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The Depth of a Pond at the Point with Coordinates h(x,y)=5x2+4y2h ( x , y ) = 5 x ^ { 2 } + 4 y ^ { 2 }

Question 32

Essay

The depth of a pond at the point with coordinates (x, y)is given by h(x,y)=5x2+4y2h ( x , y ) = 5 x ^ { 2 } + 4 y ^ { 2 } .(Assume that x, y, and h are measured in feet.)If a boat at the point (-3, -5)is sailing in the direction of the vector 5i+j5 \vec { i } + \vec { j } ,
then at what rate is the depth changing?

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