Explanation Given information: Snow depth d ( x , y ) = − 0.008 x + 0.002 y + 0.8 m , and domain is bordered by the x-axes, x ≥ 100 the line y = 80 and y = 240 − 2 x (where units are in kilometers). Formula Used: Where volume V = ∬ D d ( x , y ) d A Calculation: The snowpark volume is represented by the volume under the graph of d ( x , y ) over domain, so we compute the corresponding integral. The domain is best expressed as: 0 ≤ y ≤ 80 ; 120 − 1 2 y ≤ x ≤ 100 Thus, volume V = ∫ 0 80 ∫ 120 − y 2 100 ( − 0.008 x + 0.002 y + 0.8 ) d x d y First evaluate the inner integral treating y as constant, thus V = ∫ 0 80 ( ∫ 120 − y 2 100 ( − 0.008 x + 0.002 y + 0.8 ) d x ) d y = ∫ 0 80 [ − 0.008 × x 2 2 + 0.002 x y + 0.8 x ] 120 − y 2 100 d y = ∫ 0 80 [ − 0.008 × 100 2 2 + 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.2, Problem 52E

To determine

Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by

d(x,y)=−0.008x+0.002y+0.8m for x≥100 .

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Chapter 16.2, Problem 51E

Chapter 16.2, Problem 53E

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CALCULUS (CLOTH)

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Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by d ( x , y ) = − 0.008 x + 0.002 y + 0.8 m for x ≥ 100 .

Solution Summary: The author calculates the volume of the snowpark where depth of snow in Jocoro Provincial park is given by d(x,y)=-0.008x+0.002y+0.8m.

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Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by

d(x,y)=−0.008x+0.002y+0.8m for x≥100 .

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Chapter 16 Solutions

Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by d ( x , y ) = − 0.008 x + 0.002 y + 0.8 m for x ≥ 100 .

Solution Summary: The author calculates the volume of the snowpark where depth of snow in Jocoro Provincial park is given by d(x,y)=-0.008x+0.002y+0.8m.

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Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by d(x,y)=−0.008x+0.002y+0.8m for x≥100 .

Want to see the full answer?

Chapter 16 Solutions

Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) was given by

d(x,y)=−0.008x+0.002y+0.8m for x≥100 .