calc project - So lets do the math to find out! ( for now...

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To begin finding the minimum number of firebreaks for each of our group member’s b values we used the equation: Area Lost = 50 * 50-bx + 50bx X We then simplified this equation so that the derivative would be much easier to find. The resulting equation is: Area Lost = -2500 – 50b + 50bx X With this version of the original equation of area lost we can now find the value of the x value by taking the derivative of the area lost equation. This is how we did it: Area Lost dy = -2500 + 50b dx With the derivative of the area lost equation we can now solve for X ( ). -2500 + 50b = 0 50b = 2500 b = 50 x² = 50 b Therefore we conclude that x is equal to 50 . b Since 50 is a critical point of the original area lost equation, we know that 50 is b b either a global minimum or a global maximum. By just taking the 2 nd derivative of the area lost equation we can find whether 50 is either a global min. or max. If the 2 nd b derivative is positive then 50 will be a maximum and if negative if will be a minimum.
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Unformatted text preview: So lets do the math to find out! ( for now on let A stand for area lost). A = -2500 + 50b A = -2500x- + 50b A = 5000x-. (A is positive). Since the second derivative of the area lost is 5000x-, which is a positive number, we can now officially conclude that x = 50 is the global minimum value of b. b Now in order to find what the minimum number of firebreaks are for the four b values of our group, all we need to do is to plug the four b values into the equation x = 50 . b Here is what we got for each group members b value: Chales b value = .021km 50 for c= 101.42 (the minimal number of firebreaks for b Charles b value). Miyad b value = .01km, min. number of firebreaks = 70.21 (optimal # of firebreaks for all b values ). Tom b value = .016km, min. number of firebreaks = 88.6 Ray b value = .019km, min number of firebreaks = 96.5....
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This note was uploaded on 04/28/2008 for the course CALC 101 taught by Professor Wiesner during the Spring '08 term at Ithaca College.

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calc project - So lets do the math to find out! ( for now...

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