1) The following function, written in pseudocode, inputs INCOME as a variable and outputs the TAX corresponding to that income. You can think of this as a greatly simplified income tax. 1. IF (INCOME = 90,000) THEN a. TAX ? 14,000 + 0.3 (INCOME – 90,000) 2. ELSE a. IF (INCOME = 40,000) THEN i. TAX ? 4,000 + 0.2 (INCOME – 40,000) b. ELSE i. TAX ? 0.10 INCOME What is the pseudocode output for the following inputs? Explain your solution. a) 27,000 b) 98,000 c) 65,000 This problem is similar to Example 6 and to Exercise 1 in Appendix A of your SNHU MAT230 textbook. 2) Suppose that the array X consists of real numbers X[1], X[2], …, X[N]. Write a pseudocode program to compute the minimum of these numbers. This problem is similar to Example 12 and to Exercises 13–16 in Appendix A of your SNHU MAT230 textbook. 3) Consider the following algorithm; assume N to be a positive integer. 1. X ? 0 2. Y ? 1 3. WHILE (X a. X ? X + 1 b. Y ? Y + 2 X 4. Y ? Y / N Calculate what value of Y the algorithm will compute for the following values of N. Explain your solution. a) N = 3 b) N = 5 This problem is similar to Example 7 and to Exercise 22 in Appendix A of your SNHU MAT230 textbook. 4) Use the Euclidean algorithm to find the greatest common divisor d of 313,626 and 152,346. Then use this algorithm to find integers s and t to write d as 313,626 s + 152,346 t. Solving these types of equations, for much larger integers, is central to encryption schemes such as RSA (public key) encryption. This problem is similar to Examples 5 and 6 and to Exercises 6–9 in Section 1.4 of your SNHU MAT230 textbook.

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