10FallHwk06_Soln

10FallHwk06_Soln - Math 2413 1. (2 pts) Homework Set 6...

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Math 2413 Homework Set 6 – Solutions 10 Points 1. (2 pts) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 52 2 5 22 2 co s 2 2 si n 2 63 s 23 6 2 si n 2 s 6 2 si n2 x y x y y y yx x y x y y x y xy y ¢¢ - =+ - + = - &= + 5. (2 pts) A sketch of the tank with some water in it is to the right. We know that 6 V ¢ = and we want to find h ¢ when 12 h = . Note here is a typo in my picture. The radius should be 20. The volume of the tank is 2 1 3 V rh p = and we can use similar triangles to eliminate the r from the equation so we can get everything in terms of h (which we’ll need to do or we will end up with an r ¢ in the derivative which we know nothing about). Similar triangles gives us, 3 20 24 5 0 5 75 r h r h Vh = &= = We can now proceed as normal. ( ) 2 2 25 44 2 5 2 5 96 6 1 2 0.08289 cm/s V h h hh pp ¢ ¢ = = & == 7. (2 pts) With this problem we’ve been given the equation already. We’ll need to determine the value of P at the time in question so let’s do that first. ( ) () ( ) 6 71 2 4 71 1 0 4 00 P P P PP - -= - = -=fi= e o r4 P =
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This note was uploaded on 11/13/2010 for the course MA 141 taught by Professor Wears during the Spring '07 term at N.C. State.

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10FallHwk06_Soln - Math 2413 1. (2 pts) Homework Set 6...

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