Need help with Calculus 2 Project.

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Discussion Overview

The discussion revolves around a Calculus 2 project involving the analysis of a curve defined by a cable, specifically focusing on finding the angle and arclength of the curve. Participants are seeking clarification and assistance with the mathematical concepts and calculations involved in the project.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant has solved the first problem but struggles with problem b, specifically finding the angle related to the tangent line of the curve.
  • Another participant suggests using the tangent line to create a triangle for better visualization and understanding.
  • There is a discussion about the constant 'a', with one participant expressing confusion about its value and another clarifying that 'a' is a positive constant.
  • Participants discuss the relationship between the distance of the poles and the value of 'a', indicating that knowing the distance allows for solving for 'a'.
  • One participant expresses difficulty in simplifying an equation involving 'a' and seeks further assistance.

Areas of Agreement / Disagreement

Participants generally agree on the need to clarify the value of 'a' and the approach to finding the arclength. However, there is uncertainty regarding the simplification of equations and the intuitive understanding of the angle in problem b, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations in the clarity of the problem statement and the assumptions regarding the values of 'a' and 'b'. The discussion also reflects varying levels of understanding among participants, particularly in relation to the integration process and the geometric interpretation of the problem.

Who May Find This Useful

Students working on calculus projects, particularly those involving curves and integration, may find this discussion relevant. Additionally, individuals interested in mathematical problem-solving and collaborative learning in a homework context could benefit from the exchanges here.

Techman07
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Looking for help on a certain project. I have posted the project in pdf format


http://home.ripway.com/2005-5/317800/proj1sum05.pdf

I have already solved the first problem (a), but problem b (finding the angle) doesn't make intuitive sense to me.If you all could be so kind, all ideas are greatly appreciated. Maybe if I understood the question better that would also help.
 
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Well you are given the equation of the curve created by the cable. Thus you can find the tangent line to to curve at [itex]x=\pm b[/itex]. Thus you can create a triangle using the tangent line as the hypotenuse, a pole as a vertical leg, and the horizontal line tangent to the minimum of the curve. Try drawing a picture.
 
number one...

man i don't even think I did number one right now...
 
Maybe you'll see it better if its translated.

A curve with equation y = 2acosh(x/a) intersects the x-axis at x = -b, b. Find the arclength of the curve. All you need to do is integrate arclength for x = -50 to 50.
 
its the letter a...

I don't mind integrating it, but I just can't figure out what a is...
 
Have you read the problem? it states a is a positive constant...

Considering real valued functions, this means

[tex]\{ a \epsilon \Re | a > 0 \}[/tex]
 
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since the distance of the poles from another is 100m, then this means there are poles at [itex]x=\pm 50[/itex]. From then you can solve for [itex]a[/itex] since you know that [itex]S = 20[/itex] and you know what [itex]b[/itex] is.
 
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I end up with (a+20 = a cosh(50/a), I know that this in turn is the same as
[a + 20 = a (e^(50/a) + e^-50/a) all over 2). There are too many a's I still don't understand how to simplify, thank you for your help though.
 

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