







Five bales 
20171008 

From John:
two answers were given... I believe both to be incorrect.
five bales weighed two at a time: weightx2 given: 110,112,113,114,115,116,117,118,120, and 121. It stated all combinations ie: ab,ac,ad,ad,bc,bd,be, etc. to arrive at the above 10 combined weights. I come up with the following...
Bale A= 54lbs, Bale B=56, Bale C=58, Bale D=59. and Bale E=62 pounds.
A+B=110, A+C=112, A+D=, B+C=114, B+D=115 ,A+E=116 ,C+D=117, B+E=118 ,C+E=120, and D+E=121 Answered by Penny Nom. 





Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom. 





Complementary angles 
20170915 

From SM: The measure of angle A is 60 degrees more than its complement. Find the measure of angle A. Answered by Penny Nom. 





An impossible problem 
20170915 

From Fay: Given math homework problem of: Gary and Larry given 2 numbers and told to add together. Gary subtracted and got 14. Larry multiplied and got 799. I tried substitution:
XY=14 and X x Y=799
X= Y+14
(Y+14) Y=799 and here I'm stuck at Y squared+14 Y= 799
using substitution I got 47x17=799 but not 14b when subtracted. HELP????? Answered by Penny Nom. 





Two circles 
20170813 

From Ladines: Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 Answered by Penny Nom. 





Squares and rectangles 
20170715 

From Tront: So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole. Answered by Penny Nom. 





Yards per second to miles per hour 
20170511 

From Scott: If a soccer ball travels 30 yards or roughly .017 miles in 2 seconds how fast was the ball going in mph? 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. 





Feet per second to miles per hour 
20170127 

From ron: if a vehicle travels 50 feet in 2.5 seconds what is the speed in mph.
3600 sec in hour /5280 feet in a mile i get .68181818. how do i figure the 2.5
seconds. all the calculators I've used show 34 mph is that correct or am i forgetting the 2.5 second. please help. Answered by Penny Nom. 





A circle inscribed in an isosceles triangle 
20170114 

From Sal: There is a right isosceles triangle. Inscribed inside of it, is the largest possible circle.
Ho do you find the value of the radius?
I want to find out a way of only using the rules/laws of geometry, or is that not possible. Answered by Penny Nom. 





8^3/2(2+2) 
20170113 

From Mary: 8^3/2(2+2) Answered by Penny Nom. 





An angle and its complement 
20170110 

From Ysa: If the measure of an angle is twice the measure of its complement, what is the measure of the angle? Answered by Penny Nom. 





Two concentric circles 
20161221 

From shrestha: Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. Answered by Penny Nom. 





A sales tax of 7% 
20161207 

From Kenneth: Hello:
If a sales tax of 7% is placed on every $1.00 of merchandise for sale, is it correct to indicate
the tax as 7%/ per $1.00 or 7%/$1.00? If the calculation is expressed as 7%/$1.00 X $5.00,
the tax is not $0.35 but 0.35. Is a tax rate of 7% incorrectly represented as 7%/$1.00
since the dollar unit cancels from the multiplication?
I thank you for your reply. Answered by Penny Nom. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





Two tangent circles 
20161127 

From mikee: find the equation of a circle tangent to the circle x2+y2=4
and with the center at (0,5) Answered by Penny Nom. 





Three circles 
20161030 

From yolani: two equal circles with centre A (1;1)and B (4;5)touch a third circle with centre P as shown in the diagram. If P ,A and B Lie on a straight line find the coordinates of P Answered by Penny Nom. 





How many marbles does Haley have? 
20161019 

From Pat: Sabrina has 1/4 the marbles as Haley.
They have 305 total. How many marbles does Haley have? Answered by Penny Nom. 





Hexagonal pyramid bevel angles 
20160930 

From Peter: I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide. Answered by Penny Nom. 





A search area 
20160813 

From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom. 





The number of sides of a polygon 
20160723 

From Shriya: All the angles of a polygon are either 155° or 140°.
There are twice as many angles of 155 °or 140°.
Find the number of sides of the polygon Answered by Penny Nom. 





A congruence theorem for two right angled triangles 
20160717 

From Sayari: Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You. Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





Filling a pit with glass pebbles 
20160517 

From Sam: I need to know how many pounds of glass pebbles are needed to fill a 24 inch across circular fire pit, if 5 pounds covers 4"H x 4"W x2"D? Thank u for any assistance, Sam Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





External and interior angles of a regular polygon 
20160419 

From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20160325 

From NIHAL: A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle Answered by Penny Nom. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





Tiling a floor 
20160305 

From joanne: How many floor tiles 20x20 inch do I need for area of 8x 12 ft.? Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





The interior and external angles of a regular polygon 
20160217 

From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n Answered by Penny Nom. 





Consecutive angles of a parallelogram 
20160128 

From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom. 





The length of an 80 acre piece of land 
20160121 

From Eugene: Have to clear a piece of land 80 acres by 500 feet wide. What is the length of the property? Thanks Gene Answered by Penny Nom. 





Book sales 
20151230 

From Sandra: Your finance text book sold 56,500 copies in its first year. The publishing company expects the sales to grow at a rate of 20.0 percent for the next three years, and by 8.0 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in year 3 and 4. 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. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





The angle at the vertex of an isosceles triangle 
20151125 

From Karan: I have been given an isosceles triangle. the Top angle is what i have to find out and the two sides adjacent to it are both 4.9 cm. i have been told that the area of the triangle is 4 cm^2. i have no idea how to work this out, any ideas? Answered by Penny Nom. 





The measure of an angle in terms of its complement 
20151122 

From Pam: Can you please help me so I can help my daughter the equation is the measure of angle v is 4 time the measure of its complement what is the measure of angle v when the equation is 4x+x=90 Answered by Penny Nom. 





A conditional probability problem 
20150824 

From Faustina.: Please I have an exam tomorrow. And I have tried by best in solving this Question. An urn contains 10 white, 5 yellow and 10 black marble. A marble is chosen at random from the urn and it is noted that it is one of the black marble, what is the probability that it is yellow? Answered by Penny Nom. 





The length of a shadow 
20150801 

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





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

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





The area of an isosceles triangle 
20150611 

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





Two concentric circles 
20150528 

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





An isosceles right triangle 
20150517 

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





An octagonal frame around a pool 
20150517 

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





Sales tax 
20150505 

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





Two concentric circles 
20150421 

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





A wireless fence 
20150418 

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





The area of the ring between two concentric circles 
20150408 

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





An isosceles triangle inscribed in a circle 
20150323 

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





Two concentric circles 
20150225 

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





An isosceles triangle and an arc 
20150218 

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





Tiling a room 
20150216 

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





Jack and Jill climb two poles 
20150202 

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





The volume of Lake Utah 
20150129 

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





128/(16)/(2) 
20150128 

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





Two concentric circles 
20150125 

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





An isosceles triangle 
20141231 

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





Cutting a hexagon with a sliding miter saw 
20141123 

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





The region between two concentric circles 
20141027 

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





Building an 8 sided box 
20141014 

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





Interior angles in a parallelogram 
20140830 

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





Filling three holes with stones 
20140820 

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





A barge of triangular cross section 
20140818 

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





The length of a shadow 
20140509 

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





The derivative of sin(x) 
20140426 

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





A circle is divided into three sectors 
20140417 

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





The cost before the sales tax 
20140413 

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





Two cones 
20140409 

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





Two circles that touch each other externally 
20140408 

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





Shadows of a father and son 
20140402 

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





A circle which is tangent to two perpendicular lines 
20140309 

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





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

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





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. 





2 concentric circles 
20131127 

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





A string wrapped around three circles 
20131019 

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





Four tangent circles 
20131009 

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





Miles per minute to miles per hour 
20130908 

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





Constructing a triangle 
20130822 

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





Similar rectangles 
20130817 

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





A triangle construction 
20130727 

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





GST and PST 
20130722 

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





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

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





4 couples golfing 
20130706 

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





An isosceles tiangle 
20130616 

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





A kennel for a beagle 
20130603 

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





Four circles 
20130529 

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





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. 





An equation in two variables 
20130514 

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





A triangle and an incircle 
20130509 

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





Drawing a pentagon 
20130506 

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





Trigonometry 
20130323 

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





Tiling a floor 
20130318 

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





An electron in a TV tube 
20130215 

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





Introductory algebra 
20121030 

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





Differentiation rules 
20121023 

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





Two congruent circles in a rectangle 
20121020 

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





Percentiles 
20121017 

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





Three piles of top soil 
20121007 

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





Two circle problems 
20121005 

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





Four tangent circles 
20121004 

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





More on marbles in a jar 
20120927 

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





Three right triangles 
20120726 

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





The distance between overlapping circles 
20120726 

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





Fence post holes 
20120719 

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





The height of an isosceles triangle 
20120710 

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





An octagonal sandbox around a pool 
20120612 

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





Multiples 
20120528 

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





How fast am i driving? 
20120518 

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





Drawing an isosceles triangle 
20120510 

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





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

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





A common chord to two circles 
20120422 

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





Liters and gallons 
20120420 

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





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. 





Circles 
20120311 

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





Tiling a floor 
20120227 

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





Two circles 
20120208 

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





A fountain 
20120124 

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





Four pizzas 
20120123 

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





The derivative of x^(1/2) 
20120114 

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





An equilateral triangle and some circles 
20120110 

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





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





Two circles 
20111204 

From Luke: Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Answered by Chris Fisher. 





Solve for theta if 8cos^2 theta3=1 
20111202 

From Katherine: Hi,
I have just learned to solve trigonometric problems for theta and have one specific question in order to find the solutions to my homework.
I will use one example for this question. If I have 8cos^2 theta3=1
I first divide by 8 and get cos^2theta=3/8
then I have cos theta= plus or minus the square root of 3/8
Then I assume that I plug in inverse cos (the square root of 3/8) to my calculator.
How do I find the four solutions (we are typically supposed to find four, I believe?)
Can you help me with finding the solution to this problem? Thank you! Answered by Penny Nom. 





The total number of roles that a user can be assigned 
20111202 

From Colin: Hi, I want to define an equation for calculating the total combination of roles that a user can be assign in a system.
Here is the background: There are two types of roles that a user can be assigned. These are object roles and data roles. There must be at least 1 object and 1 data role in the system. A user must be assigned at least 1 object role and at least 1 data role. A user can be assigned as many object roles and data roles as are created in the system. There is no upper limit to the number of roles that a user can be assigned except for the total number of object roles and data roles that exist. The number of object roles and data roles in the system are independent.
Can someone please assist? Thanks. Answered by Penny Nom. 





A right angled triangle 
20111031 

From bijo: how can i find the tangent point at a circle with origin as center with radius r and the tangent pass through a given point P? I also want to find out the third point of a right angled triangle given other two points? Answered by Chris Fisher. 





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 6% commission 
20111015 

From Tamara: if you earned a gross wage of $810, which includes a salary of $90 and a 6% commission how much is the net sales? Answered by Penny Nom. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





Two great circles 
20111006 

From Jean: "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? Answered by Chris Fisher. 





Romeo throws a pebble at Juliet's wondow 
20110822 

From Natalie: There is a picture of Romeo trying to attract Juliet's attention without her nurse who is in a downstairs room, noticing. he stands 10m from the house and lobs a small pebble at her bedroom window (3.5m high). Romeo throws the pebble from a height of 1m with a speed of 11.5m/s at an angle of 60degrees to the horizontal. I have already found that it take 1.74seconds to reach the window and that it does in fact hit Juliet's window however i cannot work out the speed of the pebble when it hits the window! The answer is 9.12m/s but I cannot reach this answer. Hope you can help me :) Answered by Robert Dawson. 





Three tangent circles 
20110821 

From maribie: three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t Answered by Penny Nom. 





Three tangent circles 
20110819 

From hanniel: two coin are tangent to a third coin internally and are tangent to each other
externally. The distance between their centers are 14 mm, 17mm, and 5mm.
find their radii Answered by Penny Nom. 





concentric circles 
20110706 

From maribiie: two circles are concentric. the tangent to the inner circle forms a chord of 12cm in the larger circle. find the area of the "ring" between the two circles? Answered by Penny Nom. 





Achilles and a turtle 
20110701 

From Jean: Achilles and a turtle are having a race. The turtle starts 45m ahead of Achilles and Achilles is twice as fast as the turtle. If turtle runs at 1m/s,how far would the turtle have run before he is outrun by Achilles? Answered by Penny Nom. 





Tiles for a back splash 
20110604 

From Catherine: How man 3 11/16 tiles do I need for 28 square foot for a back splash Answered by Penny Nom. 





Three tangent circles 
20110501 

From mark: Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each
other (each is tangent to the other two). Draw a diagram and using the Law of
Cosines find the largest angle of the triangle formed by joining their centres. Answered by Penny Nom. 





Why use percentiles? 
20110429 

From Kenneth: I need some clarification regarding the word "percentile."
Here is an example and what I know: If an investor had twenty stocks in his portfolio and five of those stocks paid an annual dividend of $200.00 or more, the five stocks are in the 25 percentile.
Why is this word necessary? If my example and explanation is correct, why not simply indicate that 25% of his stocks paid an annual dividend of $200.00 or more? Answered by Penny Nom. 





Dividing a polygon into triangles 
20110416 

From Foxie: You have a given regular polygon with n vertices and you divide it into triangles(using the vertices of the polygon) which each share at least one side with the polygon. How many distinct ways can you divide the polygon if its vertices are numbered? For n=3 it's 1 way, for n=4 it's 2 ways for n=5 5 ways, I'm not quite sure but think that for n=6 it's 12 ways... thanks in advance! Answered by Claude Tardif. 





Coefficient of variation 
20110414 

From Braden: When determining coefficient of variation (CV) or %CV is it possible to calculate %CV for two variables? For instance can %CV be used to determine the precision of 5 data points on a graph using the X and Y coordinates? or does %CV need to be determined for each variable separately? Answered by Robert Dawson. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





The interior angles of a pentagon 
20110310 

From Daima: I need help!
The interior angle of a pentagon i s5 ( I hope ) or 540 degrees.
The interior angle of a pentagon is what? Explain to me please.
Daima Answered by Penny Nom. 





Fencing a park 
20110307 

From taniel: Find the number of feet of fence needed to fence a park that is 1 3/8 mi long and 5/8 wide. Answered by Penny Nom. 





A family of circles 
20110301 

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





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. 





Triangles with perimeter 16 cm 
20110222 

From Chong: How many triangles (up yo congruence) with perimeter 16 cm and whose lengths of its side are integers? Answered by Chris Fisher. 





Two tangent circles 
20110209 

From xhesika(jessica): Two circles of radius 10 are tangent to each other.A tangent is drawn
from the centre of one of the circles to the second circle.To the nearest
integer find the area of the shaded region. 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 area of isosceles triangle 
20110124 

From imraan: how to find the area of isosceles triangle by knowing only its sides Answered by Penny Nom. 





The height of a lamp 
20110113 

From Dorothy: I need to find the lamp height with casting shadow (base line of triangle where a boy 1.6m tall stands 3m from base of street lamp and has a 2m shadow. In other words, think of a right angle triangle with zero height starting at left, then 2m to right stands boy (1.6m high). Angle (hypotenuse) increases up to top of street lamp with 'x' height and 3m base. Answered by Penny Nom. 





Semicircles and the Pythagorean Theorem 
20110109 

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





What is its speed in miles per hour? 
20110106 

From Miriam: An airliner travels 125miles in 15minutes. What is its speed in miles per hour? Answered by Penny Nom. 





Draw a figure with 16 triangles using only 6 line segements 
20101216 

From Jill: How can you draw a figure with 16 triangles using only 6 line segements? Answered by Stephen La Rocque. 





Sales as a function of advertising 
20101208 

From Adori: The sales S(in thousands if units) of a product after x hundred dollars is spent on advertising is given by S=10(1e^kx). Find S as a function of x if 2500 units are sold when $500 is spent on advertising. Answered by Penny Nom. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(3,2) P(2,1) L(2,3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom. 





The base of an isosceles triangle 
20101024 

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





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. 





What are the speeds of the boats? 
20101021 

From Adori: Two boats leave the port of San Francisco traveling in opposite directions at the same time. One boat travels 8 knots per hour faster than
the other. After one day's travel they are 1920 nautical miles apart. What are the speeds of the boats? Answered by Penny Nom. 





The angles in an mgon and genrealizations 
20101016 

From Michael: Hello:
In answer to a student's question, someone named Penny from
your organization provided a proof that the sum of the interior
angles of a triangle in the plane is pi radians (or 180 degrees).
I am interested (and I'm sure many other people would be too) in
3 potential generalizations of this basic fact in plane geometry: Answered by Walter Whiteley. 





Tiles on a bedroom floor 
20101007 

From Rochelle: John's bedroom floor is square in shape. He used 625 tiles, with a side length of 200 mm, to tile the whole floor.
Calculate the area and dimensions of the bedroom Answered by Penny Nom. 





What is the average speed? 
20100921 

From Cindy: A boat travels downstream m nautical miles at d knots. It travels upstream m nautical miles at u knots. What is the average speed for the entire trip? Answered by Penny Nom. 





La racine carrée et l'exposant une demie 
20100914 

From Alain: Bonjour.
Je cherche une explication sur l'équivalence entre les exposants
fractionnaires et les racines nième.
Par exemple, comment prouvet'on que la racine carrée correspond à
l'exposant une demie?
merci Answered by PierreLouis Gagnon et Claude Tardif. 





Two overlapping circles 
20100804 

From Husen: two circles of radius 5 cm intersect each other .the distance between their centers is 5root 2.find the area of the portion common to the two circles Answered by Penny Nom. 





The suspension cables of a bridge 
20100729 

From Mike: what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span Answered by Robert Dawson. 





A spaceship playhouse 
20100726 

From Dave: I would like to build a spaceship playhouse for my grandson I want it to
be about 36" around and I want to use 5/4 decking boards that measure
5 1/2" wide how do I figure out how to lay out a base pattern to nail to
(what angle do I need to cut and how many boards will it take to go around
the circle. Answered by Penny Nom. 





Numbers that can be formed using the digits 1,2,3,4,5,8,9 
20100719 

From Donessa: write the number that is 2000 more than the difference between the largest and the smallest
number that can be formed using the digits 1,2,3,4,5,8,9 Answered by Tyler Wood. 





An octagon shaped bench 
20100709 

From rob: i am trying to build a octagon shaped bench to fit inside a 69 inch round hot tub so that the tip of each point touches the edge of the circle where it will be fastened. Answered by Stephen La Rocque. 





Rays and angles 
20100624 

From cristina: what is the formula for finding the number of angels that can be named by a given number of rays with the same endpoint? Answered by Robert Dawson. 





Going to the bike shop 
20100607 

From Omi: Marie rode her bicycle from her home to the bicycle shop in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from her home to the bicycle shop if her total travel time was 1 hour? Answered by Penny Nom. 





Four circles in a square 
20100604 

From Daniela: four circles are drawn in a square such that the circles are tangent to each other as shown. find the area of the shaded region. It the goes on to show a diagram with a square and four circles drawn in it. The length of a side of the square is 24. Please help me! Answered by Penny Nom. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? Answered by Penny Nom. 





The altitude of a triangle 
20100508 

From kylie: the vertex angle of an isosceles triangle is 57 degrees 24 minutes and each of its equal sides is 375.5 feet long. find the altitude of the triangle Answered by Penny Nom. 





An angle in a triangle 
20100506 

From Morgan: Question from Morgan, a student:
t
8 t t 8
t 78 t
t t
t t
t x t
ttttttttttttttttttttttttt
10
I'm having trouble solving for x I'm not sure where to start ( the ones in the middle of the triangle are both degrees) thanks in advance for your help i really do appreciate it Answered by Penny Nom. 





A wishing well 
20100504 

From Cassie: I'm trying to construct a Wishing Well made of treated 2x4 wood, so the actual measurement is 3 1/2 by 1 1/2. The well is going to be three feet in diameter. I'm trying to construct this as circular as possible, what angle should the wood panels be cut at? Answered by Penny Nom. 





Tiling a floor 
20100503 

From guadalupe: how many 16 x 16 inch square tiles fit into a 10 x 10 foot space? Answered by Harley Weston. 





A circle inscribed in a square inscribed in a circle 
20100428 

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





y =  log(x) 
20100428 

From Alex: y=  log(x), where y = 4.3
solve for x. Answered by Harley Weston. 





Sales taxes in Quebec 
20100428 

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





Tiles 
20100425 

From Pat: how many 6 inch tiles will I need to purchase for an area that is currently covered with 351 4 inch by 4 inch tiles.
Each box of 6 inch tiles states it contains 16 pieces and covers 4 square feet. Answered by Penny Nom. 





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. 





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. 





Tiling a floor 
20100331 

From shane: a floor in a house is 12'6" in width and 10'4" in length. Tiling the floor with each tile 5" on each side. First express the square footage into an improper fraction. Second express the area of each tile in square feet. Third how many tiles needed to tile the floor. Fourth explain how answers relate to real world Answered by Harley Weston. 





How many 20"X20" tiles do I need to cover 90 sq. ft? 
20100323 

From Karen: How many 20"X20" tiles do I need to cover 90 sq. ft. Answered by Penny Nom. 





An irregular octagon 
20100309 

From Gayle: Question from Gayle:
I am building an irregular shaped octagon wooden box.
The measurements are 291/2 inches by 211/2 inches.
Sides are 12 inches.
It will be 36 inches high.
What would the cutting angles degrees be? Answered by Harley Weston. 





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. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





How many triangles...? 
20100222 

From deciree: Given 12 points, no 3 of them on a line with 6 red, 4 blue and 2 green points.
a) How many triangles have vertices all the same color?
b)How many triangles have vertices with each vertex a different color?
c)How many triangles have at least one green vertex?
thanks to lorraine! Answered by Penny Nom. 





Triangles 
20100219 

From Wiliam: A box contains one 2 inch rod, one 3 inch rod, one 4 inch, and one 5 inch rod.
What is the maximum number of different triangles that can be made using these rods as sides? Answered by Penny Nom. 





An isosceles triangle 
20100211 

From Kim: I am given the length of the two legs of an isosceles triangle (8), and the base angles are 30 degrees...I am asked to find the area of the triangle with only this information Answered by Tyler Wood. 





Two bus routes 
20100203 

From kiyah: from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again? Answered by Penny Nom. 





An impossible isosceles triangle 
20100131 

From Hailey: An isosceles triangle has one angle that measures 50 degrees and another that measures 70 degrees. Why can't this triangle be drawn? Answered by Penny Nom. 





An isosceles triangle 
20100128 

From Jazzy: An isosceles triangle is a 2 congruent (equal) sides. Of the third side is three times the length of the congruent side(s), and the perimeter is 75 cm, find the length of all three sides of the triangle Answered by Penny Nom. 





Dividing seashells among girls 
20100106 

From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and Penny Nom. 





How many 4x4 tiles would I need for 10 sq ft? 
20100104 

From Chris: how many 4x4 tiles would I need for 10 sq ft Answered by Robert Dawson. 





Triangles on a base of 2.4 meters 
20091226 

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





A triangle with two equal medians 
20091219 

From Nazrul: If two medians of a triangle are equal , how can I prove that the triangle is isosceles. Answered by Chris Fisher. 





Polygons, diagonals and the sum of the measures of the angles 
20091218 

From jason: find the set of polygons in which the number of diagonals is greater than the sum of the measures of the angles Answered by Robert Dawson. 





Energy in calories 
20091215 

From Josephine: A soft drink manufacturer claims that a new diet soft drink is now "low Joule". The label indicates that the available energy per serving is 6300 J. What is the equivalent of this energy in calories? (1 Calorie=1000 cal) Answered by Robert Dawson. 





The height of an isosceles triangle 
20091206 

From Carl: What is the height of an isosceles triangle if its base is 12cm, and its base angle is 72degrees? Answered by Penny Nom. 





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 line through D(4, 0) and E(2, 6) 
20091116 

From Rogerson: The point F is on the line through D(4, 0) and E(2, 6) so that DF=4DE. Find the coordinates of F. Answered by Penny Nom. 





Cables in a pipe 
20091113 

From john: how many 0.28 mm diameter cables will fit into a 19.05 mm diameter pipe Answered by Stephen La Rocque. 





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. 





Concentric circles 
20091014 

From maddy: Find the exact area of the region bounded by two concentric circles with radii 10 inches and 6 inches. Answered by Penny Nom. 





The three angles of a triangle 
20091013 

From Michelle: The second angle of a triangular garden is four times as large as the first.
The third angle is 45 less than the sum of the other two angles.
Find the measure of the other two angles? Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





The maximum number of right angles in a polygon 
20091005 

From Bruce: Is there way other than by trial and error drawing to determine the maximum number of right angles in a polygon? Secondary question would be maximum number of right angles in a CONVEX polygon. Is there a mathematical way to look at this for both convex and concave polygons? Or are we limited to trial and error drawing? Answered by Chris Fisher. 





Three circles 
20091002 

From Brandon: There is a quarter circle with a radius of 1. along one eged of it,
there is a semicircl with a diameter of 1, and its center is on the
drawn line. there is another semicircle again with the center on the
other drawn line, and this one has an unknown diameter of X. both
circles are internally tangent, and are tangent to each other. Find X. Answered by Robert Dawson and Chris Fisher. 





5 x 8 + 6 divided 6  12 x 2 
20090924 

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





Seven circles 
20090920 

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





Common multiples of 36 and 48 
20090915 

From Kamaldeep: Find the first 2 common multiples of 36 and 48. Answered by Penny Nom. 





Helen has twice as many dimes as nickles. 
20090908 

From Dan: Helen has twice as many dimes as nickles. She has 5 more quarters than nickles. She has $4.75. How many nickles does she have? I know she has 14 dimes, 7 nickles and 12 quarters. How do you put this into an algebra equation? Answered by Stephen La Rocque. 





How do you convert cents/mile to dollars / hour? 
20090826 

From seanna: how do you convert cents/mile to dollars / hour Answered by Penny Nom. 





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. 





An isosceles triangle 
20090809 

From Megan: Find the perimeter of an isosceles triangle with a verticle angle of 100 degrees and a base of 25 cm.
I think I could answer this if I knew what a verticle angle was.
Thanks Answered by Stephen La Rocque. 





Two circles 
20090803 

From Karan: We are given 2 circles with radii 12cm and 3 cm. We have to find AB Answered by Penny Nom. 





Constructing an isosceles triangle 
20090727 

From Sanjay: How to construct an isosceles triangle ABC with a base BC = 5.4 centimetre and altitude AD = 4.7 centimetre? Please help. Answered by Janice Cotcher. 





How can I trisect an angle? 
20090727 

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





Two circles on a dome 
20090701 

From Beth: My question is related to a dome I would like to construct, for which I know the circumference of the base: 120ft.
I now need to figure out the diameters of two smaller circles, one at 20ft along the arc of the dome form the ground,
and the other at 30ft along the arc.
Assuming a true hemisphere, or 180 degrees total arc, how can I calculate these two circumferences?
Beth Answered by Stephen La Rocque. 





Two questions from math class 
20090618 

From Con: Hello,
My name is Con and my son is required to answer the following questions for his maths class.
He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?
He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?
Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5digit number abcde such that 4 divides a 3digit number abc, 5 divides a 3digit number bcd and 3 divides a 3digit number cde. Find the 5digit number abcde.
Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD.
Con Answered by Chris Fisher. 





Real World Applications of Mathematical Skills 
20090608 

From Kathy: I am teaching a student who is on the life skills program and is at the stage 2 level for maths but is in year 9 (stage 3). I am looking for maths lessons that will help her in life. Like maths in shopping, maths in fashion, maths in the home etc. Your help in finding lesson plans is urgently needed. Answered by Janice Cotcher. 





The position of the fulcrum 
20090523 

From jim: I think I need a formula. I need to know how far an object will be lifted.
A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side,
if I push down 36 inches on the long side of the beam, how much will the short side move up? Answered by Stephen La Rocque. 





The sum of the angles of a triangle 
20090518 

From mary: prove that the sum of the three angles inside any triangle always add up to 180 degrees? Answered by Harley Weston. 





Angles in a triangle 
20090516 

From Robert: The second angle of a triangle is twice the sizee of the first angle, the third angle is 48 degrees less than the sum of the other two angles. What are the measurements of all 3 angles?
PS: please help Answered by Stephen La Rocque. 





The hypotenuse of a right angled triangle 
20090511 

From Deb: Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. I've ended up with the hypotenuse = x+9, another side = x and the other side = x+7. what do i do next? Answered by Penny Nom. 





Rectangular prisms 
20090501 

From deborah: Could you please tell me some examples of different objects in the real world of rectangular prisms? Answered by Harley Weston. 





Common multiples of 2 and 5 
20090423 

From pat: what are the common multiples of 2 and 5, through 30, because i been working on it for hours Answered by Robert Dawson and Stephen La Rocque. 





Miles per hour and feet per second 
20090422 

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





The interior angles of a pentagon 
20090420 

From Mary: If four interior angles of a fivesided figure pentagon measure 100 degrees each, what will the fifth angle measure? Answered by Harley Weston. 





Two similar rectangles 
20090419 

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





Nickles and dimes 
20090417 

From Emily: a vending machine contains nickels and dime coins which totals an amount of $14.50. There are 95 more nickels than the number of dime coins. How many of each coin does exist? Answered by Penny Nom. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ³√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





The central angle of a chord 
20090406 

From Dale: How do I find the central angle if I only have the cord length and radius. Answered by Harley Weston. 





A fraction in its simplest form 
20090402 

From Michael: I'm in 4th grade and need to express decimals as a fraction in its simplest
form. Is there a step by step method to figure out?
ex 0.64 = 64/100 = ? Answered by Robert Dawson. 





More on the square root of 0.75 
20090330 

From Blaine: I read your response to How is the square root of 3/4 is greater than 3/4?
What I'm hoping for is a way for my students to use their own experience and number intuition to be able to make sense of the issue. As soon as my kids see "if y is this and x is this then..." their little eyes glaze over. Unfortunately, I can't come up with a way myself. Thank you for your help. Answered by Penny Nom and stephen La Rocque. 





An isosceles triangle 
20090326 

From sela: An isosceles triangle has two equal sides of length 10 cm. Theta is the
angle between two equal sides.
a) Express area of a triangle as a function of theta
b) If theta is increasing at a rate of 10 degrees/minute, how fast is area
changing at the instant theta=pi/3?
c) at what value of theta will the triangle have the maximum area?
Answered by Penny Nom. 





An infinite number of solutions 
20090324 

From Sean: this is a linear equations problem;
first:
3535.5 + Fbd (.866) + Fbc (.5)  Fab (.5) = 0
and
3535.5  Fab (.866)  Fbc (.5)  Fbd (.5) = 0 Answered by Harley Weston. 





The base and height of an isosceles triangle 
20090323 

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





Percentiles 
20090321 

From Shawn: For a normal distribution of u=654.00 and o=138.00.
What is the percentile rank for X=426? Answered by Harley Weston. 





The angles of a triangle 
20090311 

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





Triangles within triangles 
20090224 

From Mari: a large shaded triangle changes each day with a white triangle appearing
in the center of each shaded one. If this pattern continues, how many white
triangles will be there on the 6th day? On the 6th day, what fraction of
the large outer triangle will be white?THANKS! Answered by Robert Dawson. 





Trig functions without geometric data 
20090224 

From bob: I do not understand how it is possible to find the sine, cosine, or tangent of an angle if
there is no hypotenuse, opposite or adjacent side?! Answered by Robert Dawson. 





Miles per hour to kilometers per second 
20090217 

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





6^x = y 
20090212 

From Jamie: Find x:
6^x=y Answered by Harley Weston. 





Forming an arc with 2 inch steel 
20090211 

From Craige: I need to calculate the bending radius of 2" wide steel to achieve given inside and outside arc lengths Answered by Harley Weston. 





A 306090 triangle 
20090203 

From Inez: If you have a 306090 triangle and the only side you get is 73 and a 90 degree box, how do you find the area? Answered by Penny Nom. 





4 times as many or 4 times more? 
20090202 

From Jackie: Given : Here are 3 squares and 4 sets of 3 circles.
I wonder it is right to write in the below manner to represent the following Conclusion that
can be made from the above given information:
 There are 4 times as many circles as there are squares,
 There are 4 times fewer square than circles;
 There are 4 times more circles than squares.
 ...
Jackie Answered by Robert Dawson. 





The height of an isosceles triangle 
20090129 

From Mariah: An isosceles triangle has sides 10cm, 10 cm and the base 4cm.
How do you find out the height of the triangle? Answered by Penny Nom. 





20 of us golf together in groups of 4 
20090124 

From D.: Every Sunday, 20 of us golf together in groups of 4. I am looking for a
way that each of us play with 3 other people each week and ultimately get
to play in groups that are unique. For instance if week 1, I play with 2, 3, 4
and then the next week I play with 5, 6, 7, and the 3rd week I play with 8,
9, 10 and so forth until I have played with everyone. Everbody else should be
doing the same thing. Can you give me a schedule for this and how many weeks
would it take for all of us to accomplish this where we all play with different
combinations of people. (We should not play with the same person very often or even
the same pairs of people but everyone should play with everybody else) I hope
this makes sense........whew and thanks! Answered by Victoria West. 





Two tangent circles 
20090123 

From Murtaza: Two circles touch externally at T. A chord of the first circle XY is produced and touches the other at Z. The chord ZT of the second circle, when produced, cuts the first circle at W. Prove that angle XTW = angle YTZ. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20090123 

From Murtaza: Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Answered by Robert Dawson and Chris Fisher. 





The area of an isosceles triangle 
20090119 

From faris: how to calculate area of isosceles triangle with two angles of 45 degree and base of 6 Answered by Penny Nom. 





The ratio of the measures of the three angles of a triangle 
20090118 

From mary: The ratio of the measures of the three angles of a triangle is 2:5:8. What is the measure of each angle of the triangle? Answered by Robert Dawson and Harley Weston. 





A stack of rectangles 
20090111 

From ashwani: Could you please advise the area of a rectangles pyramid.
There are 5 rectangles placed one above the other. The top most rectangle has length 2 cm and height 2 cm. The subsequent rectangles length is increased by 1 cm on both the sides, while the height of the 2nd and 3rd rectangle is 2cm each, while the 4th & 5th has a height of 3 cm each. Could you please let me know the the area of the figure and the formula to calculate Answered by Penny Nom. 





A flattopped pyramid 
20090110 

From Tom: I am planning to build an open ended, flattopped pyramid with a
rectangular base 28 x 36 in.; a square top 6 x6 in.; and a vertical
height of 16 in.
I know how to calculate the dimensions of each of the pyramid sides but
I don't know how to calculate the interior angles when I bend the sheet
metal. I will cut the four sides separately and add a one inch flange
to each "vertical" edge of the two larger sides to allow for
a bonding surface for the assembly. How do I calculate that angle? I
know it will be greater than 90 degrees but by how much? Answered by Harley Weston. 





A one cubic mile lake 
20090109 

From dye: how many liters are in a one cubic mile lake Answered by Robert Dawson. 





Two angles are supplementary 
20090108 

From Stephanie: two angles are supplementary, one of the angles is 30 degrees more than double the other angle.
find the first angle, the second angle the complement of the given angle. Answered by Robert Dawson. 





660 yards = ?? miles 
20090108 

From Ashley: How do I convert yards to miles, specifically, 660 yards = x miles. Please show work so I can figure other problems out. Answered by Penny Nom. 





Pouring angles for a crucible 
20081220 

From Richard: I am trying to work at pouring angles and volume left in during pouring a crucible, The crucible is cylindrical and flat bottomed.
I know the diameter, radius and volume of the crucibles. and the volume of liquid going into it.
So lets say the crucible is only half full firstly I need to work out the angle just before its going to pour. ( I can work this out as long as there is a certain volume of liquid if its not enough I cant do it)
Now the problem I also need to work out how much I should tilt the crucible to allow a certain amount out and be able to do this untill the volume reaches 0 at 90' turn. This is where I am stuck.
The reason for needing to be able to work this out is so i can develop a constant flow for example 10Kg of metal per second.
Thank you very much for you time Answered by Harley Weston. 





Three circles inscribed in a circle 
20081218 

From seema: three equal circles each of radius 1 cm are circumscribed by a larger circle.find the perimeter
of circumscribing circle? Answered by Robert Dawson. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





The area of an isosceles triangle 
20081202 

From prateet: the area of an isosceles triangle is 60 sq cm and one of its equal sides is 13 cm. Find the base of the triangle. Answered by Penny. 





3 equidistant points 
20081201 

From Damien: How do you find 3 equidistant points (C,D,E) on a line between point A(Xa, Ya) and point B(Xb, Yb) so that AC, CD, DE and EB are all equal? Answered by Chris Fisher. 





Two tangent circles and common tangents 
20081201 

From Alan: Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Answered by Penny. 





There are 30 marbles in a bag 
20081121 

From Cori: There are 30 marbles in a bag. Twice as many red, as blue, and 1 more green than there are red. What is the probability that when one is pulled out, it will be red? 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 midpoint o a line segment 
20081115 

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





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. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





Supplementary angles 
20081110 

From Anna: <A and <B are supplementary angles. Twice the measure of <B is onefourth the measure of <A. Find the measure of both angles. Answered by Penny Nom. 





A flagpole and a yardstick 
20081107 

From Wanda: One boy holds a yardstick vertically at a point 40 feet from the base of the flagpole. The other boy backs away from the pole to a point where he sights the top of the pole over the top of the yardstick. If his position is 1 ft 9 in from the yardstick and his eye level is 2 ft above the ground, find the height of the flagpole. Answered by Penny Nom. 





The angles of a triangle 
20081031 

From kyla: an isosceles triangle has two 50 degrees angles.what is the measure of the third angle? explain how you found your answer. Answered by Penny Nom. 





Equations with the variable in the exponent 
20081028 

From fari: Solve for x
5 * 4^x3=40
5^x=25^(x+8) Answered by Penny Nom. 





A homework problem 
20081028 

From Shawn: I'm checking my son's homework and we disagree on the solution.
The problem reads:
135mn^4 (n to the 4th power) over 50n^2 (n squared)
I think the answer is: 27mn^2 (squared) over 10
Can you help? Answered by Penny Nom. 





Three congruent rectangles 
20081027 

From Meagan: Here is my problem: Three congruent (nonsquare) rectangles are placed
to form a larger rectangle. [Two are oriented the same way and the
"stacked" while the third is rotated 90 degrees and placed next to the
other two.] The total area is 1350 square cetimeters. Square ABCD is
then created that has the same perimeter as the large rectangle that was
created. E is the midpoint of line CD and F is the midpoint of BC. Find the
area of triangle AEF. Answered by Penny Nom. 





Octagon angles 
20081006 

From John: My daughter wants to build an octagon using PVC pipe fittings. There are several pipe "elbows" available, including 45 degree. I'm trying to determine if if an octagon can be constructed by using 8 pairs of 45 degree elbows, connected to each other by 8 sections of straight pipe of some equal legnth. This makes sense to me intiutively, but I do not know how this can be properly expressed in geometric terms. Answered by Chris Fisher, Victoria West and Harley Weston. 





The average rate of change of gasoline used 
20081006 

From JHulie: What is the average rate of change of gasoline used, measured in miles per gallons
if you travel 212 miles, then you fill your gas tank up again and it takes 10.8 gallons.
If you designate your change in distance as 212 miles and your change in gallons as 10.8? Answered by Penny Nom. 





The region between two circles 
20080924 

From Carol: Good day!
Here is a picture of the problem that we need to solve. (I send the picture through email.)
A small circle is inside a larger circle, the only given in the problem is the chord of the larger circle tangent to the smaller circle which measures 16cm. The question is, what is the area of the shaded region?
Can you answer this question? Thanks! :) Answered by Harley Weston. 





Probability: Marbles in a jar 
20080922 

From Andrea: Suppose you have a jar containing 100 red marbles and 100 white marbles.
A) If you draw 5 marbles in a row, throwing each marble across as you
draw it, what is the probability that at least one of them was red?
B) If you draw 101 marbles in a row, throwing each one across the room
as you draw it, now what is the probability that at least one of them was
red? Answered by Harley Weston. 





A garden in the shape of an isosceles triangle 
20080912 

From Rita: Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his garden will be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle. Answered by Penny Nom. 





Supplementary angles 
20080911 

From Shanaz: Find an angle such that 3 times its supplement equals 450. Answered by Penny Nom. 





3 miles in 6 seconds 
20080905 

From Grant: if a rocket sled is traveling 3 miles in 6 seconds, how fast is it going in miles per hour? Answered by Harley Weston. 





The length of an arc 
20080904 

From Angie: Segment PR is a diameter of circle S. If angle P =3D 25, find minor
arc QR.
This circle has an isosceles triangle in it, it is connected to the
diameter, Answered by Harley Weston. 





JeanCharles de Borda 
20080829 

From Joanne: I am researching JeanCharles de Borda as a mathmatician. What was his work focused on and where can I find more information? Answered by Penny Nom. 





Number of angles formed by rays 
20080829 

From Shon: what is the formula for finding the number of angels that can be named by a given number of rays with the same endpoint? Answered by Stephen La Rocque. 





Angles in an octagon 
20080826 

From Arvie: I have seen your answer to Kay on how she can find the length for the sides of an octagon for a 4 foot window, but what is the angle that will need to be cut to get to 4 feet Answered by Penny Nom. 





Two tangent circles 
20080822 

From Michele: A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Answered by Penny Nom. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





Metres and miles 
20080818 

From Bill: I enter a race that is 10,000 meters long,how many miles do i have to run? Answered by Victoria West. 





Similar Triangles Given a Median 
20080817 

From RAM: Sides AB , AC and median AD of a triangle ABC are respectively proportional to
PQ PR and median PM of another triangle PQR. Show that ABC is similar to PQR Answered by Janice Cotcher. 





Similar triangles 
20080812 

From ramarao: D is a point on side BC of a triangle ABC such that BD/CD=AB/AC. prove that AD is the bisector
AD is the bisector of BAC Answered by Chris Fisher. 





Solve for y in terms of x 
20080810 

From Rosie: Solve equation for y
4x=12+3y Answered by Penny Nom. 





Angles in a regular tetrahedron 
20080807 

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





Square miles 
20080806 

From Koni: I'm trying to figure out the distance our buses travel throughout our district to pick up students for school. How do you figure square miles?
If our district measures 6 1/2 miles wide and 2 3/4 miles deep, what is our total square miles? Answered by Penny Nom. 





The angle between two faces of a pyramid 
20080806 

From Carla: A pyramid has its vertex directly above the centre of its square base.
The edges of the base are each 6cm, and the vertical height is 8cm.
Find the angle between 2 adjacent slant faces. Answered by Penny Nom. 





Some angles in a pyramid 
20080804 

From Carla: A symmetrical pyramid stands on a square base of side 8cm. The slant height of
the pyramidis 20cm. Find the angle between the slant edge and the base, and the angle between
a slant face and the base. Answered by Penny Nom. 





Find the product of 2^35 and 5^38 in sci. notation. 
20080803 

From Peter: I am preparing for a competition and a lot of the noncalculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that? Answered by Penny Nom. 





Area of triangle formed by three tangent circles 
20080731 

From brian: Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles? Answered by Stephen La Rocque. 





An isosceles triangle inscribed in a circle 
20080715 

From Anne: Here is the math problem quoted from book:
"An isosceles triangle is inscribed in a circle of radius R,
where R is a constant. Express the area within the circle but outside
the triangle as a function of h, where h denotes the height of the triangle." Answered by Penny Nom. 





Hexadecagon 
20080709 

From Dave: I would like to know at what length and angle I would cut wood to make a Hexadecagon. Answered by Penny Nom. 





Fit 7 different rectangles on grid paper 
20080702 

From anonomous: I need to fit 7 different rectangles on grid paper of 1cm squared.
Each squared centimetre equals 4 squared metres, and it needs to end up as area 64 square metres. Answered by Janice Cotcher. 





Miles per hour 
20080701 

From Nedra: If I walk 1 mile and 2/10ths in 20 minutes how fast am I going?
AND how many calories have I burned off? Answered by Penny Nom. 





Kilometers per liters to miles per gallon 
20080626 

From margaret: we travelled 130 kilometers on 10 liters of gas. How many miles to the gallon did I get Answered by Penny Nom. 





The exterior angles of a polygon 
20080626 

From evelina: how many sides has a regular polygon if the measures of the exterior angle is given Answered by Walter Whiteley. 





Acres and square miles 
20080625 

From Jill: how many miles are in 417 acres Answered by Penny Nom. 





The height of an isosceles triangle 
20080622 

From Evelyn: Hi! I am facing problem finding the height of the isosceles triangle. Answered by Penny Nom. 





sin(2x)/sin(3x) 
20080619 

From matt: how does sin2x break down (not with identities) and how would sin3x be created. My
prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break
down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston. 





The angles of a parallelogram 
20080611 

From light: ABCD is a parallelogram. If angle A. = (4x=17)degrees and angle B. = (3x5)degrees , what is angle c? Answered by Penny Nom. 





Two circles 
20080610 

From cey: the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area?? Answered by Janice Cotcher. 





g(m1,2n)+n 
20080607 

From Florence: What does g(m1,2n)+n for m>0, n>=0 mean. Answered by Penny Nom. 





The two acute angles in a right triangle 
20080605 

From Crystal: In the right triangle the ratio of the measure of the two acute angles is 4:1. What is the measure in degrees of the larger acute angle? Answered by Penny Nom. 





The interior angles of an 18sided polygon 
20080604 

From Alfred: How do I find the sum of the interior angles of an 18sided polygon? Answered by Janice Cotcher. 





Three mutually tangent circles 
20080604 

From Jacob: If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular? Answered by Chris Fisher. 





The angles of an irregular pentagon 
20080520 

From victoria: The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle? Answered by Penny Nom. 





An isosceles triangle 
20080507 

From Jay: Given: An Isosceles Triangle with the area=16m squared. What would be the length of each leg. Answered by Stephen La Rocque. 





How do you reduce an equation with multiple variables? 
20080430 

From Jonathon: How do you reduce an equation with multiple variables?
For example, if 3x + y = k(x3), what would x be equal to? Answered by Penny Nom. 





The Pythagorean theorem with triangles rather than squares 
20080429 

From Zachary: I need to figure out how to prove the pythagorean theoorem using equilateral triangles
instead of using square. I know that A^2+B^2=C^2, but how do you get that by using equilateral
triangles. I know the area of a triangle is BH1/2=Area. So what i need to know is how to derieve the
formula of a triangle to get the pythagorean theorem 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. 





A 6 digit number 
20080423 

From rajiv: write the smallest 6digit number using three different digits with 6 in the ten thousands place and 1 in the hundreds place Answered by Penny Nom. 





Two intersecting circles 
20080417 

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





A tangent to two circles 
20080413 

From erson: find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other.
the illustration looks like this...hope you'll understand...
there are 2 circles  one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well
please bear with me Answered by Stephen La Rocque. 





An isosceles right triangl 
20080409 

From Stephanie: An isosceles right triangle has an area of 35 sq cm. What are the lengths of the sides? Answered by Walter Whiteley. 





Side lengths and angles in a regular octagon 
20080409 

From Lori: I am a builder and need to find the length of the sides of an octagon. I know the length between
the parallel sides (26 feet). What is the length of each side? What is the angle measurement? Answered by Harley Weston. 





1 mile per minute 
20080401 

From jennifer: If you are traveling at 1 mile per minute how fast would you need to be going Answered by Stephen La Rocque. 





A fish tank in the shape of an irregular pentagon 
20080329 

From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)
there will 3 right angles A, B, E
my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher. 





Similar triangles 
20080326 

From Nisha: In triangle ABC, LM is parallel to AB. If AL=x3,AC=2x,BM=x2,BC=2x=3. Find x Answered by Penny Nom. 





Light years to miles 
20080324 

From Robert: HOW MANY MILES ARE THERE IN 7.5 BILLION LIGHT YEARS. Answered by Penny Nom. 





A word problem about a triangle 
20080323 

From kathy: The measure of the largest angle of a triangle is twice the measure of the second largest. The measure of the second largest is 20 degrees more than the measure of the smallest. Find the measure of each angle. Answered by Melanie Tyrer. 





Angles subtended by the same arc 
20080323 

From Reid: Prove that two inscribed angles subtended by the same arc are equal. Answered by Stephen La Rocque. 





A common chord to two circles 
20080309 

From shubha: please help me out with this problem.
find the length of the common chord of the intersecting circles x2+y24x5=0
and x2+y22x+8y+9=0 Answered by Stephen La Rocque. 





Two circles and a triangle 
20080307 

From Adrian: The vertices of a rightangled triangle are on a circle of radius R and the
sides of the triangle are tangent to another circle of radius r. If the lengths
of the sides about the right angle are 16 and 30, determine the value of
R+r Answered by Penny Nom. 





A 6 pointed star 
20080304 

From Siddharth: When 2 congruent equilateral triangles share a common center, their union can be a star
If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?
a) 60 b) 70 c) 80 d)90 e)100 Answered by Stephen La Rocque. 





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

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





The angles of a triangle 
20080301 

From Allen: How to find the other two angles of a scalene triangle if one angle is given Answered by Steve La Rocque and Penny Nom. 





The base of an isosceles triangle 
20080224 

From tahrima: find the base of an isosceles triangle whose area is 12sq.cm and the length of 1 of the equal sides is 5 cm. Answered by Stephen La Rocque. 





Two right triangles 
20080218 

From Amy: Hi, I have a problem that has me stumped.
There are two right triangles that share the same adjacent side (AB) which
is 240'. The right angles of each triangle are at the opposite ends of the
shared side.
The Opposite side (AC) of Triangle ABC is 180'
and the Hypotenuse (CB) is 300'.
The Opposite side (BD) of Triangle ABD is 100'
and the Hypotenuse (AD) is 260'.
How do I figure out where the hypotenuses intersect? Answered by Stephen La Rocque and Harley Weston. 





A flagpole and a statue 
20080209 

From Krista: A flagpole casts a ten meter (m) shadow at the same time as a six metre (m) statute beside it casts a two metre shadow. What is the height of the flagpole?? Answered by Steve La Rocque and Penny Nom. 





The distance around a building 
20080206 

From olivia: If you walk around a building that is 102,869 sq ft, how many miles is that? Answered by Penny Nom. 





Multiplying decimal numbers 
20080205 

From alwyn: Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!!
In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !! Answered by Stephen La Rocque and Penny Nom. 





Tiles on a basement floor 
20080131 

From ORIETTA: I have a basement 1000 sq ft I want to purchase tile that are 18x18inches
and they are charging 4.15 sq ft how much would it cost since I will need
less tiles to cover the area since it's not 12X12 Answered by Penny Nom. 





The interior angles of a parallelogram 
20080129 

From amber: the measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find the measure of each angle. Answered by Penny Nom. 





The interior angles of a parallelogram 
20080128 

From steffie: How do you calculate the interior angle sof a parallelogram? Answered by Penny Nom. 





Finding the area of an isosceles triangle given one angle and the inradius 
20080124 

From Saurabh: Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is? Answered by Stephen La Rocque. 





The smallest possible perimeter 
20080123 

From RS: If two points of a triangle are fixed, then how can the third point be
placed in order to get the smallest possible perimeter of the triangle. Answered by Chris Fisher and Penny Nom. 





The three angles of a triangle 
20080121 

From val: two angle in a triangle equal 120 degree. what is the measure of the third angle? Answered by Penny Nom. 





Two circles in a rectangle 
20080118 

From Alex: One side of a rectangle is 10 and the other is x.
Two circles with equal radii are inscribed in the rectangle and like a Venn Diagram, the circles overlap.
Each circle touches the top and bottom of the rectangle and the left circle touches the left side of the rectangle and the right circle touches the right side of the triangle.
The distance between the centre of each circle is 2x/3.
Find x Answered by Penny Nom. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and Harley Weston. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





Seven circles in a circle 
20080110 

From fae: what is the area of the remaining portion of a large circle with radius 12cm and the seven smaller and equal circles just fit inside? Answered by Penny Nom. 





Lining up coins visually using geometry and trigonometry 
20071231 

From Jessica: a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Answered by Stephen La Rocque. 





Calculate the two possible lengths of the third side. 
20071228 

From Lisa: An isosceles triangle has an area of 25.6 sq cm.
The two equal sides are 8.4 cm long.
Calculate the two possible lengths of the third side. Answered by Penny Nom. 





How many triangles can be formed? 
20071221 

From pankaj: Q.There is 2 lines parallel to each other. If 1st has 5 points in it and 2nd 3 points in it,how many triangles can be formed? Answered by Penny Nom. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





Finding all the angles 
20071213 

From Rajesh: An eqilateral triangle is drawn in a square with one of the side as its base and draw the lines from the other angular sides such that there are four triangles
formed inside the square which includes the equilateral triangle.I want to know all the angles of all the triangles formed inside the square. Answered by Stephen La Rocque and Penny Nom. 





What angle should he turn? 
20071201 

From Jasmine: Bob is traveling due north he then turns left 45 degrees followed by four 20 degree turns to the right
What is his new heading if he needed to turn so his heading was SSW what direction and what angle should he turn? Answered by Walter Whiteley. 





Gross sales 
20071130 

From tom: here is my question: trying to determine what gross sales were.
I have.....Gross sales  (gross X .0675) = 2,245,009 Answered by Penny Nom. 





An isosceles triangle 
20071126 

From Nancy: I needed to help my 9th grade daughter regarding a geometry problem. After a while I realized I am not getting anywhere. I saw that in 2005 someone asked the same question and you gave them a hint. Unfortunately it still did not help. Because I had figured that much!Can you kindly help me proof this problem?
PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?
I am sure it is something simple I am missing, but I just can not seem to be able to see it. Thank you much. Answered by Harley Weston. 





6 consecutive multiples of 6 
20071111 

From jeff: find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18 Answered by Penny Nom. 





Related Rates (streetlamp and shadow) 
20071109 

From Casey: A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole? Answered by Stephen La Rocque and Penny Nom. 





Meters per second to miles per hour 
20071108 

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





Two triangles 
20071108 

From Barbara: If the base of a larger triangle is 34 inches long, what is the length of side A of the smaller triangle?
(the small triangle has on top the letter a on the right side of the triangle it has the letter b, and at the bottom of the small triangle it has the number 17) Answered by Penny Nom. 





Great circles 
20071105 

From Lindsay: Does a sphere have only ONE great circle? Explain? Answered by Stephen La Rocque. 





The height of an isoceles triangle 
20071029 

From Maura: I am trying to calculate the height of an isoceles triangle but in this case AB is not equal to AC.
How do I calculate this?
Thank you,
Maura age 13 Answered by Stephen La Rocque. 





Is there a practical use for radian measure? 
20071026 

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





Two mirrors 
20071024 

From Peter: The reflecting surfaces of two intersecting flat mirrors are at an angle θ (0° < θ < 90°). For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle β = 180° – 2θ. Answered by Stephen La Rocque. 





Given a six by six square, how rectangles are there in the square? 
20071024 

From Maria: Given a six by six square, how rectangles are there in the square? Answered by Stephen La Rocque. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Working with x 
20071012 

From Robert: The question: The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle, and find the sides.
41. 36 42. 18 44. 'X'
The attachment has what she has done for 41 and 42. Need help with 44 (lots of help) Thank you in advance for your site and your help. Robert Answered by Penny Nom. 





The angles in a polygon 
20071011 

From Farzan: Prove with induction that in a polygon( that may not be convex )
with n sides, the sum of the amounts of the angles become 180(n2).
If there is any easier methods to prove the problem, please write as well. Answered by Stephen La Rocque. 





Golf pairings 
20071002 

From Mike: Regarding arranging golf players so no person plays with anyone more than once.
You have given examples for 16 and 24 players. If it can be done, i need a
solution for 20 players, 4 players per team one round per day for 5 days Answered by Victoria West. 





Three circles 
20070929 

From Kevin: 3 given circles of R80, R56 & R24 are all in contact. The 2 smaller ones are inscribed in the big one.
Find by calculation or graphically (both if possible) the radiusof a 3rd circle which will be in contact with all 3 given circles. Answered by Chris Fisher. 





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

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





Metres per minute to miles per hour 
20070920 

From Angela: If a person is traveling 150 meters per minute, what is their speed in miles per hour? Answered by Stephen La Rocque and Harley Weston. 





Least Common Multiples 
20070920 

From Aiyanna: What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer....
I Worked and worked but I Couldnt Find It..... Answered by Penny Nom and Victoria West. 





Differentiate x^(1/3) using first principles 
20070914 

From Sheila: our teacher gave us this question as a challenge and even he couldnt figure it out:
Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles? Answered by Harley Weston. 





Composite angles 
20070913 

From Gilbert: what is a composite angle? please help Answered by Stephen La Rocque. 





Similar triangles 
20070829 

From James: Question: In the triangle ABC, X is a point on AC. AX = 15 m and XC = 5 m. The angle AXB is 60 degrees and the angle ABC is 120 degrees. Find the length of BC.
I am sure to an extent that this has to do with similar triangles, but I am not certain. Answered by Harley Weston. 





Reference angles 
20070825 

From Jenny: find the reference angles for the angles given below, find the quadrants in which the angles lie
1. 0=6n/7
2. 0=3.3 Answered by Stephen La Rocque. 





Two circles C1 and C2 meet at the points A and B 
20070815 

From Jerry: Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. Point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ. Answered by Chris Fisher. 





How many complete cycles does the piston make in 30minutes? 
20070811 

From San: A piston in a large factory engine moves up and down in a cylinder.
The height, h centimetres, of the piston at t seconds is given by formula
h=120sin(pi)t+200
How many complete cycles does the piston make in 30minutes? Answered by Penny Nom. 





Area of a star in a regular pentagon with side length 10cm 
20070724 

From Chetna: A regular pentagon with side 10 cm has a star drawn within (the vertices match).
What is the area of the star? Answered by Stephen La Rocque. 





What is the bearing from the port to the ship? 
20070718 

From fhay: A ship leaves a port and sails for 4 hours on a course of 78 degrees at 18 knots. Then the ship changes its course to 168 degrees and sails for 6 hours at 16 knots. After 10 hours(a) what is the distance of the ship from a port and (b) what is the bearing from the port to the ship? Answered by Harley Weston. 





The isosceles triangle of largest area with perimeter 12cm 
20070716 

From sharul: find the dimension of isosceles triangle of largest area with perimeter 12cm Answered by Harley Weston. 





Calculating sales taxes 
20070711 

From Tonya: Hi, Im having trouble calculating GST and PST
I know that in this province, GST is 6% and PST is 7%, I have a total of $275, and GST is 0.06, and PST is 0.07, so do I add those two and multiply them by the total, $275? Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





Volume in a triangular water trough 
20070624 

From David: A water trough has sloping sides of length 500mm making it triangular in cross section, with vertical ends. The width at the top is 600mm and the length is 2.0 metres.
(i) Calculate the capacity of the trough, giving your answer accurate to the nearest litre.
(ii) Find out the depth of the water when the trough is half full. Answered by Stephen La Rocque. 





The sum of angles in a square is three hundred and sixty degrees 
20070621 

From victor: can you please send to me a formalize proof for the assertion that, the sum of angles in a square is three hundred and sixty degrees. i will be grateful to hear from you Answered by Stephen La Rocque. 





How many acres is 1.8 sq miles? 
20070619 

From Jordanne: How many acres is 1.8sq miles? Answered by Penny Nom. 





A sequence of circles 
20070611 

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





A flagpole and a telescope 
20070604 

From Fabiola: A telescope is mounted on a tripod 5 ft above the ground and 20 ft from a
flagpole. The telescope must be rotated 48° from horizontal to see the top
of the flagpole. How tall is the flagpole? Answered by Stephen La Rocque. 





A regular octagon is made up of 8 identical isosceles triangles 
20070604 

From Alex: A regular octagon is made up of 8 identical isosceles triangles. If the perimeterof each isosceles triangle and the hexagon are 58 cm and 168 com respectively, find the length of the identical sides of the triangle. Answered by Stephen La Rocque. 





Area of an isosceles triangle 
20070601 

From Josh: In a previous question answered by Sue regarding the area of a regular polygon you gave a formula for the area of an isosceles. My question is how did you get this formula? Can you please explain to mean the process that you used to get that formula?
Thanks Answered by Stephen La Rocque. 





How many sales does she need? 
20070507 

From Jimi: The new businessperson hopes to earn $50,000 per year. The profit percentage for this type of business is typically 10%. How much must sales be? Answered by Stephen La Rocque. 





Finding the area of a regular polygon 
20070504 

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





Comparing two pay scales 
20070503 

From san: Mable is offered a job selling magazine subscriptions. She has the choice of two pay scales.
Pay scale 1:
She can be paid $0.65 for each subscription she sells.
Pay scale 2:
She can be paid $0.10 for the first subscription, with the wage gong up $0.05 more for each subscription after the first.
For her first sale she would make $0.10, for her second sale she would make $0.15, for her third sale she would make $0.20,
and so on.
Please compare and analyze the two scales. Which scale is better? Answered by Penny Nom. 





Two concentric circles form an annulus 
20070502 

From A student: In the diagram below, two concentric circles form an annulus. The
vertical line is tangent to the inner circle, and forms the diameter of
a third circle.
Explain why the areas of the annulus and third circle are the same. Answered by Penny Nom. 





How can I find out how many sides there are? 
20070423 

From gn: I know the angle measurements of a convex polygon. They are congruent angles. How can I find out how many sides there are? Answered by Steve La Rocque, Penny Nom and Walter Whiteley. 





A square contains five circles with the same radius. 
20070421 

From Jamie: A square has a side length on 1 m.
The square contains five circles with the same radius.
The centre of one circle is at the centre of the square and it touches the other four circles.
Each of the other four circles touches two sides of the square and the center circle.
Find the radius. Answered by Penny Nom. 





Two concentric circles 
20070419 

From James: Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is 14 cm.The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region without using a calculator. Answered by Stephen La Rocque. 





Four semicircles are drawn inside a square 
20070419 

From James: Four semicircles are drawn inside a square, with the diameter being the length of the square.The overlapping portion of the semicircles are shaded. What fraction is shaded? Answered by Penny Nom. 





All samples of size 3 
20070419 

From Liz: Consider the population of the first seven integers: 1, 2, 3, 4, 5, 6, and 7; N=7. For this population, mean = 2 and standard deviation = 2.
a. How many samples of size three can be extracted from this population (sampling without replacement)?
b. Form the complete set of samples of size three and for each sample, compute the sample mean and median. Answered by Penny Nom. 





I have an isosceles triangle. 
20070410 

From Stephanie: I have an isosceles triangle. The two equal sides are given to me, but not the
base. The equal sides are 12. I have to find the base of the triangle. Help!! Answered by Stephen La Rocque. 





Area of circles within a circle 
20070408 

From Avaline: Imagine that there are four small circles inscribed in a bigger circle. The 4 small circles are shaded. What is the ratio of the area of the shaded region to the area of the unshaded region? Answered by Stephen La Rocque. 





3 divided by 3 to it's fifth root 
20070406 

From Annie: How do I transform the equation 3 divided by 3 to it's fifth root to simple radical form
(getting the radical out of the denominator)? Answered by Penny Nom. 





Interior and exterior angles 
20070402 

From Anuj: If in a regular polygon, each exterior angle is twice the interior angle,find the number of sides? Answered by Leeanne Boehm. 





Find the measure of all 3 angles. 
20070328 

From Brittney: The smallest angle in a triangle is onethird of the largest angle. The third angle is 10 more than the smallest one. Find the measure of all 3 angles. Answered by Stephen La Rocque. 





The height of a pole 
20070322 

From clyde: I am trying to determine the height of a pole by using 3 angles top 30.8 deg, center 17.3 deg, and bottom 5.8 deg. Can you point me in the right direction ? Answered by Stephen La Rocque. 





Three equations in three unknowns 
20070318 

From Shawna: You are told that you are working with three different numbers. When the first number is added to twice the other two numbers, the result s 64( i.e x+2y+2z= 64). When the second number is added to twice the other two numbers the result is 62 (y+2x+2z=6). Finally, when the third number is added to twice the other two numbers, the resut is 59 z+2x+2y=59) Determine the three numbers? Answered by Penny Nom. 





An isosceles Triangle 
20070315 

From Devon: The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs. Answered by Stephen La Rocque. 





How many marbles are Red and how many marbles are White? 
20070313 

From Angie: A jar has 16 marbles in it. Most of the marbles are Red and the rest are
White. Two marbles are taken out of the jar at the same time. It is
equally probable that two marbles are of the same colour as the two
marbles of different colour (that is the probability that they are both red
or both white is the same as they are different). How many marbles are Red and how many marbles are White?
Could anyone help me with the above question?
Best regards,
Angie Answered by Danny Dyer. 





Can the triangle be called both an acute triangle and an equilateral triangle? 
20070310 

From Jane: If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle? Answered by Walter Whiteley. 





circles 
20070306 

From chetna: A large circle has a radius of 10cm.Given four congruent circles tangent to one another within the large circle what is the radius of the largest circle which will fit in the middle ? Answered by Stephen La Rocque. 





Walk around a 14 acre perimeter 
20070224 

From Maria: How many times would you have to walk around a 14 acre perimeter in order to walk 1 mile? Answered by Penny Nom. 





Circles 
20070222 

From Erika: I have a research paper due on real life uses of conic sections I've looked through all your conic topics and uses of them, but and i cant seem to find real life uses for circles. What are real life uses of circles? Answered by Penny Nom. 





Similar triangles 
20070221 

From Vivienne: The lengths of the sides of a triangle are 8, 15, & 17. If the longest side of a simlar triangle is 51, what is the length of the shortest side? Answered by Stephen La Rocque and Penny Nom. 





Two concentric circles 
20070211 

From maria: i have a problem with this quadratic word problem which i am trying to solve it but couldn,t get it please help me to solve this question Two concentric circles are drawn, the radius of one being 2cm greater than that of the other. The area of the ring enclosed between the two circles is one quarter of the area of the smaller circle.Calculate the radii of the circles,correct to three significant figures. (Don,t substitute for pie) Answered by Stephen La Rocque. 





The interior angles of a parallelogram 
20070207 

From jenniffeir: Can a parallelogram have two 45 degree angles and two 75 degree angles? Answered by Haley Ess. 





Angle of elevation 
20070205 

From Zee: A 55 ft. flagpole casts a 25 ft. shadow. Calculate the angle of elevation to the sun to the nearest degree. Answered by Stephen La Rocque. 





Height of a right triangle? 
20070129 

From Engelbert: The base of the right triangle is 50 ft. At the angle (on the base of the triangle) across from the right angle is labeled portion (a triangle within a triangle), the base of this little triangle is 10 ft. and the height is 6 ft. What equation can i use to solve this? Answered by Steve La Rocque and Haley Ess. 





The height of an isosceles triangle 
20070127 

From Brendan: I need to find the height of an isosceles triangle whose angles are 52, 52 and 76 degrees. The base is 100, and the two equal sides are unknown. How would I go about this? Answered by Stephen La Rocque. 





converting square miles into square meters 
20070127 

From Susan: how do you convert square miles into square meters Answered by Stephen La Rocque. 





Upper Quartiles 
20070126 

From Jamie: I see you have a question about Q3 with even numbers but what about odd numbers? I have a problem with 19 numbers 36,45,49,53,55,56,59,61,62,65,67,70,75,81,82,86,89,94,99. Is there anyway the answer could be 81.5 because every time I do it I get 82 and my teacher tells me that is wrong. So in conclusion how do you do it? Answered by Penny Nom. 





In the shadow of a building 
20070111 

From Bill: if a building b feet cast a shadow f feet long, then, at the same time of the day, a tree t feet high will cast a shadow, how many feet long? Answered by Stephen La Rocque. 





Are all rectangles trapezoids? 
20070105 

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





Tiles arranged in rows 
20070102 

From Ann: Some tiles are arranged in rows so that the number of tiles in each row is 8 more than the number of rows. The same number of tiles can be arranged in 3 more rows than the first pattern with 16 tiles in each row. Find the total number of tiles. Answered by Stephen La Rocque. 





How do the perimeters of the two pentagons compare? 
20070102 

From Robert: If the area of one pentagon is eightyone times the area of another pentagon, how do the perimeters of the two pentagons compare? Answered by Penny Nom. 





An octagonal birdhouse 
20061230 

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





An isosceles triangle 
20061229 

From Katrina: Is there any way to calculate the height or the length of the equal sides of an isosceles triangle given only the base length and the angles? Answered by Penny Nom. 





Miles, square feet and acres 
20061218 

From Emily: How do you convert miles to square feet? I have to convert 2.86 miles to square feet and then convert 72.5 acres to square feet and add them together. I looked on your website and what does the word hence mean? Answered by Penny Nom. 





Drilling holes in a cube 
20061212 

From Liz: What is the volume of the solid remaining if a unit cube has a hole drilled thru one face to the opposite side and the hole that is drilled is a cylinder of unit diameter. Then the cube is rotated and an identical hole is drilled from an untouched face to the opposite side. Then the cube is rotated and an identical hole is drilled between the last two untouched faces. This will result in the cube vertices and the remaining volume of the cube falling into 8 parts. What is the total volume of these 8 parts. How is this volume calculated? Answered by Penny Nom. 





The sum of the angles in a triangle 
20061212 

From Becky: Why does a triangle always equal 180 degrees? We know that all the angles add up to 180 degrees but cant find a valid reason for it. Answered by Penny Nom. 





Circles and polygons 
20061211 

From Irene: Can you define a circle as a polygon with an infinite number of sides which are infinitely small? If you can, can you then define a cylinder as a prism? The sides would be rectangles or parallelograms with one length infinitely small? Answered by Chris Fisher. 





Sectors of a circle 
20061130 

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





The height of a building 
20061119 

From Sweetie: I have to figure out the measure of the water towers antenna on my schools campus using up to two items created by me and a manual. I don't know far away we are going to have to be. I need to have a fool proof way to figure out the distance to the tower. I have an idea using trigonometry but its really roughly estimated. Do you have any suggestions? 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. 





"Less than" and "less than or equal to". 
20061115 

From Ross:
7 ≤ 10 and 7 ≤ 7 are both true statements. How can 7 be equal to 10, and 7 be less than 7? The book doesn't explain WHY! Answered by Penny Nom. 





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. 





A dinner group of 16 couples 
20061102 

From Nancy: This is a realworld problem. I should know the answer but I don't. A friend is starting a dinner group of 16 couples, to be distributed across 4 houses. Each month she wants to have a different set of host houses (no problem) AND she doesn't want repeats among pairs. That is, if the Smiths and Joneses are together one month, they should not be together another month until all the combinations have been exhausted. How many valid combinations are there? Is there a formula that I can convert into a computer program? I will have to get the names from my friend and give her back the combinations as she would not be able to deal with the math formulation. Answered by Denis Hanson. 





Word problem 
20061022 

From Sabrina: Thomas bought a badminton racquet and paid for it in quarters. If Thomas had used nickels and dimes, he would have needed 20 more dimes than quarters and one more than twice as many nickels as quarters. How much much did the badminton racquet cost? Answered by Stephen La Rocque. 





An equilateral triangle has been wedged in between two circles. 
20060922 

From Kim:
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Answered by Penny Nom. 





The length of the third side of a 45 degree Isosceles triangle 
20060920 

From Rusty: what is the formula to determine the length of the third side of a 45 degree Isosceles triangle? Answered by Penny Nom. 





Parameters 
20060915 

From Chase: What is the meaning of the word "parameters" when used in reference to Algebra. Answered by Penny Nom. 





The length of 2 sides of a triangle 
20060915 

From Lonnie: I need to know how to figure the length of 2 sides of a triangle, as the following example:
The length of the bottom is 12' and the angles are 45, 45 I need to know how long the other 2 sides must be to get an angle of 90 at the top. Answered by Stephen La Rocque. 





How many marbles are there? 
20060830 

From Cathey: Four children are playing with marbles. At the end of the day, one child has four less than half the marbles. The second child has six more than onefifth the marbles. The third child has one third of what the first child has and the fourth child has one less than the third child. How many marbles are there? Answered by Stephen La Rocque. 





How do i get the height of an isosceles triangle? 
20060829 

From Luis: How do i get the height of an isosceles triangle? Answered by Penny Nom. 





How high (in feet) is the mountain? 
20060829 

From Briana: A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees.
How high (in feet) is the mountain? Answered by Stephen La Rocque. 





How many miles has he walked? 
20060819 

From Ed: If a man is mowing a 100' x 100' yard with a 20" push mower, how many miles has he walked when the yard is completely mowed? Answered by Stephen La Rocque and Penny Nom. 





Mini Golf 
20060817 

From Sarah: I am a sixth grade teacher in Minnesota. I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level. Answered by Stephen La Rocque. 





An angle in a parallelogram 
20060813 

From Sam: Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC =30 degrees find the size of angle ADE. Answered by Stephen La Rocque. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





A problem with exponents 
20060809 

From A student: (8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2 Answered by Stephen La Rocque. 





How many miles are there in 30 furlongs? 
20060722 

From Jennifer: If there are 8 furlongs in a mile, how many miles are there in 30 furlongs? Answered by Steve La Rocque and Paul Betts. 





Isoperimetric quotients 
20060707 

From Jessica: How do you work out an algebraic equation for the IQ of an isosceles triangle. Answered by Penny Nom. 





Designing a garage 
20060608 

From A builder: I'm currently designing a garage and came upon this interesting math problem. I've tried using various methods to solve it but have so far been unsuccessful. I've included a picture as its far easier to show you my question than explain it verbally. I realize it could be done by trial and error but i'm looking for a real solution. Answered by Stephen La Rocque and Penny Nom. 





A bag contains 9 red, 6 white, 3 blue, and 8 green marbles 
20060518 

From Micheael: A bag contains 9 red, 6 white, 3 blue, and 8 green marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(white, then white). Make into one reduced fraction. Answered by Paul Betts and Steve La Rocque. 





What is the measure of the interior angles of a decagon? 
20060510 

From Malissa: What is the measure of the interior angles of a decagon?
And what is the measure of each interior angle of a regular decagon? Answered by Stephen La Rocque. 





5 square miles or a 5mile square? 
20060503 

From Rosemary: I am an interpreter in our Historical Museum. From what I received, I have always told my guests that when the Connecticut Land Company sold the Western Reserve land, 5 square miles constituted a township. I was corrected yesterday by someone who said it should have been a 5mile square. What is the difference? Hope you can help. Answered by Penny Nom. 





How wide is this runway? 
20060427 

From Sam: A runway is 3.75 miles long and covers a total of 5.6 acres. What is the width of the runway? Answered by Stephen La Rocque. 





Finding the supplementary angles 
20060422 

From Kendra: Angles ABC and DBA are supplementary. If m Answered by Stephen La Rocque. 





Three circles inside a larger circle 
20060416 

From Meghan: Given three congruent circles tangent to one another (radii = 1), what is the radius of a circle circumscribed around them?
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. 





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. 





Two circles 
20060407 

From Louisa: One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle. Answered by Stephen La Rocque. 





Mastering the multiplication tables 
20060404 

From Ellie: I need a detailed study plan fro helping my son master his multiplication tables.
Grade: 3 elementary Answered by Paul Betts. 





The height of an isosceles triangle 
20060401 

From Chris: how do you work out the height of an isosceles triangle if i know the length of the base but i don't know any angles or the lengths of the sides? Answered by Penny Nom. 





Solve the equation cos x = sin 20 where x is acute. 
20060326 

From Elle: Solve the equation cos x = sin 20 where x is acute. Answered by Stephen La Rocque. 





The volume of water in a cone 
20060321 

From Ghulam: A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3. Answered by Penny Nom. 





George and his car 
20060310 

From Catrina: George's car gets 3 more miles per gallon during highway driving that it does during city driving. Recently he drove 112 miles on a highway and 150 miles in the city and used exactly 10 gallons of gas. How many miles per gallon does his car get during city driving? Answered by Stephen La Rocque. 





A hat contains between 10 and 25 marbles 
20060306 

From Kerry: A hat contains between 10 and 25 marbles. Some marbles are green, and the rest are yellow. Without looking you are to reach into the hat and pull out a marble. The probability of pulling out a green marble is 2/9. How many marbles are in the hat and explain? Answered by Stephen La Rocque and Penny Nom. 





Heights and shadows 
20060306 

From Debra: A person is 7 ft tall and his shadow is 10 ft tall. using the same info what is the shadow of a person who is 5ft tall
Answered by Stephen La Rocque. 





A bag contains 6 red marbles,9 blue marbles,5 green marbles. 
20060224 

From Jen: A bag contains 6 red marbles,9 blue marbles,5 green marbles. You withdraw one marble,replace it,and then withdraw another marble. What is the probability that you do not pick two green marbles? Answered by Stephen La Rocque. 





Outliers in a box and whisker plot 
20060219 

From A student: i need help on determining if their is an outlier...i know how to find the median and the lower quartile and the upper quartile..but i don't understand about the outliers....please tell me if their is an outlier in this problem....the numbers are...63,88,89,89,95,98,99,99,100,100 Answered by Penny Nom. 





Degree 
20060209 

From Jessica: I am a 9th grade home school student and have started doing degrees of terms in my math book. The following is some examples they give:
25a to the 4th power is a 4th degree term
67c to the 9th power is a 9th degree term
x is really x to the 1st power so it is a 1st degree term
10 is really 10x to the 0 power so it is a 0 degree term
They go on to say that every constant is a zero degree term.
My question is why isn't a constant, like 10, simply to the 1st power (making is a 1st degree term) like x. Answered by Claude Tardif. 





Make 2 rows of 4 circles with only 6 circles 
20060131 

From Sarah: Moving as many circles as you need, make 2 rows of 4 circles only having 6 circles? Answered by Chris Fisher. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and Penny Nom. 





Subdividing a polygon into triangles 
20060126 

From Adam: is there an algorithm to divide a regular polygon into N
equilateral triangles having the same area (no limit on N), or if not, an
algorithm to divide a regular polygon into N triangles having the same shape
and size? Answered by Chris Fisher. 





The third side of a triangle 
20060125 

From Bob: Is there any way to obtain the third side of a triangle when 2 sides are the same length (2.18 inches). I also need to find the angles. Answered by Penny Nom. 





Sectors and arcs 
20060125 

From Wael: How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom. 





Right angles 
20060125 

From AshLee: I was recently given a challenge in my Algebra class. My teacher wanted to know about a right angle. He said he would give five bonus points to the person that could bring in information. (I know five bonus points may not seem like a lot but in this class, they are.) I looked on this site and I found out why it was called a right triangle, but my teacher want to know where did that theory come from. I was wondering too... not just because of the bonus points. Answered by Penny Nom. 





Composite triples 
20060124 

From Laeah: question 1 Find the smallest integer n such that n+1, n+2,and n+3 are all composites.
question 2 If n = 5! +1, show that n+1, n+2, and n+3 are all composite.
question 3 Find the sequence of 1000 consecutive composite numbers. Answered by Penny Nom. 





The three angles in a triangle 
20060123 

From A student: the measure of the 2nd angle in a triangle is 4 more than the measure of the 1st angle. the measure of the 3rd angle is eight more than twice the measure of the 1st angle. find the measure of each angle. Answered by Penny Nom. 





The angles in a hexagon 
20060122 

From Linda: My problem is in relation to wood and making a six sided object from it. On my saw, there is a place to set the angle to which you wish to cut. I cannot for the life of me, figure this out. I am starting with a piece of plywood (1/4" x 6" x 18") and need to know what the angle degree would be to make each of the sides match perfectly to form a hexagon. Trial and error just is not working. Can someone help me? Answered by Penny Nom. 





Interior and external angles of a polygon 
20060117 

From Anthony:
In a regular polygon, the ratio of the interior angles to the exterior angles is 3:1.
(a) Find the measure of the interior angle.
(b) How many sides are there
Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





51 acres 
20060115 

From A landowner: i just wanna know how many miles are surrounding my 51 acres? a simple answer will do. thanks:) 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. 





Blocks in a mile in Phoenix Arizona 
20051130 

From Rita: How many blocks are there in a mile in our city of Phoenix, Az.? Answered by Penny Nom. 





The sum of the angels in a triangle 
20051125 

From Rachel: how do you prove, without knowing any of the measurements or degrees, that the three angles of a triangle equal 180? what are the steps for proving that? Answered by Penny Nom. 





Find the measure of each angle 
20051125 

From Bev: in triangle abc, angle a is four times as large as angle b, angle c measures 20 degrees less than angle b. find the measure of each angle. Answered by Penny Nom. 





I = PRT 
20051116 

From Ryan: Use the formula to find the value of the variable that is not given:
I=PRT;I=$2880, R=0.08, P=$12,000 Answered by Penny Nom. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





The height of a tower 
20051108 

From Vinita: Observers at point A and B, who Stand on level ground on opposite sides of a tower, measure the angle of elevation to the top of the tower to be 33 degrees and 49 degrees respectively. Another point C is 120 m from point B, Triangle ABC =67 degrees and BAC = 31 degrees. Find the height of the tower to the nearest metre. Answered by Penny Nom. 





Triangles with integer sides 
20051104 

From Tammy: I am trying to find another pair of integer sided isosceles triangles, not the same as the ones listed below, with equal areas.
(5,5,8)
(5,5,6) Answered by Chri Fisher. 





Can we take the derivative of independent variable 
20051018 

From Mussawar: why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why. Answered by Walter Whiteley. 





What is the sum of the measures of the angles of a decagon? 
20051015 

From Dianna: What is the sum of the measures of the angles of a decagon? Answered by Penny Nom. 





Coefficients, constants and like terms 
20051005 

From Elizabeth: In the equation 8y+6ab+73ab what are the coefficients; the like terms and constants? Answered by Penny. 





What is 2,500 X 6 trillion miles? 
20050915 

From Roly: ANDROMEDA Galaxy is 2,500 light years away. A light year is 6 trillion miles. What is 2,500 X 6 trillion miles in a mathematical number? Answered by Penny Nom. 





A 306090 triangle 
20050911 

From Gary: I have the length of only 1 side of triangle with angles of 306090 degrees. How can I find the length of the other 2 sides? Answered by Penny Nom. 





One square mile 
20050911 

From Rudy: I know that there are 27,878,400 sq ft in a square mile and that there are 640 acres in a sq mile. But how do I figure out the measurement of each acre. If I could make every acre a square what would it's measurement be? Answered by Penny Nom. 





A typical farm 
20050901 

From Pagedi: A typical farm is about 700 acres. How many square miles is this? Please show me the work so, that I will know I to perform this problem myself. Answered by Penny Nom. 





Is 360 Really the correct value? 
20050815 

From Jack: Considering the circumference of a "Perfect Circle" with a Diameter of 1 meter would be something like 3.14 meters, why do we use the number 360 to represent the number of degrees within that circumference?
Would it not make more sense to express the degrees in reference to the relationship to the diameter as related to pi?
That is, let's just say our "Perfect Circle" has a circumference of 3.14 meters, therefore, what we now consider as due east would change from 90 Degrees to 78.5 Degrees. Answered by Penny Nom. 





Framing an arched wall 
20050812 

From Mike: I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs? Answered by Penny Nom. 





How many tiles do I need? 
20050720 

From Jeannette: I am putting up backsplash tile in my kitchen and I need to know how many tiles I would need to use for about 45 square feet using 4x4 tiles. Answered by Penny Nom. 





An isosceles triangle...with 
20050423 

From Shannon: If given an isosceles triangle...with
Is there any possible way to do this, without knowing a side, if so, please
explain in detail. Answered by Chris Fisher. 





The centroid of a triangle 
20050407 

From Maria: Q3)find the coordinates of the centroid of triangle ABC
i want your help here to solve the 3rd question i got stuck. 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. 





Perfecting an ideal gambling system 
20050306 

From Gaz: I am a screenwriter, currently in the fortunate position of having the development of a Screenplay funded by the South Australian Film Corporation. The (anti)hero of this screenplay is a statistician whose life is falling apart around him, thanks in part to his obsession with perfecting an "ideal" gambling system. Answered by Andrei Volodin. 





Reverse pecentage 
20050301 

From Nathan: Question for you. If I have spent $10.00, what is the mathamatical equation to
figure out what the G.S.T (7%) was?
Also if I were to spend $80.00 on a hotel, and I would like to know how much
G.S.T (7%) and how much provincial tax (6%) I spent how would I go about this.
Answered by Penny Nom. 





Each interior angle of a particular polygon is an obtuse angle... 
20050222 

From Victoria: Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have? Answered by Walter Whiteley. 





Sales before tax 
20050209 

From Lynda: I know my total sales for the month, which includes sales tax. How do I get to the sales dollars before the sales tax? Answered by Penny Nom. 





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. 





Three tangent circles 
20050125 

From Kate: Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1? Answered by Chris Fisher. 





A 6 sided (hexagonal) pyramid 
20050122 

From Steve: im trying to make a 6 sided (hexagon) pyramid, from 6 triangles of 12mm plywood, i know all the angles to cut apart from the one one to join all 6 triangles together. Rough measurements are outer edge (A) of each triangle is 13cm's, length of other 2 sides (B&C) of triangle outside to center is 14cm's with a height of the whole thing together about 6cm's. Answered by Chris Fisher and Harley Weston. 





Arcs and chords 
20050109 

From Aniesha: A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? 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. 





Irrigation and a sector of a circle 
20041223 

From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston. 





A regular hexagon is inscribed in a circle. 
20041208 

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





A belt around two pulleys 
20041207 

From Ian: a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Answered by Penny Nom. 





An arc of a circle 
20041205 

From Ruben: i have an arc 55 inches wide, 12 inches high at the centerline of the arc. how can i determine the diameter of the circle that would correspond to the arc. Answered by Penny Nom. 





Is a square a rectangle? 
20041121 

From Carol: I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.
What is the definition that makes a rectangle a square that can be taught to the students without confusing them. Answered by Walter Whiteley. 





Interior and exterior angles of a polygon 
20041116 

From Aaron: How do you find the measure of interior and exterior angles of a regular polygon when you are given the number of sides? Answered by Walter Whiteley. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





Two gears 
20041014 

From Lindsay: "There are two gears, a small one on the left and a larger one on the right. The gear on the right makes 1 revolution. The gear on the left makes two revolutions. Suppose the gear on the right is turned through an obtuse angle. Will the gear on the left make a full turn?" Answered by Penny Nom. 





Supplementary angles 
20040923 

From Rosemary: Is the term supplementary angles only applicable to 2 angles (ie. a pair of angles) or can it be used when talking about 3 or more angles that add to make 180 degrees? Answered by Penny Nom. 





Fabricating with pipe 
20040919 

From Gil: I need to fabricate a 10 section, 4" pipe circle with an inside diameter of 40". I would like to know what angles would apply and how to find them, Answered by Penny Nom. 





A travelling salesman 
20040909 

From Liz: A salesman traveled due west from city A to city B. The distance he traveled, that is the ditance from A to B, was X miles. He returned from B to A and found that he had traveled half the distance, X/2 miles. How can that be? Answered by Chris Fisher and Penny Nom. 





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. 





Percentiles 
20040815 

From Gary: Table 1
Selected percentiles for family income in the US in 1992
1 $1,300
10 $10,200
25 $20,100
50 $36,800
75 $58,100
90 $85,000
99 $151,800
Q. The percentage of families in Table 1 with incomes below $58,100 was about? Answered by Penny Nom. 





Acres and miles 
20040811 

From A student: How many acres are in 1 mile? Answered by Penny Nom. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





Two puzzles 
20040713 

From Fred: A young man's car developed a flat tire while he was driving along a deserted street. He pulled over to the curb and did all the usual things; removed the hub cap; unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them rolled down a nearby grate. Peering through the bars of the grate the man thought he could see the lugs about 6 feet below in a shallow water puddle. He had a problem, how do you think he solved it?
It is noon, your lunch hour, but you can not go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine the sun will be shining in 36 hours? Justify your answer. Answered by Penny Nom. 





A Fibonacci triangle 
20040425 

From Marcelle: Is it possible to construct a triangle with sides that are three consecutive Fibonacci numbers? Answered by Walter Whiteley. 





The "22" puzzle and the "1089" puzzle 
20040422 

From Marcelle:
1. Choose 3 digits from 19
2. Make all the 2 digit numbers you can from these (6)
3. Add the 3 original digits and divide them into the sum from step 2.
The answer is always '22'. I just can't understand why. Can you please help.
Another one related to this is it:
1. Choose a three digit number ensuring the first and third digit are differnt by at least two.
2. Make the reverse three digit number and subtract the smaller one from the larger of these.
3. Take this answer and reverse it and add these two 3 digit numbers .
eg:
643  346 = 297
297 + 792 = 1089
it doesn't matter what numbers are used, the results are alwasy the same. eg 22 or 1089
Answered by Paul Betts. 





Circles in a hexagon 
20040411 

From Crystal: step by step can you show me how to calculate the area of the region inside the hexagon but outside the seven circles. given the radius of each circle is one inch Answered by Penny Nom. 





The sum of angles in a triangle 
20040406 

From A student: How can u prove sum of angles in a triangle equal to 180 degrees? Answered by Penny Nom. 





x^2/3  7 x^1/3 + 12 = 0 
20040405 

From Jackie: I am having trouble solving this question for x:
1.) x^2/3  7 x^1/3 + 12 = 0 Answered by Penny Nom. 





Four marbles on a box 
20040322 

From Karyn: Suppose 2 solid color marbles and 2 striped marbles are placed in a box. All are the same size. If one marble is randomly drawn from the box and replaced, then a second marble is randomly drawn, what is the probability that the marble drawn both times will be striped?
I know there is a simple formula for working this out but I can't remember how.
Answered by Penny Nom. 





Sum of the angles in a pentagon 
20040311 

From Ashish: What is the sum of all the measures of the angles of a Pentagon Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





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. 





Acres and square miles 
20040217 

From Richard:
How many acres are in .17 square miles? and How many acres are in .6 square miles?
The two areas I am requesting information about are Vatican City and San Marino, the two smallest countries in the world. If I can transfer the sq. miles into acres , I can relate the size of these countries to our school grounds and the students will better understand their sizes.
Answered by Penny Nom. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Bundles of asphalt shingles 
20040124 

From Larry: According to my study material 4:12 multiplying factor for shingles is 1.054. The question reads as follows: A building with a floor plan of 3350 sq. ft. and a roof slope of 4:12 will require _______ bundles of standard asphalt shingles. Answered by Harley Weston. 





What is the speed of the automobile? 
20040120 

From Rita: An automobile travels toward Nashville from Cookeville. It takes 33 minutes to travel from Cookeville to Manchester, which is a 36 mile distance. If the driver continues at this pace, what is the speed of the automobile? Answered by Penny Nom. 





Cubic furlongs 
20040111 

From A student: 1 mile=8 furlongs, how many cubic furlongs in a cubic mile? Answered by Penny Nom. 





Reflex angles 
20040109 

From Sonya: My daughter is searching for examples of reflex angles. We already have the hands of a clock but still need another example. Can you help us. Answered by Chris Fisher. 





The angles in a regular polygon 
20031221 

From Ernie: If i have a measure of one interior angle of a polygon, how can i find the number of sides it has? Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





An octagon shaped bed frame 
20031123 

From Trish: My son and I are making an octagon shaped bed frame. We are going nuts trying to figure out what angle to cut the boards to make an outline of an octagon. It seems that the 8 inside angles of the 8 "corners" are 120*, but what is the angle that the 2x6 wood should be cut so that they will angle together to form the outline of the octagon? Answered by Penny Nom. 





Three problems 
20031116 

From Megan: My name is Megan and I am a junior in high school. Our teacher gave us a few xtra credit questions and I need some help. Answered by Penny Nom. 





Divisibility by 7 
20031114 

From A student: how do you test a number to see if it is divisible by 7 or not? Answered by Penny Nom. 





Lines 
20031114 

From A student: What is a name that a group of lines pass through? Answered by Chris Fisher. 





Odd Pythagorean triples 
20031023 

From Kathleen: in a triple can a and b be odd numbers Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





A theorem in geometry 
20030902 

From Diego: Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT^{2} = AP x BP. Answered by Dieter Ruoff and Penny Nom. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





Cutting some wood 
20030725 

From Betty: My husband is building a six sided wood circle and would like to know the angle to cut the pieces. Answered by Penny Nom. 





pst and gst 
20030624 

From Robin: I need to find an easy solution to remembering how to calculated the gst and pst once I have the total amount. ex: my total is $154.40, I have to find the gst and then the pst. I live in bc so the taxes are 7% for gst and 7.5% for pst. Answered by Penny Nom. 





Definitions and descriptions 
20030608 

From Tammy: MY DAUGHTERS TEACHER ASKED HER TO GIVE BOTH A DESCRIPTION AND A DEFINITION OF THE FOLLOWING ... CIRCLE, SQUARE, TRIANGLE,HEXAGON...... THE LIST GOES ON. WHAT IS THE DIFFERENCE BETWEEN DEFINITION AND DESCRIPTION ? DO A CIRCLE FOR AN EXAMPLE PLEASE. Answered by Penny Nom. 





A radio controled car 
20030608 

From Robert: I have a radio controled car (scale size 1/43). This car can travel 490 ft. per minute. I would like to know how fast that is at that scale size in miles per hour (and Kilometers per hour)? Answered by Penny Nom. 





Spacing the spindles for a railing 
20030606 

From Jennifer:
Scott is a homebuilder. He builds railings in which he places spindles. Spindles ar evertical posts taht are equally spaced beneath a horizontal bar. Scott would like a mathematical model to help him determine the amount of space to put between each spindle. The railing must follow the following criteria: The spaces between each spindle must be equal except for the ones at either end. Theses spaces are smaller. They are half the width of a spindle less than the other spaces. The number of spindles needs to be minimized since spindles are costly. Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4" Generalize you model to determine the width of spaces for total railing of length L and spindle width s Answered by Penny Nom. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





Rules of exponents 
20030505 

From Carl: Hi, I am a student who would like to recall how to multiply exponents. Here is such an equation: 6.02569 X 10^{25} X 5.25^{4} =?
Also, adding exponents. Don't I just add subtract the exponents separately? Such as 5^{23} +15^{12} =?? Answered by Penny Nom. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





An equilateral triangle 
20030317 

From Shirley: An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible? Answered by Penny Nom. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





A regular polygon 
20030226 

From Melissa: The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? Answered by Penny Nom. 





A section of land 
20030225 

From Bev: How many acres in a section of land? How many square miles is in a secion of land? Answered by Penny Nom. 





The area of an isoceles triangle 
20030207 

From A student: I have to find the area of an isoceles triangle with one angle side of 30 degrees, and length of base 5. Could you please help me solve this problem? Answered by Penny Nom. 





I have three circles... 
20030130 

From Tony: I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. Answered by Penny Nom. 





Radians 
20030116 

From Erikson: I am a student in the 10th grade and attending advanced math at my high school. I was assign to do a report about the unit circle and the radian. But there seems to be no information available about the history of the radian; who first found out about them, which civilizations used it if any. Well, hopefully you'll assist me in this troubling question. Thank you for your kind consideration. Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





Miles per hour 
20021128 

From Liz: If a car has traveled 16 miles in 30 minutes, how many miles per hour did they go? Answered by Penny Nom. 





Subdividing a circle 
20021111 

From David: Say you have a cirlcle. Then you draw 2 dots on the circle. Then you connect the dots with lines. The circle is divided into 2 parts. If you do the same with 3 dots and connect each dot to each dot with a line then you get a circle with 4 parts. 4 dots with lines connecting all (6 lines) = 8 parts.... Answered by Claude Tardif. 





Three bags of marbles 
20021108 

From A student: I have 3 bags of marbles 1 bag is labeled blue; 2nd bag is labeled red; 3rd bag is labeled blue & red all the bags are mismarked your job is to take one marble from 1 bag look at it and correctly label all the bags Answered by Penny Nom. 





An isosceles triangle 
20021030 

From Stan: What two different base lengths can an isosceles triangle have with sides on both remaining at 13 inches? How do I show this? Answered by Paul Betts and Peny Nom. 





Kilometers to miles 
20021009 

From A student: how many miles are in 16 kilometers? Answered by Leeanne Boehm. 





Fractional exponents 
20020920 

From Jill: The problem is with fractional exponants: 10 1/3 mult. by 10,000 The 1/3 is an exponant of 10. Answered by Penny Nom. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





How many cubic feet are in a cubic mile? 
20020830 

From William: How many cubic feet are in a cubic mile? Answered by Penny Nom. 





A square of tiles 
20020830 

From Rosa: How do I go about finding a formula for the number of tiles I would need to add to an arbitrary square to get to the next sized square? Answered by Penny Nom. 





< and > 
20020830 

From Kelsey: What is the origin of the greater (>) than and less (<) than signs? Answered by Harley Weston. 





The circumference of a 72 
20020814 

From Linda: What is the circumference of a 72" diameter circle? Answered by Penny Nom. 





Musical Scales 
20020724 

From Terence: Given that there are 12 notes in a musical octave, what is the maximum number of musical scales possible within that octave, if each scale has a minimum of 5 notes and a maximum of 9 and we start all the scales from the same note? In case you don't know anything about music, a scale is a progression of notes where you start on a specific note and end on that same note an octave higher. There are twelve different notes between these two similar notes. Which notes you choose to play determine the sound of the scale. Anything less than five notes would not make for a very interesting scale. Anything more than nine and you would be playing almost 'every' note in the scale, not leaving much room for distinction in how you organize these notes. I assume you first have to figure out the maximum number of variations possible in a 5note scale (with 12 notes at your disposal). Then do the same for a 6note scale, then a 7note, then an 8note, and so on. Then add up the results. How to find this maximum number of variations for each scale size though is what I don't know. Answered by Leeanne Boehm. 





20 men dig 40 holes in 60 days 
20020724 

From Lindsey: 20 men dig 40 holes in 60 days. So, 10 men can dig 10 holes in how many days? Answered by Penny Nom. 





7th grade math lesson plans 
20020723 

From Peter: Where can I get samples of 7th grade math lesson plans and curriculum for the whole year? Answered by Leeanne Boehm. 





As much greater than 47 as it is less than 105 
20020723 

From Joe: To find the number in question you need to find the number exactly halfway between 47 and 105. Another way of thinking about the number that is halfway between two other numbers is as the average of the two numbers given. Answered by Leenaan Boehm. 





The base 10 multipliction table 
20020707 

From A student: These are two questions from Math for Elementary Teachers and they have me stumped. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins? The product of the diagonals of any 2x2 matrix in the base 10 multiplication table are equal. Why? Answered by Penny Nom. 





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. 





Find the angle measures 
20020518 

From Amanda: In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures. Answered by Penny Nom. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Answered by Penny Nom. 





The law of cosines and obtuse angles 
20020509 

From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom. 





Designing a ballot 
20020426 

From Kelley: I want to design a ballot for four elections. Actually all the candidate races are on 1 ballot. I need to know how many different ballot styles would be needed for all of the candidates to be in each rotation an equal number of times. For example:  A,B,C & D are running for mayor
 E,F,G & H are running for congress
 I,J & K are running for senate
 L,M & N are running for governor
They are all on the same ballot. But in each race their name (for instance A) has to be in the #1 rotation, #2 rotation, #3 rotation, and #4 rotation for his race on this ballot an equal number of times as B,C and D. The same goes for the other candidates for their perspective races. How many total ballot styles will there be? Answered by Penny Nom. 





Two triangles 
20020403 

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





What fraction of the world's motor vehicles are built in Canada? 
20020320 

From A student: About 1/4 of the world's motor vehicles is built in Canada or the United States. About 1/5 of the world's motor vehicles are built in the United States. What fraction of the world's motor vehicles are built in Canada? Answered by Claude Tardif. 





The isosceles triangle of smallest area 
20020308 

From Lettie: can you find the isosceles triangle of smallest area that circumscribes a circle of radius of one? Answered by Walter Whiteley. 





Factor completely 
20020307 

From Taylor: I'm supposed to completely factor this but I don't know what to do with all the variables. a^{3}b^{5}  a^{2}b^{5}  12ab^{5}. Does it have anything to do with b^{5} being a common factor or am I completely off? Answered by Penny Nom. 





The median with ties 
20020227 

From Marcel: What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median. Answered by Harley Wston. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





36 is 20% less than _____? 
20020213 

From Lori: 36 is 20% less than _____? Answered by Walter Whiteley. 





Miles and kilometers 
20020122 

From Dennis: I'm in the middle of purchasng a vehicle and it was built in Canada. Therefore it is in kilometers and not in miles. I forgot how many kilometers are in a mile. It registers as 183,049 kilometers. Answered by Penny Nom and Judi McDonald. 





Nickles, dimes, quarters and fifty cent pieces 
20020108 

From A parent: The total for all coins counted is $4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there? Answered by Penny Nom. 





Piles of coins 
20011205 

From A student: Sharon has less than 20 coins. When she puts them in piles of 5, she has 1 left over. When she put them in piles of 3, she also has 1 left over. How many coins does Sharon have? Answered by Penny Nom. 





Box and Whisker plots 
20011119 

From Rod: In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect. My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not? Answered by Penny Nom. 





Rules of exponents 
20011014 

From Carissa: how do you work this out? Investigate the relationship between a,b,c and d if 2^{a}*2^{b}=4^{c}/4^{d}? Answered by Leeanne Boehm. 





Acres 
20011010 

From Allison: how many feet are there in an acre? Answered by Chris Fisher. 





Pythagoras & magic squares 
20011009 

From John: My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 345 triangle, and the fact that his teacher told him there was also a 51213 triangle, i.e. both rightangled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on. I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7order square would also generate a rightangled triangle for him. He found that 72425, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...  Is there a rightangled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and
 Is each triangle unique (or, as he put it, can you only have one wholenumbersided rightangled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. 





A bag with 3 red marbles and 
20010927 

From Mike: In a bag, there are 3 red marbles and "B" blue marbles. Two marbles are randomly selected from the bag without replacement. The probability that the two marbles are the same color is 0.5. Calculate the sum of all possible values of B. Answered by Claude Tardif. 





Bicycles and tricycles 
20010926 

From Sally: A bicycle shop has 5 bicycles and tricycles to repair. They have 12 wheels. What strategy would you use to determine how many bicycles and tricycles need to be repaired? Answered by Claude Tardif, Diane Hanson and Penny Nom. 





A polygon 
20010911 

From Sueling: what is the smallest polygon. what is a polygon. Answered by Penny Nom. 





Similar triangles 
20010908 

From Dave: I am standing on the bank of a river ( whose banks are parallel here) directly opposite a boathouse, B, on the opposite bank. I walk along the bank of the river past a signpost, S, until I reach a point C distant 60 metres from where I started walking. I then walk away from the bank, at right angles to the bank, until I reach a shady tree at D. Attached to teh tree is a sign stating that this spot is 45 metres from the signpost. C is 36 metres beyond S and B and S are in line from D. (a) How far did I walk away from the bank of the river?? (b) Calculate the width of the river? Answered by Penny Nom. 





Bisecting angles 
20010827 

From Monica: Ray QS is the bisector for angle PQR. Find the measure of angle PQS and PQR if the measure of angle SQR is 52 degrees. Answered by Penny Nom. 





Standard angles 
20010805 

From Nagaraj: Why 0^{o} , 30^{o} , 45^{o} , 60^{o} ,and 90^{o} are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles? Answered by Chris Fisher. 





Radian measure 
20010726 

From Amy: i have to find out what is meant by the radian measure of an angle and compare it to the measure of an angle in degrees. Answered by Harley Weston. 





Rhombus 
20010716 

From William: Calculate the internal angles of a rhombus given measurments of all four sides only. Answered by Walter Whiteley. 





Three chords 
20010628 

From Paul: AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. Answered by Harley Weston. 





Three tangents to a circle 
20010627 

From Stephanie: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT. Answered by Chris Fisher. 





An inequality involving triangles 
20010612 

From Sandra: The triangle inequality guarantees that the sum of the lengths of two sides of a triangle is greater than the length of the third. As a consequence, if x and y are legs of a right triangle, with x less than or equal to y, and z the hypotenuse, then x + y is greater than z, so x is greater than z  y. Under what circumstances will x is greater than 2(z  y) be true? Answered by Chris Fisher and Penny Nom. 





Geometry problems involving triangles 
20010607 

From Sandi: Find the radius of the largest circle contained in a right triangle whose legs are 8 and 15 and hypotenuse is 17. If the right triangle has legs a and b and hypotenuse c, find an expression for the radius of the circle. Answered by Penny Nom. 





The angles in a triangle 
20010511 

From Nikki: Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths. 26, 35, 40 Answered by Penny Nom. 





Circles, ellipses, parabolas and hyperbolas 
20010509 

From Colleen: How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Answered by Pnny Nom. 





How many acres are in a square mile? 
20010504 

From Terri: How many acres are in a square mile? Answered by Judi McDonald. 





Triangles and fractions 
20010427 

From Constance: My name is Constance and I am thirteen years old (I am a student). The question that I am queering about I don't understand why you do ONE HALF x the base x the width WHEN YOU WANT TO FIND the area of a triangle? My second question is if you multiply one half and 10 together why does it come out as 5? Answered by Penny Nom. 





Isoscles and scalene 
20010417 

From Autumn: explain where the term isoscles and scalene came from? Answered by Chris Fisher. 





Squares on a chess board 
20010411 

From Tom: It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures. How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures. Answered by Penny Nom. 





The bond angles of a tetrahedral polygon 
20010314 

From Nishi: how do i prove (a simply as possible) why the bond angles of a tetrahedral polygon are 109.5 degrees? *i already have two explanations that i don't understand. one is about "theory of dot products" and "vectors" and a hooklike symbol w/ a cosine, and the other has an incomprhensible diagram w/ difficult notation PLEASE BE SIMPLE! thanks sooo much Answered by Harley Weston. 





Powers 
20010304 

From A student: Hey, can you show me how you do .. (2xy)to the 3rd power (x) to the 2nd power? Answered by Penny Nom. 





How tall is the tree? 
20010302 

From Ronda: a tree's shadow is 42 ft. long. There is a stop sign that is right next to it and it is 18 ft. tall and it's shadow is 12 ft. long. How tall is the tree? Answered by Penny Nom. 





Solve for two variables 
20010225 

From A student: How do I solve for %1 and %2 in the following formula when T1, T2 and T3 are known? %1 and %2 are ratios of the same element, therefore %1 + %2 = 100%
(%1 x T1) + (%2 x T2) = T3 Answered by Penny Nom. 





Mr. Moser's roof 
20010221 

From Michelle: Mr. Moser is planning to replace the roof of his home. He needs to order a pack of shingles. Each pack covers 100 sq. ft. of roof. Without a ladder, Mr. Moser can not climb to the roof to measure it. Instead, he measures his attic and finds it to be 40 ft. long, 24 ft. wide, and 5 ft. high at the peak of the roof which is in the center of the house. Although the roof is even with the side walls, he estimates the roof line continues 1.5 ft. beyond the front and back walls. How many full packs of shingles should Mr. Moser order to cover his roof? Answered by Penny Nom. 





Angles in a polygon 
20010217 

From Joan: How many sides does a polygon have if its smallest interior angle is 120 degrees and each sucessive angle is 5 degrees greater than the predecessor? Answered by Penny Nom. 





Bicycles and phone calls 
20010208 

From Sarah:
 A bicycle has a diameter of 66 centimeters. How many times must the tire rotate to travel 1 kilometer?explain answer.
 Becky want to make a long distance call to her friend Sarah from a pay telephone.She has $5.00 in change.The call costs $0.90 for the first three minutes and $0.24 for each additional minute.How long can Becky talk to Sarah?
Answered by Leeanne Boehm. 





Conversions 
20010124 

From Tanya: I have 2 questions  covert 628 kilometers to miles.(round off your answer to two decimal places.)
 a new clerk in your office is to earn $200 per week. If she works 30.5 hours each week, what is her hourly rate? (round off your answer to the nearest hundreth, that is, to the nearest cent.)
Answered by Penny Nom. 





The sum of the angles in a polygon 
20010123 

From A student: What is the sum of the measures (interior angles) in an octagon ... heptagon ... decagon. Answered by Penny Nom. 





Some complex problems 
20010115 

From Nick: I am having enormous difficulty with one question in my maths homework. The question is shown below. If anybody out there can find the answers and show the workings and help me to understand. Answered by Harley Weston. 





Is n^2  2 a multiple of n  4? 
20010110 

From John: Find all positive integers n so that n^{2}  2 is a multiple of n  4. Answered by Sukanta Pati. 





A quartercircle and two semicircles 
20001231 

From Christopher: Inside the quartercircle are two semicircles with the same radius, (r). Which has a greater area, G or L? Answered by Penny Nom. 





A lampost and its shadow 
20001224 

From Laura: A lamppost line EC casts a shadow line AC. A 30 cm ruler line DB has been moved from A so that it's shadow falls just within the shadow of the lamppost.  Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?
 Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?
Answered by Penny Nom. 





Is this a right triangle? 
20001208 

From Alicia: How would you setup and answer a problem like these one? Triangle ABC has vertices A(2,2), B(1,2), and C (1,2). Use slopes to determine if the triangle is a right triangle. Answered by Penny Nom. 





< and > Which one is which? 
20001206 

From Alice: This grandmother forgot and wants to know the correct for greater and the one for lesser..... the two are < and > Which one is which? Answered by Penny Nom. 





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. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





An integration problem 
20001130 

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





What are adjacent angles that equal 360 called? 
20001122 

From David: I know that supplementary angles add to 180 degrees and that commplementary angles add up to be 90 degrees, but what are adjacent angles that equal 360 degrees called? Answered by Chris Fisher. 





Length of a shadow 
20001101 

From Jessy: A man who is six feet tall is walking away from a street light that is fifteen feet tall. How long is the man's shadow when he is ten feet away from the light? Answered by Penny Nom. 





The ages of three daughters 
20001025 

From Andrea: An encyclopedia saleman call at a home. The woman who answers the door says she will buy something from him if he can give the ages of her three children. The first clue, she says, is the three ages multiplied together equal 36. he responds that he needs more infomration, so she says that the threee ages add up to the number of the bus that passed by (the prof did not give us this number) He thinks for a while and says he needs one more clue. So she says, my youngest child has red hair, and he is able to answer and make the sale. what are the ages of the three children? (hint: the salesman needed all three clues to get the answer). Answered by Penny Nom. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





Larger and smaller 
20001010 

From Nicole: which one of these arrows < , > points to the greater number? which arrows points to the smaller number. Answered by Penny Nom. 





Trigonometry 
20000902 

From david: determine the sum of the angles A,B where 0 <= A , B <= 180 (degrees) sinA + sinB = sqr(3/2) , cosA + cosB = sqr(1/2) Answered by Chris Fisher. 





Rectangles and algebra 
20000613 

From Kirstin: A rectangle's length is 4 more than twice its width. The area of the rectangle is 336m squared. What is its length? Answered by Paul Betts and Penny Nom. 





Projecting a line segment onto a plane 
20000608 

From Monica: What is the measure of the angle determined by a 14 inch segment and its projection into a plane if the length,in inches, of the projection into the plane is 7 inches? Answered by Penny Nom. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. Answered by Harley Weston. 





Adjacent Angles 
20000521 

From Katherine Keys: Can a straight angle be an adjacent angle to another angle? Answered by Chris Fisher. 





Supplementary angles 
20000509 

From Suzanne: We know that: Supplementary angles are two angles whose sum equals 180 degrees and complementary angles are two angles whose sum equals 90 degrees. Are supplementary and complementary angles necessarily adjacent? or can they be nonadjacent? Answered by Chris Fisher. 





sin(7pi/12) 
20000504 

From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts. 





Monica's geometry problem 
20000427 

From Monica: Given: ABCD is a square; AX is perpendicular to BY Prove: Angle 1 is congruent to Angle 3 Answered by Chris Fisher. 





The side length ratios of some triangles 
20000404 

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





Why a Right angle? 
20000403 

From Joseph Mizerek: I was wondering why a 90 degree angle is called a Right angle. I mean why isn't called a left angle. Answered by Haragauri Gupta. 





Reflex angles 
20000322 

From D. Reed: What is the name of an angle that exceeds 180 degrees? Answered by Penny Nom. 





Grazing area for a goat 
20000310 

From Amy: A goat is tied in the middle of a side of a square building whose sides are 2 yards long. The rope is 4 yards long. What is the grazing area for the goat? Answered by Harley Weston. 





Pythagorean triples 
20000301 

From Bob Ross: Could you please tell me what pythagoria triad is.I am a year 10 student. Answered by Chris Fisher. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Building a pyramid 
20000226 

From Francis X. Hines Jr.: I am presently trying to build a pyramid. I can understand that the base has 90 degree angles on the first plane which is the outline of the square that makes up the floor. As close as I can figure the slope of each wall face is 35 degrees or 35.7 to be exact if I am correct by using 360 as the total of the three interior angles.Now , I run into a compound angle where the corners meet what would be the angle created by the two 35 degree angles that would allow for the 90 degree edge to continue. Because I'm working in three dimensions I also need to be sure that my math would be correct when I substract 35 from 90 to aquire the angle of the narrow edge as to allow for a 90 degree surface to be present ..to allow for another level to be added with only the base line being shortened. I hope you can understand what it is that I'm asking assistance with.I would greatly appericate your help. Answered by Chris Fisher. 





Weighing bales 
20000215 

From Thinh Than: You have 5 bales of hay. and they were weighed but they didn't weigh them individually, they were weighed in pairs. The pairs were 1&2, 1&3, 1&4, 1&5, 2&3, 2&4, 2&5, and so on. The weights of the pairs were 80,82,83,84,85,86,87,88,90, and 91. Can you tell me how much the bales weigh individually. Answered by Claude Tardif. 





Tennis doubles 
20000204 

From Brittany Allinson: Cheri, Beth and Jacinta are daughters of Mr. Sullivan, Mr. Marchand, and Mr. Benoit. Four of these people are playing tennis doubles. Mr. Benoit's daughter and Mr. Sullivan are partners. Cheri's father and Mr. Marchand's daughter are also partners. There aren't any father/daughter combinations. Who is Cheri's father? Answered by Penny Nom. 





Angles 
20000106 

From Rayna: I am doing a presentation report on angles which has to be fun and entertaining as well as educational. I am having problems locating resources on angles that give me ideas of fun entertaining projects. My lecture is to be about 20 minutes long infront of a class of 11th and 12th graders. Please Help if you can. Answered by Claude Tardif and Walter Whiteley. 





Two candles 
19991124 

From Skip Simpson: You have two candles the same length. They are lit at the same time. One burns down in 4 hours; the other in 5 hours. How long does it take before one candle is three times the length of the other candle? Answered by Walter Whiteley. 





The number of city blocks in a country mile 
19991124 

From Gloria Hearst: For years my family has had an on going debate on the number of city blocks in a country mile. We vary from a minmum 8 blocks per mile to a maximum of 12 blocks per mile. Answered by Nadine Griffiths and Penny Nom. 





Area of a quadrilateral 
19991119 

From Zane Cram: I need the formula to calculate the area of an irregular sided rectangle. Each side has a different measurement or length. Answered by Walter Whiteley. 





Trolls and Gargoyles 
19991102 

From TexGrimm: How can you seat 6 monsters  3 Trolls and 3 Gargoyles at a circular table if the trolls look alike and the gargoyles look alike? Does your formula work for 9 monsters  4 trolls and 5 gargoyles? Answered by Penny Nom. 





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

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





Isosceles triangles 
19991012 

From Amber: In defining the types of triangles, our class was stumped by a question asked by one of the student. Maybe you could help. The definition of an equilateral triangle is a triangle with three congruent sides. The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle? Answered by Penny Nom, Walter Whiteley and Chris Fisher. 





Two 12sided polygons 
19990925 

From Kelly Boulton: Two 12sided polygons are similar. A side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon. wHAT IS the ratio of the area of the larger polygon to the area of the smaller polygon. Answered by Walter Whiteley. 





Bales of hay 
19990913 

From Ivy: You are given 5 bales of hay. Two bales are weighed at a time, which equal the following weights: 110, 112, 113,114,115,116,117,118,120,121. What does each individual bale weigh? Answered by Harley Weston. 





Rolling Circles 
19990912 

From Craig Ellis: We have a circle of radius 3. inside the circle and tangent to the circle of radius 3 at one point is a circleof radius 1. The question is if we could roll the smaller circle around the inside of the larger circle how many revolutions would it take to get around to where we started. Answered by Chris Fisher and Walter Whiteley. 





Degrees and triangles 
19990909 

From Sandra Mills: Are there any triangles which are not 180 degrees? I am also in need of information on the history of degree measure for an angle. Answered by Walter Whiteley. 





The number of acres in a square mile 
19990709 

From Rita Murphy: What is the # of acres in square mile Answered by Harley Weston. 





Circles, cirmcuference and area 
19990516 

From Stephen Ehrler: I would appreciate if you could please tell me if what I discovered here is something or my ignorance? I noticed that a circle with r radii has the folling characteristic. r = [2 * ( pi * r^{2} / pi * 2r)] The equation states that the ratio of a circles area over its circumfrence = 1/2 that of the circles radii. It works every time. Did you know this ? Is it some kind of therom and can it be used for any thing? I thought this was intresting and would appreciate any input you may have. Thank you. Answered by Chris Fisher. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Circles 
19990421 

From Alex Elkins: How do you find the circumference of a circle if you only know the radius and the square feet or inches of the circle if the radius is 18 inches, If done in inches do you multiply by 12 to get the square feet? Answered by Jack Lesage and Harley Weston. 





Finding a rule for a sequence 
19990217 

From Lindsey Masters: I'm doing a maths investigation and i have a sequence which goes: 13,16,25,32,45,56,73. Our teacher told us we have to find a rule by looking at the differences of the terms until we find a constant. The first differences are: 3,9,7,13,11,17. The differences of these are: ...... Please could you tell me how to work it out so that I could work out the rules of similar sequences. Answered by Penny Nom. 





Angles in Polygons 
19990121 

From Jen:
 How do u find the interior angles of a pentagon when you are given 4 of the angles and you need to find the fifth?
 If you are given the measure of each exterior angle of a regular polygon, how do you figure out how many sides the polygon has?
 i need all information on polygons and how to find their angles!!!
Answered by Jack LeSage. 





Geometry patterns lesson plans 
19981231 

From Vicki: hi,,, my name is Vicki and I am a new 5th grade teacher.... Anyway, I'm supposed to come up with a lesson plan to  Explore patterns that result from cominations of "reflections, rotations, and translations of geometric figures.
The plan is to include:  writing/metacognition, assessment strategies, interdisciplanary connections, supplemental materials, or textbook, and Bloom's taxonomy level.
Any help you could give would be greatly appreciated. Thanks Answered by Jack LeSage. 





Divisibility by 11 
19981028 

From Pat Duggleby: I am an upgrading instructor at a dropin program in Regina. One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows:  If the difference between the sum of the oddnumbered digits and the sum of the evennumbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.  . . . Answered by Penny Nom. 





Complementary and Supplementary Angles 
19981021 

From Christina Saunders: I am in 9th grade and my math teacher wanted us to find out why complimentary angles are called complimentary and why supplimentary angles are called supplimentary. I have looked everywhere and asked numerous people, but I have yet to find an answer. My math teacher said it had something to do with trigonometry. Do you have an answer for me? Answered by Chris Fisher and Penny Nom. 





A Kite 
19981007 

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





Probability 
19980917 

From Chris: Six marbles are placed in one of three boxes. What is the probability that each box contains two marbles? What is the formula used? Answered by Penny Nom and Chris Fisher. 





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. 





The origin of angles 
19980224 

From Marc Poulin: I'm currently teaching angles to students in grade 10 and I've been asked what's the origin of the terms degrees, radians and gradians. I know that the radians come from the sexagesimal numerical system of the Babylonians but my kids wanted to know dates and persons who would have brought these terms first. Answered by Harley Weston. 





(50^20)(20^50) 
19980224 

From fion: 50 power of 20 X 20 power of 50? How many zero can be found in the answer and why? Answered by Penny Nom. 





The sum of the angles of a triangle is 180 degrees 
19980219 

From Quin Liu: How do you prove that the sum of the angles of a triangle is 180 degrees? Is there a proof? what is it? Answered by Chris Fisher. 





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. 





Trigonometric functions 
19971221 

From Calvin Cheng: My name is Calvin and I have a year 12 question for you to help me with. From a point S, the angle of elevation of the top of a tower due north of it is 20 degrees. From R, due east of the tower, the angle of elevation is 18 degrees. S and R are 100m apart. Find the height of the tower. Answered by Harley Weston. 





Pythagorean Triples. 
19971204 

From Shameq Sayeed: I've got a couple of problems which I hope you'll be able to solve for me. I'm investigating pythagorean triples, and I have found a trend for the triples themselves, and thus have been able to form a general equation, i.e. a=2x+1, b=2x^2+2x, and c=b+1. Now, I sure this equation works, because I've tried it out and have come up with triples that adhere to a^2 + b^2 = c^2. But I was wondering WHY c=b+1. Is it possible to have c=b+2, and if not why not? THAT is the first problem. Answered by Chris Fisher. 





Shimin's Geometry Problem 
19971202 

From Ong Shimin: ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Answered by Chris Fisher. 





A geometry problem 
19971120 

From Herman: When produced, two equal chords AB and CD of a circle meet at P in an angle of 24 degrees. If H is the midpoint of AB and K is the midpoint of CD, calculate the size of angle HKD. Answered by Penny Nom. 





Rowing on the Charles River. 
19970917 

From Fawwaz Muraisi: On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.How fast is the river flowing? Answered by Harley Weston. 





The Length of a Chord. 
19970726 

From Nathan Arthur: Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Answered by Chris Fisher. 





Area Between Two Sectors 
19970302 

From Rebecca Henry: Points A,B,C,D,E,F are equally spaced on a unit circle. Arc CGE has a center A. Find the number of square units of area in the shaded region. Answered by Walter Whiteley. 





Some Circle Questions. 
19970225 

From Staci Vawser: A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Answered by Harley Weston. 





Triangles, The Pythagorean Theorem and Pizzas. 
19970223 

From Sherryle Mathis: I am a graduating senior presently teaching geometry as part of my student teaching. I will do my CUP on Right Triangles and Pythagorean theorem. I am looking for a fun activity as part of my unit plan. Answered by Walter Whiteley. 





Mathematics of Schedules 
19970116 

From Byron Krull: I was asked if there was a mathematical method to work with schedules. The problem is this. There are 24 teams playing weekly on 4 sheets at 3 different times of the day as follows... Answered by Denis Hanson. 





Sides in a Regular Polygon 
19961206 

From Rick Moss: If you are given the measure of each interior angle (162 degrees) of a regular polygon. How many sides does the polygon have? Answered by Penny Nom. 





Height of a Hotel 
19961107 

From Irene: "Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel? Answered by Penny Nom. 





Why is a circle divided into 360 degrees? 
19960930 

From Kurtis Kredo: I was recently wondering why a circle has been divided in to 360 degrees. When I asked my physics teacher he could not think of an answer. His guess is that it probably has to do with people long ago using the base 6 number system. I have a small inkling that it has to do with easy conversion or usage with radians or grads. Answered by Chris Fisher. 





calcul de durée 
20120903 

From laila: un bus démarre de paris à 8h 45mn s'il fait 42h 20 mn de trajet entre paris et la ville suivante à quelle heure il arrivera à la ville suivante.
est ce qu'il ya un shema pour calculer ou comment procéder. je sais qu'il faut additionner 8h 45 mn à 42h 20mn, mais comment on trouve le résultat rapidement. merci Answered by Claude Tardif. 





Les dérivées partielles 
20120516 

From Haddouche: Bonjour,
Je vous demande de bien vouloir m'éclaircir comment on calcule les dérivées partielles généralement étudiées dans les modèles de la concurrence fiscale à titre d'exemple celui de Wildasin ""NASH EQUILIBRIA IN MODELS OF TAX COMPETITION "", dont j'ai essayé toutes les méthodes et aucune d'elle n'est arrivée à trouver le résultat des dérivées de ce dérnier papier, à cet effet, je vous serais reconnaissant de m'éclaicir la méthode afin de résoudre ce problème qui pour moi un vrai mistère à percer.
Je vous remercie infiniment à l'avance.
Et comptant sur votre compréhension, mes salutations les meilleures.
HA Answered by Claude Tardif. 





Les calcules avec les heures 
20110909 

From johanna: bonjour
je voudrais pouvoir expliquer a mon fils ces calcules avec les heures, mais franchement je n'y comprend rien, pouvez vous m'aider.
voilà le premier calcul:
1h35min29s  46min37s
deuxiéme exercice:
calculer la durée d'une emission télévisé qui débute à 20h40min et se termine à 22h17min.
troisiéme exercie:
je suis partie en vacances le 25 juillet. Mes vacances ont durées 2 semaines. Quel jours suisje revenu?
quatroéme exercice: je pars de stpierre, je prend le bus.
je veut arrivé à stdenis à 10h et demi.
je sais que la durée du trajet stpierre /stdenis est de 1h50min.
a quel heure doisje partir de stpierre. Answered by Claude Tardif. 





Quel est le 6e nombre dans la serie suivante 
20100813 

From jeff: Quel est le 6e nombre dans la serie suivante: 1,2,6,42,1806,... Answered by Stephen La Rocque and Claude Tardif. 





Un bénéfice de 5% 
20080311 

From mahiques: Un propriétaire decide de vendre deux parcelles de terrains pour un montant total de 141750 F. Il fait un bénéfice de 15% sur la première et une perte de 10% sur la deuxième. L'ensemble de la transaction lui a rapporté un bénéfice de 5%.combien atil vendu chacune des parcelles ? Answered by PierreLouis Gagnon. 





800 poules pondent 800 oeufs en 8 jours 
20071217 

From LINDA: 800 POULES EN 8 JOURS PONDENT 800 OEUFS, COMBIEN 400 POULES
VONTELLES PONDENT D'OEUFS EN 4 JOURS? Answered by Claude Tardif. 





Problème de géométrie 
20050429 

From Christian: C un cercle de centre I et de rayon 3 cm.
SORT est un carré inscrit dans le cercle C
M est un point quelconque de C Calculer la somme des carrés des distances de M aux sommets du carré (MS2 + MO2 +MR2 + MT2)
Cette somme dépendelle de la position de M sur le cercle ? Answered by Claude Tardif. 





6 poules pondent 6 oeufs en 6 jours 
20050301 

From Nathalie: SACHANT QUE 6 POULES PONDENT 6 OEUFS EN 6 JOURS, COMBIEN 12 POULES PONDENT D'OEUFS EN 12 JOURS? Answered by Claude Tardif. 





les formules d'aire et de volume de les solides 
20030201 

From Annie: Je cherche le nom des mathématiciens qui ont découvert les différentes formules d'aire et de volume de tous les solides ( boule, cube, les prismes, cylindre, cône, pyramide, polyèdres réguliers). Je cherche aussi à trouver comment ils ont démontré l'exactitude de ces formules. L'important, c'est de connaître le nom des mathématiciens qui ont découvert ces formules. Answered by Claude Tardif. 





Ses points de discontinuités est les irrationnelles 
20020108 

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





Les tableaux de conversions 
20010503 

From JeanJacques: Sur quel site est il possible de trouver tous les tableaux de conversions de mètres,kg,litre,m2,m3 Quelle est la relation entre les m^{3} et les litres 1 m^{3} = 1000 litres = 1000 kg? Answered by Claude Tardif. 





Un polyedre ayant comme face 20 triangles 
20000802 

From Sonia: J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux. Answered by Chris Fisher. 





Maths 
19990111 

From Stephane Roissard: Soit ABC un triangle dans lequel les trois médianes sont de meme longueur. Montrer que ce triangle est quilatéral. Answered by Jack LeSage. 





Le sang humain 
19981006 

From Golden: Le sang humain contient approximativement 2,5 x globules rouges. Chaque globule a un rayon de 0,004 mm. Si on le place ces globules bout a bout, quelle est la longeur de la chaine en millimetres? En kilometres? Compare toi avec la circonference de la terre (24 000 km) (Travail avec exposants) Answered by Claude Tradif. 





les fractions 
19980224 

From Colette Huguenin: Bonjour je révise mes math de tout les secondaire et le livre louer la bibliothèque n'est pas entier voici le genre de problêmes qui me bloque (5 4/5+1/2)divisé 1/3 je sais que je dois commencer par la parenthèse mais...je fait quoi comme opération avec le 5? doisje le multiplier ou l'additionner ou.......????? si je pouvais seulement avoir la base des fractions je redébloquerais surement Answered by Diane Hanson. 





Question de trigonométrie 
19971211 

From JeanPierre Quesnel: Je suis dans le désert et je parcours 1000 km à partir du point "A" jusqu'au point "B". Si je reviens au point "A" et fais une rotation de 8 degrés en faisant un autre 1000 km, quelle sera la distance en km entre les points "B" et "C". Answered by Diane Hanson et Penny Nom. 

