







The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





The distance between the origin and a moving point on a graph 
20171016 

From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom. 





A trapezoid inscribed in a circle 
20170517 

From Kameron: I have been given a challenge problem that states that Diameter AB is drawn in a circle if 10 inch. Chords AC and BD are drawn so that each is of length 12inch and ACDB is a trapezoid. Find the height, in inches, of the trapezoid Answered by Penny Nom. 





The height of a isosceles trapezoid 
20170403 

From Riham: Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance. Answered by Penny Nom. 





Covering the ceiling of a garage 
20170220 

From DeAnna: I am trying to drape a 15 x 30 garage with yards of fabric. If the yard of fabric is 60 inches wide, would 10 1/4 yards be enough for my space? Answered by Penny Nom. 





A pie chart 
20161205 

From vickie: Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant Answered by Penny Nom. 





2^x= 2x  11 
20161127 

From Kathy: I don't know how to start this problem:
2^x= 2x  11 Answered by Penny Nom. 





The amount of material remaining on a roll 
20161111 

From Yoh:
Question from Yoh:
Hello,
I am trying to find impressions on a roll (either full roll or partial).
Let's say I have the following information.
 Outer Diameter of roll
 Inner Diameter of roll (cardboard core)
 thickness per layer
 Each cut off length (impression length)
Now let's say a roll has a 40in outer diameter, the cardboard core has a 3.75in diameter and a thickness of .002. Each impression has a cut off of 14inches.
With this the roll will have approximately 2,700 impressions. How would I find the remaining impressions if the outer diameter of the roll is only 6.5inches?
Thank you. Answered by Penny Nom. 





A stained glass cone lamp 
20160409 

From Edwin: In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Answered by Penny Nom. 





A block wall 
20160315 

From Robert: I have a wall 40 ft. long and 4 ft. tall as well as another one that is 30 ft by 3.5 ft. tall that I am trying to build. how many 6 inch by 12 inch landscaping blocks do I need? Answered by Penny Nom. 





The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





The volume of a silo 
20160118 

From Clinton: Can you show me how to calculate the ground corn capacity in a steel silos of 10' x 10' high and 10' x 20' high and 10' x 24' high and 10' x 28' high Answered by Penny Nom. 





A triangular shaped garden 
20160113 

From Demetrie: Dwayne's garden is triangleshaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side? Answered by Penny Nom. 





The perimeter of a triangular plot of land 
20160111 

From Janelle: I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off? Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





The angles of a triangle 
20151217 

From Faith: Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Answered by Penny Nom. 





The positive root of sin(x) = x^2 
20151213 

From Kemboi: Find the positive root of the equation sin(x) = x^2 Answered by Penny Nom. 





The area of a domed roof 
20151113 

From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom. 





Why are bags of soil measured in litres? 
20150619 

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





A piecewise function 
20150425 

From uday:
f(x)={x^2+3x+2 / x+2, x(not equal to)=1
{4, x=1
how to find domain and how the graph looks like 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. 





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. 





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. 





Is a square a trapezoid? 
20150126 

From Katie: Can a trapezoid sometimes be a square? 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. 





A truncated, squarebased pyramid 
20141123 

From Hannah: A designer vase has the shape of a truncated, squarebased pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface
area of the vase. Answered by Penny Nom. 





An arithmetic progression 
20141119 

From Gbenga: In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression.. Answered by Penny Nom. 





A piecewise graph 
20140510 

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





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. 





Graphing piecewise functions 
20140329 

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





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. 





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. 





The graph of y=2x+4 
20140218 

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





The graph of f(x)=x^24 
20140207 

From Allison: Graph f(x)=x^24 and give the five point of the x/y intercepts. 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. 





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. 





What does y= f(x) actually mean? 
20131231 

From John:
I don't understand how to pick coordinates for y=f(x).
I took a look at your answer to a previous question here:
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/monica2.html
What does y= f(x) actually mean? Answered by Penny Nom. 





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. 





How do I graph y=2x1? 
20131207 

From cindy: How do I graph y=2x1? 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. 





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. 





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. 





How can we draw the equation "x+y=1" in 3d? 
20130503 

From shimaa: how can we draw the equation "x+y=1" in 3d Answered by Robert Dawson. 





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. 





An arithmetic progression 
20130206 

From loberto: the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term Answered by Penny Nom. 





Plotting y=f(x)+2 
20130121 

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





A bipartite graph 
20121029 

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





A 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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





Using Newton's Method to find a root 
20120409 

From Nancy: Use Newton's method to find the real root function, accurate to five decimal places
f(x) = x^5+2x^2+3 Answered by Penny Nom. 





A lot with a slope 
20120330 

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





Two overlapping circles 
20120321 

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





A trapezoidal prism filled with sand 
20120312 

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





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

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





Wallpapering a room 
20120208 

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





The graph of a quadratic function 
20111227 

From Thomas: sketch a quadratic function with zeros at 3 and 1 Answered by Penny Nom. 





2 + f(x) and f(x) + 2 
20111121 

From Beth: Do you do y=2+f(x) the same way as if the 2 came after the equation such as y=f(x) +2 when graphing? Answered by Penny Nom. 





The end of a trough 
20111021 

From Lorraine: The vertical end of a trough has the following dimensions: width at top 4.4 ft., width at bottom 3.2 ft., depth 3.5 ft. Find the area at the end of the trough. Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





A trapezoid inscribed in a circle 
20111002 

From Greg: A trapezoid is inscribed within a circle.
The two interior angles who share the longest side are 70 and 80.
The arc whose chord is the longest side has a length of 120.
Find the other two interior angles of the trapezoid, and the other three arc lengths. Answered by Chris Fisher. 





A step function 
20110822 

From Giovanna: An average school bus holds 45 people. Show a graph between the relationship of students who need bus transportation and number of buses required? Answered by Robert Dawson and Penny Nom. 





A trapezoid 
20110802 

From Nazrul: How can I draw a trapezoid whose parallel sides and other two sides are given. Answered by Chris Fisher. 





A stained glass lamp 
20110725 

From Guy: Like Kay, I also work in stained glass, but in 3dimensions. I am
frequently asked to replicate lamp shades in stained glass where the
diameter of the top is different (narrower) from the diameter of the
bottom (which is wider). Some people want 5, 6, 7, 8, 10, 12, 16, ,,,
nsided shades. Is there a formula I can use to determine the width
of the sides using the angle, if I remember correctly, I think it's
called theta. In other words, is there a formula where I can plug
in the angle which describes the arc of the circle. For instance, if
someone asks for a 7 sided shade, plugging in 51.43 (360/7). I
could then use that to determine the width at the top and bottom
rings to create the appropriate trapezoids. I've visited a few sites
so the formula looks like its a function of sin & cos but they are
presented like proofs for teaching. Your site appears to want to
actually answer questions without making the inquirer feel stupid. Answered by Harley Weston. 





A reel of paper 
20110603 

From keith: if a full reel of paper has 7750 metres on it with a diameter of 1240mm and a core diameter of 100mm how can work out the thickness of each strip of paper therefore allowing me to work out the metreage of the roll when its half in diameter at say 620mm Answered by Penny Nom. 





The volume of a triangular shaped aquarium 
20110507 

From Jeff: HI, I searched the site but really couldn't find my answer,
at least that I could understand! I have a triangular shaped aquarium
( think of a cube, except its an equal triangle shape). all 3 sides are 48 inches,
and it is 34" tall. Can you please tell me what the volume is in gallons?
Thanks! Answered by Penny Nom. 





cos(x) = 1/(square root of 2) 
20110427 

From Shelby: Find exact value of x for 1 <(or equal to) x < 2pi
a) cos(x) = 1/(square root of 2) Answered by Penny Nom. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You! Answered by Penny Nom. 





6 faces and 8 corners 
20110304 

From noemi: jeff made a figure with 6 faces the figure has 8 corners all of the faces are the same size and shape what figure did jeff make Answered by Penny Nom. 





At what rate is the grain pouring from the chute? 
20110226 

From MJ: Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Answered by Penny Nom. 





A circle is inscribed inside an isosceles trapezoid 
20110225 

From priyam: a circle is inscribed inside an isosceles trapezoid (with parallel sides
of length 18 cm and 32 cm) touching all its four sides.
find the diameter of the circle.
thanks for help!! Answered by Penny Nom. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





Points on a graph 
20110215 

From Maggie: Which set of ordered pairs can be used to graph y = 2x1.
A.(5,9),(1,3),(4,9) B. (2,5),(1,1),(5,9)
C.(2,5),(0,1),(4,3) D. (5,9),(2,3),(4,9)
I cannot figure it out. Could you help me? Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

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





The height of the trapezoid 
20101201 

From Ryan: A trapezoid has an area of 10.5 cm squared and parallel sides that
measure 5.0 cm and 2.0 cm what is the height of the trapezoid Answered by Penny Nom. 





Intersecting polygons 
20101117 

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





The sides of a trapezoid 
20101103 

From Bobbi: Isosceles Trapezoid base=60”; two 45⁰angles at base, two 135⁰ angles at the top, vertical distance between base & top=16”. What is the length of the top line and the two equal side lines? Answered by Penny Nom. 





A water trough 
20101022 

From Jasmine: A water trough is 8 m long and its crosssection is an isosceles
trapezoid which is 90 cm wide at the bottom and 120 cm wide
at the top, and the height is 30 cm. The trough is not full.
Give an expression for V , the volume of water in the trough in cm^3,
when the depth of the water is d cm. Answered by Stephen La Rocque. 





The equation of a line 
20101019 

From Sava: I have to write an equation and sketch a graph for the line that meets the given conditions:
A line with slope 15/5 that passes through the point (2.5,4.5) Answered by Penny Nom. 





A taxi ride 
20100922 

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





How many labels are left on a roll? 
20100813 

From Melissa: Is there a simple way to calculate how many labels are left on a roll? I thought there was a way to look at the individual label length, the label thickness and the core diameter and then measure the overall diameter to calculate how many pieces were left, but I'm struggling. I've seen a tool before I thought we called it a circle calculator, but those parameters were all that I needed to input to spit out the correct count. I never saw what was behind the scenes for this calculation. Ie factoring in revolutions or the number of pieces on each layer, etc. Please let me know if you have any suggestions. Any assistance will be greatly appreciated!!! Thanks! Answered by Penny Nom and Tyler Wood. 





The intersection of two graphs 
20100627 

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





The outside surface area of a U shaped tube 
20100603 

From Adolfo: What is the formula for calculating the outside surface area of a U shaped tube? Answered by Robert Dawson. 





graph y=(2x^23x)e^ax 
20100531 

From James: graph y=(2x^23x)e^ax Answered by Robert Dawson. 





Which values of x satisfy (x2) / (x+4) <7 
20100523 

From Rocco: Which values of x satisfy (x2) / (x+4) <7 Answered by Harley Weston. 





Two overlapping circles 
20100412 

From Scott: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^2 (half the area of the small circle). The Question is: suppose we have known the radius r of the small circle, and the distance between the two circle centers, what should the radius R of the large circle be? Answered by Chris Fisher. 





Vapor trails 
20100412 

From Frank: I'm not sure if this is a proper question to ask so if I have misdirected my question I apologize and no response is expected. I am trying to figure out a way to measure vapor trails from my back yard in Phoenix Arizona. If I used a compass and spread each point of the compass to the start and finish of the vapor trail I would have the angle of an isosceles triangle. The other two angles would be identical. The height of from the inverted base of the triangle to my standing spot on the ground would be about 35,000 feet. I'm thinking that there should be a way to figure out the length of the inverted base (vapor trail) but I'm devoid of mathematical skills and can't seem to figure out how to do this. Is it possible to figure out the length of a vapor trail using this method or do you have an easier way to accomplish the task?
Any help you could offer would be most appreciated.
Thanks....Frank Answered by Harley Weston. 





An isosceles trapezoid is inscribed in a circle 
20100406 

From Abby: An isosceles trapezoid whose bases have lengths 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid Answered by Penny Nom. 





A roll of paper 
20100325 

From keith: how many yds of paper for a roll with a width of 6.875 and a core of 3 in and a diameter of 40in? Answered by Robert Dawson. 





Modelling the roof of a house 
20100323 

From Sandi: This question has been haunting my dreams at night. It states the cross section of the roof of a house is modelled by the function y= 5\12x12+5, where y>0 or y. Now I'm suppose to graph the function. b) Find the slope, height, length of sides, and base of the isosceles triangle. c)Explain what transformation must be applied to the graph of y=x to obtain the graph of y= 5\12x12+5, where y>0 or y=0. 1st I put the equation into my calculator and graphed it. I got 10 for the height. We have had 2 sub teachers this past week. The first one told me the height should be 12 the other one told me 5. So I'm really confused. If I use my 10 units as height and the Pythagorean Theorem I get my sides to be 26 units the base 48 and my slope I calc to be 5/12. Both teachers are pretty sure I'm wrong and they are right but we all have different answers. Please help put this problem to rest so I can rest soundly at night. Thank you for your time. Answered by Penny Nom. 





A quadratic equation 
20100315 

From rachelle: under certain condition, it is found that the cost of operating an automobile as a
function of speed is approximated by a quadratic equation. use the data shown
below to find the function. then use the function to determine the cost of operating
the automobile at 60mph.
speed
(in miles per hour) 
operating cost
per mile(in cents) 
10 
22 
20 
20 
50 
20 
Answered by Penny Nom. 





Two overlapping circles 
20100307 

From Hayden: I have two circles of equal size. The radiuses of the circles are 30ft. The two circles are positioned 40ft apart and I need to find the area where they overlap. Answered by Harley Weston and Tyler Wood. 





Sketch the graphs of the following 
20100302 

From musaf: without detailed plotting of points,sketch the graphs of the following
showing relevant information on the graphs:
a) y=(x3)2 +5
b)y=4xx2 Answered by Penny Nom. 





The area of a trapezoid 
20100301 

From mariah: the height of a trapezoid is 6 centimeters. one of the bases is three times the height, and other base is four times the height . find the area of the trapezoid Answered by Penny Nom. 





A paper tube 
20100221 

From shailesh: How can i estimate weight of paper tube from size. i have paper tube
inner diameter : 22mm, thickness : 2mm, length : 14mm. so how can i got weight
of paper tube? Answered by Harley Weston and Tyler Wood. 





Bending a wire to form shapes 
20100204 

From Geraldine: a wire bent into the shape of a square encloses an area of 25cm squared. then the same wire is cut and bent into two identical circles. what is the radius of one of the circles round to the nearest hundred Answered by Penny Nom. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





The adjacency matrix of an undirected graph 
20100115 

From Bhavya: Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2 Answered by Robert Dawson. 





The area of a trapezoid 
20100106 

From maureen: the question asks for the area of a trapezoid with parallel sides 5m and 6m and height of 2.5m
I have done it by dividing the trapezoid into 2 triangles and reach the same answer as my manual11.25 sq. m
My question...how would you illustrate this? I read this to mean to sets of parallel sides, which would mean it is a parallelogram and not a trapezoid.
Any suggestions? Answered by Robert Dawson. 





Cutting a square into four shapes 
20100105 

From Tracy: A square with a side of 4 ft needs to be cut into four shapes with the same area. can you find six different was to cut the square? Answered by Robert Dawson. 





Using graphs 
20100104 

From Armstrong: Given that 50 litres of kerosine costs 6000 nira. Draw a graph and read off;
A: The costs of 15 and 34 liters.
B: The number of litres that can be bought for 2300 nira. Answered by Robert Dawson. 





A Lagoon, free form, inground swimming pool 
20091222 

From donna: What is the linear footage of a 14 x 23, Lagoon, free form, inground swimming pool? Answered by Robert Dawson. 





Figure out the square root of something 
20091220 

From eric: is there an ez equation to figure out the square root of something? Answered by Harley Weston. 





The acute angle formed by intersecting lines 
20091217 

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





f(x)=x+2sinx 
20091212 

From amroziz: for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Answered by Harley Weston. 





The graph of f(x)=1/x 2 
20091129 

From Kapilan: Please answer the following question:
Sketch the graph of f(x)=1/x 2 Answered by Harley Weston. 





Two overlapping circles 
20091119 

From Raraa: There are two identical circles . The edge of one circle is at the middle point of the other circle. There were overlapped . The area of the overlapped surface is 20000 square centimetres . How do I find the radius of the circle rounded to the nearest whole centimetre ? Answered by Penny Nom. 





The graph of f(x2) 
20091119 

From Kapilan: Hi please answer the following question:
Given the function f(x)=x^2 sketch the graph of f(x2) Answered by Robert Dawson. 





An isosceles trapezoid 
20091112 

From lyjah: what is parallel sides of an isosceles trapezoid measure 5cm and 11cm long.and
oneof the other sides also measures s5cn long what of the isosceles trapeziod Answered by Penny Nom. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





f(x)= (e^x) / [(e^x)+(ex^2)] 
20091110 

From natalie: I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator.
thanks,
natalie Answered by Chris Fisher and Harley Weston. 





The intersection of two graphs 
20091030 

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





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

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





The intersection of two graphs 
20090902 

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





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





Graph 2x3y+15=0 
20090820 

From Diem: Graph 2x3y+15=0 Answered by Leeanne Boehm. 





A paper towel roll 
20090819 

From Jeff: I am making a spiral tube with paper that is 2" in dia. and 102" long
I will be using paper that is slit 3" wide how many lineal feet of paper will
I need to to cover the 102"
I will be using 3 rolls of paper that will over lap the other by half to make
a hard tube (paper core) in a roll of paper towels
Thanks Jeff Answered by Penny Nom. 





The volume of a telephone pole 
20090811 

From robert: 12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions? Answered by Harley Weston. 





The volume of a tapered pole 
20090809 

From robert: what is the formula to use to come up with cubic feet in a tapered pole Answered by Harley Weston. 





The length of tape on a reel 
20090806 

From Philiip: What diameter reel would be required to roll up 1000 meters of tape that is 0.01 mm thick such that the final role left 10 mm empty space between the top of the roll and the outside of the reel, the hup that the tape was wound on was 2 cm? Answered by Stephen La Rocque. 





Buying pens and staplers 
20090722 

From Ellen: one more math question,
six pens and four staplers cost $7.10. four pens and seven staplers cost $9.50
find the cost of one pen and one stapler. Answered by Penny Nom. 





A roll of paper 
20090705 

From mark: is there a simple way of finding out how much is left on a roll of paper. i have read similiar questions and answers on here but all seem very complicated and not being very good at maths does not help me much. some are in inches and all have different figures to mine so if i give my figures hopefully i wil understand it better. the radius of the cardboard core is 52.25mm, the radius of the paper at 2000 linear meters is 158.625mm. the thickness is 0.17mm. when nearing the end of the paper how do i work out how much is left in a simple way. thank you in advance for any help you can give me Answered by Harley Weston. 





The surface area of a tank 
20090625 

From Charles: I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high. Answered by Penny Nom. 





How many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? 
20090527 

From Henry: how many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? Answered by Penny Nom. 





The Smythe family lot 
20090524 

From Shrima: We must determine the size of the lot. The Smythe family lot is 235ft
across the front and 212ft down the side and 254ft down the other side.
The sides of the lot are parallel to each other and perpendicular to the front.
The size of the lot is two dimensional measure therefore you need to find
the areaenclosed by the lot line.
Question:
What is the size of the Smythe lot including the unit? Answered by Penny Nom. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





Stairway construction 
20090502 

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





Winding paper after a break 
20090410 

From Olen: Question from Olen:
I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston. 





The graph of y = 4x^4 
20090407 

From lyric: tell whether the graph opens up or down.write an equation of the axis of symmetry
y=4x^4 Answered by Penny Nom. 





A triangle inside a trapezoid 
20090406 

From rohan: i have a diagram with a triangle inside a trapezoid.trapezoid is PQRS ,
PQ being the line above and RS THE LINE BELOW.The area of this is 12.
If RS is twice PQ what is the area of PQS. Answered by Penny Nom. 





Conversion factor 
20090323 

From kab: Would like to photocopy a Landscape Design. What is the Conversion Ratio or magnification required to convert 1" = 10 feet to 1/4" = 1 foot? Answered by Harley Weston. 





A 1.5:1 rectangle 
20090323 

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





A simple digraph 
20090323 

From Shabkhal: Show that the sum of in degrees of all the nodes of a simple digraph is equal to the sum of out degrees of all its nodes and this sum is equal to the number of edges of the graph. Answered by Victoria West. 





An equation for a line with a changing slope 
20090321 

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





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

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





A shape with 10 sides 
20090303 

From Sandra: One of my son's math questions is as follows:
Suppose I have a shape with 10 sides. I choose a vertex then draw lines to the other vertices that dont share sides with the first vertex. How many vertices will that be and why? Answered by Penny Nom. 





An octagonal landscaping frame 
20090301 

From Richard: Hi
I am trying to put landscape timbers down in octagon shape that measures 6
feet across and outside measures 360 degrees.. The timbers are 4 inches by 4
inches. I need to know at what angle to cut boards and at what length i need to
complete octagon.
Thanking you in advance for your kind assistance.
Richard :) Answered by Harley Weston. 





The graph of y = 6 
20090221 

From Barb: I was given the problem that says "graph the line y = 6" how do I find all the set points that have a y coordinate of 6? I am so lost lost and have no clue how to start. Can you help me please? thanks. Answered by Penny Nom. 





Making shapes with straws 
20090206 

From Melissa: suppose you have 60 straws. How many of each shape could you make
a) Triangles
b) squares
c) pentagons
d) hexagons Answered by Stephen La Rocque. 





The intersection of two lines 
20090130 

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





Shapes 
20090129 

From Rana: I want to know about Circumference / Area / Volume of different shapes ie Circle , Oval , An Arc Trapezide etc Answered by Robert Dawson and Harley Weston. 





y = x  4 
20090128 

From tiana: how do you find where to plot Y in a problem that states y=x 4? Answered by Robert Dawson and Penny Nom. 





Graphing a parabola 
20090127 

From Kimberly: I need help with this parabola: graph y=5x^25x6. I am not really understanding how to graph parabolas in general. Can you help me? Answered by Penny Nom. 





A applied math trig problem 
20090113 

From Simon: I wish to find all the answers for the following equation over the interval (0,1):
cos^2(pi * n^x) + cos^2(pi * n^(1x))  2 = 0
where n is any integer > 0 Answered by Robert Dawson and Harley Weston. 





Surface area of an irregular shape 
20081215 

From Patrick: An irregular shaped object (lets say a gold nugget, not smooth with
pockets) can have its volume determined by comparing its mass in
water.
Is there any method or means or anything that could be used to
determine the surface area of this shape? Whether that be theoretical
mathematical formula to using a special infrared technique,etc...
The problem I foresee is that the component parts cannot be divided
into smaller geometric shapes. I would propose an answer although I
don't know if it is a good one: A liquid material that dries superthin, but
has a very specific and easily determined volume/mass is coated over
the object. Measure the mass difference between the beginning sample
of fluid and the mass after the object has been coated. Then determine
the surface area of the same mass of fluid in a geometric shape.
Is this feasible? Answered by Robert Dawson. 





Wall covering 
20081210 

From Jeanie: I need to convert 14 LY of wallcovering (54" wide) to square feet. Can you please help me? Answered by Penny Nom. 





A quadrilateral with exactly 1 pair of parallel sides and no congruent sides 
20081210 

From alie: a quadrilateral with exactly 1 pair of parallel sides and no congruent sides is what? Answered by Robert Dawson. 





Graphing 
20081209 

From Natasha: 2x+y=5 Answered by Robert Dawson. 





Graphing Rational Functions 
20081205 

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





Evaporation of waste water 
20081121 

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





Four circles in a square 
20081119 

From Anthony: I have a square where one side measures 10cm and within that square
There are four equal quarter circles. Each quarter circles starts in a
different corner of the square and I am trying to find area inside the
overlap on the quarter circles. Answered by Janice Cotcher, Chris Fisher and Penny Nom. 





The diagonals of an isosceles trapezoid 
20081114 

From hazel: how to solve the diagonals of an isosceles trapezoid? what is the formula? Answered by Harley Weston. 





Filling a tank with 2 taps 
20081110 

From Murray: 2 taps turned on together can fill a tank in 15 minutes. By themselves, one
takes 16 minutes longer than the other to fill the tank.Find the time taken to
fill the tank by each tap on it's own. Answered by Penny Nom and Victoria West. 





The area of a trapezoid 
20081104 

From kelsey: The area of a trapezoid is approximately 150cm2...the length is 26 cm, the
weight is 5cm...what is the height????
(show me the work that you did so i can understand) Answered by Penny Nom. 





The volume of a pond 
20081104 

From Malcolm: I am looking for a formula to find the volume of my pond. I know the average surface diameter and the average bottom arc length.(The arc from one bank through a point in the bottom and on to the surface on the other bank. I am not able to get a good measurement of the depth at this time. Can the volume be figured with the known measurements (the cord and the arc)? Thanks: MS Answered by Harley Weston. 





Scaling a logo 
20081020 

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





Concavity and the second derivative 
20081015 

From Christina: I'm having trouble solving for a second derivative for the following graphing question.
f(x) = (X^2+2x+4)/2x
using the quotient rule, I found:
f'(x) = (x^24)/(2x^2)
however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)(x^24)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3(4x^3 16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3
and making the equation equal to zero result in 0=4 which doesn't seem to make sense... Answered by Penny Nom. 





Compatible numbers 
20080925 

From Katie: I am having trouble remembering how to find compatible numbers used to find the estimate in the foloowing problem. Can you please help me solve it and explain it to me? My son is in 5th grade and I need help. Thank you. Here is the problem: 2,752 / 28 estimate: 90 Answered by Penny Nom. 





Graphing a piecewise function 
20080812 

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





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





The cube root of a really big number 
20080717 

From Pete: Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator? Answered by Harley Weston. 





Graphing Using Double Angle Identities 
20080716 

From Hodan: the Question is:
Describe how you could use your knowledge of Double angle formulas to sketch the graph of each function. Include a sketch with your description.A) F(x)=sin x cos x
B)F(x)=2 cos(squared)x
C) F(x)= tan(x) (divided) by 1tan(squared) x Answered by Janice Cotcher. 





Domain & Range of a Periodic Function 
20080711 

From Michelle: The depth, w metres, of water in a lake can be modelled by the function,
w=5sin(31.5n+63) +12 where n is the number of months since
January 1, 1995. Identify and explain the restrictions on the domain and
range of this function. Answered by Janice Cotcher. 





A point on a graph 
20080708 

From Rita: If (2, b) is a point on the graph of y = (x^2) + 4x, find the value of b. Answered by Leeanne Boehm. 





Points on a graph 
20080703 

From Rita: Dertermine if the given 3 points are on the graph of the equation.
Equation: y = (x^3)  [2(sqrt{x})]
Points: (0, 0); (1, 1); (1, 1) Answered by Penny Nom. 





A piecewise equation 
20080616 

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





How do i find the area of an irregular figure? 
20080610 

From DAVE: How do i find the area of an irregular figure? Answered by Penny Nom. 





Geometric shapes that are the same 
20080609 

From tia: what is the name used for shapes that are exactly the same? Answered by Harley Weston. 





The area of a regular pentagon 
20080602 

From Jenna: I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given. Answered by Penny Nom. 





Applications of trigonometry 
20080524 

From Mohita: I have got a project in the school and i am not getting anything about the topic. The topic is that we need to find the application of trigonometry on any one of the real life situations using 3dimensional figures. I mean how can trigonometry can be used in real life situations like navigation, architecture, survey, astronomy etc. Answered by Penny Nom. 





The wedges in a circle graph 
20080518 

From Libby: I don't understand how to do this word problem:
The cafeteria workers distributed a survey to the student body asking students to pick 1 from a list of 5 choices for their favorite lunch. The circle graph below gives the results of the survey for the students who responded. What is the measure, in degrees, of the central angle for each choice?
And there is a pie chart that has food choices with these percentages: 25%, 20%, 15%, 10%, and 30% Answered by Leeanne Boehm and Penny Nom. 





The area of a trapezoid 
20080515 

From Ashley: what is the formula for area of a trapezoid Answered by Penny Nom. 





The fourth side of a property 
20080514 

From Penny: Property has 3 measurements and 2 angles and I want the altitude at a particular point. Corners are sw, nw, ne and se. 1 want the 4th saide measurement confirmed (we think 146.07') and the altitude measurement at 25' from sw (on the swse side)
The angles provided are interior at nw 67.38 degrees and the opposing corner se interior appears to be 68.58 degrees. the 3 sides with measurements are: sw to nw=54.07'. sw to se 146.07' and se to ne 53.57'. If you would help, we would really appreciate it. Thanks! Penny Answered by Harley Weston. 





Identify the graph 
20080505 

From A parent: Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer.
y = 2x
y = log2x
I can figure out what line on the graph is which equation but unsure what is meant by justify your answer. Answered by Penny Nom. 





Two overlapping circles 
20080426 

From Michelle: Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Answered by Penny Nom and Walter Whiteley. 





What shape(3D) has 5 vertices,8 edges,and 5 faces? 
20080425 

From stacy: what shape(3D) has 5 vertices,8 edges,and 5 faces? Answered by Penny Nom. 





Naming a figure 
20080424 

From P.: What is the name of a figure that has 2 sides that measure
25 feet each and 2 sides that measure 10 feet each? Answered by Penny Nom. 





A solid figure with 3 rectangular faces and 2 triangular faces 
20080417 

From Emily: I am in the 3rd grade and my teacher gave us a question. What is a
solid figure with 3 rectangular faces and 2 triangular faces? Answered by Penny Nom. 





The capacity of a silo 
20080412 

From Candonn: I have a cement silo that is 30 ft. high and has a diameter of 12 ft.
I was wondering what the capacity of the silo is in tons of dry material.
The silo is flat on the bottom also. Answered by Penny Nom. 





A shape 
20080403 

From Joshua: what shape has 4 faces, 4 corners and 9 edges. Answered by Penny Nom. 





The square root of 21 between what two numbers? 
20080403 

From Danielle: The square root of 21 between what two numbers? Answered by Penny Nom. 





The cube root of 198 
20080327 

From bobby: what is the cubed root of 198 Answered by Harley Weston. 





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

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





Graph the equation P(x)= x^3 + x^2 12x 
20080318 

From Sean: I want to graph the equation : P(x)= x^3 + x^2 12x I was thinking that I would combine
the xvalues, but then I could not use the complete the square technique. Would I have to
just solve the second half of the equation and then graph x^3 seperately Answered by Penny Nom. 





Determine the capacity of Farmer John's silo 
20080316 

From paula: Farmer John stores grain in a large silo located at the edge of his farm. The cylindershaped silo has one flat, rectangular face that rests against the side of his barn. The height of the silo is 30 feet and the face resting against the barn is 10 feet wide. If the barn is approximately 5 feet from the center of the silo, determine the capacity of Farmer John’s silo in cubic feet of grain. Answered by Penny Nom. 





Estimate the cube root of 270 
20080311 

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





An incorrect Babylonian formula 
20080310 

From Martin: Given the area of an isosceles trapezoid is 150, that the difference of its bases is 5 (that is b1  b2 = 5), and that its equal sides are 10 greater than twothirds of the sum of its bases (that is, s1 = s2 = 2/3(b1 +b2) + 10
Solve the problem using an incorrect Babylonian formula for the area of a trapezoid A = (b1 + b2)/2 x (s1 + s2)/2 Find the length of the sides of the isosceles trapezoid. Answered by Penny Nom. 





A roll of paper 
20080305 

From Sheik: How I Convert My Roll Weight Into Meters?
Roll Width : 241mm
Thickness : 56gsm
Weight :81 Kg Answered by Harley Weston. 





Pythagorean equation 
20080227 

From Judy: X^2 + Y^2 = 5^2
Graph all ordered pairs in the coordiante plane that satisfy the Pythagorean equation, x squared plus y squared equals five squared Answered by Stephen La Rocque. 





How do I graph y = 2x^2? 
20080212 

From Max: How do I graph y=2x^2? Answered by Penny Nom. 





A three sided shape 
20080209 

From Tim: Question from Tim:
How would I calculate the area in square feet of a "triangle" with sides:
Base is 36 feet; height is 70 feet; and the thirs side is an arch (curve) of 77 feet. Answered by Harley Weston. 





Out of school applications of Pythagoras Theorem 
20080123 

From Laura: Hi,
I am currently working on a math summative in which I have to choose a real life subject and relate it back to the material in my grade 12 math class. I find the history and discovery behind the Pythagorean Theorem and Identity very interesting, but I have yet to find a reallife application of the equations. Yes, I know they are used for finding distances, heights etc., but realistically, how many people actually use it in those situations? Very few. I was hoping for a new application. Is the pythagorean theorem (sin^2x + cos^2x = 1) even applicable? Thank you,
Laura Answered by Harley Weston. 





Graphing a parabola 
20080116 

From Sean: How do I find the roots and describe the roots when graphing a parabola?
y =  x^2  4x 3 Answered by Stephen La Rocque. 





Pie graphs 
20080115 

From amarilis: explain why circle graphs are called pie graph or pie charts Answered by Stephen La Rocque. 





Hoisting an anchor 
20080110 

From ron: four men on a boat are using a capstan for hoisting an anchor weighing 2000lbs. The diameter of the barrel of the capstan at the section in use is 8in., and the pull on the chain carrying the anchor and passing around the capstan barrel is assumed to act at a distance of 1in. from the surface of the barrel. If the distance from the axis of the barrel to each point at which effort is applied to a capstan bar is 40in., what force must be applied by each man hoisting the anchor? Answered by Stephen La Rocque. 





Practical applications of sequences 
20080101 

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





Finding the equation of a line from its graph 
20071225 

From ken: I have a graph and it is asking me to find the slope of each line, and
then write its equation. the graph show a negative slope. Would
appreciate the answer if you could show me how to do this question.
Kind regards: Ken Answered by Stephen La Rocque. 





Solve sin(x)=x^2x 
20071211 

From ming: is there anyway you can solve
sin(x)=x^2x without a calculator? Answered by Stephen La Rocque. 





Pictographs 
20071211 

From eniyah: The title of my pictograph is Favorite pets. I have two columns. in my first column is the kind of pet and the second column is the numbers of students, the dogs have 16 student that like them and cats have ten students the likes them. each pictures equals 2 stodents my question is. i have to draw paictures to show the number of students for each row. the key says each symbol equals 2 students. since 16 divided by 2 is 8 can you show me how to make this in a graph Answered by Stephen La Rocque. 





Plotting a function 
20071206 

From Paula: My son has a problem that says plot the point:
2x3y=9
I have explained to him that there must be a function for y in order to plot that point, but he doesn't think so. The question above that one says find the function for y, and I assume we should use that function. Am I wrong? Can we plot a point without a y function. Answered by Stephen La Rocque. 





A mystery shape 
20071126 

From Daniel: I am in year 3 and have been given some homework to do with my mum.
Question is: my shape has two circular faces and one curved face. It has two edges and no vertices. Can you help me identify the shape please. Answered by Penny Nom. 





A curve sketch 
20071122 

From Ahson: Find critical points, determine the monotonicity and concavity and sketch
a graph of f(x) with any local maximum, local minimum and inflection
points labeled:
1. f(x) = x^4  x^3  3x^2 + 1 Answered by Harley Weston. 





Two lines 
20071118 

From Kate: represent qraphically the equations of these lines and their intersecting points
xy=2
3x+y=11 Answered by Penny Nom. 





The area of a trapezium (trapezoid) 
20071105 

From Scott: How can we calculate this I do not understand?
A trapezium of area 126m2 has parallel sides of length 3m and 4m. How far apart are the parallel sides? Answered by Stephen La Rocque and Harley Weston. 





Area of a triangle formed by three points on a graph 
20071026 

From Betty: My question is 'find the are of a triangle whose vertices have
coordinates (3,5),(6,5), and (4,10) Answered by Stephen La Rocque. 





A graph with 100 vertices 
20071024 

From amarjeet: let g be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent only if ij=8 or ij=12. The number of connected components
in g are:
1. 8
2. 12
3. 4
4. 25 Answered by Penny Nom and Victoria West. 





A conical cup 
20071018 

From Nicholas: Water is leaking out of a small hole at the tip of a conical paper cup at the rate of 1cm^3/min. The cup has height 8cm and radius 6cm, and is initially full up to the top. Find the rate of change of the height of water in the cup when the cup just begins to leak.
Since V= (pi/3)r^2h, how do I eliminate a variable or change the equation so I that I can answer the question? Thanks. Answered by Penny Nom. 





The normal approximation to the binomial 
20070930 

From m.j.: Slot Machines The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. Answered by Harley Weston. 





The area of a roof 
20070927 

From RANDY: I have an area of roof. It's in a sort of triangle.
it's 25' across the top
30' at each edge
86' across the bottom Answered by Stephen La Rocque. 





Grade 5 shapes and measurements 
20070923 

From Marina: I'm helping my grade 5 son in this assignment but I don't know how. There are 2 question I would like you to help me:
1.How can the shapes used to form a larger similar figure using 4 shapes: ( a 3 by 3square is drawn in a 6 by 6 dot figure,drawing attached)
2.You are planning to build a birdhouse measurement is attached,. You are going to cut the pieces from a board that is 12 inches wide. How long should the board be? Answered by Penny Nom. 





Are the diagonals of a trapezoid ever perpendicular? 
20070923 

From Amanda: Are the diagonals of a trapezoid ever perpendicular? Answered by Harley Weston. 





x = y^2 and x = 4 y^2 
20070911 

From Jil: My question is when dealing with parabolas, x=y^2, so that they are sifted on their side you could say,
what will happen to the graph if you change it to x=4y^2. I understand
that the  flips the graph in the other direction but can you simply just plug
in numbers and increase the stretch of the y? Answered by Penny Nom. 





Is there a way I can calculate correct square footage for odd shapes? 
20070831 

From Tom: I manage a golf course, and we are about to over seed the course for the upcoming winter months. We will be over seeding all greens, fairways, and tee boxes. Noone of the area that we will be placing seed on is a regular shape. The closest shapes they would be is a circle, rectangle or square, but most of them are all odd CURVED shapes. I know what the equation is for Square ft., and I know how many Square ft. are in an acre, but I need to be precise with the amount of seed I order. Is there a way I can calculate correct square footage for odd shapes. Answered by Harley Weston. 





Applications of sequences and series 
20070827 

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





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





Explain how you can shift a parabola up two units 
20070814 

From Marsia: Explain how you can shift a parabola up two units (y axis). Answered by Stephen La Rocque. 





Paying off a loan 
20070808 

From Iona: I borrowed $6000. 00 from a friend to pay school fee.
He said I should not pay back any interest but pay $350.00
monthly after graduation.
(1) Make an equation from the above
(2) make a graph
(3) what is the relationship between the months after graduation and the loan?
(4) what is the horizontal and vertical intercept relate to the problem? Answered by Stephen La Rocque. 





The irrationality of PI 
20070807 

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





Subdividing a property into half acre parcels 
20070731 

From Pamela: We need to divide a large property with five sides and strange angles into 1/2 acre parcels from the top down. We want to know where along the eastern and western borders of the large property to make the divisions. Answered by Stephen La Rocque. 





The graph of a log function 
20070730 

From Marsia: How would you describe to another student what the graph of a logarithmic function looks like? Answered by Penny Nom. 





Dried grapes and percentage of water content 
20070709 

From Jyoti: Fresh grapes contain 90% water by weight while dried grapes contain 20 % water by weight. what will be the weight of dry graprs available from 20kg of fresh grapes? Answered by Stephen La Rocque. 





Period of a sum of trig functions 
20070617 

From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque. 





What is the name of the shape that is 3D and irregular? 
20070614 

From alan: What is the name of the shape that is 3D and irregular? Answered by Stephen La Rocque and Penny Nom. 





More on quadrilateral shape names 
20070526 

From Don: If North Americans call a quadrilateral with no parallel sides a trapezium, is a kite merely a special type of trapezium? Can a rhombus be a kite? Answered by Walter Whiteley and Penny Nom. 





Is a square also a right trapezoid? 
20070524 

From Don: Is a square also a right trapezoid? Answered by Stephen La Rocque. 





Finding square roots 
20070517 

From Chandler: I would like an easy way to find the square root of a number. Answered by Gabriel Potter. 





Parabolas 
20070516 

From Andy: How do you write an equation of a parabola that opens to the left with a vertex of (2,6)? Answered by Stephen La Rocque. 





Pattern for a truncated cone 
20070511 

From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque. 





Finding a parabola's equation by looking at its graph 
20070430 

From Kenzie: The graph shows an arrow going upward crossing at the 2 on the x line
and crossing the 3 on the x line and the vertex on the 6 on the y line. Answered by Stephen La Rocque. 





How do i form a paper cone 
20070414 

From Sash: How do i form a paper cone with the height of 25 cm, the slant height
of 25.8 cm, and the radius of 6.2 cm? Answered by Stephen La Rocque. 





A sketch of a quadratic equation 
20070414 

From Fee: A ball is thrown upward from the roof of a 25m building. The ball reaches a height of 45m above the ground after 2s and hits the ground 5s after being thrown.
Use the fact that the realtion between the height of the projectile and time is quadratic to draw an accurate graph of the relation on graph paper. Answered by Penny Nom. 





Graphing a line 
20070323 

From mitchell: Graph each equation.
y = 2x + 4 Answered by Jaymi Peterson and Haley Ess. 





A pictograph 
20070314 

From Angie: I am confused! I have to include a title, labels, and a key: Here is the problem
Snickers 45
Kit Kats 65
Nerds 30
Kisses 50
Suckers 75
With the above information please help me make a candy pictograph
I would gladly like your help as my child is a second grader and can not tell me anything about a pictograph Answered by Penny Nom. 





Using complex numbers 
20070312 

From Kara: Do you use complex numbers in your job? Answered by Stephen La Rocque and Penny Nom. 





Statistics data 
20070308 

From Parnini: The following table shows the expenditure on different household items by a family. Draw a line graph for the following data: Items : Food Rent Cloth Education Saving Others Expenditure : 2000 2.500 1.500 1.200 4000 3.500 Answered by Stephen La Rocque. 





The area of a decagon 
20070228 

From heather: how do i find the apothem and area of a decagon that has a perimeter of 60? Answered by Penny Nom. 





The area of an Lshaped polygon 
20070223 

From Louanne: How do I find the surface area of a L shaped polygon? Answered by Melanie Tyrer. 





x^x = 2x 
20070222 

From ramsay: This has been bugging me for ages. How do find both real solutions to x^x = 2x? Obviously I have x=2, and there's another at about 0.35, but I can't work it out properly. Any help? Answered by Penny Nom. 





The length of the side of a hexagon 
20070219 

From Nick: if the area of a regular hexagon is 259.807 how do i find the length of each side, and the apothem? thanks if you can help Answered by Penny Nom. 





a specific 3d shape 
20070212 

From Robby: What three dimensional shape has 6 vertices, 5 faces, and two congruent triangular bases? I can't find the answer to this question anywhere. Your help will be appreciated. Thanks, Robby Craig Answered by Pam Fowler, Gabe Potter and Walter Whiteley. 





Large exponents 
20070209 

From Nick: I am trying to figure out an extremely large number. It relates to the estimated number of bacterial divisions in 12775 generations of bacteria. The problem I need to solve is: 2^12775 or 2 to the power of 12,775. Answered by Stephen La Rocque and Penny Nom. 





The capacity of a tank 
20070208 

From lorn: what is the capacity of a tank height is 110 feet diameter is 24 feet Answered by Brennan Yaremko. 





The cube root of 8000 
20070131 

From Jacqui: How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it? Answered by Penny Nom. 





Splitting a 5 acre piece of property 
20070125 

From John: I have a 5 acre piece of property that I wish to split into 5 individual 1 acre parcels. The 5 acre parcel 1s 660 feet in length and 330 feet in width. The first two parcels are 264'x165', but I am asking for help getting the perimeters of the last 3 lots, one of which is a irregular pentagon. All of the one acre parcels must have an area of 43,560 square feet each. Answered by Penny Nom. 





Line segments on dot paper 
20070121 

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





y = x^2  2 
20070108 

From Mike: Graph the quadratic equation: y=Xsq2 Answered by Penny Nom. 





Are all rectangles trapezoids? 
20070105 

From Sarah: Are all rectangles trapezoids? Answered by Chris Fisher. 





A linear system 
20070104 

From Harold: System A (4, 2/3) 2x3y=6 and x3y=2
I approached this problem using the addition method.
Could i have found the answer using the graphing method? Answered by Penny Nom. 





A trapezoid with one right angle? 
20061209 

From Andre: How do you draw a trapezoid with one right angle? Answered by Stephen La Rocque. 





Conic sections 
20061119 

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





Motorcycle expansion chamber design 
20061114 

From David: I'm interested in calculating cone information regarding motorcycle expansion chamber design for example. I guess it's called a truncated cone, from what I've read so far. If I know the center line height, small radius, and large radius of a truncated cone then, how can I calculate the angle (included angle?) the cone forms? I'd like to know the variations of the formula so I can calculate for angle, or length, or one of the diameters if I know the other two measurements. Answered by Stephen La Rocque. 





Apples and plums 
20061113 

From Saif: the problem i am stuck with is, nicole buys 2.3kg apples 1.8kg plums she pays £7.18 total plums cost £2.20per kg cost 1kg apples what is the cost of 1kg of apples Answered by Stephen La Rocque. 





Some applications of conic sections 
20061113 

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





The name of a shape 
20061111 

From Valentina: I have a shape of 4 sides 3 are the same length (2cm each) and the other smaller (1.5cm) Answered by Chris Fisher. 





y = x  10 
20061103 

From Pam: what is the process for finding the vertex point for an equation such as this, y= x  10. Answered by Penny Nom. 





How does knowing the sum for 2+7 help you find the sum for 6+1 
20061026 

From Andrea: How does knowing the sum for 2+7 help you find the sum for 6+1 Answered by Haley Ess. 





An approximation 
20061022 

From Ellen: consider the curve 8x^2 +5xy+y^3 +149 =0 Write an equation for the line tangent to the curve at (4, 1) use this equation to approximate the value of K at the point (4.2, K) Answered by Penny Nom. 





Is a circle a regular shape? 
20061010 

From David: Is a circle a regular shape or an irregular shape? Answered by Stephen La Rocque. 





Plotting a linear equation 
20061009 

From Jennifer:
I am having problems explaining how to do these problems to my child .
graph:2=xy
graph the equation: 2y+x=3
Answered by Penny Nom. 





The focus of a parabola 
20061001 

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





Your birthdays until your one hundredth 
20060909 

From Alan: which of your birthdays until your one hundredth, fall on the same day of the week as the day you were born? Answered by Chris Fisher. 





Find the points of intersection 
20060818 

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





A hamiltonian circuit 
20060724 

From Tom:
1)Prove that every simple not directed graph with 21 vertices and 208 edges has
a hamiltonian circuit but not an Euler circuit.
(I have proved that if we give the 2 edges for each vertices then after a few
steps I have 21 vertices of odd degree and 19 edges.So in the end I have 2
vertices of odd degree.So I have not an Euler circuit.But how can I prove that
there is a Hamiltonian one?)
2)If G is a tree and has a virtex k degree,prove that it also has at least k
vertices degree 1.
Answered by Penny Nom. 





Area of a trapezium demonstration 
20060718 

From Karthik: how can u " SHOW THAT THE AREA OF THE TRAPEZIUM IS EQUAL TO HALF THE PRODUCT OF ITS ALTITUDE AND THE SUM OF ITS PARALLEL SIDES." in an Innovative And Creative way..... Answered by Stephen La Rocque. 





The area of a sector and a triangle 
20060623 

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





As close to 841 as possible 
20060621 

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





What will the graph of y=x2  2x  3 be? 
20060617 

From Byrony: What will the graph of y=x2  2x  3 be? Answered by Steve La Rocque. 





A truncated cone 
20060528 

From Phil: Hi, I am an art student and I am trying to make a "truncated cone" (ie: a cone with the top cut off) out of sheet metal. I need to design a template first and am having problems working out the angles. The truncated cone is 250mm high, 550mm wide at the bottom and 290mm wide at the top. Can you help? Answered by Stephen La Rocque. 





How do you graph 3x + 6y = 9 by axis intercepts? 
20060522 

From Crystal: How do you graph 3x + 6y = 9 by axis intercepts? Answered by Penny Nom. 





The interior angles of a right triangle 
20060520 

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





Landscaping 
20060511 

From Luke: HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE TO FILL UP A BOX 20FT.X20FT.X6IN DEEP?
HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE; I HAVE A 12FT.IN DIAMETER POND AND I WANT TO PUT A 3FT.SIDEWALK AROUND THE OUTSIDE OF IT? Answered by Stephen La Rocque. 





Geometric sequence and basic functions (graphs) 
20060420 

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





Cubic yards of landscape stone 
20060419 

From Janet: I need to spread landscape stone around my pool. A landscaper said I need 16 yards. What is the area of a cubic yard if I want the stone 3" deep? Answered by Stephen La Rocque. 





Overlapping area of two circles 
20060415 

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





The area of a regular hexagon 
20060410 

From A student: find the area of a regular hexagon with a apothem of 9 Answered by Stephen La Rocque. 





An epicycloid 
20060410 

From Sharon: What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Answered by Stephen La Rocque and Penny Nom. 





A table of values 
20060328 

From Cindy: Create a table of values for each of the following functions: y=5x, y=52, and y=5x. I dont know to do this. Answered by Stephen La Rocque. 





Linear feet on a paper roll 
20060320 

From Vishal: I WOULD WISH TO KNOW OF A STANDARD FORMULA BY WHICH I CAN CALCULATE THE LINEAR FEET OF A PAPER ROLL AS PER THE FOLLOWING DETAILS:
THICKNESS: 150 GSM (GRAMS PER SQUARE METER)
REEL WIDTH: 85 CM
REEL DIAMETER: 140 CM
REEL INNER CORE: 10 CM
REEL WEIGHT: 946 KG's
Answered by Stephen La Rocque. 





The shape of an egg 
20060319 

From Vinson & Julie: What is the proper mathematical term for the geometric solid that is represented by an egg? Answered by Chris Fisher. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





The area of a parallelogram 
20060312 

From Shayne: Is there a method of finding the area of a trapezium or/and parallelogram even if the height is not given? Could you also explain how to find the height? Answered by Penny Nom. 





What names are known for the quarter circle shape? 
20060306 

From Christina: What names are known for the quarter circle shape? Answered by Stephen La Rocque and Penny Nom. 





The graph of y = 2x + 1 
20060223 

From Geneva: I'm having trouble with graphing equations like y=2x+1 which is my homework I'm not sure how to graph it. I'm in the 8th grade taking a 9th grade course algebra I. Answered by Penny Nom. 





Whose photo is he looking at? 
20060219 

From Adeyeri: Looking at a picture a man says, that the father of the person (in photo) is the son of my father. whose photo is he looking at? Answered by Penny Nom. 





Brokenline graphs and histograms 
20060216 

From George:
1. What is the main difference between a brokenline graph and a histogram? Both represent continuous variables.
2. What is the correct way to read a multiplication array: xaxis first and then yaxis, other way around or it doesn't matter?
Answered by Penny Nom. 





Intercepts and slope 
20060115 

From Anthony: Given 1.7x + 0.8y=7.1:
(a) state the intercepts and slope for the graph
(b) Draw the graph Answered by Penny Nom. 





Folding a sheet of paper 
20051215 

From Victoria: The current problem is to take a normal 8 1/2 x 11 sheet of paper, take a corner and fold it to meet the opposite corner, and (without actually measuring) produce a formula to describe the result fold/crease. Answered by Penny Nom. 





Four tangent circles 
20051206 

From Ananth:
I have one bigger circle A with radius 15.
Inside this bigger circle i have another circle B with radius 3 which touch this bigger circle. Have another circle C with radius 4 which touches A and B. I would like to draw a biggest circle which touches A,B and C.
Answered by Chris Fisher. 





Graphing two lines 
20051120 

From A student: About y = 5x + 24 and y = 3x  8
1. Graph both equations on the same set of axes. When you made your graph, how did you choose the range of x and y values?
2.Find the point of intersection for the graphs.
3. Test the point of intersection you found by substituting its coordinates into the equations. Do the coordinates fit the equations exactly? Answered by Penny Nom. 





What shape do I say a football is? 
20051114 

From Peter: I am a 43 year old man. I am no longer in school, I have a bachelors degree. I like to tell stories about sports in ways to make people think about the amount of time they devote to the sports. For example, while attending a church in Chicago on the north side, I would pass by Wrigley field.
I began to call it the church of the flying orb or sphere. Now if I want to tell a similar story about football (not soccer), what shape do I say a football is? Answered by Chris Fisher. 





Shapes 
20051112 

From Tonya and Hailey: MY THIRD GRADERS TEACHER HAS SENT HOME HOMEWORK ASKING FOR THEM TO FIND REALWORLD OBJECT IN MANY DIFFERENTS SHAPES A FEW HAVE US STUMPED Answered by Penny Nom. 





The diagonals of a trapezoid 
20051111 

From Chris: Is there ever a case where the diagonals of a trapezoid bisect each other? Answered by Walter Whiteley. 





Painter's caps 
20051019 

From Duk: The equation C=10 +2n represents the cost in dollars, C, for n painter's caps advertising the walkathon. Which pair of values could represent a number of caps and the cost for that number of caps, (n, C)?
(0, 10) (7, 24) (15, 30) Answered by Penny Nom. 





Open dots and closed dots 
20050929 

From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny. 





A 3dimensional pie shape 
20050917 

From Bill: Your site appeared in my search for the name of a 3dimensional pie shape. 2d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it? Answered by Chris Fisher. 





Graphing a linear inequality 
20050826 

From Gina: When graphing a linear inequality, how do you know if the inequality represents the area above the line? Answered by Penny Nom. 





Graphing an inequality 
20050502 

From Janice: I need to know how to graph inequalities. I need to know just abot everything. From graphing an equation to shading. Answered by Leeanne Boehm. 





Area of a region on a map 
20050428 

From Balachandar: Pl. find the attached map.
1. Can u pl. find out the total square are of WLMZ
2. Can u pl .find out the total square are of WXYZ  { A }
3. Can u pl .find out the total square are of XLMY  { B }
Pl .help me to find out the above.
..... Answered by Chris Fisher and Penny Nom. 





A roll of paper 
20050416 

From Tuomas: How would you calculate a diameter of a paper reel when the paper is 0,04 millimeters thick and for example 5000 meters of it is winded on a 76 mm (3inch) core. Answered by Penny Nom. 





Two overlapping circles 
20050320 

From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom. 





The capacity of a dryer 
20050223 

From Darlene: I am trying to figure out the capacity of my dryer. I need to know the size in order to buy a new one. The drum within measures 27" in diameter and 18" deep. I know that I am looking for an answer in cubic feet but am not sure how to determine this.
Answered by Penny Nom. 





Graphing inequalities 
20050215 

From Melanie: Solve and Graph the following variable inequalities:
y<2x+4
y>2x+6
3x+4y<24
4x6y>24 Answered by Penny. 





The diaonals of an isosceles trapezoid are congruent 
20050202 

From Daniel: I am currently unable to find a proof that the diaonals of an isosceles trapezoid are congruent. Might you happen to have one? Answered by Walter Whiteley. 





Approximating an integral 
20050127 

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





The area of a trapezoid 
20050115 

From Doak: What is the total acreage of a pieshaped piece of land that is:
146' f ront
85' back
246' each side
The front and back lines are fairly straight....a trapezoidal shape. Answered by Penny Nom. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





A graph with certain properties 
20041122 

From A student: i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root Answered by Penny Nom. 





The points of intersection of two graphs 
20041105 

From Benjamin: How do I find the points of intersection of the two functions:
1) y = 2  ex
2) y = 1 + x2 Answered by Harley Weston. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





The area of a lot 
20040928 

From Stan: I own a parcel of land (lot 20) that is assessed at 9127.00 square feet and has a frontage of 99.90 feet according to the tax roll. I don't know how large my property actually is since I feel that the tax assessment and the survey map don't jive Answered by Harley Weston. 





f(x) = x4 if x<2 
20040921 

From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Answered by Penny Nom. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





An isosceles trapezoid 
20040831 

From Bruce: An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid. Answered by Penny Nom. 





The intersection of two graphs 
20040728 

From JJ: Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Answered by Penny Nom. 





The commuter 
20040714 

From JJ: A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time.
Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Answered by Penny Nom. 





12(1.221)^t = t + 3 
20040714 

From Jay: This problem has me stumped since i cannot separate the t and the 3. Here it is:
12(1.221)^{t} = t + 3
It's on a logarithm worksheet, but how do i figure it out?! Answered by Harley Weston. 





Programming without trig functions 
20040525 

From Derek: I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston. 





The problem of Apollonius 
20040425 

From Mitja: There are given 2 circles lying one out of another and one point out of both circles. How to construct a circle passing through a given point and internally tangent to one and externally tangent to the other cirlce? Answered by Chris Fisher. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) Answered by Penny Nom. 





The degree sequence of a graph 
20040331 

From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom. 





A fifteen sided polygon 
20040305 

From Joann: WHAT IS THE NAME OF A FIFTEEN SIDED SHAPE? Answered by Penny Nom. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





Nonconvex shapes 
20040218 

From Merrill: Draw 4, 6 and 8 sided shapes so that ONE straight line can be drawn through each side Answered by Chris Fisher and Penny Nom. 





A pyramidshaped tank 
20040213 

From Annette: The base of a pyramidshaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston. 





Graphing lines 
20040208 

From A student: how do you solve y=1\3x+3 and y=1\3x3 by graphing? Answered by Penny Nom. 





Logarithms 
20040201 

From A student: Where did the word logarithmic come from? Where/whom did it originate? Answered by Harley Weston. 





The trapezoidal rule 
20031231 

From Prashanth: I have a set of XY coordinates(say 49 points),I want to find the area enclosed by the curve joining them and the axes.I do not have an equation for the curve and I am not able to fit a curve given the points.I use the trapezoidal rule
(Y1+Y2/2)*(X2X1),
Is it right? can I do this with any other method? Answered by Penny Nom. 





Intercepts 
20031104 

From A student: I am totally confused on how to determine intercepts of an equation and then to graph the line. For example, how to determine the intercepts of 2x3y12=0. Answered by Penny Nom. 





Trees 
20031028 

From Ali: Is there any formula for counting the number of trees (graphs)? Answered by Denis Hanson. 





A parabola 
20031024 

From Delores: Given the vertex (4, 2) y intercept = 6 find if/where the parabola crosses the x axis? Answered by Penny Nom. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





Functions, graphs and derivatives 
20031005 

From Jathiyah: I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other? Answered by Walter Whiteley. 





Applications of logarithms 
20030916 

From A student: I have a project due in my algebra two class dealing with logs and where they are used in life, but I am having trouble finding websites that relate. So I would really appreciate it if you couldhelp me. Answered by Penny Nom. 





Graphing a piecewise function 
20030824 

From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom. 





The area of an odd shaped piece of property 
20030724 

From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom. 





Some shapes 
20030429 

From Suzanne:
 What shape has 12 edges all the same length?
 What shape has 3 surfaces and 1 is curved?
Answered by Penny Nom. 





Two intersecting graphs 
20030423 

From Patty:
a) graph the equation x^{2}  y  4 = 0
x^{2} + y^{2} = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places. Answered by Penny Nom. 





Area of a trapezoid 
20030413 

From A road builder: My husband works with asphalt building roads. There are times when one end of the road will be (for example) 100ft wide the other end would be( for example) 200ft wide and he must figure the area in square feet. So far it has been a guessing game because he dosen't have the formula to figure the square feet. Answered by Penny Nom. 





y < 2x + 1 
20030301 

From Erika: how can I solve and graph y<2x+1 and which side in the graph should i shade after i finish solving my inequality? Answered by Penny Nom. 





y = 1  sin(x + 60) 
20021210 

From Eman: Sketch the graph of y = 1  sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis. Answered by Penny Nom. 





A lampshade from a cone 
20021126 

From Ellsie: I need to make a pattern to cover an old lampshade. This is actually the bottom portion of a cone. Please help me figure out how to draw this pattern, so that we can complete our project. Answered by Penny Nom. 





Performance reviews 
20021121 

From Lara: Perhaps you can help. He's doing performance reviews at work. The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year. The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year. How do I solve for the other performance review numbers. Answered by Penny Nom. 





Rounding 27.27 
20021103 

From A parent: If you have a problem 27.27 and you need to round to the first 7 the answer would be 27 Would 27.0 be acceptable as well or is it completely wrong. Answered by Penny Nom. 





The four colour theorem 
20021027 

From Rhonda: is there an actual equation for the four colour map theorem??? i cannot find it anywhere!! if so can you give a breif description on how it works!! Answered by Penny Nom. 





x^{ 4} + x^{ 5} = 100 
20021027 

From Bill: One of my students has stumped me. He asked how to solve the equation 4^{ x} + 5^{ x} = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston. 





Intercepts 
20020904 

From Tamara: Why is it that the x intercept the value of y is 0 and at the y intercept the value of x is 0? Answered by Leeanne Boehm. 





A schedule for a fantasy football league 
20020901 

From Steve: i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 15 = division 1 team 610 = division 2 team 1 should play teams 25 twice and teams 610 once. Answered by Claude Tardif. 





When does an inequality represent the area above the line? 
20020825 

From Tamara: How do you determine that an inequality represents the area above the line and when do you include the line in the solution? Answered by Penny Nom. 





Conics 
20020529 

From Brooke: Which conic cannot be generated by an intersection of a plane and a double napped cone? Answered by Chris Fisher. 





Overlapping circles 
20020529 

From Naman: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Answered by Harley Weston. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. Answered by Penny Nom. 





Cube roots 
20020326 

From Kathy: My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without? Answered by Penny Nom. 





x and yintercepts 
20020310 

From A student: I have the problem f(x)= ^{X5}/_{X2+X6} and I have to find the vertical asymtope, horizontal asymtope, xintercept, and yintercept. And graph the problem. I am having problems finding the yintercept. Answered by Harley Weston. 





When will the calendar be the same as 2002? 
20020220 

From John: When will the calendar be the same as 2002? I know the answer is 2013, but I don't know how to answer this mathematically, or if it is possible to do so. This is a ninth grade level algebra question my daughter received from her teacher. Any ideas? Answered by Chris Fisher, Patrick Maidorn and Penny Nom. 





Papy's Computer 
20020111 

From MaryAnne: My secondgrade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston. 





Maple trees and pine trees 
20020106 

From A student: A team of scientists found that in a forest there was four maple trees for every nine pine trees.How many maple were there if they counted 45 more pine than maples? Answered by Penny Nom. 





A quadrilateral with 0 sets of parallel sides 
20011212 

From Jess: Ok well for quadrilaterals a parallelogram is a 4 sided figure with 2 sets of parallel sides and a trapezoid is a 4 sided figure with 1 set of parallel sides. So is there a name for a quadrilateral with 0 sets of parallel side? Answered by Chris Fisher. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





The median of a trapezoid 
20011001 

From Laura: Given: A (1,2) B (9,2) C (7,2) D (3,4) Find the endpoints of the median. Use exact values. Write the equation using the letters from the given trapezoid. Verify the theorem using algebra. Answered by Penny Nom. 





An egg shaped island 
20010922 

From Karen: I am a civil engineering designer trying to design an egg shaped island. I want a 30' radius at the top and a 40' radius at the bottom and the longest length of the egg to be 125'. Is there standard geometry for an egg shape? I am not held to exact radii or the length given. Answered by Chris Fisher. 





Double bar graphs 
20010909 

From Leslie: My daughter has a homework problem in which she is graphing data from two frequency tables onto a double bar graph. The graph shows how many students worked in a program in two different years, grouped by age. In the first age group, one of the years has no students working, while there were students in that age group in the other year. Answered by Penny Nom. 





Graphing equations 
20010501 

From A student: If, for example, 4x^{2}12x+9=0 and 4x^{2}+12x9=0, which I'm assuming it does since you can derive that equation from the first, why do those two equations have different graphs? Answered by Penny Nom. 





f(x), f(x) + 2, f(x +2) 
20010404 

From Monica: Could you explain to me how one should go about graphing functions such as f(x), f(x+2), and so on. Also, how should you explain things such as constants and relationships among functions? Answered by Penny Nom. 





Approximating 260 divided by 3 
20010402 

From Andrew: Choose the letter of the best estimate. 260 divided by 3 a. 60 b. 70 c. 90 d. 100 Answered by Paul Betts. 





Dots on squared paper 
20010330 

From Tom: Consider some squared paper with lines 1cm. apart and dots where the lines cross. Place squares whose sides are whole numbers of centimetres on the paper in such a way that the sides of the squares always lie along the lines on the paper. For each square, find (a)the number of points inside the squares; (b)the number of points on the square and (c)the area of the square. How are these quantities related? Answered by Leeanne Boehm and Penny Nom. 





Cube roots on a calculator 
20010324 

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





Shape names 
20010226 

From Paul: I have been asked to give names of shapes from A to Z . I can only find 14 shapes can you help..... I'm missing letters b, g, j, l, m, n, u, v, w, x, y, z. Answered by Harley Weston. 





Shape, symmetry, measurement and space 
20010224 

From Marilyn: I have to write in detail about how young children learn about shape, symmetry, measurement and space. It is not activities I need it is how the children learn. How/why their brain takes it all in Answered by Walter Whiteley. 





What is my name? 
20010223 

From Julia: My perimeter is 12 cm. My sides are all equal. The sum of half my sides is equal to 6 cm. How many sides do I have? What is my name? Answered by Penny Nom. 





Finding roots 
20010201 

From A student: My math problem is right now we are working on roots. I don't quite understand how to find the answer to the problems, i was wondering what is the easiest, and fastest way to find the answers to roots? Answered by Penny Nom and Claude Tardif. 





Polynomials and exponents 
20010115 

From A student: I am duing a project in math on polynomials and exponents. I need a real life usage of polynomials and exponents for my project. Answered by Penny Nom. 





The Pythagorean Theorem 
20010108 

From Megan: Why the Pythagorean Theorem so important in our lives and what is it's history? Answered by Penny Nom. 





The pythagorean theorem in everyday life 
20010106 

From Josh: What are some ways that we use the pythagorean theorem in jobs, or even in everyday life? Answered by Claude tardif. 





Solving x  sin(x) = constant 
20001229 

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





A Trapezium problem 
20001215 

From Ben: A trapezium has a perimeter of 22cm. The 2 parallel sides are such that the length of one is three times the length of the other. The nonparallel sides are equal. If the distance between the parallel sides is 4cm, find the lengths of the 4 sides. Answered by Claude Tardif. 





Parabolas in life 
20001203 

From Ashley: I am a student and my teacher recently gave us the assignment of writing a portfolio on parabolas in life and finding examples, three to be in fact, only we have to go into detail about only one. We have been instructed to include such terms as: axis of symmetry, completing the square, parabola, quadratic formula, standard form (vertex form) and vertex. We also must include in our detailed example an equation of the parabola and very specific details, PLEASE HELP! Answered by Harley Weston. 





Graphing F(x) = 3^{x} 
20001106 

From Jose: graph the exponential problem F(x)=3^{x} Answered by Harley Weston. 





Tapes and CD's 
20001022 

From Arnold: Nicole has 25 CDs and tapes altogether. When she tries to pair them up, she has 4 CDs left over. How many tapes does Nicole have? Answered by Penny Nom. 





The scale on a map 
20001021 

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





Where will we use this in the real world? 
20001011 

From Jane Ann Musgrove: As a teacher of mathematics, I am always asked "Where will we use this in the real world?". I am seeking ideas/sites via the internet where students can find answers to this type of question. Can you help me? To be more specific, right now I am interested in finding careers where the employees would use the concepts of "Radicals", "Matrices", and "Logarithms". This information will be used by students to make presentations to the class on their findings from internet searches. Answered by Harley Weston. 





Leap Year 
20000920 

From Jennifer: The earth revolves around the sun in 365.24 days. How does our calendar deals with the extra 0.24 day? Answered by Penny Nom. 





Graphing an inequality 
20000802 

From Lori: How do I find x and y and graph this problem 3x + y < 5 Answered by Penny Nom. 





Making a paper cone 
20000730 

From John: The question of how to lay out & cut out of paper, cones came up. I would like the cone have : A base of 4 inches and height of 4 inches, 6 inches, 8 inches. Answered by Harley Weston. 





An Area 
20000626 

From Frank: Can you tell me what the sq. ft. are of and area measuring: __________58____________
 
 
 
 
 
76  70 
 
 
_____21________ 
Answered by Harley Weston. 





4 Color map Theorem 
20000602 

From Rick Slen: I am challenging my students to find a map that can not be coloured using only 4 colours. I know that it is not possible, but one boy drew a map with a "country" totally surrounding all the others so of course it touched all other colours. How do I explain that this type of map is not permissable? Answered by Denis Hanson. 





Graphing a linear function 
20000517 

From Chelsea: I need help with grahing linear functions.If you could email me back the basics and how tos I would be much appriciative. Answered by Penny Nom. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Two calculus problems 
20000501 

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





Graphing cube roots 
20000427 

From Heather Jones: What do the graphs of cube roots look like? Answered by Walter Whiteley. 





Rounding 
20000415 

From Tawana Brown: I was uncertain as to whether a number such as 85.25 rounding to the nearest tenth would be 85.3 or 85.2. I thought I had heard somewhere that if 5 is the last number that you don't round up. But I have also heard that anything 5 and above you do round up. It's been awhile since I've done rounding, so I need a refresher course. Answered by Walter Whiteley and Harley Weston. 





Estimates 
20000411 

From Sue Jordan: I am looking for examples of estimates for underestimating and overestimating. When would you do each one. For my child age 11 6th grade. Answered by Penny Nom. 





Putting in a pool 
20000316 

From Katie: If your digging a hole for a pool and the pool is: Length= 11m Width= 6m Sallow Depth= 1.1m graduating to 'Deep' Depth= 1.8m What is the volume of soil that will be taken out? And if a bobcat can excavate and remove 10m3 (qubed) of soil an hour how long will it take him to excavate the soil. Answered by Penny Nom. 





A valentines project 
20000221 

From Courtney Dohoney: I was assigned a valentines project. Our job is to make a valentines card that has a math theme. On my valentines card I would like to include the set of equations that when graphed look like a heart. If you can figure out a set of equations and get it back to me I would be very happy. Answered by Harley Weston. 





Functions 
20000123 

From Tara: Hi my name is Tara, I have two math problems that I need help with in my calculus math class.  If f(x)= x  2 show that (x+3)f(x)(x+2)f(x+1)+4=0
 Graph this function and use the graph to determine the range y=2x^{2}  8x  3
Answered by Harley Weston. 





A roll of paper 
20000115 

From Richard: I have a roll of paper, wrapped around a corrugate core, whos diameter is 10.750 in. The outer diameter of the roll is approx. 60 in. The thickness of the paper is .014 in. I am trying to find out how much linear feet of paper is left on the roll, given only the diameter of paper remaining on the core. Answered by Chris Fisher and Harley Weston. 





Bar graphs and histograms 
20000111 

From Raeluck: What is the difference between a bar graph and a histogram? Answered by Harley Weston. 





Factoring by graphing 
20000111 

From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom. 





Capacitor discharge rate 
20000109 

From Bill Phillips: I need to be solve for t in the following rate problem for an electrical capacitor. Vr = E(e^t/RC), e=nat. log 2.718 raised to the t/RC power. Answered by Harley Weston. 





Yintercept 
20000103 

From Kayla Boylan: How do you use and find the yintercept? Answered by Penny Nom. 





Graph of a sine function 
19991223 

From Pierre: Given; amplitute:1 period: 540 Phase shift: 60 degree,right I am ask to right the equation: sin 2/3 (value 60degree) When I am asked to graph the equation, the period is mixing me up. Answered by Harley Weston. 





Approximations 
19991220 

From Adrian Valc: Longtime ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source? Answered by Chris Fisher. 





Cutting a carpet 
19991215 

From Heather: A rectanglular piece of carpeting is 90 inches long and 90 inches wide. How can the carpet be cut into two pieces of equal sides and shape to cover an area of 100inches? There can only be one cut and no scraps. Please show me how. Answered by Penny Nom. 





Two calculus problems 
19991213 

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






Age in minutes 
19991121 

From Mesha Jackson: How old would I be in minutes if I were 12 Answered by Penny Nom. 





Crossing number 
19991106 

From Christian: The crossing number of a graph G, denoted cr(G) is defined to be the minimum number of (pairwise) crossings of edges among all drawings of the graph in the plane. For example, cr(K5)=1 and cr(K3,3)=1. What is cr(K7,7)? I figured out that the answer is 81. Now I am trying to figure out if K7,7 can be drawn in the plane with less than 81 crossings? I'm not sure how to approach this one. Other than actually drawing it out and checking by trial and error, I am not sure how to approach this problem. Please help! Answered by Denis Hanson. 





A pictograph 
19991028 

From Ali: Please tell me how to make a pictograph.I am 2 grade student. Answered by Penny Nom. 





Calculating a square root 
19991028 

From Jonathan: What is the formula for calculating a square root? Answered by Penny Nom. 





Broken line graphs 
19991019 

From Lori Samara, Kristi Cameron and the 4th grade students: Students in Ms. Cameron's grade 4 class were wondering if a broken line can be used anywhere in the range on the y  axis when creating a broken line graph? They understand that the broken line can be used at the 0 on the broken line but what if there is a large gap in the data from 100  200? What do we do? The text book and mathematics dictionary do not answer these questions. Answered by Penny Nom. 





Regular and irregular shapes 
19991003 

From Samuel Tighe: What is the difference between a regular shape and an irregular shape? Are a rectangle and a triangle regular or irregular shapes? Answered by Walter Whiteley. 





Intercepts 
19990924 

From Cassandra: My book says to find where the X and Y intercept, i dont understand who to do this problem. Can you please help here is the problem. it didnt quite explain the instructions. Answered by Penny Nom. 





Square roots without a calculator 
19990914 

From Josh Weiner: Is there any way to find out a square root without a calculator? Answered by Harley Weston. 





Stem and Leaf Plot 
19990914 

From Jeanette Sovick: My 5th grade son brought home a math paper, the title of which reads, Reading StemandLeaf Plots...can you explain this so I can explain it to him...There is no book, his teacher just sent this practice sheet home for him to complete and I have no clue! Answered by Penny Nom. 





Spreading a rumor 
19990913 

From Bornstar14: There is someone who wants to spread a rumor within 7 days to 250,000,000 people. he wants to know how many people he should tell on the first day (assuming the rumor is passed by everyone who was told to the same amount of people) so that everyone knows on the 7th day. What I did is the 7th root of 250,000,000. this answer is not possible unless rounded. is it okay for the number to be approximate? Answered by Penny Nom. 





Liquid capacity 
19990615 

From Bernard Antill: Would you please tell me how many litres of water in a swimming pool that is 24 feet long, 16 feet wide & 4 feet deep. I would appreciate you showing the formula for this calculation. I am a 74 year old male and I cannot find a formula in which I have any faith! I would also appreciate the answer in Imperial gallons. Answered by Penny Nom. 





Graphing a linear equation 
19990527 

From Dylan Bradley: Im in Grade ten and am doing linear equations, I cann't figure out how to make a chart for questions like y = 2x + 3 Answered by Penny Nom. 





Shapepreserving transformations 
19990504 

From J McAndrew: A shape preserves its shape if a rotation, translation or scaling is performed on it. Are these the only continuous transformations which have this property? These transformations if performed on the parts and then summed have the same effect as the transformation being applied to the whole; are these linear transformations? Who, and what area of mathematics has classified all transformations of this type completely? Answered by Chris Fisher. 





Parabolic shapes 
19990504 

From Justin Ailor: Can you give me some parabolic shapes? Answered by Penny Nom. 





Dotted graph paper 
19990408 

From Bridget Winward: A teacher at our school is trying to locate dotted graph paper online or in print. His class would like to make three dimensional, geometerical drawings. Please let us know if you have a good source. Answered by Jack LeSage. 





Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





Area of an irregular shaped objects. 
19990407 

From Jesse Townsend: How do I find the surface area of an irregulary shaped object such as someone's knee from the thigh to shin? Thanks. Answered by Walter Whiteley. 





Resources for realworld math activities 
19990326 

From Kate O'Brien: Where is there a collection of math acitivities or projects to use in high school Algebra I, Algebra II, or Trigonometry that tie concepts to realworld careers? Answered by Jack LeSage. 





John Napier and e 
19990206 

From Shimin: I would like to ask about the exact definition of e, its history (like how John Napier came about discovering it) and its applications in problems and real life situations. Thank you! Answered by Chris Fisher. 





Graphing the Derivative 
19990118 

From Milena Ghebre: This question has been nagging me for sometime now. Is there a way of finding out the derivative of a function, just by looking at the graph of it? Answered by Walter Whiteley. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





Logs 
19981021 

From Benny: What does log means? How come we have to use log Answered by Chris Fisher. 





A Kite 
19981007 

From Paul Scott: What is the mathematical term for the kite shape? Answered by Walter Whiteley. 





Points on a Graph 
19981003 

From Nouver Cheung: If the point P(3,2) is on the graph of y=f(2x1), what point must be on y=f(x)3? Answered by Harley Weston. 





Radicals 
19980915 

From Lana Sabo: Question: fifteen times the square root of twenty, divided by the square root of 2. nine subtract the square root of fortyfive, divided by 3. the square root of 18 plus the square root of 12, divided by the square root of 3. Answered by Harley Weston. 





Snake Eyes 
19980720 

Would you please advise me what the probability is of rolling snake eyes on a pair of dice is? My recollection is 1 out of 6 multiplied by 1 out of 6 = 1 out of 36 is this correct? Answered by Jack LeSage and Penny Nom. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





Isosceles trapezoid formula 
19980512 

From Donna McMullin: The teacher of Gifted and Talented Math has been trying to locate the formula for anisosceles trapezoid and we can't find it anywhere. Could it be the same formula for that of a parallelogram ? Please advise. Answered by Walter Whiteley. 





Graph Distortion 
19980219 

From Dana Steffan: What exactly is graph distortion? I have to explain it for a project and I can't seem to find anything on it. Answered by Penny Nom. 





Two Inscribed Trapezoids 
19980127 

From James: A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Answered by Haragauri Gupta. 





The twodigit numbers from 1099 
19980121 

From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a twodigit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the twodigit numbers from 1099? Please help and thank you for any assistance you can give me. Answered by Penny Nom. 





Quadratic Graphs 
19980113 

From Simon Batten: How does varying the values a,b and c affect the graph of y=ax^{2} + bx + c? Answered by Harley Weston. 





(2)^x 
19971212 

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





The Area of a Trapezoid. 
19970507 

From Mary George: I am doing the area of trapezoids and mixed polygons and I was wondering if you can help me figure out this problem. A line segment drawn parallel to a leg of a right triangle divides the other leg into segments of 3cm and 6 cm and the hypotenuse into segments of 5cm and 10 cm. The two figures formed are a triangle and a trapezoid. Find the area of each. I would appreciate if you would email me back the solution. Answered by Harley Weston. 





Graphing Inequalities of Conic Sections 
19970324 

From James Sheldon: I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade: x^2+y^2 is greater than or equal to 16 xy > 4 So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it... Answered by Penny Nom. 





Approximating pi. 
19961104 

From Ben Dixon: How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Answered by Chris Fisher. 





Approximating roots. 
19961104 

From Ben Dixon: How do you calculate a square root? eg the square root of 2.There is obviously some sort of successive approximation type algorithm for doing it to however many decimal places is required, but what is the algorithm? Answered by Harley Weston. 





Where do 2^x and x^2 intersect? 
19960723 

From Darin M Selfridge: The intersecting points of y=2^x and y=x^2, graphed along with x^2=2^x, are obviously three... (2,4), (4,16) and (?,?). I am having problems figuring out the value, and even an equation for the (?,?). Can you help? Answered by Harley Weston Chris Fisher. 





Show that this construction yields a rhombus. 
19960616 

From LennyB: Hello, I have a problem. I doubt you can help me. If you have an isosceles trapezoid, and you connect the midpoints of the four sides of the isosceles trapezoid forming a quadrilateral, how do you prove that it's a rhombus in a 2 column proof?? Answered by Penny Nom. 





How do you graph these inequalities? 
19960517 

From Robert: How do you graph the inequalities 5+gg, and g+h>6 on one coordinate plane? Answered by Harley Weston and Maxine Stinka. 





How do you graph these equations? 
19960430 

From David Gamble: How do you graph the equation x=3 on a x,y graph? Also how do you graph f(x)=3x + 2 on the same graph? Answered by Harley Weston and Maxine Stinka. 





An application of Pythagoras' theorem 
19960409 

From Mike Jones: We'd like to know what practical applications there may be for the Pythagorean theorem. Answered by Penny Nom and Maxine Stinka. 





Combien de bonds auratil besoin 
20120410 

From zachary: Un lapin fait toujours un bond de 3m suivi d'un bond de 5m. S'il maintient ce rythme de combien de bonds auratil besoin pour franchir une distance de 584m ?? Answered by Claude Tardif. 





la capcite en metre cube de ma remorque 
20080322 

From pages: je voudrai connaitre la capcite en metre cube de ma remorque les dimensions font 12495 34 merci Answered by PierreLouis Gagnon. 





Problème avec rapport point, prix... 
20050908 

From Nico:
Le prix d'un diamant est proportionnel au carré de son poinds. Un diamant de 0.45 g vaut 7500euros.
1. Combie coute un diamant de 0.693 g ?
2. Quel est le poids d'une diamant valant 45000 euros ?
Je vous demande pas de le raisoudre à ma place mais j'aimeré comprendre comment je peut calculé le rapport entre le point et le prix.
Answered by Claude Tardif. 





La traduction anglais 
20020527 

From Une etudiant: je voudrais savoir la traduction anglais de :
homothétie (mot de niveau intermédiaire (69)) apothème (mot de niveau internédiaire (69))
parce que je ne les trouve pas. Answered by Chris Fisher at Claude Tardif. 





l'équation d'une rotation dans un graphique cartésien 
20011114 

From Ghaith: je d6sir que vous me rafraichissez un peu la mémoire s.v.p. j'aimerai savoir l'équation d'une rotation dans un graphique cartésien merci Answered by Claude Tardif. 





la pantographie 
19991118 

From Erick et Christine: Nous recherchons la définition de pantographie voltaïque, que représente cette "figure" ? estce qu'on peut en définir une unité de mesure ? Answered by Claude Tardif. 





logarithme neperien 
19991110 

From Louise Kieffer: D'où provient la valeur e ( 2,7....) des logarithmes népériens ? Answered by Claude Tardif. 





Application surjective 
19990930 

From Charass: je suis étudiant en premiere année de deug et je cherche apres une definition si vous pouviez m'aider, ça serait sympa. qu'est ce qu une application subjective? Answered by Claude Tardif. 

