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Stitz-Zeager_College_Algebra_e-book

# Find the vertex focus and directrix include the

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Unformatted text preview: , the higher the entropy, the stronger the password. 1. If a 7 character case-sensitive16 password is comprised of letters and numbers only, ﬁnd the associated information entropy. 2. How many possible symbol options per character is required to produce a 7 character password with an information entropy of 50 bits? Solution. 1. There are 26 letters in the alphabet, 52 if upper and lower case letters are counted as diﬀerent. There are 10 digits (0 through 9) for a total of N = 62 symbols. Since the password is to be ln(62) 7 characters long, L = 7. Thus, H = 7 log2 (62) = 7 ln(2) ≈ 41.68. 16 That is, upper and lower case letters are treated as diﬀerent characters. 6.5 Applications of Exponential and Logarithmic Functions 387 2. We have L = 7 and H = 50 and we need to ﬁnd N . Solving the equation 50 = 7 log2 (N ) gives N = 250/7 ≈ 141.323, so we would need 142 diﬀerent symbols to choose from.17 Chemical systems known as buﬀer solutions have the ability to adjust to small changes in acidity to maintain a range of pH values. Buﬀer solutions have a wide variety of applications...
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