







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. 





Why are bags of soil measured in litres? 
20150619 

From Cheryl: Why are bags of soil measured in litres? Answered by Penny Nom. 





My final exam score 
20150619 

From Deirdre: Hi,
I got 69% on a question worth 20%
68% on a question worth 20%
And the final exam was worth 60%
My final grade overall was 63%
Did I do very bad in the exam???? Answered by Penny Nom. 





1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? 
20150618 

From Sharon: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?
I got 1 as my answer despite BODMAS making it 12 because logic tells
me I ought to place brackets around the first set of repeated addition. Could you
please clarify this for me? Thank you 😊 Answered by Harley Weston. 





A waste oil tank 
20150613 

From Angela: a waste oil tank is 5 feet wide and 20 feet long, the empty tank on your truck holds 5000 gallons. If 7.48 gallons are in every cubic foot, what is the maximum depth the oil can be to completely fit into your truck? Answered by Penny Nom. 





The amount before profit and overhead 
20150612 

From kelly: I have an existing amount of $22,750.00. this includes the profit at 10% and overhead at 10%.
How do I remove the profit and overhead in order to come up with the original starting figure? Answered by Penny Nom. 





The area of an isosceles triangle 
20150611 

From Pradipta: Find the area of an isosceles triangle having two equal sides of 20 cm each and angle between them 45 degree ? ( solve without trigonometric function). Answered by Chris Fisher. 





A fantasy football league 
20150611 

From Jason: Hello. We have a fantasy football league with 14 teams. The season is 13 weeks long and we would like to figure out a way to have two divisions of seven teams each with each team playing their interdivision opponents twice. Is there a way to set this up? I cannot seem to find a way to do it. Thanks! Answered by Victoria West. 





8 golfers playing 5 round 
20150611 

From Simon: We have 8 golfers playing 5 rounds, and want to make the pairings as even as possible (ie all play against everyone else)
2 of the players however must play together each day  due to a buggy being required.
If anyone has a formula to work this out I'd be appreciated Answered by Victoria West. 





An equilateral triangle inscribed in a circle 
20150611 

From Casey: I have an equilateral triangle inscribed in a circle  this triangle
has been bisected to give me 2 right triangles. I know the length
of the line bisecting the equilateral triangle is 36 inches. How do
I figure out the circumference of the circle and the length of the
sides of the equilateral triangle? Answered by Penny Nom. 





Is 22/7 is an irrational number? 
20150607 

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





The surface area of a round bar 
20150606 

From chirag: Please tell me the formula for finding round bar surface in square inches/ mm Answered by Penny Nom. 





Manipulating an equation 
20150605 

From Leigh: Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=ymx. Could you please assist me with this Answered by Penny Nom. 





A two digit number 
20150605 

From Madison: Trini took some photos. The number of photos she took is a two digit number.
The sum of the digits is 11. The tens digit is 3 more than the ones digit.
How many photos did Trini take? Answered by Penny Nom. 





The surface area of a triangular prism 
20150603 

From Alex: Find the surface area of a triangular prism with Isoceles triangles and dimensions 4 feet by 6 feet Answered by Penny Nom. 





The volume of a pipe 
20150602 

From gordon: What is the formula to find out how many gallon of water in a length of pipe tried your answer on 8inch at 50feet did not work out Answered by Penny Nom. 





A tangent to y = x^3 
20150531 

From Brayden: Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Answered by Penny Nom. 





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





A stone walkway around a pool 
20150529 

From Jerri: I have a rectangular pool 15x30 and it will require stone placed around it 4 feet out and 4 inches deep how much will I need? Thanks, jerri Answered by Penny Nom. 





The perimeter of a rectangle 
20150528 

From Imran: The length of a rectangle is x+3 centimetres.
The width of the rectangle is x1 centimetres.
Find an expression in terms of x for the perimeter of the rectangle.
The perimeter of a rectangle The perimeter of a rectangle
Give your expressions in it's simplest form.
The perimeter of a rectangle The perimeter of a rectangle
Thank You. Answered by Penny Nom. 





Two concentric circles 
20150528 

From Shannan: Two concentric circles have radii of 24cm and 26cm. What is the length of the chord that is tangent to the inner circle? Include a sketch Answered by Penny Nom. 





The perimeter of a quarter circle 
20150521 

From Bethany: The perimeter of a quarter circle is 3.57. What is the quarter circle's radius? Answered by Penny Nom. 





Golf for 14: 2 fourballs and 2 threeballs 
20150520 

From martin: I have to organize 14 players to play four rounds of golf. Each round comprise two fourballs and two three balls .
What's the best combination to ensure that each persons plays with as many of the others as possible without playing with somebody more than twice? Answered by Victoria West. 





Manipulating an expression using logarithms 
20150518 

From Katie: Solve x=At^be^ct for b in terms of c.
The e is Euler's number, not a letter or random placeholder. v
I've tried 2 methods on my calculator, and I am unsure as to why they give me different answers, and which one is correct.
For some reason, when placing a multiplication sign in between the A and the first t, I get a completely different answer. Why is this?
Also, which is the right answer for the question I have?
Thank you!
Katie :) Answered by Penny Nom. 





An isosceles right triangle 
20150517 

From Ari: In a 454590 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom. 





An octagonal frame around a pool 
20150517 

From James: I have a 20' pool and need to put a frame around it using 2by 4 what r the lengths and angle cuts Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





A pile of mulch 
20150515 

From Justin: I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have.
Please help and help with the formula for further use. Thank you! Answered by Penny Nom. 





Two lorries approaching an intersection 
20150515 

From Nuraini: Two straight roads intersect at the right angles. Lorry A, moving on one of the roads,
Approaches the intersection at 50mi/h and lorry B, moving on the other roads, approaches the intersection at 20mi/h.
At what rate is the distance between the lorry changing when A is 0.4 mile from the intersection and B is 0.3 mile from the intersection? Answered by Penny Nom. 





An angle of depression problem 
20150514 

From haxir: find the height of the balloon directly above a town if the measure of angle of depression of another town 5km from the first town is 20°!6` Answered by Penny Nom. 





A calculus optimization problem 
20150514 

From Ali: Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Answered by Robert Dawson. 





Folding a rectangle to preserve the aspect ratio 
20150509 

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





Repeated decimals 
20150509 

From Vir: Years ago I (re?)discovered 'cyclic division'. For example: if you arrange the number along a circle and put the number 142857 at the centre
all the numbers taken cyclically, starting with 1, are fully divisible by 37. Whatever the starting point of this number, it remains fully divisible by 37.
what is more, the number can be formed by taking the digits clockwise as well as anticlockwise..This I call "full cyclic divisibility". In many cases, only clockwise cyclic divisibility is possible. But I have not come across a case where ONLY anticlockwise divisibility occurs. Thus clockwise cyclic divisibility seems to be favoured. Could this be construed as a sign of chirality in mathematics?.. Answered by Chris Fisher. 





A word problem 
20150508 

From JAMES: A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought? Answered by Penny Nom. 





A triangle inscribed in a circle 
20150507 

From R2D2: A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees find the length of the side opposite the third angle? Answered by Chris Fisher. 





A circle is tangent to the yaxis 
20150506 

From Elynna: What does it mean when a circle is tangent to the yaxis?
Thanks, Answered by Penny Nom. 





Sales tax 
20150505 

From Adalyn: Hello i've been having some trouble with math, The question is asking for a GST
and a PST
of a 30.00 dollar shirt. I don't know how to find the GST or the PST please help Answered by Penny Nom. 





The number of possible musical notes using an nkey instrument 
20150504 

From Farihin: Lets say that i have keys, and each key is for notes of a musical instrument,
So i wanted to find out the number of notes i can get for a certain number keys,
of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100.
Notes in real life is not as such, but ignore reality.
I tried doing this but i can't seem to find a formula for it.
For example, i have 4 keys, say A, B, C, and D.
so, for notes that uses one key are 4, which is A, B, C, and D themselves.
for notes that uses two keys are 6,
AB, AC, AD, BC, BD and CD.
for notes that uses three keys are 4,
ABC, ABD, ACD and BCD.
lastly for notes that uses all four keys is 1, ABCD.
So, the total will be 4+6+4+1=15#
The nth term for the first equation is n, the second is [(n^2)n]/2
the third and the fourth, i don't know but the final answer should be like,
n + [(n^2)n]/2 + [3rd] + [4th]
Sorry for the long question though... Answered by Penny Nom. 





13 games, 3 possible outcomes 
20150501 

From Kennedy: Hello, hope it finds you well.
Am not that good with numbers, can you please help me get all the possible outcomes of 13 games, with a home win, draw or an away win as three possible results for each of the 13 games.
Thanks in advance Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





A square and a rectangle 
20150501 

From nick: why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ? Answered by Penny Nom. 





Filling a pool with dirt 
20150501 

From Mike: I have a hole which a 24 ft pool in it is 10" deep in the the centre and goes to 1" inch at the edge want to fill it in with dirt how many yards of dirt would I need to fill it in Answered by Penny Nom. 





The volume of a sphere 
20150430 

From Cassidy: How do you find the radius of a sphere that has volume 36pI? Answered by Penny Nom. 





The volume of a cube 
20150430 

From megan: What's the volume of a cube with a side length of 6? Answered by Penny Nom. 





Locating the center of a circle that forms an arc 
20150423 

From Ken:
Find the Cartesian coordinates of the center of an arc with the given location of the beginning and end points and radius length. Not the midpoint of the circumference but the actual point that the arc
is drawn around.
I know their are two answers depending on the direction of the arc. Unless we assume that all arcs are drawn counter clock wise.
Thanks
Ken
Answered by Harley Weston. 





A word problem with fractions 
20150423 

From Cecilia: if one third of a pole is red, one quarter is white and 15m is black what is the height of the entire pole Answered by Penny Nom. 





Expand and Simplify (3x+5)(5x9) 
20150423 

From chloe: Expand and Simplify (3x+5)(5x9) Answered by Penny Nom. 





Two concentric circles 
20150421 

From Juniper: Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment? Answered by Penny Nom. 





A circle inscribed in a square 
20150419 

From michael: A circle is drawn in a square PQRS. If the total area of the shaded portion of the square is 42 cm square, calculate the radius of the circle Answered by Penny Nom. 





An inequality 
20150419 

From mr.: Simplify the inequality √x>x and represent on a number line Answered by Penny Nom. 





A wireless fence 
20150418 

From Dave: I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be? Answered by Penny Nom. 





Two cars approaching an intersection 
20150416 

From Engabu: Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection? Answered by Penny Nom. 





How many boats total are in the marina? 
20150415 

From Carla: In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong. Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





Constructing a box of maximum volume 
20150414 

From Margot: I need to do a PA for maths and I'm a bit stuck.
The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.
8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. Answered by Penny Nom. 





Team selection 
20150413 

From Peter: I manage a football team with a list of 28 players.
Only 24 can play each game.
The season is 16 games.
How do I fairly select 24 players each week. Answered by Robert Dawson. 





The area of a circle given the circumference 
20150412 

From F: How do you find the area of a circumference of 6?
Thanks. Answered by Penny Nom. 





Excavating a basement 
20150412 

From Randy: The cost of excavation is $4.50/ cu yd. Find the cost of excavating a basement 87 ft long, 42 ft wide, and 8 ft deep. Answered by Penny Nom. 





An 8 pointed star inscribed in a circle 
20150410 

From Kermit: How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10. Answered by Penny Nom. 





The perimeter of a quarter circle 
20150410 

From Riley: How do you find the perimeter of a quarter circle when the radius is 56? Answered by Penny Nom. 





A word problem with fractions 
20150409 

From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.
If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.
Let x be the numerator and let y be the denominator of the original fraction.
Write down two simultaneous equation in x and y.
Solve these equations to find two possible values for the given fraction. Answered by Penny Nom. 





The area of the ring between two concentric circles 
20150408 

From Conner: The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is? Answered by Robert Dawson. 





A circle graph 
20150406 

From Davis: i don't know how to answer this question. please help!
a survey about student government shows the following results
110 like the program
120 think the program is unnecessary
210 plan on running for student government next year
if this information is put in a circle graph,what is the central angle for the students who like the program? Answered by Penny Nom. 





On what day of the week did 1994 begin? 
20150405 

From tayyaba: there were 365 days in the year 1993
the first day of the year was friday.
on what day of the week did 1994 begin? Answered by Penny Nom. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





The weight of a steel block 
20150404 

From Mark: the weight of a steel cube 37 inches X 28 inches X 7 inches Answered by Penny Nom. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





Dealing cards to Melissa and Robert 
20150324 

From Karena: 92 cards in all. Melissa has 3 times as many cards as Robert. How many cards does Robert have? Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20150323 

From Rachel: Triangle ABC is an isosceles triangle inscribed in circle O. If each leg of the triangle is 13cm and the altitude to the base of triangle ABC is 5cm, find the radius of the circle. Answered by Penny Nom. 





16 golfers for 18 weeks 
20150322 

From Rose: We could use a schedule to include the following:
16 golfers
4 foursomes
Each person plays once a week for 18 weeks.
No one plays in same foursome more than 1 or 2 times, or the least
amount of time.
Thank you for your kindness. Answered by Victoria West. 





8 golfers playing in 2x2 balls in 5 games 
20150318 

From Brian: We are 8 golfers who will be playing in 2x2 balls in 5 games.
is there a formula to minimize the chances of playing with a partner or opponent
too often please ? Answered by Victoria West. 





The weight of two dogs 
20150317 

From Renee: Darlene's dog weighed 5 times as much as Leah's dog. Together, the dogs
weighed 84 pounds. How much did each dog weigh?
Write an equation and solve Answered by Penny Nom. 





A region defined by three lines 
20150316 

From Lucinda: find the area of the figure formed by the line y=5x+9 and the xaxis and yaxis. Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





Average rate for a return trip 
20150314 

From Michael: Jeffrey drove to a town 25 miles away at an average speed of 50 miles per hour. The return trip along the same route took 20 minutes longer than the trip to town. Determine the average speed in miles per hour for Jeffrey's round trip. Answered by Penny Nom. 





The side length of a gazebo 
20150314 

From Dennie: From middle of side to middle of opposite is 14'6". What is the length of the side? Answered by Penny Nom. 





A limit 
20150313 

From arthur: sin(x1)/x^+x2 Answered by Penny Nom. 





A fishfinder 
20150313 

From Dave: I have a fishfinder that has a 20 degree cone on bottom of boat going to the bottom of the lake.
How do I know the size of base diameter of the cone on the lake bottom depending on depth...
such as 10 feet deep, for example? Answered by Penny Nom. 





Olivia and Ray walk to school 
20150312 

From Rebeccah: Olivia and Ray walk to school. Olivia walks 1/4 of a mile to school. Her walk is 2/3 of the distance that walks Ray to school. What is the total distance,in miles,that Ray walks to school? Answered by Penny Nom. 





Two sunflowers 
20150312 

From Maurice: Sam and sally planted two sunflowers.Each sunflower grows 1cm each day. Sally's sunflower is 4cm high. Sam's is 12cm high. How high will each sunflower be when Sam's sunflower is twice the height of Sally's? Answered by Penny Nom. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





The height of an equilateral triangle 
20150312 

From anna: I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches Answered by Penny Nom. 





The volume of a trench 
20150311 

From Kim: A trench 60m long and 15m deep, 12m wide at the top and 8m wide at the bottom.How many cubic meters of earth have been removed? Answered by Penny Nom. 





The area of a quadrilateral 
20150311 

From Joel: Diagonal ac of quadrilateral ABCD is 60cm and the lengths of perpendiculars to
It from the opposite vertices are 4.2cm and 5.8 cm find the area of the quadrilateral
ABCD Answered by Penny Nom. 





What is 1000 billion billion? 
20150310 

From LeRoy: what does this mean? 1000 billion billion Answered by Penny Nom. 





Angles of elevation and depression 
20150308 

From Timmy: Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
A. If there was a piece of rope from the top of the building to Joel, how long would it be?
B. What is the angle of elevation from Joel to the top of the building?
C. Margaret says that she could find the angle of depression from the top of the building to Joel by subtracting the angle of elevation from 90°. Is she correct? Explain. Answered by Penny Nom. 





Extraneous solutions 
20150307 

From Emily: I have a question about Extraneous Solutions, Because I was recently researching to figure out
on how to determine that a solution is extraneous and many of the answers talked about how if a answer is negative
that it should always be extraneous but now I found out that positive solutions can also be considered as extraneous solutions
so that is why I am really confused Extraneous Solution's.
I would really appreciate it if you could clearly explain to me how to determine an extraneous solution from a normal solution.
Thanks,
Emily Answered by Chris Fisher. 





A lot on a culdesac 
20150306 

From ana: Julie lives on a culdesac and wants to know if the city calculated the area of her plot of land correctly (see diagram below). We can assume the culdesac is a circle and it has radius 40 feet.The boundary of the lot along the culdesac (the arc from A to B) is 78.21 feet. The city found the area to be 7012.5 square feet–are they correct? Answered by Penny Nom. 





A man is standing on top of a building 
20150306 

From kiki: a man of height 1.5m standing on top of a building of height 48.5m views another building across the square. he observe that the angle of depression of the bottom of the building is 40 degrees and the angle of depression of the top of the building is 5 degrees. Both buildings stand on the same level
a) calculate the distance of the man from the base of the building across the square measured along the line of sight Answered by Penny Nom. 





Two parallel tangents to a circle 
20150305 

From Samantha: The equation of a circle is x^2+y^2=25. Determine
the equation of the parallel tangent lines to this
circle, for which the slope is 4/3. Answered by Penny Nom. 





The length of a ramp 
20150305 

From Jaylynn: Hi, I've been trying to figure out how long my ramp would have to be in order to reach a height of 3.5 feet at a 30 degree angle for a sugar glider enclosure? Answered by Penny Nom. 





Bricks around a fire pit 
20150305 

From Jayson: I have a round fire pit. It measures 25 inches in diameter. I have 12 inch long square bricks to go around it . My question is what degree do I cut the ends of these bricks to make them fit around this circle? The brick dimensions are 12"Lx6"Wx4"D. Answered by Harley Weston. 





Istanbul to Lagos 
20150303 

From Victor: A plane flies from Istanbul to Lagos at 800km/h and then returns to Istanbul at 900km/h. The return trip takes 1 hour less than the flight to Lagos. What is the distance between Istanbul and Lagos? Answered by Penny Nom. 





The radius of a cylinder 
20150226 

From Rose: Hi. I want to know how to find the radius of cylinder.
When I have height (35cm) and area of the curved surface(880sq.cm).
I know the formula is 2πr(h+r). But I can't understand how to find it's radius.
Please help me. I really need your help. Answered by Penny Nom. 





Two equations with fractions 
20150226 

From Pulane: Hi math centre I've been trying to solve these equations for days now please help
(6/x)(1/y)=4
(9/x)+1=(2/y)
Please help me solve them simultaneously
Thank you Answered by Penny Nom. 





Two concentric circles 
20150225 

From Manasi: The area between 2 concentric circles is 6 times the smaller circle. Radius of small circle is 7 cm. Find the difference in the circumference of the bigger circle ad the smaller circle? Answered by Penny Nom. 





3 over "x" plus 5 
20150223 

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





f(x)=(x^21)/(x1) 
20150221 

From Ahmed: Is f(x)=[(x^21)/(x1) and x=2 at x=1] differentiable at x=1 ? Why ? Answered by Penny Nom. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





Column vectors 
20150221 

From jill: A has co ordinates (7,1) and B has coordinates (3,5).write these as column vectors Answered by Penny Nom. 





A limit 
20150219 

From genc: Lim (27x^31) / (3x1)
X> 1/3 Answered by Harley Weston. 





The height of a building 
20150218 

From prateek: the height of a flagpole on top of a building is 6m.
the angle of elevation of the top and bottom of the flagpole are 45 and 30 respectively.
find the height of the building Answered by Penny Nom. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





5000 gallons in cubic yards 
20150217 

From Miguel: If I have a cube shaped tank in the ground that holds 5000 gallons and I want to take it out and fill the hole in with dirt, how much dirt will I need in yards? Answered by Penny Nom. 





Tiling a room 
20150216 

From Owen: nicolas room is 56m2 she wants to put tiles down which are 50cm by 50cm each cost £4 how much money will she spend Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





A 330 foot long fence 
20150215 

From Marsha: I am putting up a fence 330 feet long and want to put the t post every 4 feet
how many t post do i need? Answered by Penny Nom. 





Distance, time and rate for three people 
20150215 

From Mubashir: Steven left Town A and walked towards Town B at a speed of 100m/min. At the same time, Jason and Melvin started from Town B and walked towards Town A at a speed of 80m/min and 75m/min respectively. If Steven met Melvin six minutes after passing Jason, find the distance between Town A and Town B. Answered by Penny Nom. 





Bearings and a rectangular plot 
20150214 

From Mubashir: A,B,C,D are the four corners of a rectangular plot marked on level ground. Given that the bearing of B from A is 040 degrees and that the bearing of C from A is 090 degrees. Calculate the bearing of
(a)B from C
(b)A from C
(c) D from C Answered by Penny Nom. 





Stopping distance 
20150211 

From Audrey: A Harley Davidson motor cycle weighing 650 lbs with a rider weighing 175 bs
was going 40 miles per hour. He had to make a sudden stop . Slammed on brakes. How long a distance for him to stop? Answered by Penny Nom. 





A word problem with fractions 
20150211 

From Omokayode: A vehicle tank was 3/5 full of petrol. When 21 litres of fuel was added it was 5/6 full. How many litres of petrol can the tank hold? Answered by Penny Nom. 





A fence post problem 
20150208 

From Nicole: In Susan's rectangular garden plot, she put 12 posts on the long sides
and 8 posts on the short sides. How many posts did she use altogether?
(The answer is not 40.) Answered by Penny Nom. 





A circle and a chord 
20150207 

From Dakota: If the diameter of a circle is 48 cm, find the shortest distance from a chord of length 34 cm to the center of the circle Answered by Penny Nom. 





Speed, distance and time 
20150206 

From Terry: How many seconds would it take to travel 0.18 km at a speed of 130km per hour? Answered by Penny Nom. 





The product of a 2digit number and a 3digit number 
20150206 

From Nathaniel: The product of a 2digit number and a 3digit number is about 50 000 what are the products Answered by Penny Nom. 





2x^22x+1=4x+1 
20150206 

From Caitlyn: 2x^22x+1=4x+1 Answered by Penny Nom. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





A parallelogram inscribed in a circle 
20150204 

From narendra: how can we prove that a circular parallelogram is a rectangle? Answered by Chris Fisher. 





Two cars pass each other going in opposite directions 
20150203 

From Caroline: Two cars pass each other going i opposite directions. One car is going 100 km/h and the other is going 80 km/h. How far apart will the two cars be after driving 45 minutes at these rates of speed? Answered by Penny Nom. 





A train from Vancouver to Whistler 
20150202 

From Tea: Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train?
Thanks :) Answered by Penny Nom. 





Jack and Jill climb two poles 
20150202 

From APRIL: Two vertical poles are 3 meters apart. Jack is climbing one pole while Jill climbs the other. If the distance between Jack and Jill is 5 meters, how much higher is Jill than John? Answered by Penny Nom. 





Ratio of gas to oil 
20150202 

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





The volume of Lake Utah 
20150129 

From Hannan: Lake Utah has a surface area of 3,846 square miles and an average depth of 10.5 feet. In cubic miles, how much water does it hold?
How would you approach this question? Where would you start? Answered by Robert Dawson and Penny Nom. 





128/(16)/(2) 
20150128 

From jackie: 128/(16)/(2) I was wondering if you can show me how to work this question out Answered by Harley Weston. 





What is our cost? 
20150127 

From Johanna: I have a pieces of 3/4" sch40 (round tube) 240" long at $70. What is our cost. We also add 35% to our cost for selling price. How do I figure this out? Answered by Penny Nom. 





The height of an obelisk 
20150127 

From Fabian: Two observers on level ground position themselves 50 meters apart so that an obelisk is due north of position A and due west of position B. The angle of elevation to the top of the obelisk at position A and B is measured to be 29.9 degrees and 37.5 degrees respectively. Use this information to estimate the height of the obelisk. Answered by Penny Nom. 





Is a square a trapezoid? 
20150126 

From Katie: Can a trapezoid sometimes be a square? Answered by Penny Nom. 





Russell is 6 years older than Samantha 
20150126 

From Kelli: Russell is 6 years older than Samantha.
In 4 years the sum of their ages will be 78. How old is Russell now? Answered by Penny Nom. 





A road around a garden 
20150125 

From hahha: a garden 150 m long and 80 m wide has a road 4 m wide all around on the out side find the cost of paving at the rate of 12 per s.q m Answered by Penny Nom. 





Two concentric circles 
20150125 

From nazneen: select the correct answer from the given four options
given are two concentric circles. radii of outer circle & inner circle are r1 & r2 respectively.
the areas of inner circle & shaded ring are equal. the radii r1 & r2 are related by?
1. r1 = r2
2. r1 = r2*square root 2
3. r1 = r2*square root 3
4. r1 = 2r2 Answered by Penny Nom. 





A schedule for observing our peers 
20150123 

From Jennifer: I am a sales trainer. Each month we need to observe one of our peers and give feedback. What this means is every month, not only am I observing someone, but someone is also observing me. For example, in January, Amy observes Tracy, Tracy observes Rachel, Rachel observes Ryan, and so on. The last person would then observe Amy, bringing it full circle. There are 10 trainers on my team. How do I set it up to where each trainer observes another trainer only once over the course of the year (and in return, each trainer is only being observed once by each person)? I know they will eventually repeat but would that start in the 10th month? Answered by Robert Dawson. 





A schedule for 5 employees working 2 at a time 
20150123 

From Cynthia: We have 5 employees and need only 2 to work on Saturdays. what is the best
way to fairly schedule everyone. PS. from time to time a sixth person will be
thrown in to make things really interesting. Answered by Victoria West. 





Scheduling meetings with pairs of people 
20150122 

From Jacey: I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done? Answered by Victoria West. 





Math in the universe 
20150121 

From GA: I want to find out examples in universe for this equation:
sin(x)/cos(x)=1 or tan(x)=1. I know the mathematical answer of pie/4 or 45 degree angle.
What I need to know is to find examples of this. I found an example in construction, for example, which is the shape of attic in the house.
I want to find examples in universe like in solar system, in quasars or jets coming out of them, in galaxies, in stars, in black holes, etc
Do you know of any such examples? Answered by Robert Dawson. 





The volume of a swimming pool 
20150121 

From kirara: Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the water line is 50 ft. And the breadth is 20 ft. The bottom of the swimming pool is a plane sloping gradually downward so that the depth of the water at one end is 4 ft. And at the other end is 8 ft. Answered by Penny Nom. 





The height of a building 
20150120 

From Emily: A man 2m high observes the angle of elevation to the top of the building to be 70 degrees. And the angle of depression to the bottom of the building to be 19 degrees. How tall is the building? Answered by Robert Dawson. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Answered by Penny Nom. 





An input/output table 
20150113 

From Rose: How do you create an input/output table when the rule is: the output is a +5? Answered by Harley Weston. 





$xx,xxx million 
20150112 

From sherry:
as a financial editor, for years I've seen $\$$ amts like this:
$\$xx,xxx$ million (ie, with a comma, not dec point)
Isn't that thousands of millions, which would equal 'billions'? Answered by Penny Nom. 





An investment for 20 months 
20150112 

From rose: Darnell wants to have 2700$ to purchase a tv in 20 months. what will he need to deposit today if he earns 5% annual interest compounded monthly Answered by Penny Nom. 





h+h+h = 9 
20150112 

From juanita: How to solve h+h+h = 9 Answered by Penny Nom. 





The length of a roll of paper 
20150112 

From Peggy: roll of paper 3ft wide and roll equals 500 sq ft how long would the roll be? Answered by Penny Nom. 





The volume of a lake 
20150110 

From Peter: If a lake is 8 acres in size and 10 feet deep how many gallons of water does it contain Answered by Penny Nom. 





Mutually prime composite numbers 
20150109 

From nivedita: Two composite number that is mutually prime? Answered by Penny Nom. 





Scheduling 12 for lunch 
20150105 

From Sabrina: I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks! Answered by Victoria West. 





The degree of a polynomial 
20150105 

From Nichole: How do I determine the degree of polynomials? I've searched this on sites but they are
all so confusing! Is there a simple explanation or way to find what the degree is? Some
examples are: 6x^4 10x^2yz^5 and 3m^2n^710m^8. I also have to say that I am
under the impression that this symbol ^ means the number after it is an exponent. Answered by Robert Dawson and Harley Weston. 





A silo is composed of a hemisphere and a cylinder 
20150103 

From Ami: A silo is composed of a hemisphere and a cylinder. The total height for the silo is 20m and the diameter of the silo is 8m. What is the volume of the silo to the nearest cubic meter? Answered by Penny Nom. 





Filling a tub 
20150102 

From Mr: The cold tap can fill a bath in 5minutes,the hot tap in 15,and the waste pipe empty the full bath in 10 minutes. All three are fully open for 2 minutes,after which the wastepipe is closed. How much longer will it take to fill the bath? Answered by Penny Nom. 





An isosceles triangle 
20141231 

From ahmadmahmoud: an isoseles triangle is such that each of the base angles is twice the vertical angle.Find the angles of the triangle Answered by Penny Nom. 





1.5% of 1 trillion 
20141230 

From Kgosi: How much is 1.5% of 1 trillion? Answered by Penny Nom. 





Rates, percentages and units 
20141230 

From Kenneth: Hello:
If percentages have no units, why are some percentages called rates, as in interest rate, or
perhaps a tax rate of 7% as an example? A rate has units of different quantities.
I thank you for your reply. Answered by Robert Dawson. 





The perimeter of a quarter circle 
20141226 

From Maisy: This is the question that I got for a math worksheet.
The radius of a quarter circle is 5 miles. What is the quarter circle's perimeter?
Use 3.14 for pi. Answered by Penny Nom. 





A trip to Ottawa from Toronto 
20141222 

From Kristy: A trip to Ottawa from Toronto will take 4 1/2 hours. Assuming we are 2/3 the way there, how
much longer will the trip take? Answered by Penny Nom. 





A tangent to a circle 
20141222 

From azman: Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5). Answered by Penny Nom. 





A line segment of length root 5 
20141215 

From angela: On the dot grid below, draw and label a line segment with length square root 5
the dot grid is 8 by 10 Answered by Penny Nom. 





A cone is 2/3 full of sand 
20141214 

From Janice: A cone with a radius of 3.5 cm and a height of 12 cm is 2/3 full of sand.
What is the volume of the sand inside? Answered by Penny Nom. 





A right triangle 
20141213 

From Katie: the shorter leg of a right triangle measures 2 feet less than the longer leg. the hypotenuse measure 10 feet. find all three sides Answered by Penny Nom. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? Answered by Penny Nom. 





A circle through 3 points 
20141204 

From priyanka: Find the equation of a circle passing through the origin and intercept on axes are a and b. Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





Exponential notation 
20141127 

From Jaqui: May sound super easy, but how would you SHOW that you simplified
3x3 to the power of 2 (the little 2)?
thank you!
Jaqui Answered by Penny Nom. 





What is 20 and 3/5 of 10? 
20141126 

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





Mark's book case 
20141124 

From anne: mark has 312 books in his case. he has 11 times as many fiction books as non fiction books. how many fiction books does mark have? Answered by Penny Nom. 





Cutting a hexagon with a sliding miter saw 
20141123 

From Joseph: I need the angles in degrees for a hexagon one side is 18inches on the outside the problem I am having is in the angle of the cut and I am using a sliding miter saw which only goes from0 degrees to 45 degrees so I need help in getting the angle of the cut Answered by Harley Weston. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





An age related word problem 
20141118 

From Cole: Susan and Russell are brother and sister. Susan says that in two years she will be twice Russell's current age. Russell says that he's only three years younger than Susan. How old is each of the siblings? Answered by Penny Nom. 





How many square feet in 10 gallons of liquid at 1/4 in thick? 
20141114 

From Rich: How many square feet in 10 gallons of liquid at 1/4 in thick Answered by Penny Nom. 





(x3)^2(x+3)^2 
20141113 

From Bernice: (x3)^2(x+3)^2 Answered by Penny Nom. 





1/6k=11 
20141113 

From Marty: Using the balance method, what is the answer to 1/6k=11, trying to find what k equals. Thanks Answered by Penny Nom. 





An irregular convex octagon 
20141113 

From james: I have an irregular convex octagon, alternating between 4 large edges, say 'a' mm long and 4 small edges, say 'b' mm long, is there a formula available so that I can work out the minimum size sit a circle with a radius of 34.25mm inside it thank you Answered by Chris Fisher. 





The area of a circle in terms of the circumference 
20141104 

From Sarah: How do you find the area of a circle if you already have the circumference?
There was one answer to this question already but it didn't make sense to
me, because they rounded up pi which you can't do so the answer is
incorrect. thanks Answered by Penny Nom. 





A quadratic function modelling the heightof a flea jump 
20141102 

From Hannah: A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is located at the point from which the flea jumped. Determine a quadratic function in vertex form to model the height of
the flea compared to the horizontal distance travelled Answered by Penny Nom. 





Jason's speed 
20141031 

From jason: the speed of Jason is 12 times faster than everyone. The speed of Jason is 108mph. Write the equation and solve to find the speed of everyone else. Answered by Penny Nom. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





What is the speed of the boat in still water? 
20141030 

From Adam: The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water? Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

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





The region between two concentric circles 
20141027 

From Ray: two circles, concentric; Given the length of chord of outer circle that is tangent to inner circle. what are the areas of both? how to calculate? Answered by Penny Nom. 





logbase4 (sin x) = 0.5 
20141026 

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





6 bolt holes around a circle 
20141026 

From Bobby: What Is The Cord Dimension For 6 Holes On A 24" Bolt Circule Answered by Penny Nom. 





Revolutions per minute 
20141024 

From Edward: Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM
of that tire is at 8 MPH and 64 MPH. Thank you.
Sincerely; Edward Answered by Penny Nom. 





A 10foot piece of PVC pipe 
20141021 

From David: A plumber has a 10foot piece of PVC pipe. How many 9/5foot pieces can be cut from the 10foot piece ? Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

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





Water in a spherical container 
20141017 

From Natalie: A spherical container with radius 10cm being filled with water such that the water level, h cm, in the container increase at a rate of 0.5 cm s^(1). Show that the area of the horizontal surface of water, A cm^(2), in the container is given by A = π(20h  h^(2) ). Answered by Penny Nom. 





A poorly worded question 
20141014 

From Marjorie: How do I figure out the following? Dylan's dog weights 12 times more than his pet rabbit. The dog and the rabbit weight 104 pounds. How much does Dylan's dog weigh? Would you explain in detail how I would arrive at the answer so I can convey same to my grandson who is in the 5th grade.
Thanks. Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





A fact family containing 4, 4 and 16 
20141014 

From Leslie: I am helping my son and the question is 4,4,16 in fact family what does that mean Answered by Penny Nom. 





How does pir^2 = 1/4pid^2? 
20141014 

From al: Hi I cant work out the algebra. How does pir^2 = 1/4pid^2 Thanx Answered by Penny Nom. 





Building an 8 sided box 
20141014 

From Michael: I want to build an 8 sided box. The North, East, South, and West sides I want them to be 4 feet in length.
The NE, SE, SW, and NW sides I want to be 2 feet in length. What angles do I need to cut my angles.
Thanks Michael Answered by Penny Nom. 





15  (5x)/ x = 30 
20141013 

From AMANDA: 15  (5x)/ x = 30
I thought you had to multiply both sides by x in order to remove the fraction?
15x  5x  x2 = 30x
then combine 10x  x2 = 30x
x2 =20x
then take the sqrt of each side...
what am I doing wrong?? Answered by Penny Nom. 





Pre algebra 
20141012 

From mohamed: i want to know the meaning of pre algebra Answered by Penny Nom. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? Answered by Penny Nom. 





Why express fractions in lowest terms? 
20141009 

From John: I teach in a Faculty of Education. A colleague in the university asked me about fractions and lowest terms. I am quoting the person below, and would appreciate your insights into the question/thought.
"One I'm struggling with is why (for example) 6/18 is not considered as good an answer to a fraction question as 1/3. The traditional response is that 6/18 is not in lowest terms so the question has not been finished until the fraction is reduced, but what actually makes the lowest terms answer the better one? Is it convention? Is there a way to explain why simplest form answers in fractions are right and and anything else is considered incorrect without alluding to some need for this 'good habit' elsewhere in math or science? Is there a reallife reason?"
Thank you for any insights and if you have nothing to offer to this query, that is fine too. I appreciate your consideration.
John Answered by Robert Dawson. 





One zero to a quadratic expression 
20141006 

From Kevin: Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question? Answered by Penny Nom. 





A tennis ball in a triangular prism 
20141006 

From Anna: Hi, I need to find the the base and the height of a triangular prism, but I only know the diameter of a tennis ball that fits exactly in the triangular container.. The diameter for the ball is 8.50cm.
Can you help me find the formula?
Thank you! Answered by Penny Nom. 





Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





A lost combination 
20140928 

From Kim: I cannot remember my combo to this simple lockbox. It is 3 digits from 09. They can be used more than once . I thought it was 117..but no joy. I am fairly sure it was using those digits 1, and 7. can you give me a list of all possible combinations, using 1s and 7s, for the 3 number code? Thank you and I am in awe of people who have math skills, for I certainly do not. Answered by Penny Nom. 





A rectangle and a triangle 
20140927 

From rajesh: The perimeter of a rectangle is equal to the perimeter of a rightangled triangle of height 12 cm if the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle? Answered by Penny Nom. 





A wire is bent to form a right triangle 
20140925 

From Lorena: A wire 24 dm is bent to form a right triangle. The ratio of the shorter leg to the hypotenuse is 3:5. Find the length of the longer leg? Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Continuity on a closed interval 
20140921 

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





The perimeter of a parcel of land 
20140918 

From Shirley: What is the perimeter of a parcel of land that is 564 acres square Answered by Penny Nom. 





Meetings for 77 students 
20140918 

From Adam: We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice.
We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this?
I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group.
Thanks! Answered by Victoria West. 





Two equations in two variables 
20140918 

From Susan: (28x + 36y)  [20000  .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables Answered by Penny Nom. 





How much did each dog weigh? 
20140916 

From Fred: LJ owned two dogs that weighed a total of 140 pounds. If one dog weighed 10 pounds more than the other, how much did each dog weigh Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





A six team track schedule 
20140915 

From Paul: I need to make a six (6) team track schedule. It needs to be five (5) triangular (3 team) meets with each team playing each team twice Answered by Victoria West. 





Two chords in a circle 
20140913 

From Carlos: Find the length of the radius of a circle in which a
chord of length 6 units is twice as far from the
center as a chord of length 12 units Answered by Penny Nom. 





The average of 9 numbers is 45 
20140912 

From rizza: The average of 9 numbers is 45. If 90 and 88 are added to the set of numbers. What will be the resulting average? Answered by Penny Nom. 





The average age of a group of 10 students 
20140911 

From sujan: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group . What is the average age of the two new students who joined the group? Answered by Robert Dawson and Penny Nom. 





The perimeter and diagonal of a rectangle 
20140910 

From niniha: the perimeter of a rectangle is 68cm.if the diagonal is 26, find its dimensions Answered by Penny Nom. 





A second grade word problem 
20140909 

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





Problem solving 
20140908 

From hubert: a car left the house and travelled at an average speed of 60 kph.how many minutes will it take for the car to reach the school which is 8 km away from the house Answered by Penny Nom. 





A secret number 
20140908 

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





The diagonals of a cube 
20140904 

From Rukshanth: How many diagonals does a cube have? Answered by Harley Weston. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





Interior angles in a parallelogram 
20140830 

From xavier: so, one of my math homework questions requires me to know how to find out how to find the interior angles in a parallelogram, the question is, "how many interior angles does a parallelogram have?" Answered by Penny Nom. 





Water usage in Ames 
20140829 

From Abigail: The City of Ames water treatment plant treats 7 million gallons of water per day on
average to meet water demands. Hypothetically, if water is withdrawn from a
groundwater system with an area of 51.6 square miles
(approximate area of Ames and surrounding area),
what is the depth of water in inches that would have to be added to
the groundwater system annually to replace the water that is withdrawn by the city? Answered by Penny Nom. 





Three collinear points 
20140828 

From jhanavi: p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R Answered by Penny Nom. 





Logarithms 
20140828 

From effaryna: how logarithms is applied in everyday life? Answered by Penny Nom. 





Using a bucket to fill a tub 
20140827 

From Charlotte: A bathtub needs to be filled with water. To fill the tub, a bucket needs to be filled then dumped into the tub. If the bucket is a cylinder with a radius of 6 in. and a height of 12 in, how many buckets will it take to fill the 5 ft x 3 ft x 3 ft tub. Answered by Penny Nom. 





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

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





A car passing a bus 
20140824 

From Athish: the driver of the car is travelling at 36 km/hr and spots a bus 80 m ahead of him after 1 hr the bus is 120 m behind the car what is the speed of the bus Answered by Penny Nom. 





The perimeter of a triangle 
20140821 

From Phyllis: What is the perimeter of a five acre triangle with one side being 250 feet and the second side would be at a 90 degree angle.
Thank you. Answered by Penny Nom. 





Filling three holes with stones 
20140820 

From mark: how many tonnes of hardcore/crushed stone would it take to fill
1 hole 9ft diameter 5ft deep
and 2 holes both 3ft diameter and 5ft deep Answered by Penny Nom. 





Revisiting 8 golfers in two foursomes 
20140819 

From steve:
I noticed you had an answer on how can you put 8 golfers in even foursomes over 7 games so that everyone plays with everyone equally. However the formula showed the following sequence that was used but did not go past the second day. Can you change the 0s and 1s into the numbers 1 to 8 instead. Here is what you have written:
Day 0 : (0, 0, 0, 0, 1, 1, 1, 1)
Day 1 : (0, 0, 1, 1, 0, 0, 1, 1)
Day 2 : (0, 1, 0, 1, 0, 1, 0, 1)
Day 3 : (0, 1, 1, 0, 1, 0, 0, 1)
Day 4 : (0, 0, 1, 1, 1, 1, 0, 0)
Day 5 : (0, 1, 0, 1, 1, 0, 1, 0)
Day 6 : (0, 1, 1, 0, 0, 1, 1, 0)
Thank you so much for your anticipated help.
Steve Answered by Harley Weston. 





A barge of triangular cross section 
20140818 

From tushar: a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement Answered by Penny Nom. 





4 rounds of golf as three foursomes 
20140818 

From Christopher: For our golf trip, we will be playing 4 rounds of golf as three foursomes. We would like to have each person play with everyone at least once. Is this possible? Answered by Victoria West. 





The equation of a circle 
20140814 

From jennifer: hi there My name is Jennifer and residing in Denmark. I am a student and I wrote to you because i am having trouble in finding out the equation for the circle using
(xa)^2 + (yb)^2 =3D r^2.The diameter of this circle is d=3D 44,514 cm.
I have attached a drawing of my problem..thanks Answered by Penny Nom. 





Distance, speed and time 
20140813 

From abdel: Mac walked to a park from the college at 5 km/h. 10 minutes later, Steve started
riding his bike at 15 km/h to the same park to meet Mac. They arrive at the same
time at the park. How far is the park from the college? Answered by Tyler Wood. 





Speed, distance, time 
20140813 

From Aarti: a theif running at 8 km/hr is chased by a policeman whose speed is 10km/hr.if the thief is 100 m ahead the policeman then what will b time required for the policeman to catch the thief? Answered by Tyler Wood. 





Golf for 10 
20140812 

From Fred: We have 10 golfers playing 4 rounds: one 4some and two 3somes each round.
Can you suggest the best distribution of players? Answered by Victoria West. 





Golf for 15 
20140811 

From Brian: I am trying to arrange 5 rounds of golf for 15 golfers. We will play 5 in a group, 3 groups per round, 5 rounds. I would like everyone to play with everyone else. Secondary objective would be for no one to play with anyone else more than 2 times.
Thank you. Answered by Victoria West. 





Multiplication in base five 
20140807 

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





4821x14y is an 8digit number divisible by 72 
20140806 

From RAYA: if 4821x14y is an 8digit number divisible by 72. How many values can x and y take? Answered by Penny Nom. 





A chord and an arc of a circle 
20140806 

From Luis: Hello I am trying to figure out how to get chord lengths of quarter points for a circle. I work with large diameter circles and I need to be able to find chord length from 0 degrees to 90 degrees, 0 degrees to 270 degrees, 270 degrees to 180 degrees and 90 degrees to 180 degrees. Can you please use 100ft. diameter as example and work out the problem. I'm sorry if I use wrong terminology, I'm really bad at math . Thank you in advance for your time and help I really appreciate it. Answered by Harley Weston. 





The area of a quadrilateral 
20140806 

From Rahul: find the area of the quadrilateral whose side measure9cm,40cm,28cm,15cm and in which the angle between the first 2 sides is a right angle Answered by Penny Nom. 





The dimensions of a rectangle 
20140803 

From Jamaica: if the perimeter of a rectangle is 30m and its area is 56 m2.find its length and width? Answered by Penny Nom. 





A 6 team sports schedule 
20140802 

From Daniela: Hello,
My husband and I are volunteering at our church's Jrs camp and we were given the task of making the schedule for sports. There will be 6 teams and a total of 3 games for two days. We would like for every team to play each other but we cannot figure it out.
Pls help!
Thanks. Answered by Victoria West. 





A word problem with fractions 
20140801 

From nathanielcabalan: The denominator of a fraction is one more than the numerator. If the numerator is increased by three, the resulting fraction is one more than the original fractional. Find the original fraction. Answered by Penny Nom. 





A word problem concerning averages 
20140726 

From Bernie: The average weight of a team of children is 50kg, Todd who weighs 56 kg then joins the team. The average weight of the new team is 51. How many children in the original team? Answered by Penny Nom. 





60% as much as $30. 
20140718 

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





Selecting a meal at a school cafeteria 
20140718 

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





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

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





An octagon around a tree 
20140716 

From floyd: I want to build an octagon 4 feet from base of tree from 4x4's. What length do I cut my pieces Answered by Penny Nom. 





16 golfers over 15 weeks 
20140711 

From Steve: I need a schedule for 16 golfers over 15 weeks, where each golfer is paired with a different golfer each week and plays 4 matches per week against 4 different pairs (each pair does not have to play each week) Answered by Penny Nom. 





A 14 team golf league 
20140711 

From Pat: We have a 14 team golf league that plays a 16 week schedule. Playing once per week, I need a schedule where each team plays every other team at least one time. Answered by Victoria West. 





A 5 sided lot 
20140710 

From mia: have the feet numbers of three sides, but the forth side is in a "V" so it has two figures.
Question: can i add the two figures of the "v" together to get one figure, so then I would have the figures for all four sides. Answered by Harley Weston. 





4/9 of a set of story books cost Rs 630. 
20140709 

From YASIN: If 4/9 of a set of story books cost Rs 630. What will the rest of the set cost? Answered by Penny Nom. 





A ladder against a wall 
20140709 

From thabo: A ladder 6.5m long,leans against a wall so that the top of the ladder is 4.8m from the ground.what is the angle of elevation of the ladder to the top of the wall Answered by Penny Nom. 





A rotation schedule for 14 teams 
20140708 

From Daniel: I am organizing team activities for a summer camp. We have 14 teams and 7 rotations and 7 different games. every team will play a different game each rotation. Where I am having trouble is I would like each team to play a different team each rotation without a repeat. Is that possible? if so what is the formula? Answered by Victoria West. 





14 golfers, 7 men and 7 women 
20140706 

From John: I have to schedule 14 golfers, 7 men and 7 women, into 4 teams each day, playing for 3 days. So each player plays with as many different players as possible for 3 games. Answered by Victoria West. 





An antenna is atop a building 
20140705 

From Andrew: If an antenna is atop a building 70 feet tall and the antenna has a beamwidth of 30 degrees how far from the building does the beam first touch the ground? Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





Quarters 
20140704 

From kamal: how many quarters in the sum of 8 and 12 ? Answered by Penny Nom. 





Sum of 22, product of 125 
20140703 

From marj: find two real numbers whose sum is 22 and whose product is 125. Answered by Paul Betts, Robert Dawson and Penny Nom. 





The width of a rectangle 
20140702 

From john: if the area of a rectangular field is 90 sq. m and its length its is 19 m find its width Answered by Penny Nom. 





Covering a 12 inch by 12 inch square hole 
20140702 

From Patricia: I am putting in a new bathroom fan. I am wondering if a new light with a 15 inch diameter will cover the existing square hole which is 12 by 12 inches? If the existing hole is 11 1/2 by 11 1/2 inches?
Also, if the 15 inch diameter does not cover the 12 by 12 hole, what size diameter would?
Thank you. Answered by Penny Nom. 





A six digit number 
20140630 

From anupam: hi,
my daughter asking a solution for the below question, kindly help.
Write the smallest 6 digit number wit digits ( 2,4,3,0,5,7).
plz this is an urgent requirement.
regards,
anupam Answered by Penny Nom. 





Angular speed 
20140629 

From andrea: a wheel having a radius of 10cm rotates such that the linear speed at its rim is 30mls.
what is the angular speed of the wheel in rpm? Answered by Penny Nom. 





Differentiate ln[x(2x4)^1/2] 
20140628 

From Igwe: If y=In[x(2x4)^1/2],find dy/dx at x=3 Answered by Penny Nom. 





A triangle on the surface of the Earth 
20140626 

From Christine: A, B and C are three towns, the bearing of B and C from A being 310 degrees and 220 degrees, and their distances from A are 510km and 700km respectively. Find the bearing of B from C to the nearest minute. Answered by Robert Dawson. 





The largest odd number using the digits 08672 
20140624 

From audrey: what is a 5 digit greatest odd number out of this given digits? 08672 Answered by Robert Dawson. 





12 golfers 
20140623 

From Derek: I have a golf group that is set up as follows.12 players broken into 2 teams of 6.We play as a 4 ball ie 2 from each group.I am looking for a formular to have the 2 players from each group not play with each other again & also both of the 2 in each group not play with others in the other group more than once.I don't believe it is possible,so will accept as little duplication as possiblemany thanksDerek Answered by Victoria West. 





An oval pool 
20140621 

From steve: I have a 16' x 28' oval pool that is buried 24" deep inground. The dig site is dug
2' wider all the way around the pool. I need to back fill this area with stone. I want to fill this area with 6 to 8"
of stone. How many tons of stone will this take?
Thanks you
Steve Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





How many kilometers to a longitudinal degree? 
20140619 

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





A reversed curved on a railroad track 
20140619 

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





Two regression lines 
20140614 

From catherine: Given a set of data values ,we can get two regression lines .Explain. Answered by Robert Dawson and Penny Nom. 





A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





A small solid silver pyramid 
20140613 

From Jenesis: For Awards Night at Baddeck High School, the math club is designing small solid silver pyramids.The base of the pyramids will be a 2 in by 2 in square. The pyramids should not weigh more than 2.5 pounds. One cubic foot of silver weighs 655 pounds. What is the maximum height of the pyramids? Answered by Penny Nom. 





The area of a circle of circumference 32.69 meters 
20140611 

From coco: Find the area of a circle with a circumference of 32.69 meters. Answered by Penny Nom. 





Forming a cylinder from a square 
20140608 

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





Another conditional probability problem 
20140608 

From PAVITHRA: Two dice are thrown. What is the probability that sum of the numbers appearing on the die is eleven, if five is appear on the first die Answered by Penny Nom. 





Bags of sand 
20140606 

From Robert: We have a section that is 20ft long by 14ft wide and 4inches deep, the bags of sand are
.5 cubic ft. How many bags of sand do we need to fill this space evenly. Answered by Penny Nom. 





Factorials 
20140606 

From penny: What is factorial? For eg. Like 2!, 3! 4! Etc. Answered by Penny Nom. 





20 teams and 10 competition stations 
20140604 

From Joel: I have 20 teams. There are 10 competition stations.
Each station will accommodate exactly 2 teams to compete with each other at a time.
Each of the 20 teams needs to compete at each of the 10 stations exactly one time.
Here's the catch I cannot solve: how to schedule it so that each team plays EVERY OTHER TEAM once and only once, while never repeating a station. Answered by Victoria West. 





10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball 
20140604 

From adrian: Hi,
We are off to Scotland on our yearly golfing trip soon.
Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball.
I would like to ensure that each golfer plays with the other guys an equal amount of times,
guess 3ish? and we share the amount of times each player plays in the 4ball.
Hope you can help? Answered by Victoria West. 





How do we use logarithms in our daily life 
20140601 

From ss: how do we use logarithms in our dailylife Answered by Penny Nom. 





6 inches of dirt in a baseball field 
20140601 

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





How do I make fractions into decimals? 
20140531 

From jay: Hi,
I wanted to know how do I make fractions into decimals example 1 3/8? Answered by Penny Nom. 





An equilateral triangle with vertices in 3 parallel planes 
20140531 

From prajay: How to construct an Equilateral Triangle whose vertices lie on three
parallel lines, if the distances of two lines are 'a' and 'b' units
from the middle line.What is the length of the side of the
Equilateral Triangle ? Answered by Chris Fisher. 





A word problem with fractions 
20140530 

From shadab: A container of milk is 4/5 full. When 10l milk is poured into it, the container becomes 9/10 full. What is the capacity of the container ? Answered by Penny Nom. 





A rotating schedule for 9 individuals 
20140529 

From Josh: I need to set up a rotating schedule for 9 individuals.
The individuals will be pairing each week in groups of two.
Thus, every week there will be 4 groups of two individuals and one individual not paired with anyone (i.e. a "bye week").
The rotating schedule should not repeat any pairing and it will continue until each individual has been paired with every other individual once.
Thank you Answered by Victoria West. 





A word problem with fractions 
20140523 

From Tanzeela: There are 1200 pupils in a school. 2/3 of them are girls. 1/4 of the boys are overweight.
How many boys are overweight? Answered by Penny Nom. 





Overlapping sets 
20140523 

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





The volume of a wedge 
20140521 

From steve: I need to figure the volume of a wedge / right triangle, the dimensions of the right triangle is L1(10'5"), L2 (10'6"), H (14'9.5") height of L1 is 0'0" height at intersect L2/H is 3'3" Answered by Penny Nom. 





The volume of hexagonal pyramid and hexagonal prism 
20140518 

From visshwam: how to find volume of hexagonal pyramid and hexagonal prism?
my measurements are each side of pyramid's triangle is 1"x2"x2".
hexagon prism is 2"x1" each side Answered by Penny Nom. 





14 golfers for 13 weeks 
20140517 

From Judi: I want to schedule each of my 14 golfers to play each of the other girls one time during a 13 week period. We would golf in foursomes , threesomes or twosomes to make this happen. Can you send me a grid that would do this scheduling? I'm at a loss as to how to do it!! Answered by Victoria West. 





The weight of salt in a basket 
20140517 

From Sumit: I want to determine how many kg of salt or XYZ thing can be filled in a basket
Length = 4.5"
Breadth = 5"
Height = 6"
Even its formulae
is kg quantity can be different for semi solid thing Answered by Penny Nom. 





The equation of a line 
20140516 

From Michael: Find the equation of a line that passes through (2,1); the sum of the x and yintercepts is 2. (There are two answers) Answered by Penny Nom. 





A hexagon with different side lengths 
20140516 

From Grace: Sorry if this is a simple question, but I can't seem to understand how to solve it. I am Trying to find the area of a hexagon with measurements 6x7x6x6x7x6, or 2 sets of opposing sides with 6, and one set with 7. Thank you. Answered by Penny Nom. 





Golf for 14 players over 12 weeks 
20140516 

From Judi: How would I develop a playing schedule using foursomes and one twosome for 14 players who will play 12 weeks and each person would play all but one of the others? Answered by Victoria West. 





A problem with numbers 
20140514 

From Justina: Okay so I don't understand how to equal this equation to 10 using bedmas.
I've been stuck on it for a few days now. Is there different ways you can show me
Using these same numbers?
5 2 4 3 1 = 10
Help! Thanks. Answered by Robert Dawson and Penny Nom. 





18 golfers for 5 rounds with a teaching Pro 
20140514 

From Maree: We are taking 18 golfers on Tour with a teaching Pro. There are 5 rounds of golf and we want everyone to play with the Pro once, but everyone else to play with as many different people as possible Answered by Victoria West. 





A circle a square and a rectngle 
20140512 

From mazhar: suppose the length and breadth of the rectangle are 5 cm and 10 cm respectively and M is a point along the corner of the circle. what is the radius of the circle?(diagram is given..but i didn't mention it..actually the diagram looks like a circle inscribed in a square and the right bottom corner one rectangle will be given ,it is touches to circle at a point M that I've already mentioned and the dimensions of that rectangle also I've mentioned) please help me out.. Answered by Penny Nom. 





Travelling upstream and downstream 
20140512 

From Mohanad: Howie Sorkin can travel 8 miles upstream in the same time it takes him to go 12 miles downstream. His boat goes 15 mph in still water. What is the rate of the current? Answered by Penny Nom. 





A 12 week poker tournament 
20140512 

From Jamie: Looking to schedule a 12 week poker tournament with 18 players ...playing 2 separate 9 person tables...I'm looking to have a balanced schedule where everyone player with each other an equal amount of time Answered by Victoria West. 





Mary's height as a percentage of Michael's height 
20140511 

From Lauren: Mary is 1.4m tall and her brother Michael is 1.2m tall.
Express Mary's height as a percentage of her brother's. Answered by Penny Nom. 





The length of a shadow 
20140509 

From vijay: A girl of height 80 cm is running away from the base of a lamppost at a speed of 2 m/s. If the lamp is 4 m above the ground, find the length of her shadow after 5 seconds. Answered by Penny Nom. 





A question concerning two lines 
20140509 

From Hela: The equation of the line L is 6x+5y=3, and the equation of line Q is 5x6y=0, which statement below about the line is true?
A) same y intercept
B)parallel
C) Same x intercept
D)perpendicular Answered by Penny Nom. 





How many boards did the carpenter start with? 
20140508 

From Yanly: A carpenter has several boards of equal length. he cuts 3/5 of each board.
After cutting the boards, the carpenter notices that he has enough pieces
left over to make up the same length as 4 of the original boards.
How many boards did the carpenter start with? Answered by Penny Nom. 





A schedule for 2 teams of 10 
20140507 

From John: How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 110, Team B would consist of players 1120. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!! Answered by Victoria West. 





A 5person golf flight 
20140505 

From Jeremy: can you have a 5person golf flight and play only 3 matches so that one person plays one match each? Answered by Victoria West. 





Golf for 8 
20140505 

From Ivan: We have an eight member golf team. We field one foursome each week for 16 weeks of league play. How do I roate the eight members so each team member plays with each team member and all play an approximately equal number of times? Answered by Victoria West. 





4 golfers in twosomes 
20140504 

From Lori: 4 golfers want to play as 2 somes every week, but rotate the 2 players so we all play together
With each other evenly thru out the summer Answered by Victoria West. 





Golf :15 players over 4 days 
20140502 

From michael: We are playing with 15 players over 4 days. We plan to have 3 people in each group. A total of 5 groups with 3 players each. Can I arrange for each player to play with other players only 1 time? Answered by Victoria West. 





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

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





11 golfers going on a golf trip for 4 rounds 
20140501 

From David: I have 11 golfers going on a golf trip for 4 rounds of golf. I want to make sure that everyone gets a chance to play with everyone at least once but not more than twice.
Also, as we are n = 11, we will be composed of 344 everyday. I am trying to ensure that as few as people as possible play in the group of 3 (golf seems to be more enjoyable for whatever reason in foursomes). i have tried 3 differemt times and can seem to figure it out. Can you assist? Answered by Victoria West. 





2 teams of six playing each other 4 times 
20140501 

From Steve: I have 2 teams of six (Team A & B) playing each other 4 times.
Is it possible to have a player from Team A play with a different partner from Team A for each of the 4 rounds,
and likewise for Team B.
Whilst no player from either team plays an opponent more than twice during the 4 rounds? Answered by Victoria West. 





If x+y+z=1 then x^2 + y^2 + z^2 = ? 
20140430 

From Nitin: If x+y+z=1
then
x^2 +y^2+z^2 = ? ? Answered by Robert Dawson. 





Profit and loss 
20140429 

From Anoushka: A man sells two tables of the same price. On one he makes a profit of 10 percent and on the other he suffers a loss of 10 percent.Find his loss or gain percent on the whole transaction. Answered by Robert Dawson. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





The volume and radius of a sphere 
20140427 

From grace: How do you find the radius of a sphere when all you know is the volume? Answered by Penny Nom. 





The derivative of sin(x) 
20140426 

From Lucky: f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem. Answered by Penny Nom. 





A schedule for 9 teams on 3 fields for 18 days 
20140425 

From Scott: I need to schedule 9 teams on 3 fields for 18 days with no buys. Two teams play while other practices in field(little guys). Two fields have backstops and other is open field. Would like to have even time on each diamond if possible. Thank you Answered by Victoria West. 





Solve for theta 
20140425 

From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta.
Substituting for cos2th either 12sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom. 





An octagonal pad 
20140425 

From George: Hi,
I need to pour a cement pad in the shape of an octagon that allows
for 12" of clearance around the tank I will be putting on it.
The tank has a radius of 16'. Answered by Penny Nom. 





A trig problem 
20140425 

From srishti: Consider the points P= (sin(ab),cosa), Q=(cos(ab),sina), R=(cos(ab+c),sin(ac), where 0 Answered by Chris Fisher. 





What was the selling price? 
20140425 

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





What time was it when joe's brother passed him? 
20140425 

From Nathan: joe left home in his bike at 10:00 am, traveling 21 km/h. At noon, his brother set out after him on his motorcycle, following the same route. if the motorcycle traveled at 63 km/h, what time was it when joe's brother passed him? Answered by Penny Nom. 





Two 9 hole golf leagues 
20140423 

From Sally: I need help scheduling two 9 hole leagues. Here are the variables:
 Leagues alternate each week starting on the front and back
 League A starts at 4:30 with 7 groups and League B starts at 5:15 with 8 groups (all use carts and must be teed off by 5:30)
 Regular play must continue, customers who have started before league play begins have preference to continue their round whether they are playing 9 or 18 holes.
Thank you!!! Answered by Victoria West. 





Golf for 6 
20140421 

From barbara: We are a group of 6 golfers. We play in groups of 3 for 5 days.
How can I arrange the groups that everybody plays with everybody else at least once?
Thanks. Answered by Victoria West. 





Golf with 3 teams of 20 
20140421 

From Joshua: Thank in advance for this great service
Golf  new  3 teams of 20  to create 20 unique groups of 3
For example use 3 teams of 3
1a 2a 3a
1b 2b 3b
1c 2c 3c
So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c
Groups can only have one a, one and one c  and that combo should be unique Answered by Victoria West. 





A 22 team golf league 
20140421 

From Terry: We have a team league at our local golf course.
We have 22 teams, we would like it so that each team plays the other team only once.
I have tried the scenario.
1,21;2,20;3,19;4,18;5,17;6,16;7,15;8,14;9,13;10,11;12,X X+1=1 scenario
2, 1;3,21;4,20,5,19,6,18;7,17;8,16;9,15;10,14;11,13;1,X
using formula from other post in your forums.
I can get all the possible playing arrangements. The big quandary is setting up the schedule
so that each week, each team would start on a different hole.
I can get the first 11 weeks scheduled very easily, it is just trying to get the last 11 weeks scheduled?
Any help would be greatly appreciated. Answered by Victoria West. 





Golf League Schedule for 15 weeks and three flights 
20140421 

From bigdog: I need help setting up a 12 team (3 flights with 3 teams in each flight) 15 week league play schedule. Each team must play teams in there perspective flight twice during the 15 week season. Answered by Victoria West. 





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 