Explanation Given: In measuring the length of the object, when the length of the ruler is reduced by a factor of 5 the number of area elements increases by a factor of 30. Formula used: Fractal dimension D of the object is found from N=R D Where, N is the factor by which number of element increases when ruler is shortened by a factor R. Taking logarithm on both the sides- log(N)=log(R D ) log(N)=D log(R) [applying the rule log(a x )=x log(a) to right hand side] D = log ( N ) log ( R ) An object is defined as fractal if it has a non-integer dimension. Calculation: Here, the length of the ruler is reduced by a factor of 5 i...

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

7th Edition

ISBN: 9780134715919

Author: Bennett

Publisher: PEARSON

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Chapter 10.C, Problem 25E

To determine

The dimension of an object and state whether or not it is a fractal, given that in measuring the length of the object, when the length of the ruler is reduced by a factor of 5 the number of area elements increases by a factor of 30.

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Chapter 10.C, Problem 24E

Chapter 10.C, Problem 26E

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Chapter 10 Solutions

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

Ch. 10.A - Prob. 1QQ Ch. 10.A - Prob. 2QQ Ch. 10.A - An acute angle is a. less than 90°. b. exactly...Ch. 10.A - 4. A regular polygon always has a. four sides. b....Ch. 10.A - 5. A right triangle always has three equal-length...Ch. 10.A - 6. The circumference of a circle of radius r...Ch. 10.A - The volume of a sphere of radius r is a. \[\pi...Ch. 10.A - Prob. 8QQ Ch. 10.A - If you triple the radius of a sphere, the volume...Ch. 10.A - Suppose you cut a large stone block into four...

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