These are Matlab program problems. Please help. Please run files to make sure they work thank you.
ENGR1140: COMPUTATIONAL ENGINEERING METHODS. Spring 2017
PROJECT 3.
For all problems
1. Write a MATLAB script and name it appropriately. For instance you can name the first file Proj1_1 (representing project 1 problem 1.). Make sure your script has enough comments to bring the meaning of the code out.
2. Save your file
3. Clear your workspace
4. Run the file in the MATLAB command window
5. Copy your script and paste it as specified in page 3 below.
6. Copy all your outputs (exactly as displayed) and paste them as specified in page 3 below.
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Problem 1: DRAWING BUTTERFLIES
This problem requires you to use a combination of the while loop, the for loop and the if statement to generate a figure that looks just like this.
These are butterflies.
Write a function called butterfly that returns the x and y values that can be used to plot a single butterfly. The equations to draw a butterfly with x and y points are:
?=??+?∗?∗???(?)
?=??+?∗?∗???(?)
??,??, ?? ?ℎ? ?????? ?? ?ℎ? ????????? ??? ? ?????? ?ℎ? ℎ???ℎ? ?? ?ℎ? ?????????.
Use 0≤ t ≤ 40*pi with and increment of 0.1.
Use a while loop to allow the user to continuously input the center coordinates, the height scale and the color of the butterfly. Use an if statement to terminate the loop once the user is done imputing the properties of all the four butterflies. For each set of inputs, use a for loop to compute x and y values that will plot a butterfly and plot it with the assigned color. Use the following butterfly properties.
Problem 2: LOAN AMORTIZATION TABLE
When you borrow money from a bank to buy a house, the loan generally comes with the loan amount and the interest rate that is quoted annually. If the loan is paid monthly, then the interest on the loan is calculated monthly. The monthly payment is calculated by using the equation below.
where:
M is the monthly payment, P is the principal left to be paid at any given time, i is the monthly interest rate calculated by dividing the annual interest rate by 12, n is the term of the loan or number of payments (the number of months you will be paying the loan).
The interesting thing about mortgage payment is that the monthly interest payment changes every month and it is calculated on a monthly basis based on the principal left.
Example calculation: Suppose the initial loan is $200,000, the annual interest rate is 5%, the term of the loan is 30 years (n = 30*12 = 360 payments). Here the monthly interest rate is calculated as i = 0.05/12 = 0.0041666667. Using the formula above, the monthly payment is $1073.64. The interest on the loan is calculated always on the balance left to pay on the loan. For the first month, the interest component of the monthly payment is calculated as: interest = balance left * 0.0041666667= 200000*0.0041666667=833.33. This means the principal component for the first monthly payment will be: Principal paid = monthly payment -interest= 1073.64-833.33 = 240.31. The balance left on the loan after the first payment will then be calculated as: balance left = 200000-240.31 = 199759.69. This new balance is used to start the process for the next payment. This is done until the loan is fully paid for at the end of the term of the loan. The table that shows the payment plan is called a loan amortization table. An example is shown below:
⦁ Write a function called amorttable that asks the user to input the following: the loan amount, the interest rate, and the term of the loan in years.
⦁ Use a for loop in your function to develop the loan amortization table similar to the one below. Note that the table shows the total interest paid on the loan. Use a loan amount of $250,000. a 30 year loan term, and an interest rate of 5%. Use an if statement to force a negative balance to zero.
⦁ Repeat the process using a while loop. The two tables should be exactly the same.
⦁ Run your code again except that in this case use 15 years as the term of the loan.
Problem 3: SUMMER TRAVEL
Every summer, many people travel by road to various locations across the country. With low fuel prices this summer, there will be lots of travel. The purpose of this program is to determine the total miles of travel and also compute the cost of travel using various travel route options. The excel sheet named project3.xlsx has data for this work. The table represents 55 families travel plans. Each family is identified by a family ID. Each travel plan consists of 10 road segments whose distances are given in miles. Column 11 is the average speed of the family and column 12 is the fuel efficiency of the family’s vehicle. For example, for family 1, the average speed is 65mph and they have a vehicle that does 35 miles per gallon. Write a function called summetravel that uses a for loop to generate the table below. Your table should show all the outputs from 1 to 55. Use $2/gallon as the average fuel cost.
SEGMENT (MILES)
FAMILY 1 2 3 4 5 6 7 8 9 10 11 12
1 40 150 70 100 140 202 51 44 12 95 65 35
2 100 121 57 105 66 182 54 87 8 141 75 20
3 66 147 64 115 206 100 57 78 45 135 68 25
4 89 88 67 130 25 99 60 98 120 158 65 26
5 90 125 68 150 58 68 63 78 145 141 70 25
6 45 102 78 175 157 159 66 41 22 107 75 33
7 60 99 77 205 149 171 69 15 23 84 77 30
8 91 218 81 140 204 21 72 25 36 108 79 32
9 24 192 79 140 116 228 75 47 99 87 49 28
10 57 188 82 150 150 57 78 102 97 88 66 29
11 89 140 75 160 139 140 81 55 72 45 60 20
12 97 167 76 170 179 125 84 48 42 77 75 19
13 67 183 119 180 170 122 87 77 20 98 76 60
14 54 125 113 190 104 109 90 99 5 45 58 52
15 100 98 85 200 128 210 93 87 55 23 63 22
16 120 82 86 210 137 214 91 78 88 12 65 21
17 96 75 87 220 111 183 94 79 48 10 60 20
18 201 69 87 230 215 122 97 69 78 9 55 18
19 77 132 90 55 159 221 100 63 74 77 58 19
20 123 59 139 50 137 194 103 158 41 9 59 66
21 143 57 100 60 160 212 106 45 40 12 76 25
22 119 160 131 108 44 91 109 60 145 120 77 54
23 102 123 104 112 17 59 112 91 22 88 74 25
24 70 75 105 116 120 157 115 24 23 45 71 24
25 72 123 109 120 175 207 113 57 36 98 70 26
26 74 52 112 124 111 138 116 89 99 32 69 27
27 76 93 116 128 159 181 119 97 97 78 66 29
28 78 89 119 132 162 179 122 67 72 79 58 30
29 80 74 122 136 154 166 125 54 42 69 59 31
30 82 63 128 140 44 157 128 100 20 63 63 35
31 84 339 127 144 45 14 131 120 5 158 60 32
32 86 227 133 148 66 87 134 96 55 45 58 36
33 88 243 133 152 36 88 137 105 22 60 55 34
34 44 78 142 156 30 47 140 93 45 91 54 41
35 92 209 125 160 28 45 143 89 78 24 71 22
36 94 125 125 58 156 50 141 45 98 57 72 20
37 96 144 75 154 90 84 102 113 12 89 65 18
38 98 158 52 172 200 55 147 33 100 97 69 17
39 100 56 44 176 172 68 150 77 78 67 66 19
40 102 90 25 180 207 4 153 47 79 100 67 32
41 104 78 134 92 96 75 156 128 98 87 55 19
42 106 144 58 94 163 62 159 59 78 52 55 22
43 108 258 144 96 178 87 162 389 45 65 58 25
44 110 243 87 98 164 9 121 58 52 49 59 24
45 55 243 90 100 108 98 123 45 47 48 63 21
46 47 58 99 87 95 117 125 54 22 43 60 20
47 116 100 150 11 171 69 127 78 111 50 58 23
48 118 22 47 106 189 87 129 89 20 66 55 33
49 120 58 87 108 194 77 131 65 69 69 54 35
50 22 25 8 60 45 59 133 47 86 61 71 30
51 48 78 165 10 116 45 135 102 38 63 72 30
52 20 98 17 114 88 130 87 12 72 48 65 36
53 102 78 158 87 195 192 77 201 55 88 69 19
54 66 44 163 48 144 122 141 125 65 73 70 22
55 132 89 171 120 207 47 44 88 60 70 69 28
