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Title: Calculus : Optimization Problem Post by: nappy110 on Mar 5, 2015 A girl athlete can run faster, then she swims. She can run maintaining the speed of 10
kilometers per hour. She can swim maintaining the speed of 7 kilometers per hour. Her task is to cross a perfectly circular lake of the radius R= 1 kilometer, from a point A to the diametrically opposite point B at a minimal time tmin. She may either run only or swim only or combine the running and the swimming What is the minimum time needed tmin to cross the lake? Approximate your results to two digits after the decimal points. The angle in (a) should be in radians. Here's what I have so far. Run=10km/hr Swim=7km/hr Rad=1 Dswim/Vswim+Drun/Vrun ==================== 2Rcos(theta)/7 + R*2(theta)/10= 2(1)cos(theta)/10 + 1*2(theta)/10 = (2/7)cos(Theta)+(1/5)(theta)=t(Theta) tderivative= -(2/7)sin(theta)+(1/5) -(2/7)sin(theta)+(1/5)=0 sin(theta)=7/10 or 44.4 degrees or 11pi/45 How am I doing so far? am I doing this correctly? Obviously this isn't done yet but maybe someone can help check my work or do your own work and compare what I have. Thanks in advance. Title: Re: Calculus : Optimization Problem Post by: bio_man on Mar 5, 2015 Hi Nappy, this should help:
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