Explanation Given information: S − 5 p w = 3 p w 2 − 6 p q and p and q are positive constants. Formula used: If f ( x ) = a x 2 + b x + c , its extreme is at x = − b 2 a . Calculation: S − 5 p w = 3 p w 2 − 6 p q (Given) ⇒ S = 3 p w 2 + 5 p w − 6 p q By the formula that if f ( x ) = a x 2 + b x + c , its extreme is at x = − b 2 a , we have for the above equation w = − 5 p 2 ( 3 q ) w = − 5 p 6 q Then to find the minimum value w = − 5 p 6 q

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ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 4.3, Problem 47P

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The value of w minimizes S if S−5pw=3pw2−6pq and p and q are positive constants.

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Chapter 4.3, Problem 46P

Chapter 4.3, Problem 48P

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 4 Solutions

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The value of w minimizes S if S − 5 p w = 3 p w 2 − 6 p q and p and q are positive constants.

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To find: The value of w minimizes S if S−5pw=3pw2−6pq and p and q are positive constants.

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Chapter 4 Solutions

To find:

The value of w minimizes S if S−5pw=3pw2−6pq and p and q are positive constants.