Define "catenary curve"?
963383
That's the curve a rope makes when you let it hang loose.
534463
All kinds of things. All of a cars mechanisms are based on physical laws. I suppose this is for a school project so it might be enough if you talk about speed, acceleration etc...and maybe about the chemical energy that is being converted to heat energy which is being converted to kinetic energy (in school terms). When going through a curve you can talk about centripetal acceleration etc etc
557771
Draw a straight line.\nDraw a good cuve (mirror), using a compass or a protractor(for later mark a point as centre and place the protractor on this point coinciding with the axis.)\nThe curve should be of equal length on each side of principle axis.\nNow mark the pole, radius and focal point (twice the radius).\nIn case u use protractor, take focal lenght as twice the distance between the marked pont and pole.\n\nRemember how the rays reflect/refract, and accordingly draw two incident and two reflected/refracted rays.\nGive the standard sign convention...I hope plane mirror and prism are easier.
16095
It is called a ray.\nA ray is a half-infinite line with one end-point.
864285
A rollercoaster is traditionally an amusement park ride where up to a half-dozen "cars" riding on rails move very fast up and down hill and around corners, propelled by gravity.  Modern innvations include twists, turns, spiral and loops, dramatic speeds (approaching 200mph), dramatic climbs and drops (hundreds of feet), variations where the "car" consists of a mere "seat" or where you stand up, etc.
601313
Yes, there is - called inflexion points. A linear equation has none, all points lie on a straight line; a quadratic has one, while a cubic has 2 inflexion points.\n\nInflexion point is a point where the curve basically changes direction. Thus, a quadratic equation, if you plot it on an X/Y graph, will rise (or fall) to a highest (or lowest) point, and then will fall (or rise).\n\nThus, a quadratic graph looks like an U (or an inverted U), while a cubic will look like an S on its side.\n\nMultiple regression technique is a way to see the effect of several variables on an outcome that you are interested in. By this method, you can find out how much is the result influenced by one or more of the variables.\n\nThere are several sites where this is explained in more details, if you google it. One such site is http://www.statsoft.com/textbook/stmulreg.html\n\nHope this helps
1111034
Perhaps the link will help a little.  If you bend a pipe or metal bar, some of the metal will be in tension (stretched) and some will be in compression (squeezed).  There is a neutral plane between the two conditions that is neither stretched nor squeezed.  Often the plane passes through the centroid of the pipe (or bar).  This is easy to find if the cross-section is regular (round, square, etc.) but more difficult to find if the area is irregular or of variable properties such as density.  The centroid is similar to the center of gravity for the shape.  Hope that helps a little.
908963
There doesn't seem to be any connection to conic curves in braid theory.  See:\nhttp://en.wikipedia.org/wiki/Braid_group
898061
No.\n\nIt means that the slope of the curve y = x^2 at a given point is equal to twice the value of x at that point.\n\nThe change in y for an infinitesimally small change in the value of x is equal to twice the value of x at that point.\n\nYour interpretation, "for every change in x there is a change of 2 [in y]", would correspond to a derivative (or slope) of 2, not of 2*x.  The function, y = 2*x + constant would have a derivative dy/dx = 2.
575551
I recommend Unit 5 of this course:\nhttp://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/\n\n(Construction of Bézier Curves, De Casteljau's Algorithm, Subdividing a Bézier Curve)\n\nand the software "DesignMentor V2: Curve":\nhttp://www.cs.mtu.edu/~shene/NSF-2/DM2-BETA/index.html
140255
A graph of many rates (rate of reaction, population growth, etc.) produce exponential curves (asymptotic).\nThese are difficult to interpret.\nTo linearise the curve plot log y against x, or log y against log x. The properties of the rate can now easily be established.\nHave a look here (note, second reference is PDF format):
658342
There are two that I've seen used:\n\n-margin for error\n-probability curves (discrete or continuous)
217051
An approximation for the length is the circumference of cylinder for each turn (as discussed in previous answer).\nThe exact helix angle is inverse tangent of elevation through one turn divided by the approximate length you just calculated.\nThen the exact length is the approximate length divided by cosine of angle you just calculated.
179742
Various springs (flat or helical) deflect linearly with load and resistance of certain wires (nichrome, etc.) varies linearly with length.  If your experiment allows or expects large deflections you may be able to combine the spring/resistors into a circuit that calibrates force/deflection/resistance-reading suitable for measurement on an ohmmeter or perhaps a strip chart recorder.  Good luck.
160513
Timeline: a curve formed by tracking initially adjacent particles in time. It shows how particles deform. Consider a curve drawn through adjacent particles at t=0. At some other time t>0, the particle may no longer be adjacent. The curve connecting them at t>0 is the timeline.\n\nPathline: the path or trajectory traced out by moving particle. It tells how the particle has translated. \n\nStreakline: curve formed by connecting all fluid particles passing through a fixed point in space. This is formed by picking any point and letting the flow pass through it. Then at some later time, you "freeze" the flow and draw a curve connecting the particles that passed through that point in the order in which they passed.\n\nStreamline: curves drawn in flow at a fixed instant which are tangent to the direction of flow at every point. Basically a streamline is a curve drawn tangent to the velocity vector of fluid. \n\nBTW, for steady flow, the pathline, streamline, and streakline are identical.
1116918
In Calculus of Varations deals with minimization problems the most elementary of which is the Brachistochrone.  This is the problem of the shape of a wire which provides the fastest path between two points for a marble sliding down it.  I don't know what applications of differentiation is.
129186
Per Wikipedia: "The spirochaetes (or spirochetes) are a phylum of distinctive bacteria, which have long, helically coiled cells. They are distinguished by the presence of flagella running lengthwise between the cell membrane and cell wall, called axial filaments. These cause a twisting motion which allows the spirochaete to move about. Most spirochaetes are free-living and anaerobic, but there are numerous exceptions."