(a) Explanation Given Information: The data: Calculation: The function y = a x 2 + b x + c defines the given data, where x is the hour after 6 and y is the amount of pollutants in the air. The values of a , b , c can be obtained by putting the values from the table. Substituting x = 2 , y = 98 in the above equation we get: y = a x 2 + b x + c 98 = 4 a + 2 b + c (I) Now, Substituting x = 4 , y = 138 in the above equation we get: y = a x 2 + b x + c 138 = 16 a + 4 b + c (II) Now, substituting x = 10 , y = 162 in the above equation we get: y = a x 2 + b x + c 162 = 100 a + 10 b + c (III) Subtracting (I) and (II) as follows: 138 − 98 = 12 a + 2 b 40 = 12 a + 2 b (IV) Subtract (III) and (II) as follows: 162 − 138 = 84 a + 6 b 24 = 84 a + 6 b 24 3 = 84 3 a + 6 3 b (b) To determine To calculate: The time when the pollution level is maximum and the maximum level itself as per the data. The data is

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8, Problem 6RE

(a)

To determine

To calculate: The function y=ax2+bx+c to model the data.

(b)

To determine

To calculate: The time when the pollution level is maximum and the maximum level itself as per the data. The data is

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Chapter 8, Problem 5RE

Chapter 8, Problem 7RE

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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.

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Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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The function y = a x 2 + b x + c to model the data.

Solution Summary: The author explains how the function y=ax2+bx+c defines the given data.