MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
9th Edition
ISBN: 9780136415893
Author: Tannenbaum
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Chapter 7, Problem 36E

The 4 by 5 grid shown in Fig. 7-37 represents a network of streets (4 blocks by 5 blocks) in a small subdivision. For landscaping purposes, it is necessary to get water to each of the corners by laying down a system of pipes along the streets. The cost of laying down the pipes is $40, 000 per mile, and each block of the grid is exactly half a mile long. Find the cost of the cheapest network of pipes connecting all the corners of the subdivision. Explain your answer. (Hint: First determine the number of blocks in the MST.)

Chapter 7, Problem 36E, The 4 by 5 grid shown in Fig. 7-37 represents a network of streets 4 blocks by 5 blocks in a small

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(4) (8 points) (a) (2 points) Write down a normal vector n for the plane P given by the equation x+2y+z+4=0. (b) (4 points) Find two vectors v, w in the plane P that are not parallel. (c) (2 points) Using your answers to part (b), write down a parametrization r: R² — R3 of the plane P.
(2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3 and 2x + z = 3. Then determine a parametrization of the intersection line of the two planes.
(3) (6 points) (a) (4 points) Find all vectors u in the yz-plane that have magnitude [u also are at a 45° angle with the vector j = (0, 1,0). = 1 and (b) (2 points) Using the vector u from part (a) that is counterclockwise to j, find an equation of the plane through (0,0,0) that has u as its normal.

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MYLAB MATH FOR EXCURSIONS IN MATHEMATIC

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