Application of differential: jet is flying due east at 12mil/min...

crankerbeat

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Hi all.. I'm newbie here. FYI, i'm still new in calculus and a little bit slow for solving the problem regarding in this course. Is there anybody can help me to solve this problem? :(

1. At time t= 0, single engine military jet is flying due east at 12mil/min. At the same altitude and 208 miles directly ahead of the military jet, still at time t=0, a commercial jet is flying due north at 8mil/min. When are the two planes closest to each other? What is the minimum distance between them?:(


2. Suppose that it costs 1+(0.003)v^3/2 dollars per mile to operate a truck at v miles per hour. If there are additional costs (such as the driver's pay) of $10/hr, what speed would minimize the total cost of a 1000-mil-trip?

3. Find the volume of the unbounded solid generated by rotating the unbounded region of the graph y=e^-x and the x-axis for x>=1. (Hint: Firstly sketch the graph and compute the volume from x=1 to x=b, where b>1. Then find the limit of this volume as b-->infinity.) What happen if y=1/root(2,x) instead?At time t= 0, single engine military jet is flying due east at 12mil/min. at the same altitude and 208 miles directly ahead of the military jet, still at time t=0, a commercial jet is flying due north at 8mil/min. when are the two planes closest to each other? what is the minimum distance between them?

Can somebody show me the solutions with steps. Thanks a lot.
 
Hi all.. I'm newbie here. FYI, i'm still new in calculus and a little bit slow for solving the problem regarding in this course. Is there anybody can help me to solve this problem? :(

1. At time t= 0, single engine military jet is flying due east at 12mil/min. At the same altitude and 208 miles directly ahead of the military jet, still at time t=0, a commercial jet is flying due north at 8mil/min. When are the two planes closest to each other? What is the minimum distance between them?:(
Set up a coordinate system so that the origin is at the position of the military jet, the positive x-axis to the east, the positive y axis to the north. The path of the military jet is x= 12t, y= 0, where x and y are in miles, t in minutes. The commercial jet is initially at (208, 0) so x= 208, y= 8t. The distance between them at any given minute is \(\displaystyle \sqrt{(12t- 208)^2+ (0- 8t)^2}\). \(\displaystyle \sqrt{f}\) is minimum if and only if f is so this problem is the same as minimizing \(\displaystyle (12t- 208)^2+ 65t^2\). That is quadratic so you can minimize by taking the derivative and setting it equal to 0 or by completing the square.

2. Suppose that it costs 1+(0.003)v^3/2 dollars per mile to operate a truck at v miles per hour. If there are additional costs (such as the driver's pay) of $10/hr, what speed would minimize the total cost of a 1000-mil-trip?
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Traveling at v miles per hour, it will take 1000/v hours to go 1000 miles so the additional costs are 10000/v dollars. The total cost, then, of going 1000 miles at v miles per hour is \(\displaystyle \frac{10000}{v}+ 1+ 0.003v^3/2\). Take the derivative and set it equal to 0.

3. Find the volume of the unbounded solid generated by rotating the unbounded region of the graph y=e^-x and the x-axis for x>=1. (Hint: Firstly sketch the graph and compute the volume from x=1 to x=b, where b>1. Then find the limit of this volume as b-->infinity.) What happen if y=1/root(2,x) instead?
This question is incomplete. Rotate this area around what axis?

Can somebody show me the solutions with steps. Thanks a lot.
 
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