Explanation Given information: Snow depth d ( x , y ) = − 0.01 x + 0.004 y + 1.3 m , and domain is bordered by the coordinates axes, and 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 ; 0 ≤ x ≤ 120 − 1 2 y Thus, volume V = ∫ 0 80 ∫ 0 120 − y 2 ( − 0.01 x + 0.004 y + 1.3 ) d x d y First evaluate the inner integral treating y as constant, thus V = ∫ 0 80 ( ∫ 0 120 − y 2 ( − 0.01 x + 0.004 y + 1.3 ) d x ) d y = ∫ 0 80 [ − 0.01 × x 2 2 + 0.004 x y + 1.3 x ] 0 120 − y 2 d y = ∫ 0 80 [ − 0.005 ( 120 − y 2 ) 2 + 0

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Chapter 15.2, Problem 51E

To determine

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

d(x,y)=−0.01x+0.004y+1.3m.

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Chapter 15.2, Problem 50E

Chapter 15.2, Problem 52E

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Chapter 15 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) is given by d ( x , y ) = − 0.01 x + 0.004 y + 1.3 m .

Solution Summary: The author calculates the volume of the snowpark where depth of snow in Jocoro Provincial park is given by d(x,y)=-0.01x+0.004y+1.3m.

Concept explainers

Videos

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

d(x,y)=−0.01x+0.004y+1.3m.

Want to see the full answer?

Chapter 15 Solutions

Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) is given by d ( x , y ) = − 0.01 x + 0.004 y + 1.3 m .

Solution Summary: The author calculates the volume of the snowpark where depth of snow in Jocoro Provincial park is given by d(x,y)=-0.01x+0.004y+1.3m.

Concept explainers

Videos

Volume of the snowpark where depth of snow in Jocoro Provincial park (example 6) is given by d(x,y)=−0.01x+0.004y+1.3m.

Want to see the full answer?

Chapter 15 Solutions

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

d(x,y)=−0.01x+0.004y+1.3m.