Explanation Given information: The total memory of the tablet is 32-GB. The total memory used by apps A, B, and C is 4%. The 6% of total memory used by two more apps each using the same amount of memory as app A. The 13.5% of total memory used by eight apps in which 3 times of app A, 4 times of app B, and one time of app C can be included. Calculation: Write the general form of equations using given information. Use the percentage in numerical. Consider total memory used by apps A, B, and C. A + B + C = 4 % of 32 GB =0 .04 × 32 A + B + C =1 .28 Consider 6% of the tablet’s memory. 3 A + B + C = 6 % of 32 GB = 0 .06 × 32 3 A + B + C =1 .92 Consider 13.5% of the tablet’s memory. 3 A + 4 B + C = 13.5 % of 32 GB = 0.135 × 32 3 A + 4 B + C = 4.32 Write the given equations in general matrix form [ A ] . [ A ] = [ 1 1 1 3 1 1 3 4 1 ] Here, [ A ] is the matrix form of coefficients A , B , and C and [ X ] is the constants of equations. Find the determinant | A | of matrix A . | A | = | 1 1 1 3 1 1 3 4 1 | Expand matrix A by first column. | A | = 1 ( 1 − 4 ) − 1 ( 3 − 3 ) + 1 ( 12 − 3 ) = − 3 + 0 + 9 = 6 Replace the coefficients of A (elements of column 1) with constant [ X ] to form matrix [ X A ] . [ X A ] = [ 1.28 1 1 1.92 1 1 4.32 4 1 ] Find the determinant | X A | of matrix X A . | X A | = | 1.28 1 1 1.92 1 1 4.32 4 1 | Expand matrix X A by first row. | X A | = 1.28 ( 1 − 4 ) − 1 ( 1.92 − 4.32 ) + 1 ( 7.68 − 4.32 ) = − 3.84 + 2.4 + 3.33 = 1.89 Find number of megabytes (MB) of memory required for app A using the equation: A = | X A | | A | Substitute 1.89 for | X A | and 6 for | A | . A = 1.89 6 = 0.32 GB × 1 , 000 MB 1 GB = 320 MB Therefore, number of megabytes (MB) of memory required for app A is 320 MB _

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.6, Problem 38E

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Find the number of megabytes (MB) of memory required for each app A, B, and C.

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Chapter 16.6, Problem 37E

Chapter 16, Problem 1RE

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