







A kinky curve 
20161006 

tammie pose la question : Koch’s kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segment is replaced by four segments, and so on. How many bends does the curve have at the third stage? Penny Nom lui répond. 





A metal gate 
20160206 

Carl pose la question : 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. Harley Weston lui répond. 





Planar curves 
20141213 

ann pose la question : what does planar curve mean in your definition of a cone? Penny Nom lui répond. 





A reversed curved on a railroad track 
20140619 

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





The parameterisation of of a curve 
20140401 

Eunice pose la question : Let C be the path along the curve given by y−80=−5x2 that moves from the point (5,−45) to the point (0,80).
Find r(t) the parameterisation of C in that direction as t∈[0,5]. How am I suppose to find the parametric of both x and y?
can I let x=t, then y=5t^2+80? thanks Penny Nom lui répond. 





Equal ordinate and abscissa 
20130815 

sonit pose la question : the slope of tangent to the curve y=(4x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Penny Nom lui répond. 





A curve in 3space 
20130214 

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





Lines tangent to y^2=4x 
20111111 

Reuchen pose la question : Find equations of the lines tangent to y^2=4x and containing (2,1). Penny Nom lui répond. 





Lissajous curve 
20100303 

Nikki pose la question : I'm interested in information about a particular mathematical figure. My memory is that it is called a "liciju figure", but obviously my spelling of this is incorrect because a google search of this and it's variants has revealed nothing. I believe it's related to the Moebius strip and probably connected with radio waves. It is used as the logo for our national broadcaster (The Australian Broadcasting Corporation) and you see exactly what I'm talking about by going on their website: www.abc.net.au. I have tried contacting them directly, but have received no response in over a month now! Harley Weston lui répond. 





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

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





Fitting the curve y=a*exp(b*x)+c 
20090812 

aika pose la question : Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Robert Dawson lui répond. 





The area of a region bounded by two curves 
20090107 

Rogerson pose la question : Find the area, S, enclosed by the given curve(s) and the given line.
y = x^2  x  1, y = x+2 Harley Weston lui répond. 





The area enclosed by a curve and the xaxis 
20090104 

Rogerson pose la question : Find the area, S, enclosed by the curve y = x^2 + 6x  5 and the xaxis in the interval 0≤x≤4. Harley Weston lui répond. 





A normal to a curve 
20081011 

sundar pose la question : How do I find a normal to a curve defined by equation y = a*x^3+b*x^2+c*x+d Penny Nom lui répond. 





I need an equation that best fits these numbers. 
20080903 

Vallatini, pose la question : Attached, please find a plotted curve (pdf file). I have pulled values from this curve (see below). I need an equation that best fits these numbers. Can you help? Harley Weston lui répond. 





A tangent to a curve through a point not on the curve 
20080723 

Carter pose la question : How does one find the tangent points on a curve, given only the curve's function
and the xintercept of that tangent line?
i.e. Find the point(s) on the curve y = (x^2) + 1, where the tangent line passes
through the point (2, 0).
I know that there will be two such points, one where y is very close to 1, and the
other point where y is a large negative number. However, I do not recall how to
figure out the tangent line equation given a single intercept and solving to find the
tangent points. Penny Nom lui répond. 





Chord, radius, arc length and central angle 
20080415 

Cindy pose la question : There is a railroad curve with a chord length of 2000 ft. and a central angle of 35 degrees. What is the radius and arc length of the circular arc? Stephen La Rocque lui répond. 





The area bounded by 3 curves 
20080413 

Sabahat pose la question : Hi, I have enclosed a diagram.
The diagram shows the curve y=(2x5)4. The point P has coordinates (4,81) and the tangent to the curve at P meets the xaxis at Q.
Find the area of the region (shaded in the diagram) enclosed between the curve, PQ and the xaxis . (Please note that the equation y is read as y=2x 5 whole raise to power 4.) Stephen La Rocque lui répond. 





A curve sketch 
20071122 

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





Parameters 
20060915 

Chase pose la question : What is the meaning of the word "parameters" when used in reference to Algebra. Penny Nom lui répond. 





An epicycloid 
20060410 

Sharon pose la question : 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. Stephen La Rocque and Penny Nom lui répond. 





The bathtub curve 
20051013 

David pose la question :
My father asked me to submit a question about the socalled 'bathtub
curve'. If you cut a bathtub in half lengthwise down it's middle, the
edge of the tub would describe the 'bathtub curve' which can be used
to demonstrate typical failure rates of products. This curve is
characterised by high initial (infant mortality) failure rates at
it's beginning, which drop quickly to a very low level. Failures then
increase gradually to the "end of life" stage where the failure rate
takes off dramatically again.
If anyone in the math department knows about the socalled 'bathtub
curve' my father would really appreciate the equation.
Chris Fisher and Edward Doolittle lui répond. 





A line from the center of the patch to the periphery 
20050101 

Sandrine pose la question : I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Denis Hanson and Harley Weston lui répond. 





A rate of change problem 
20041015 

Frank pose la question : Find the rate of change of the distance between the origin and a moving point on the graph of y = x(squared) + 1 if dx/dt = 2 centimeters per second. Penny Nom lui répond. 





Intersecting a line and a curve 
20040129 

Senthil pose la question : between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Penny Nom lui répond. 





Making a windmill 
20040102 

Matthew pose la question : I am a farmer in Ontario. It has been almost 20 years since high school. I am toying with making a windmill. The output chart for the the old generator I have is shown below. Before I tear it appart I would like to develop a formula from the chart that can predict the output at various speeds. Penny Nom lui répond. 





The tangent to a curve and the tangent of an angle 
20020826 

A teacher pose la question : Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Chris Fisher lui répond. 





Asymptotes 
20011109 

Frank pose la question :
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Chris Fisher and Penny Nom lui répond. 





Fourier transform 
20010807 

Adbul pose la question :
 Sir, we have the Dirichlet's condition for the Fourier transform : " The function should be integral over the real line " But why we are we neglecting this for example when we take the Fourier transform of an impulse train?
 Suppose we want to travel from one corner of a square of side 'a' to the diagonally opposite corner. We can travel along the sides which gives a pah length of '2a'. We can also do it in steps as shown below:
_  _PATH  _ _____
Suppose The step size =DELTA x Then the path length will be again '2a'. Now in the limit DELTA x >0 again we get '2a' But when we take the limit we get the straight line diagonal whose length is 'SQRT(2)X a' Where did I go wrong? Chris Fisher lui répond. 





Area between curves 
20010613 

Phil pose la question :
question 1 find the area bound by the curves y = x^{2} + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x^{2} + y^{2} = 9 about the xaxis Harley Weston lui répond. 





The area between two curves 
20010508 

Esther pose la question : Find the area of the region enclosed by the graphs of y = x^{3}6x and y = 2x between their points of intersection. Harley Weston lui répond. 





Length of a line 
19991010 

Dagmara Sarudi pose la question : My question has to do with the length of a diagonal. This problem came up when I thought about the shortest distance between two points, for example walking from one point to another in my neighborhood. I can choose a zig zag route and assuming the blocks I walk are exactly the same length, it shouldn't matter what route I took, the distance I travel should still be the same when I reached my goal. If, on the other hand I could travel in a diagonal line, the distance would be shorter. But what if, in my zig zag motion, the sections get so small the route approaches a diagonal. Shouldn't it be that each separate section added together equals the value of the two original sides? Or would it suddenly equal the value of the diagonal (which, of course was shorter than the two sides added together)? What gives? Chris Fisher and Harley Weston lui répond.






Slopes of curved lines 
19990609 

Stephen Ehrler pose la question : When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Harley Weston lui répond. 





Fitting a Curve 
19990119 

Kirk Doward pose la question : Hello my name is Kirk from Scarborough, Ontario. I have been out of a formal education system for thirty years. I program microcontrollers in my spare time. I have built a temperature sensing device ready to go but, thermistors are very nonlinear. I do know that there is a way to calculate the input condition of the thermistor and display the correct temperature in degrees C. I am sending a file to show my progression so far. Harley Weston lui répond. 

