







Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





A metal gate 
20160206 

From Carl: I am a welder and I build gates. I have to put holes in a rail and then bend the rail
in a curve. The problem is that the holes in the curved rail must line up with holes
in the other straight rails. How do I calculate where to put the holes in the rail
before I bend it? I will send a drawing if necessary. Answered by Harley Weston. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





A circle through 3 points 
20141204 

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





Three collinear points 
20140828 

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





A circle through three points 
20140222 

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





Intersection points and diagonals 
20130911 

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





Percent and percentage point 
20130719 

From Kenneth: Hello:
Does 0.01 represent both one percentage point and one percent in decimal form?
What is, for example, 2/100 of one percentage point, and what is 2/100 of one percent?
Are the answers the same.
I thank you for your assistance. Answered by Penny Nom. 





Points of intersection 
20130502 

From Bianca: Find the sets of values of k for which the line y=kx4 intersects the curve y=x^22x at two distinct points. Answered by Penny Nom. 





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

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





Points per quarter 
20120514 

From debbie: A basketball team scores 216 points in 8 quarters . Find the teams point per quarters rate Answered by Penny Nom. 





Simplify the expression 
20120212 

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





Two line segments in the plane 
20110815 

From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.
Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points. Answered by Chris Fisher. 





Points on a graph 
20110215 

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





3 equidistant points on a circle 
20100621 

From Brian: We have to line up 3 pins on a lifting bridle to be 120 degrees apart from each other to connect into a lifting assembly.
I know pi*d. I know straight lines connecting these points to each other will result in an equilateral triangle.
How does one find these points without using a protractor? There must be a formula (formulae) to work this out mathematically.
r = 10.5 inches
pi*d = 65.9736
3 segments( arcs) = 21.9912 which is the distance along the circumference that the points are from each other. Answered by Penny Nom. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





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. 





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. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20080722 

From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom. 





A point on a graph 
20080708 

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





Points on a graph 
20080703 

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





Inflection points 
20080125 

From Armando: Hi, Im trying to write a program that takes an equation ( f(x) = 0 ) and returns a list of the inflexion points in a given interval.
there must be (I think) a mathematical method or algorithm to do this, probably involving the (second) derivate of the function.
However I have not found such a method yet. Any help on this will be much appreciated. Answered by Stephen La Rocque and Harley Weston. 





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. 





Local maxima, minima and inflection points 
20071113 

From Russell: let f(x) = x^3  3a^2^ x +2a^4 with a parameter a > 1.
Find the coordinates of local minimum and local maximum
Find the coordinates of the inflection points Answered by Harley Weston. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Points that are 15 units from the origin 
20070920 

From Paula: Find the coordinates of any point(s) 15 units away from the origin with an
xcoordinate of 9.
I was given the answer: (9,12) and (9,12), but I do not understand how these numbers
were calculated. Thank you for your help! Answered by Stephen La Rocque. 





Points in a plane 
20070601 

From Gabrielle: In general how many planes are there which contain two given points, three given points, and four given points? Answered by Steve La Rocque and Walter Whiteley. 





A set of points in space 
20070404 

From Lenny: What is a set of points in space the same given distance from its center point called? Answered by Stephen La Rocque. 





Maximizing profit 
20070123 

From Denise: Total Profit= Total RevenueTotal Cost P(x)=R(x)C(x) Where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to get that profit. R(x)=5x C(x)=.001x^2+1.2x+60 Answered by Stephen La Rocque. 





Points of intersection 
20070118 

From Mark: Find the points of intersection of the given pair of curves. 2x  3y = 8 and 3x  5y = 13 Answered by Steve La Rocque and Haley Ess. 





Points of intersection 
20060820 

From Gianella:
Find the points of intersection by solving this problem analytically.
y= x cubed
y= x
Answered by Stephen La Rocque. 





Find the points of intersection 
20060818 

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





What's the difference between percentages and points? 
20060421 

From Sayed: What is the difference between percentages and points? Answered by Stephen La Rocque. 





Find the point of inflexion for the curve y = e^x/(x^21) 
20060331 

From Sam: Hi, i am trying to find the point of inflexion for the curve y = e^{x}/(x^{2}1) and i got a really complex expression for y". I can't seem to solve x^{4}4x^{3}+4x^{2}+4x+3=0 so does that mean there is no point of inflexion? Answered by Penny Nom. 





The centroid of a triangle 
20060118 

From Andrea: I am trying to find the centriod of a triangle. I have been given the three vertices of the triangle: A (25, 20), B (5, 40), and C (15, 30). I believe I calculated the correct midpoints: AB(E) (5, 5), BC(D) (5, 5), and AC(F) (15, 30). When I graphed these points I came up with the solution (5, 10), but I can't seem to write the answer out (equations of the lines, etc) correctly. Any help would be greatly appreciated! Answered by Penny Nom. 





A point is twice the distance from y = 5 + 2x as it is from y = 5  2x 
20051209 

From Hazel: A point moves so that its distance from the line y=5+2x is twice its distance from the line y=52x. Find the general form of the equation of its locus. Answered by Penny Nom. 





A fixed point problem 
20041114 

From Bob: I am trying to solve an existence of fixed point problem. I need to show that a function f (on reals) with f'(x)=>2 has a fixed
point. Answered by Claude Tardif. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





Compass points 
20021105 

From Mhairi: I was asked this in maths but I am not sure if it is geography. Name all the compass points? We have been given 8 but he told us there is more and we have to name them. Answered by Chris Fisher. 





A set of points in space 
20020318 

From Victoria: Describe the given set with a single equation or a pair of equations: The set of points in space that lie 2 units from the point(0,0,1) and at the same time 2 units from the point (0,0,1). Answered by Penny Nom. 





Midpoints and endpoints 
20000215 

From Jessica Sipes: I need to know how to find and endpoint using the midpoint and the other endpoint. Answered by Penny Nom. 





Graph question 
19980512 

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





How many intersections? 
19971008 

From James: (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Answered by Chris Fisher. 

