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I'm having trouble trying to figure out how to solve question 8 and 9. I just don't get it and would appreciate any help in figuring these two problems out.
MAT 230 Module Three Homework
General: Before beginning this homework, be sure to read the textbook sections and
the material in Module Three. Type your solutions into this document and be sure to show all steps for
arriving at your solution. Just giving a final number may not receive full credit. You may copy and paste mathematical symbols from the statements of the
questions into your solution. This document was created using the Arial
Unicode font. These homework problems are proprietary to SNHU COCE. They may not be
posted on any non-SNHU website. The Institutional Release Statement in the course shell gives details about
SNHU’s use of systems that compare student submissions to a database of
online, SNHU, and other universities’ documents. SNHU MAT230 Page 1 of 4 Module Three Homework 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-income is less than 40k so .10(27,000) =2,700
b) 98,000-income is more than 90,000 so 14,000+.3(98,000-90,000)
=16,400
c) 65,000-income is greater than 40,000 less than 90,000 so
4,000+.2(65,000-40,000) =9,000
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.
1. Min ←(x)1
2. For I= 2 thru N
a. If (min < x [1]) then
i. Min ← x [I]
3. Return (min)
3) Consider the following algorithm; assume N to be a positive integer.
1. X ← 0
2. Y ← 1
3. WHILE (X < N)
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.
A) X=0, y=1, x<3
X=0+1=1
Y=1+2(1) =3
X=1<3
X=1+1=2 Y=3+2(2) =7
X=2<3
X=2+1=3 y=7+2(2) =13 SNHU MAT230 Page 2 of 4 Module Three Homework Y=13/3
N=5; x=0; y=1
X=0<5
X=0+1=1 y=1+2(3) =3
X=1<5
1+1=2
y=3+2(2) =7
X=2<5
X=2+1=3 y=7+2(3)=13
X=3<5
X=3+1=4 y=13+2(4)=21
X<5
X=4+1=5 y=21+2 (5)=31
Y=31/5
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.
313626-(152346*2)=8934; 152346- (8934*17)=468; 8934- (468*19)=42;
468-(42*11)=6 42- (6*7)=0 GCF=6 s=8934 t=17
This problem is similar to Examples 5 and 6 and to Exercises 6–9 in Section 1.4
of your SNHU MAT230 textbook.
5) If f6 is the mod-6 function, compute each of the following.
a) f6(22) + f6(27)
f622=6*3+4 so f6=4
f627=6*4+3 so f6=3
so 4+3=7
b) f6(22 + 27)
f6(49)=6*7+2 so f6(22+27)=2
c) f6(22) × f6(27)
f622=6*3+4 so f6=4
f627=6*4+3 so f6=3 so 4*3=12
d) f6(22 × 27)
f6 (594)=99
This problem is similar to Example 9 and to Exercises 16–17 in Section 1.4 of
your SNHU MAT230 textbook.
6) Write the binary (base 2) and hexadecimal (base 16) expansions for each of the
following numbers:
a) 46 (this represents the symbol for the period in Unicode) 00101110; 3436
b) 945 (this represents the symbol for the Greek letter “alpha” in Unicode)
10110001 393435
This problem is similar to Example 13 and to Exercise 43 in Section 1.4 of your
SNHU MAT230 textbook. SNHU MAT230 Page 3 of 4 Module Three Homework 7) Use Bacon’s code to create a dummy message for THEORY. For the sake of
readability, use lowercase letters “a”, “b”, etc. for letters corresponding to 0 and
uppercase letters “A”, “B”, etc. for letters corresponding to 1. For example, in
Example 15, the letter F would be coded as onCeU.
This problem is similar to Examples 15 and 16 and to Exercise 45 in Section 1.4
of your SNHU MAT230 textbook.
BAABBAABBBAABAAABBBABAAABBBAAA
8) Prove, for n ≥ 1, that 7 + 14 + 21 + … + 7n = 7 n (n + 1) / 2
This problem is similar to Example 1 and to Exercise 4 in Section 2.4 of your
SNHU MAT230 textbook.
9) Prove that, for if C, D1, D2, …, Dn are n + 1 sets, that
n n i=1 i=1 C ∩ ( U Di )=U (C ∩ Di ) This problem is similar to Example 2 and to Exercises 18 and 19 in Section 2.4 of
your SNHU MAT230 textbook. SNHU MAT230 Page 4 of 4 Module Three Homework