 yds away, traveling at 92 mph, the suspects car 5 ft long and the officers car is 5.3 ft long, how long will it take to have the front of the officers car, equal to the front of the suspects car down to the tenth of a second. Answered by Harley Weston. 





If a parallelogram is a cyclic quadrilateral then it is a rectangle 
20120201 

From Kim: Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle.
Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA. Answered by Robert Dawson and Chris Fisher. 





Properties of real numbers applied to subsets 
20120201 

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





The dimensions of a rectangle 
20120131 

From Dazz: Hi I was wondering how to find the length of a rectangle if you know the area is 484 square inches And the length is 10 square inches or 22 square inches?
Thanks~Dazz Answered by Penny Nom. 





A two digit number 
20120129 

From Christine: Five times the sum of the digits of a two digit number equals the number. If the digits are reversed, it becomes nine more than the original number. What is the original number?
I really don't understand this question, help me please Answered by Penny Nom. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





The volume of a dugout 
20120128 

From Jan: is there a formula for calculating the cubic yardage removed from a dugout
for example that is forty feet wide by one hundred and twenty feet long by
twelve feet deep with a three to one slope? It is the slope that makes it a
little tricky. Thank you. Answered by Penny Nom. 





Tons of fill dirt 
20120127 

From Brian: about how many tons of fill dirt would I need to level a area 30 foot by 30 foot
and 6 foot deep Answered by Penny Nom. 





The area of a triangle 
20120127 

From mary: I have a scalene triangle and the base is 33m, side is 52m and the unparallel side is 25m but i drew a dotted line down and that s 20m
how do i figure the area?
thanks Answered by Penny Nom. 





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

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





Rolling three dice 
20120126 

From Aishwarya: A red, a blue and a green die are all thrown at the same time. Display all the possible outcomes in a suitable way. Find the probability of obtaining:
1. A total of 18 on the three dice
2. a total of 4 on the three dice
3. a total of 10 on the three dice
4. a total of 15 on the three dice
5. a total of 7 on the three dice
6. the same number on each die.. Answered by Robert Dawson. 





The difference in the latitudes of Lynchburg and Myrtle Beach 
20120126 

From Sarah: Assuming that the earth is a sphere of radius 6378 kilometers, what it is the difference in the latitudes of Lynchburg, Virginia and Myrtle Beach, South Carolina, where Lynchburg is 400 kilometers due north of Myrtle Beach? Answered by Robert Dawson. 





A circular cylinder circumscribed about a right prism 
20120125 

From Noriz: A cylinder is circumscribed about a right prism of altitude 12.6cm.
Find the volume of the cylinder if the base of the prism is an
isosceles triangle of sides 3cm by 3cm by 2cm.
Hope you can help me with this. Answered by Penny Nom. 





Great circle course 
20120125 

From Hervé: On the earth, the mathematical formula giving the distance
between two points, and the initial course for a boat on the great circle
is well known.
I need to find the inverse formula, ie knowing an initial position on earth,
and the initial course of the boat, and the distance to run on the great circle,
the formula gives the final position (longitude and latitude). Answered by Robert Dawson. 





Today is Emma's Birthday. 
20120125 

From Mike: Today is Emma's Birthday.
Emma's mother is four times as old as Emma is today.
In four years, Emma's mother will be three times as old as Emma.
How old is Emma today? Answered by Penny Nom. 





A fountain 
20120124 

From kris: A fountain has a radius of 14 meters to its outer edge. Their is an inner ring in the center of the fountain, where a statue of Sir Isaac Newton stands, that does not contain water. The inner ring has a diameter that is 6m less than the diameter of the outer ring of the fountain. What is the circumference of the inner ring? What is the area that is covered by water in the fountain? Answered by Penny Nom. 





Four pizzas 
20120123 

From kris: a pizza company wishes to put 4 medium pizzas in a box to sell as a party pack. The box they want to use the square and has dimensions of 60cm by 60cm. They need you to help them calculate the dimensions of the pizza that will fit in the box. Calculate the following: area, radius, diameter, circumference Answered by Penny Nom. 





A problem in logic 
20120119 

From Ghader: The puzzle below I know the answer to; because someone told me! My question is: how could I answer it using logic, maths, etc. what field of inquiry does this kind of problem fall into?
Puzzle: You are in a room with two men: one is a compulsive liar and the other is a compulsive honest. There are two doors: one leading to heaven, the other to hell. The two men know which door leads to where. You want to go to heaven but are allowed only ONE question from one or the other of the two men. What would that question be?
[The question to ask, from either man, is: "if I asked the OTHER man which door leads to heaven, which door would he point?". You would then choose the other door.]
Has this answer got any basis in logic or maths at all? Answered by Robert Dawson. 





8(3x+4)+6x=4(x8 )+4x 
20120118 

From bianca: 8(3x+4)+6x=4(x8 )+4x Answered by Penny Nom. 





A limit 
20120118 

From Neil: The limit of [(1/x)^3  1/8]^1/3 all over (x  1/2) as x approaches 1/2 to positive infinity. How to answer that? Answered by Harley Weston. 





The difference in latitudes of two cities 
20120118 

From Renee: Assuming that the earth is a sphere of radius 6378 kilometers, what is the difference in latitudes of two cities, one of which is 600 kilometers due north of the other? Answered by Robert Dawson. 





A circle inscribed in a regular octagon 
20120116 

From Eric: I have a circle inscribed in a regular octagon. How do I determine the length of one side of the octagon if I know the radius of the circle (2.75 inches) ? Answered by p. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





The derivative of x^(1/2) 
20120114 

From Eric: I have an problem figuring out the derivative of the negative square root of x i.e. x^(1/2) using the first principle.
Could someone please show me?
Thanks in advance! Answered by Harley Weston. 





How many gallons of water to fill my pool? 
20120113 

From Don: How many gallons of water do you need to fill a 22 feet long and 13 feet wide rectangular pool if it is 3 feet deep on one end and 7 feet deep on the other end? Answered by Penny Nom. 





Four apples and two oranges cost Rs. 30... 
20120113 

From nasr: Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost? Answered by Harley Weston. 





Lost in the woods 
20120112 

From Liz: I am lost in the woods. I believe that I am in the woods 3 miles from a straight road. My car is located 6 miles down the road. I can walk 2miles/hour in the woods and 4 miles/hour along the road. To minimize the time needed to walk to my car, what point on the road should i walk to? Answered by Harley Weston. 





The radius of a circle 
20120112 

From Janie: Find the radius of a circle knowing that a chord of 24.6 inches has a corresponding arc of 70°. Answered by Penny Nom. 





Running 5 km 
20120112 

From Fayeann: What amount of time will it take a person running 7 m/s to travel a distance of 5 km? Answered by Penny Nom. 





What is the height of the triangle? 
20120112 

From Hailey: The area of a triangle is 77ft2. if the base is 11ft. how tall is the height? 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. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





A picture in a frame 
20120110 

From nnadozie: a picture, which measures 46cm by 38cm, is surrounded by a frame, which is 2cm wide, find the area of the frame. Answered by Penny Nom. 





Designing aluminum cans 
20120108 

From swathi: A company manufactures aluminum cans. one customer places an order for cans that must be 15 cm high, with a volume of 1200cm cube.
a) use the formula V= pie r squared h to determine the radius that the company should use to manufacture these cans
b) graph the function that corresponds to 0 = pie r squared h minus V to determine the radius. Answered by Penny Nom. 





A wire spiral 
20120107 

From Pinar: I am trying to help my daughter with very challenging maths questions which sometimes I get stuck
If someone help me with one of them I would appreciate it.
Jane is making a spiral out of wire. She bends the wire after 1 cm, then bends the wire
after 2cm, then 3cm and continues in this manner. After 4 bends she used 15 cm of wire
For each bend how many cm wire was used? After 6 bends how many cm wire will she have used?
How many bends will she have made if she uses 66 cm of wire?
I would appreciate if somebody would help me with this.
Thank you!
Pinar Answered by Penny Nom. 





The dimensions of a rectangle 
20120106 

From joseph: The perimeter of a rectangle is 72 inches. The length of the rectangle
is three more than 2 times the width of the rectangle. What is the
length of the rectangle? Write and solve an equation to determine the
dimension of the rectangle. Answered by Penny Nom. 





A straight line distance 
20120106 

From Margaret: If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line? Answered by Penny Nom. 





Two shapes 
20120106 

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





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





Lotto tickets 
20120103 

From Ashley: Hi. I play the lotto a lot, and have yet to win. How many combinations can I make with 6 numbers 153? I am trying to come up with a dollar amount so I know how much I would have to spend to guarantee a win. Thank you in advance. (I'm no good at math) Answered by Robert Dawson and Penny Nom. 





Triangles, area and perimeter 
20120101 

From Panny: I saw a question asked on your board without an answer.
How do I find the area of a triangle any triangle if I only know the perimeter.. Answered by Penny Nom. 





Sum and difference of squares 
20111231 

From Anne: Se x e y são números reais distintos, então:
a) (x^2 + y^2) / (x  y) = x + y
b) (x^2 + y^2) / (x  y) = x  y
c) (x^2  y^2) / (x  y) = x + y
d) (x^2  y^2) / (x  y) = x  y
e) Nenhuma das alternativas anteriores é verdadeira. Answered by Harley Weston. 





Limits and composition 
20111230 

From Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function Answered by Penny Nom. 





Triangular numbers that are square 
20111227 

From Luke: The “TnS” is a positive integer which is both Triangular number
and Square number. For example, 36 is a “TnS” number
since 36=1+2+3+4+5+6+7+8 (Triangular number)
and 36=6x6 (Square number).
What is the next “TnS” which is greater than 36? Answered by Penny Nom. 





The graph of a quadratic function 
20111227 

From Thomas: sketch a quadratic function with zeros at 3 and 1 Answered by Penny Nom. 





The volume of a frustum of a cone 
20111224 

From CV: If I know the height, taper, and volume of a frustum cone,
what are its Radii?
Calculating frustum cone volume is straight forward.
v=Pi/3*h*(R*R+r*r+R*r) where;
v=volume;
h=frustum height;
R=major radius;
r=minor radius;
Pi=3.1415926;
t=taper, ('slant angle' where t=0 is a disk)
Here is the tricky part.
Knowing 'h', 't', & 'v';
Calculate one or both of 'R' & 'r'.
Specifically, what is the formula for 'R=' or 'r='? Answered by Penny Nom. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





The volume of a cylinder 
20111222 

From luke: what is the volume of a cylinder that is 30 mm in diameter and 70 cm high?
can you please write the equation out in full for me to help understand it better. thanks Answered by Penny Nom. 





The weight of 36 inch steel pipe 
20111222 

From Keith: What is the weight of 36 inch steel pipe 3/4 wall per foot in lbs. Answered by Penny Nom. 





Water is flowing into a cup 
20111219 

From Tim: A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Answered by Penny Nom. 





The number of gallons in a box 
20111218 

From matt: i need to know how many gallons a 16 inch square box will hold Answered by Penny Nom. 





Displacement 
20111217 

From faisal: a helicopter takes off and travels 300 km due north then returns to its landing field. what is its displacement? Answered by Penny Nom. 





Rounding 
20111214 

From seth: A decimal number rounded changed to 23.7 after it was rounded.
Give a decimal number that is less than 23.7 and another that is greater than 23.7 that each round to 23.7.
Explain to what place each number was rounded. Answered by Penny Nom. 





Augmented matrix 
20111214 

From Britney: Write Augmented matrix and use row reduction to solve.
I need major help with this problem! Tomorrow is my semester test and I have no idea how to do this.
2x+5y=8
yx=10 Answered by Robert Dawson. 





The circumference and area of a circle 
20111213 

From Mable: A circle that going 70mi across using 22/7 I need the area,radius, and the circumference
and how to set up the steps can you help? Answered by Penny Nom. 





i+i^2+i^3+i^4...+i^102 
20111213 

From megan: how do you solve i+i^2+i^3+i^4...+i^102 Answered by Robert Dawson. 





Extended real numbers 
20111212 

From Justin: Hi there, I was wondering does +infinity=+infinity in the extended real number system? Basically, I was wondering does +infinity=+infinity since infinity and any extended real number (except +infinity) are less than +infinity?
Sincerely,
Justin Answered by Robert Dawson. 





Exponential form 
20111212 

From Zoey: What is the exponential form of 1/8?? Answered by Penny Nom. 





Simple interest 
20111211 

From sandeep: Use the formula I = Prt to solve.
Damon deposits $500 into a savings account that pays simple interest
at a rate of 0.65% per year. How long will it take Damon to earn $130
in interest? Answered by Penny Nom. 





factor 6x219x+3 
20111210 

From pedro: factor 6x219x+3 Answered by Penny Nom. 





Jennifer wants to fence in her backyard 
20111209 

From Val: Jennifer wants to fence in her backyard. A yard is rectangular and is 15 feet by 12 feet. One 12foot side is against the house so it does not need fencing. How many feet of fencing does Jennifer need? Answered by Penny Nom. 





A 3000 gallon tank 
20111208 

From Delores: I need to know what size to build a tank to hold 3000 gallons of water
one side needs to be 8 ft width X 6 ft height how long does it need to
be? Answered by Penny Nom. 





What does 2xy mean? 
20111207 

From dana: I don't know what is 2xy what does that mean? is it 2x+2y or 2x times y
Please help! thank you for your time!! :) Answered by Penny Nom. 





The height of a flagpole 
20111207 

From Grail: at a certain point the angle of elevation of the top of a flagpole which stands on a level ground is 35 degree. 75 ft. nearer the pole, the angle of elevation is 50 degree. How high is the pole Answered by Penny Nom. 





Two trains passing each other 
20111207 

From Tamkeen: two trains 245m and 315m long are travelling toward each other at 90km/h and 54km/h respectively on parallel lines . how long do the train take to pass one another train the time they meet each other? Answered by Penny Nom. 





How many rpm does a 3.5 in. diameter wheel turn at 7 miles per hour? 
20111206 

From Al: how many rpm does a 3.5 in. diameter wheel turn at 7 miles per hour 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. 





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





The arc of a bridge 
20111205 

From Marioneta: Two same columns placed symmetrically, 40 m apart.
The height of columns is 8 m.
If the origin of the coordinate system is placed at the foot
of the left column the equation of the arc of the bridge:
f (x) =1/80x^2+1/2x+8
What is the maximum height of a boat sailing under the bridge and
identify its path. Answered by Penny Nom. 





A cube of ice is melting 
20111205 

From Emily: a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm? Answered by Penny Nom. 





What is the altitude of the balloon? 
20111204 

From C: Chelcy and Jorgeare 2.32 miles apart. The observe a hot air balloon directly overhead between them Chelcy's angle of elevation is 28 degrees. Jorge's Angle of elevation is 37 degrees. What is the altitude of the balloon? Answered by Penny Nom. 





Two circles 
20111204 

From Luke: Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Answered by Chris Fisher. 





Two parallel chords 
20111204 

From violet: Two parallel chords of a circle AB and CD on the same side of the centre measure 6 cm and 11 cm respectively. Find the radius. Answered by Chris Fisher and Walter Whiteley. 





Repeating a medication 
20111202 

From ivan: One person received the recommendation of a doctor taking the drug "Passaneura" every 10 hours. After a few days, noted that the time you should take the medication had not been repeated once. How many days since the first dose, will have to pass the time until recur Answered by Penny Nom. 





Solve for theta if 8cos^2 theta3=1 
20111202 

From Katherine: Hi,
I have just learned to solve trigonometric problems for theta and have one specific question in order to find the solutions to my homework.
I will use one example for this question. If I have 8cos^2 theta3=1
I first divide by 8 and get cos^2theta=3/8
then I have cos theta= plus or minus the square root of 3/8
Then I assume that I plug in inverse cos (the square root of 3/8) to my calculator.
How do I find the four solutions (we are typically supposed to find four, I believe?)
Can you help me with finding the solution to this problem? Thank you! Answered by Penny Nom. 





The total number of roles that a user can be assigned 
20111202 

From Colin: Hi, I want to define an equation for calculating the total combination of roles that a user can be assign in a system.
Here is the background: There are two types of roles that a user can be assigned. These are object roles and data roles. There must be at least 1 object and 1 data role in the system. A user must be assigned at least 1 object role and at least 1 data role. A user can be assigned as many object roles and data roles as are created in the system. There is no upper limit to the number of roles that a user can be assigned except for the total number of object roles and data roles that exist. The number of object roles and data roles in the system are independent.
Can someone please assist? Thanks. Answered by Penny Nom. 





A suspension bridge 
20111130 

From jennifer: suspension bridges like the golden gate bridge, are used to span large distances.
when the main curved cables are attached to the deck by vertical cables they will end
up in the shape of parabola. assume that we need to build a bridge that spans
2,400 feet. the two towers 165feet tall each where placed at 400feet from either
side. the lowest point of the center of the bridge at 10feet. vertical suspension cables
where placed at 25foot interval. how many feet of cable are needed to connect
the deck to the main cables between the two towers? show all working. Answered by Penny Nom. 





Four carpenters can build eight houses in 10 days. 
20111123 

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





A railway bridge over a road is in the shape of a parabola 
20111123 

From Brennen: A railway bridge over a road is in the shape of a parabola,
and the bridge is 3 m high in the middle and 6 m wide at its base.
A truck that is 2m wide is approaching the bridge.
What is the maximum height that the truck can have and
still pass under the bridge? Explain.
Thank you!! Answered by Penny Nom. 





The average age of 300 cars 
20111122 

From Jason: I have 300 used cars built from 1970 to 1980, I would like to know the average
age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?
Total built 
50 
56 
30 
10 
30 
25 
64 
9 
12 
14 
Year built 
1971 
1972 
1973 
1974 
1975 
1976 
1977 
1978 
1979 
1980 
Thanks Answered by Penny Nom. 





The height of a flag pole 
20111121 

From Micah: A flagpole stands vertically at the edge of a roof of a building 200 ft high. the angle of elevation of the pole from a point 100 ft from the bottom of the building is 67 degrees. Find the length of the pole in meters. Answered by Penny Nom. 





Water pouring into a conical tank 
20111121 

From Patience: Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you Answered by Penny Nom. 





Reducing by a scale factor of 1/3 
20111121 

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





A triangle problem 
20111120 

From May: In triangle ABC, AB=AC, angle A=20,
D lie on AB making DC=AD,
E lie on AC making angle EBC=70.
Find angle DEB. Answered by Chris Fisher. 





15 pigs and 6 pens 
20111116 

From Mike: I have 15 pigs and 6 pens, I have to put them in odd numbers, how do I do it. Answered by Chris Fisher. 





The 3, 4, 5 right triangle 
20111115 

From rishil: to the nearest degree,what is the measure of the smalles angle in a rightt triangle with sides of length 3,4 and 5? Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





Lines tangent to y^2=4x 
20111111 

From Reuchen: Find equations of the lines tangent to y^2=4x and containing (2,1). Answered by Penny Nom. 





The dimensions of a rectangle 
20111111 

From Ivan: The length of a rectangle is 31 centimeters less than five times its width. Its area is 72 sq centimeters. Find the dimensions of the rectangle. Answered by Penny Nom. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





The slope of a line 
20111110 

From Sara: Line k lies in the xyplane.
The xintercept of line k is 4.
And line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0).
What is the slope of line k?
Give the answer as a fraction. Answered by Penny Nom. 





What was the cost price of the article? 
20111110 

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





The perimeter of a quarter circle 
20111110 

From sierra: how do you figure the perimeter of a quarter circle that has a radius of 12 Answered by Penny Nom. 





A word puzzle 
20111110 

From kevin: ABCD
ABCD
ABCD
ABCD

EBEA
What does each letter stand for?
I've been at it for days and still have nothing.
Thank you,
Kevin Answered by Robert Dawson. 





Uses of logarithms 
20111109 

From BEA: what is the use of logarithmic functions in real life or daily life? Answered by Penny Nom. 





0.5 acres of land 
20111109 

From Kim: I have .5 acres of land. I want to divide it into 20x20 squares. How many squares will I have? Answered by Penny Nom. 





The volume of a berm 
20111104 

From Roy: I need to know how many cubic yards are in a berm 100 ft long 8 ft high and 32 ft wide at the bottom? Looking from the end of the berm it would look like a trangle. Thanks for the help. Answered by Penny Nom. 





A right angled triangle 
20111031 

From bijo: how can i find the tangent point at a circle with origin as center with radius r and the tangent pass through a given point P? I also want to find out the third point of a right angled triangle given other two points? Answered by Chris Fisher. 





The area of a triangular garden 
20111031 

From tasha: a garden has sides of 6m,8m and 10m find the area Answered by Chris Fisher. 





A scale drawing 
20111030 

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





Modular arithmetic 
20111030 

From Kim: Hello,
I am editing a resource for students, and I think some of the answers may be incorrect.
The text I was given and my questions are in the attachment.
Any help you could give would be appreciated.
Thanks,
Kim Answered by Harley Weston. 





The LCM of 6,15 and x is 90 
20111030 

From Richie: Hi there,
There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5
#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?
From #1, since 90=6x15, how can this be used to work out possible values of x?
Thanks in advance,
Richie Answered by Penny Nom. 





The average speed for the whole journey 
20111030 

From Shahzad: a train travels 68 Km at an average speed of 51Km/h. It then travels another 20Km at an average speed of 40Km/h before reaching its destination. Calculate the average speed for the whole journey? Answered by Penny Nom. 





A mythical soccer ball 
20111027 

From Joel: We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes.
The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball? Answered by Robert Dawson and Lorraine Dame. 





The square root of z=3+4i 
20111027 

From dianah: how to find the square roots of complex number, z=3+4i Answered by Robert Dawson. 





3 fish 
20111027 

From Ann: You have 3 fish weighing a total of 21 lbs. The largest fish weighs twice as much as the second fish and the third fish weighs half the amount of the second fish.
So how much does the third fish weigh? Answered by Penny Nom. 





A spherical ball in a conical wine glass 
20111026 

From Jules: A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is w. Show that the greatest overflow occurs when the
radius of the ball is (h*sin(w))/(sin(w)+cos(2w)). Answered by Claude Tardif. 





The number of People who Know Each Other 
20111021 

From Ted: I'm trying to prove that at a party
where there are at least two people,
there are two people who know the
same number of other people there. Answered by Robert Dawson and Penny Nom. 





37 miles in 3 seconds 
20111020 

From Joyce: Jake can travel 37 miles in 3 seconds,please calculate jake's rate of speed.(round to 2 decimal places) Answered by Penny Nom. 





Implicit differentiation 
20111020 

From Monica: Find dy/dx in terms of x and y, if sin(xy)=(x^2)y. Answered by Penny Nom. 





The end of a swimming pool 
20111017 

From Jim: "The end of a swimming pool is a rectangle inclined 45° to the horizontal.
The edge at the surface is 12 feet long and the submerged edge is 10 feet long.
Could you draw a diagram for me ? I don't understand the Problem. Answered by Penny Nom. 





The area of a circle 
20111017 

From Winney: If the diameter of a semicircle is 3 feet what is the area. Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





Expanding the size of a table 
20111016 

From Ericka: You are working as a carpenter in an industrial Shop. A customer came to you and inquired about the size of the table which would be fitted in her room. She informed you that she had already a 1.5 x 1m table in her room but she wanted to maximize the space by adding the same amount to is length and width. She is planning to occupy a 3 square meter place on her room for her to work comfortably. She is requesting you a written recommendation before she asked to make a table. What amount should be added to both sides to maximize a 3 square meter area? Answered by Penny Nom. 





A 6% commission 
20111015 

From Tamara: if you earned a gross wage of $810, which includes a salary of $90 and a 6% commission how much is the net sales? Answered by Penny Nom. 





Expanded form 
20111012 

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





Twice an even number 
20111010 

From Ron: The number of dollars that Tracy has in her pocket is an odd number.
Hal gave Tracy $2 more than she already had in her pocket.
The number of dollars Tracy now has cannot be _________.
a) $60 b) $62 c) $64 d) 68 Answered by Penny Nom. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





What is the speed of the boat in still water? 
20111007 

From Hannah: The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water Answered by Penny Nom. 





Three consecutive odd integers 
20111007 

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





Linear equations 
20111006 

From Hannah: I am confused about a question on my homework, here is an example on what I need to do:
You own a sightseeing boat tour. Kids' admission costs $5, adults' admission costs $8.
During that day you get (madeup number) $521 with 71 admissions.
How many of each passenger boarded?
I tried something like
5x + 8y = 521
x + y = 71
But, I still don't understand how to solve it! Help? Answered by Penny Nom. 





Two great circles 
20111006 

From Jean: "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? Answered by Chris Fisher. 





Six golphers for 27 weeks 
20111004 

From ken: I have 6 golfers alternating playing in a group of 4 each week for 27 weeks.
How can I create a schedule so that each golfer both plays equally and plays against the other golfers an equal amount of time Answered by Victoria West. 





A reservoir has the shape of an inverted cone 
20111003 

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





A trapezoid inscribed in a circle 
20111002 

From Greg: A trapezoid is inscribed within a circle.
The two interior angles who share the longest side are 70 and 80.
The arc whose chord is the longest side has a length of 120.
Find the other two interior angles of the trapezoid, and the other three arc lengths. Answered by Chris Fisher. 





Drawing three coins from 10 coins 
20110929 

From Michelle: Three coins are chosen at random from a purse containing 6 dimes & 4 quarters. What is the probability that the selection will contain at least one quarter? Answered by Penny Nom. 





3digit, daily numbers 
20110929 

From Margaret: I need the list/group for a raffle that would contain the combinations
for a 3 digit (000999) daily number. There would be 100 tickets sold
with 10 3digit numbers from each numerical group beginning
from 000's, 100's 200's, 300's,...900's. No duplicates/replacement. What would be the
list of possible combinations of each group of 100 tickets, keeping each
different group/list of combinations in separate blocks of 100 tickets
without duplication. So I could use 1 list of 100 this year and the next list of
combos next year and so forth. Please help!
Example: 000,197,245,367,445,569,618,777,842,964
What would be the possible lists of each 100 tickets?
Thank you Answered by Penny Nom. 





Three men sharing a task 
20110927 

From Olaniyan: Three men do a piece of work, the first does 7/15, the second does 5/6 of the remainder while the third does the rest.if the rest done by the third person equals 24 units, find the whole piece of work? Answered by Penny Nom. 





A hemispherical bowl with a lead ball inside 
20110927 

From Jean: "(a) Water is being poured into a hemispherical bowl of radius 3 inch
at the rate of 1 inch^3/s. How fast is the water level rising when the
water is 1 inch deep ?
(b) In (a), suppose that the bowl contains a lead ball 2 inch in
diameter, and find how fast the water level is rising when the ball is
half submerged." Answered by Penny Nom. 





90 cm of pipe 
20110926 

From margie: A 90cm pipe is cut into two pieces so that one pieces is 6cm shorter than the other. how long was each piece? Answered by Penny Nom. 





A tank is 3/8 full 
20110924 

From Olaniyan: When 150 liters has been drawn from a tank, it is 3/8 full; how many liters will the tank hold? Answered by Penny Nom. 





The sides of a regular octagon of area 800 sq. ft. 
20110921 

From Susan: Help please. I am building an octagon tree house to live in. I would
like the total square footage to equal 800 to 1,000 sq ft. How long
should each side of the octagon be.
tx, susan Answered by Penny Nom. 





Place value 
20110920 

From Ivana: the digit in the ones place is a hand with out a thumb(4)
2) the digit in the thousands place is 2 less than the digit in the one's place.
(42=
3) the digit in the ten's place is the sum of 2 and 6 (2+6=
4) the digit in the hundreds place is what you get when you get when you subtract 5 from the digit in the ten's place (ten's5=
what is the number? Answered by Penny Nom. 





The volume of a hexagonal prism 
20110919 

From Denise: I am being asked to find the volume of a hexagonal prism, base edges are 3cm, and a height of 15cm. The book that I am working from says that the answer is 77.94cm(cubed) but no matter what the equation I use I always get the answer 116.9/117. Please help! Thank you! Answered by Penny Nom. 





5 crayons 
20110917 

From John: How many four color combinations are possible with 5 crayons Answered by Penny Nom. 





A rectangle of largest possible area 
20110916 

From mary: Steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle Answered by Penny Nom. 





A four digit number 
20110916 

From gina: i am having a hard time figuring this out.. i believe the answer is 3105 but the 0 is throwing me off... i am a 4 digit number between 3100 and 3200, none of my digits are even, the sum of my digits is 9, the largest digit is in the ones place, what number am i ?? Answered by Penny Nom. 





A rectangular wall 
20110912 

From Jimi: The area of a rectangular wall of a barn is 110 square feet. It's length is 12 feet longer than twice its width. Find the length and width of the wall of the barn. Answered by Penny Nom. 





Blocks in a wall 
20110912 

From JOHN: HOW MANY BLOCK WILL IT TAKE TO BUILD A 28*48 HOME, ON A FOOTER THAT IS DONE ALREADY, I WANT TO GO TEN HIGH. Answered by Harley Weston. 





A beginning algebra question 
20110910 

From Tobby: A=1/2 solve for h.area of a rectangle with b and h Answered by Penny Nom. 





Decartes' circle theorem 
20110907 

From Joseph: Given 3 circles of diameters 50, 55, and 60 units,
Place them externally tangent.
What is the diameter of the outer circumscribing circle,
tangent to all 3 circles? I can attach a pdf if this description is not clear.
Not urgent, this has nothing to do with current assignments,
just wondering if I have developed the best methods? Answered by Chris Fisher. 





The derivative of f(x) = (x+1)^1/2 
20110905 

From Carla: Find the derivative using the limit process of
f(x) = (x+1)^1/2 Answered by Harley Weston. 





Geometry Related Careers 
20110901 

From Richard: Good morning,
I am hoping to find a list of careers that would relate to geometric constructions and tessellations.
I have searched the internet some and some of the sites I have found are a bit questionable or dated. Are there sites that Math Central would recommend?
I could not find anything when I did a search on the site.
Thanks in advance,
RVD Answered by Walter Whiteley. 





4 x 2 
20110830 

From Lucjan: how to sketch a diagram that shows 4x2 expression? Answered by Penny Nom. 





Exponential form? 
20110830 

From Emily: I have a 6th grader that needs to find out what is the exponential form of 461,885,811 Answered by Penny Nom. 





A coin toss game 
20110829 

From Aniish: A and B alternately toss a coin.The first one to turn up a head wins.If no more than 5
tosses each are allowed for a single game,find the probability that the person who tosses
first will win the game?What are the odd's against A losing if she goes first? Answered by Penny Nom. 





A border around a flower garden 
20110828 

From jessica: A Landscaper, who just completed a rectangular flower garden
measuring 6 feet by 10 feet, orders 1 cubic yard of premixed
cement, all of which is to be used to create a border of uniform
width around the garden. if the border is to have a
depth of 3 inches, how wide will the border be?
( 1 cubic yard=27 cubic feet) Answered by Penny Nom. 





An antifreeze solution 
20110827 

From aniish: The radiator of a jeep has a capacity of 4 gallons. It is filled with an antifreeze solution
of water and glycol which analyzes 10% glycol.what volume of the mixture must be drawn off and replaced with glycol to obtain a 25% glycol solution? all percentages are by volume Answered by Penny Nom. 





25 billion dollars 
20110826 

From Bill: If you have $25billion dollars, what would the value of this amount become if you inflated it at 4% per year for 55 years?=C2=A0 My TVM calculator will not go this high. Answered by Penny Nom. 





The cost of petrol 
20110826 

From Sam: Hi, i'm confused about this question from my textbook, here goes:
The cost of petrol for a 240 km journey for a car which runs 12 km on
each litre of petrol is $24. What would be the cost of petrol for a 500
km journey for a van which runs 11km on each litre of petrol?
please answer in detail and thanks in advance :) Answered by Penny Nom. 





Driving to meet Mary 
20110824 

From Denise: mary leaves St Paul traveling 2000 miles @ 55 MPH; John leaves LA traveling 2000 miles @ 45 MPH how many miles will John had traveled to meet mary? Answered by Penny Nom. 





The length of an arc 
20110824 

From nuel: Is there any formula to calculate the arc length from only the chord length and angle between the chord and tangent of the arc at its endpoint ? Answered by Penny Nom. 





Exponential form 
20110823 

From kiara: The African bush elephant is the largest land animal and
weighs about 8 tons . Write the amount in exponential form . Answered by Robert Dawson. 





Romeo throws a pebble at Juliet's wondow 
20110822 

From Natalie: There is a picture of Romeo trying to attract Juliet's attention without her nurse who is in a downstairs room, noticing. he stands 10m from the house and lobs a small pebble at her bedroom window (3.5m high). Romeo throws the pebble from a height of 1m with a speed of 11.5m/s at an angle of 60degrees to the horizontal. I have already found that it take 1.74seconds to reach the window and that it does in fact hit Juliet's window however i cannot work out the speed of the pebble when it hits the window! The answer is 9.12m/s but I cannot reach this answer. Hope you can help me :) Answered by Robert Dawson. 





Three tangent circles 
20110821 

From maribie: three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t Answered by Penny Nom. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





Three tangent circles 
20110819 

From hanniel: two coin are tangent to a third coin internally and are tangent to each other
externally. The distance between their centers are 14 mm, 17mm, and 5mm.
find their radii Answered by Penny Nom. 





3.8 x 2.2 
20110818 

From Isaac: Question from isaac, a student: I am struggling in math & I need help on multiplying 3.8 x 2.2. Can you helpme Answered by Melanie Tyrer and Harley Weston. 





Ordering fractions 
20110817 

From Myon: My problem is putting fractions from least to greatest and they are 1/4 2/5 1/3 4/6 1/2 8/9 3/4 1/1 2/6 1/10 thanks Answered by Penny Nom. 





Two line segments in the plane 
20110815 

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





A cyclic quadrilateral 
20110815 

From Tim: Hi! I've been working on this for a while and I'm quite stuck. If anyone can help that would be great.
The sides BC and AD of a quadrilateral ABCD are parallel. A circle meets the side AB at B and E and the side CD at C and F. Prove that the quadrilateral AEFD is cyclic. Answered by Chris Fisher. 





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. 





Infinite Logarithmic Series 
20110808 

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





A concrete octagonal pad 
20110804 

From Tina: I have a project where I need to construct a concrete octagonal pad. Each side is 12' and it is 5" deep. Please tell me how to calculate square yards of concrete. Thank you. Answered by Penny Nom. 





A 3 foot circle using 1/2" cord 
20110804 

From Cindy: To make a 3 foot circle using 1/2" cord  how many lineal feet of cord
do I need? Answered by Robert Dawson. 





A lock box 
20110803 

From Tom: I need to open a lock box from my parent's estate. The combination is a simple 4 number lock. The last two numbers are 33. Numbers can be used more than once.What are the possible combinations?
WP Answered by Harley Weston. 





Ben's favourite numbers 
20110803 

From Luke: Ben challenges you to guess his favourite numbers by using the following three clues:
Each number is a fourdigit odd number.
Each is a palindrome
The digits of each number add up to 10
None of the numbers are divisible by 5 Answered by Robert Dawson. 





A cone with an oval as a base 
20110803 

From Emily: Hi, I was wondering how to calculate the surface area of a cone with an oval as a base (which I think is referred to as an elliptic cone or something like that). I have the both the maximum and minimum radius as well as the height, but I don't have a slant height and I'm not sure how to calculate it and then calculate surface area. I would really appreciate some help. Thanks! Answered by Robert Dawson. 





A point on a circle 
20110802 

From George: I know the center location (x,y) of the circle, I know the radius of the circle, I know the location (X,Y) of one point on the circle, and I know the angle (in degrees not radians) between the known point location (X,Y) and an unknown point location (let's call it (A,B) for reference). What formula(s) can I use to find out the coordinate position of (A,B)? Answered by Chris Fisher. 





An equation in the form Ax+By=C 
20110728 

From Mike: I need to write an equation in the form Ax+By=C
The points I was given are (5,0) and (3,5)
I know how to find the slope I got 5/8 and wrote it out as y=(5/8)x+b however I'm not quite sure where to go from here.
Any help would be greatly appreciated. Answered by Penny Nom. 





A stained glass lamp 
20110725 

From Guy: Like Kay, I also work in stained glass, but in 3dimensions. I am
frequently asked to replicate lamp shades in stained glass where the
diameter of the top is different (narrower) from the diameter of the
bottom (which is wider). Some people want 5, 6, 7, 8, 10, 12, 16, ,,,
nsided shades. Is there a formula I can use to determine the width
of the sides using the angle, if I remember correctly, I think it's
called theta. In other words, is there a formula where I can plug
in the angle which describes the arc of the circle. For instance, if
someone asks for a 7 sided shade, plugging in 51.43 (360/7). I
could then use that to determine the width at the top and bottom
rings to create the appropriate trapezoids. I've visited a few sites
so the formula looks like its a function of sin & cos but they are
presented like proofs for teaching. Your site appears to want to
actually answer questions without making the inquirer feel stupid. Answered by Harley Weston. 





The height of a fluid in a horizontal tank 
20110724 

From jason: Same set up as many others, cylindrical tank on its side, but I am interested in defining the change in volume and/or fluid level as a function of time at a constant volumetric outflow. I plan on hooking a pump to the tank so "gpms' will be constant. I have a couple different sized tanks and pumps so I want a general equation. Thanks for your help. Answered by Harley Weston. 





A cylinder fits perfectly in a box 
20110718 

From Brix: A cylinder fits perfectly in a box. 76 cubic inches of oil is poured into the space between the cylinder and the box, filling the space halfway. If the box is 3ft wide, how tall is the cylinder in inches? Answered by Stephen La Rocque. 





A regular hexagon inscribed in a circle 
20110718 

From Courtney: If ABCDEF is a regular hexagon inscribed in a circle of
radius r, prove that the length of each side of the hexagon
equals r. Answered by Penny Nom. 





A rectangle is inscribed in a circle 
20110717 

From Alexea: A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x. Answered by Penny Nom. 





A linear equation with fractions 
20110713 

From Simon: I would like to ask if you would be able to explain : linear equation: 2 1/2 (X1)  x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) .
Thanks for your help. Answered by Penny Nom. 





Fencing around a pool 
20110712 

From Anita: The measurement of a swimming pool are 32 feet by 18 feet. How much fencing is needed if the fence is to be built 7 feet from each side of the pool? Answered by Penny Nom. 





A group of 40 golfers 
20110711 

From Doug: We are a group of 40 golfers who play in 10 x foursomes playing 3 rounds. Can we all play with different players each round yet maintain the foursomes format. Answered by Victoria West. 





Golf for 14 
20110711 

From Doug: We have 14 players playing over 4 days. can we play with different players every day and keep the 3 x foursomes and 1 x pair format Answered by Victoria West. 





Two piles of cards 
20110709 

From maribie: a standard deck of playing cards contains 26 black cards and 26 red cards, or 52 cards in all. a deck is randomly divided into two unequal piles, such that the probability of drawing a red card from the small pile is 1/3. at the same time, the probability of drawing a black card from the larger pile is 5/14. how many cards are in the larger pile? Answered by Penny Nom. 





Golf for 12 
20110707 

From Jim: I have a golf trip scheduled with a total of 12 guys. We are playing
three rounds of golf. For round 1 Players A B C D must play together.
Is there a formula that would allow me to set up the other 8 foursomes
with no repeats or minimal repeats?
Thanks. Answered by Victoria West. 





concentric circles 
20110706 

From maribiie: two circles are concentric. the tangent to the inner circle forms a chord of 12cm in the larger circle. find the area of the "ring" between the two circles? Answered by Penny Nom. 





Achilles and a turtle 
20110701 

From Jean: Achilles and a turtle are having a race. The turtle starts 45m ahead of Achilles and Achilles is twice as fast as the turtle. If turtle runs at 1m/s,how far would the turtle have run before he is outrun by Achilles? Answered by Penny Nom. 





A column and a sloped ceiling 
20110610 

From Tom: Hi! I am a woodworker who needs some help finding a formula. I have to make a cylinder shape column that butts up against a sloped ceiling using bending plywood. I need to figure out how to cut the shape on this flat piece of material. The diameter of the column is 54.375". The tallest point is 9 13/16" and the shortest point is 4 7/16". Any help would be greatly appreciated. Answered by Harley Weston. 





Construct a 30 degree angle 
20110610 

From Ella: they give you a simple straight line and ask you to construct an angle of 30 degrees at one end of the line using only a ruler and a compass? Answered by Penny Nom. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





Tiles for a back splash 
20110604 

From Catherine: How man 3 11/16 tiles do I need for 28 square foot for a back splash Answered by Penny Nom. 





A reel of paper 
20110603 

From keith: if a full reel of paper has 7750 metres on it with a diameter of 1240mm and a core diameter of 100mm how can work out the thickness of each strip of paper therefore allowing me to work out the metreage of the roll when its half in diameter at say 620mm Answered by Penny Nom. 





The volume of a decagonal prism 
20110529 

From Susan: How do you find the volume of a decagonal prism? Answered by Penny Nom. 





How tall is the pole? 
20110527 

From cynthia: 20 foot rope is tied 2 feet from the top of a pole and secured 8 feet from the base of the pole....How tall is the pole? Answered by Penny Nom. 





How many meters long should the race be? 
20110526 

From Lee: Nathan can walk at a rate of two meters per second while David can
easily go threeandahalf meters per second. David offers Nathan
a 45 meter head start. How many meters long should the race be in
order for Nathan to win by a nose Answered by Penny Nom. 





16 golfers and 8 rounds 
20110526 

From Gerry: 16 golfers and 8 rounds. To have each player play with as many others as possible. Answered by Victoria West. 





pi/2 + 12/13 
20110524 

From Jen: If you have (pi/2) and you want to add it to (12/13), how would you go about it? Answered by Chris Fisher. 





Problem solving with fractions 
20110521 

From emilyd: I had a packet of sweets. I put 1/5 of the sweets into Container A, 1/3 of them in Container G, 10 sweets in container C and the rest in container D. If the number of sweets in container D is equal to 75% of the total number of sweets in container A and B, how many sweets are there altogether? Answered by Penny Nom. 





What is the angle of decent? 
20110520 

From Taten: So you have an airplane with an altitude of 5.8KM. It has 46KM till the run way. What is the angle of decent? Answered by Penny Nom. 




