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HW3 even solutions

# HW3 even solutions - Homework 3 Solutions 12.1.2 The...

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Homework 3 Solutions 12.1.2 The distance of a point P = ( x, y, z ) from the yz -plane is | x | , from the xz -plane is | y | , and from the xy -plane is | z | . So A is closest to the yz -plane, since it has the smallest x -coordinate in absolute value. B lies on the xz -plane, since its y -coordinate is 0. C is farthest from the xy -plane, since it has the largest z -coordinate in absolute value. 12.1.6 The distance formula d = p ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 + ( z 2 - z 1 ) 2 , gives us the distance between any pair of points ( x 1 , y 1 , z 1 ) and ( x 2 , y 2 , z 2 ) . Thus, we find Distance from P 1 to P 2 = 2 2 Distance from P 2 to P 3 = 6 Distance from P 1 to P 3 = 10 So P 2 and P 3 are closest to each other. 12.1.22 (a) The total cost C in dollars of renting a car is 40 times the number of days d plus 0.15 times the number of miles driven m . So C = f ( d, m ) = 40 d + 0 . 15 m. (b) We have f (5 , 300) = 40(5) + 0 . 15(500) = \$245 . Renting a car for 5 days and driving it 300 miles costs \$245. 12.1.31 The edges of the cube have length 4. The center of the cube is the point ( x, y, z ) where the coordinates are found by taking the midpoint of the edges of the cube: x = 2 + 6 2 = 4 , y = 5 + 9 2 = 7 , z = - 1 + 3 2 = 1 . Thus, the center of the sphere is the center of the cube which is the point (4 , 7 , 1) and the radius is r = 2 . Thus an equation of the sphere is ( x - 4) 2 + ( y - 7) 2 + ( z - 1) 2 = 4 . 12.2.2 (a) The value of z only depends of the distance from the point ( x, y ) to the origin. Therefore, the graph has a circular symmetry around the z -axis.

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HW3 even solutions - Homework 3 Solutions 12.1.2 The...

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