How to calculate the total length of a line given a graph.?

Question

Here is the graph:
http://i39.tinypic.com/2hxsmc.jpg
Is there a way to know how long the length of the line is?

Answer 1

For parametric curves, where x = x(t), y = y(t), the arclength is found by the integral:



∫ (t = 0 to 1) √( (x'(t))² + (y'(t))² ) dt



Most of the time for high order Beziers, it cannot even be evaluated exactly. Numerical methods have to be employed for approximate answers.



In fact, most mathematical curves that "loops" are usually very difficult or impossible to evaluate. For this reason, engineers use low order Beziers to piece together complicated curves that have loops, so that it would be more analyzable.

Answer 2

1) You know that area is equal to length times width, so all you have to do is multiply both 8x-4 and 3x+6 using the distributive property of multiplication (8x-4) (3x+6) 4(2x-1) 3(x+2) - take out the GCF 12(2x^2 + 4x - x - 2) - Distribute 12(2x^2 + 3x - 2) = area 2) This problem is easy... all you have to do is find the GCF (4) 8n+12 4(2n+3) 3) When writing to the power of powers, do this - x^2 x^2+3x - find the GCF (x) x(x+3) - Your answer 4) Correlation indicates the strength and direction of a linear relationship between two random variables. 5) I honestly don't know, check your math book or google it. 6) You know selecting a nickel is 1/3rd probability (2/6th reduced to 1/3). Once 1 nickel is gone, you are left with 3 pennies, 1 nickel, and 1 dime. The chance of getting that 1 dime is 1/5 now. After you get that probability, all you have to do is multiply the chances of the first and second event. 1/3 x 1/5= 1/15 1/15 is your answer 7) V = 1/3~r^2h I put ~ as pi because i dont know where the actual pi symbol on my computer is. I hope that helps.

Answer 3

Yes there is.

Mathematically there is a formula to determine length of curve if you know the function of the curve. Since you apparently don't you could approximate by taking points along the curve and then find the best fit formula. You could do this stepwise and get several functions and add up their values. The formula is ∫_{a}^{b}[2]√(1+(((dy)/(dx)))²)dx.

There is a much easier way here:

http://akamai.backcountrystore.com.edgesuite.net/images/items/medium/SCA0001.jpg

With this gadget your roll along the curve and read of the length. Don't forget scaling.