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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 5 2 2 5 2 2 5 2 2 cos 2 2 sin 2 6 3 2 cos 2 3 6 2 sin 2 2 cos 2 3 6 2 sin 2 x y x y y y y x x y x y x y y x y x y y x 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 r h 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 2 4 50 5 75 r h r h V h p fi = ° = = We can now proceed as normal. ( ) 2 2 25 4 4 25 25 96 6 12 0.08289 cm/s V h h h h p p p ¢ ¢ ¢ ¢ = fi = ° = = 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.

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

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