Explanation Given Information: The cost of producing a box on June 1 is $ 5 . Formula Used: The sum and difference rules for an integral is, ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Where, f ( x ) and g ( x ) are two functions. The rule for integral of constant term ∫ a d x = a x + C . If the function is f ( x ) = sin x , then the formula for the integration of the function is, ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function 0.05 + 0.4 cos [ π 6 ( t − 11 ) ] . To evaluate the integral 0.05 + 0.4 cos [ π 6 ( t − 11 ) ] , suppose that the function f ( u ) is 0.05 and g ( u ) is 0.4 cos [ π 6 ( t − 11 ) ] . Apply the sum rule, ∫ [ f ( u ) + g ( u ) ] d u = ∫ f ( u ) d u + ∫ g ( u ) d u ∫ 0.05 + 0.4 cos [ π 6 ( t − 11 ) ] d t = ∫ 0.05 d t + ∫ 0.4 cos [ π 6 ( t − 11 ) ] d t Now, evaluate the integral of the function ∫ 0.05 d t by applying formula for constant integration and evaluate the integral of ∫ 0.4 cos [ π 6 ( t − 11 ) ] d t by applying constant multiple rules and using shortcut formula of ∫ cos ( a x ) d x = 1 a sin ( a x ) + C to determine the cost C ( t ) . ∫ 0

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.3, Problem 60E

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To calculate: The cost C(t) at time t of producing a box of holiday tree decorations which is changing at rate of 0.05+0.4cos[π6(t−11)] dollars per month, t months after January.

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Chapter 9.3, Problem 59E

Chapter 9.3, Problem 61E

Chapter 9 Solutions

Applied Calculus

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The cost C ( t ) at time t of producing a box of holiday tree decorations which is changing at rate of 0.05 + 0.4 cos [ π 6 ( t − 11 ) ] dollars per month, t months after January.

Solution Summary: The author calculates the cost of producing a box of holiday tree decorations, which is changing at rate of 0.05+0.4mathrmcosleft, t months after January.

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To calculate: The cost C(t) at time t of producing a box of holiday tree decorations which is changing at rate of 0.05+0.4cos[π6(t−11)] dollars per month, t months after January.

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Chapter 9 Solutions