Write a MATLAB program in a script file that fmds a positive integer n suchthat the sum

Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) 12-4<5x3 (b) y = 8/4>6x3-42>-3 (c) y = -3 < (8 - 12) + 2 X (5 > 1 8/6 -4)2 (d) (5+0) X 6==3+3 xO

Given: a = -2 , b = 3 , c = 5 . Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) y = a- b>a-c<b (b) y = -4<a<0 (c) y = a-c < = b >a+ c (d) y = 3 x (c+aalb-b)==(a+c)=b

Given: v = [4 -1 2 3 1 -2 5 0] and u = [ 5 -1 0 3 -3 2 1 5 ]. Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) (b) v== (c) u = = abs(v) (d) v >= u + v

Use the vectors v and u from Problem 3. Use relational operators to create a vector w that is made up of the elements of u that are smaller than or equal to the elements of v.

Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) -3&3 (b) 5<4&0>-3 (c) -2&2>318/3 ( -3<-1<0 1 5<4<3

Use loops to create a 3 x 5 matrix in which the value of each element is its row number to the power of its column number divided by the sum of its row number and column number. For example, the value of element (2,3) is 23/(2+3) = 1.6.

A symmetric (5 x 5) Pascal matrix is displayed on the right. Write a MATLAB program that creates an n x n symmetric Pascal matrix. Use the program to create 4 x 4 and 7 x 7 Pascal matrices.

The average monthly precipitation (in.) for Boston and Seattle during 2012 are given in the vectors below (data 1 1 1 1 1 1 2 3 4 5 1 3 6 10 15 1 4 10 20 35 1 5 15 35 70 from the U.S. National Oceanic and Atmospheric Administration). BOS = [2.67 1.00 1.21 3.09 3.43 4.71 3.88 3.08 4.10 2.62 1.01 5.93] SEA= [6.83 3.63 7.20 2.68 2.05 2.96 1.04 0.00 0.03 6.71 8.28 6.85] where the elements in the vectors are in the order of the months (January, February, etc.) Write a program in a script file to answer the following: (a) Calculate the total precipitation for the year and monthly average precipitation in each city. (b) How many months was the precipitation above the average in each city? (c) How many months, and on which months, was the precipitation in Boston lower than the precipitation in Seattle?

Write a program in a script file that fmds the smallest even integer that is divisible by 13 and by 16 whose square root is greater than 120. Use a loop in the program. The loop should start from 1 and stop when the number is found. The program prints the message "The required number is:" and then prints the number.

Fibonacci numbers are the numbers in a sequence in which the first two elements are 0 and 1, and the value of each subsequent element is the sum of the previous two elements: 0, 1, 1, 2, 3, 5, 8, 13, ... Write a MATLAB program in a script file that determines and displays the first 20 Fibonacci numbers.

The reciprocal Fibonacci constant v is defmed by the infinite sum: 1 v= nL F I n where Fn are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ... . Each element in this sequence of numbers is the sum of the previous two. Start by setting the first two elements equal to 1, then Fn = Fn _ 1 + Fn _ 2 Write a MATLAB program in a script file that calculates 'II for a given n. Execute the program for n = 10, 50, and 100.

Write a program in a script file that determines the real roots of a quadratic equation ax2 + bx + c = 0 . Name the file quadroots. When the file runs, it asks the user to enter the values of the constants a, b, and c. To calculate the roots of the equation the program calculates the discriminant D, given by: D = b2-4ac If D > 0, the program displays message "The equation has two roots," and the roots are displayed in the next line. If D = 0, the program displays message "The equation has one root," and the root is displayed in the next line. If D < 0, the program displays message "The equation has no real roots." Run the script file in the Command Window three times to obtain solutions to the following three equations: (a) 3x2+6x+3 = 0 (b) -3x2+4x-6 = 0 (c) -3x2+7x+5 = 0

The value of 1t can be estimated by: Write a program (using a loop) that determines the expression. Run the program with n = 100, n = 10000, and n = 1000000. Compare the result with pi. (Use format long.)

The value of 1t can be estimated from the expression: = J2. JUJ2 . J2+JUJ1 1t 2 2 2 Write a MATLAB program in a script file that determine 1t for any number of terms. The program asks the user to enter the number of terms, and then calculates the corresponding value of 1t. Execute the program with 5, 10, and 40 terms. Compare the result with pi. (Use format long.)

Write a program that generates a vector with 20 random elements between -10 and 10 and then finds the sum ofthe positive elements.

Write a program that (a) generates a vector with 20 random integer elements with integers between -10 and 10, (b) replaces all the negative integers with random integers between -10 and 10, (c) repeats (b) until all the elements are positive. The program should also count how many times (b) is repeated before all the elements are positive. When done, the program displays the vector and a statement that states how many iterations were needed for generating the vector.

Write a program that asks the user to input a vector of integers of arbitrary length. The program then counts the number of elements, the number of positive elements, and the number of negative elements divisible by 3. The program displays the vector that was entered and the results in sentence form, i.e. "The vector has XX elements. XX elements are positive and XX elements are negative divisible by 3 ", where XX stands for the corresponding number of elements. Execute the program and when the program ask the user to input a vector type randi ( [- 2 0 2 0] , 1, 16) . This creates a 16-element vector with random integers between -20 and 20.

A vector is given by x = [4.5 5 -16.12 21.8 10.1 10 -16.11 5 14 -3 3 2]. Using conditional statements and loops, write a program that rearranges the elements of x in order from the smallest to the largest. Do not use MATLAB 's built-in function sort.

The Pythagorean theorem states that a2 + b2 = c2 Write a MATLAB program in a script file that fmds all the combinations of triples a, b, and c that are positive integers all smaller or equal to 50 that satisfy the Pythagorean theorem. Display the results in a three-column table in which every row corresponds to one triple. The first three rows of the table are: 3 4 5 5 12 13 6 8 10

A twin primes is a pair of prime numbers such that the difference between them is 2 (for example, 17 and 19). Write a computer program that finds all the twin primes between 10 and 500. The program displays the results in a two-column matrix in which each row is a twin prime. Do not use MATLAB's built-in function isprime.

An isolated prime is a prime number p such that neither p - 2 nor p + 2 is prime. For example, 47 is an isolated prime since 45 and 49 are both not primes. Write a computer program that fmds all the isolated primes between 50 and 100. Do not use MATLAB's built-in function isprime.

A list of 30 exam scores is: 31, 70, 92, 5, 47, 88, 81, 73, 51, 76, 80, 90, 55, 23, 43,98,36,87,22,61, 19,69,26,82,89,99, 71,59,49,64 Write a computer program that determines how many grades are between 0 and 19, between 20 and 39, between 40 and 59, between 60 and 79, and between 80 and 100. The results are displayed in the following form: Grades between 0 and 19 2 students Grades between 20 and 39 4 students Grades between 40 and 59 6 students and so on. (Hint: use the command fprintf to display the results.)

The Taylor series expansion for cos(x) is: x2 x4 x6 (-1)n Zn cos(x) = 1-21 + 4i- 61 + ... = ..... (2n)! x n = 0 where x is in radians. Write a MATLAB program that determines cos (x) using the Taylor series expansion. The program asks the user to type a value for an angle in degrees. Then the program uses a loop for adding the terms of the Taylor series. If an is the nth term in the series, then the sum Sn of then terms is sn = sn-I + an . In each pass calculate the estimated error E given by E = 1Sn-8n-II Stop adding terms when:5:0.000001. The program displays sn-1 the value of cos(x). Use the program for calculating: (a) cos(35) (b) sin(125) Compare the values with those obtained by using a calculator.

Write a MATLAB program in a script file that fmds a positive integer n such that the sum of all the integers 1 + 2 + 3 + ... + n is a number between 100 and 1000 whose three digits are identical. As output, the program displays the integer n and the corresponding sum.

The following are formulas for calculating the training heart rate (THR) for men and women: For men (Karvonen formula): THR = [ (220-AGE)-RHR] x INTEN + RHR For women: THR = [(206-0.88xAGE)-RHR]xiNTEN+RHR where AGE is the person's age, RHR the resting heart rate, and INTEN the fitness level (0.55 for low, 0.65 for medium, and 0.8 for high fitness). Write a program in a script file that determines the THR. The program asks users to enter their gender (male or female), age (number), resting heart rate (number), and fitness level (low, medium, or high). The program then displays the training heart rate. Use the program for determining the training heart rate for the following two individuals: (a) A 21-year -old male, resting heart rate of 62, and low fitness level. (b) A 19-year-old female, resting heart rate of 67, and high fitness level.

Body Mass Index (BMJ) is a measure of obesity. In standard units, it is calculated by the formula w BMI = 703- H2 where W is weight in pounds, and His height in inches. The obesity classification is: BMI Classification Below 18.5 Underweight 18.5 to 24.9 Normal 25 to 29.9 Overweight 30 and above Obese Write a program in a script file that calculates the BMI of a person. The program asks the person to enter his or her weight (lb) and height (in.). The program displays the result in a sentence that reads: "Your BMI value is XXX, which classifies you as SSSS," where XXX is the BMI value rounded to the nearest tenth, and SSSS is the corresponding classification. Use the program for determining the obesity of the following two individuals: (a) A person 6ft 2 in. tall with a weight of 180 lb. (b) A person 5ft 1 in. tall with a weight of 150 lb.

Write a program in a script file that calculates the cost of shipping a package according to the following price schedule: Weight Type of 0--0.5lb 0.5-5lb More than 5 lb service Ground $0.70+ $1.18 + $0.42 for every $4.96 + $0.72 for every (5-7 days) $0.06/oz additional 0.5lb (or additional lb (or fracfraction). tion). Express $2.40+ $4.40 + $1.20 for every $15.20 + $1.80 for every (3-4 days) $0.25/oz additional 0.5lb (or additional lb (or fracfraction). tion). Overnight $12.20+ $18.60 + $4.80 for every $61.80 + $6.40 for every (One day) $0.80/oz additional 0.5lb (or additional lb (or fracfraction). tion). The program asks the user to enter the type of service (Ground, Express, or Overnight) and the weight of the package (two numbers. First for number of pounds and second for number of ounces.) The program then displays the cost for the shipment. Run the program three times for the following cases: (a) Ground 2 lb 7 oz. (b) Express 0 lb 7 oz. (c) Overnight 5lb 10 oz.

Write a program that determines the change given back to a customer in a self-service checkout machine of a supermarket for purchases of up to $50. The program generates a random number between 0.01 and 50.00 and displays the number as the amount to be paid. The program then asks the user to enter payment, which can be one $1 bill, one $5 bill, one $10 bill, one $20 bill, or one $50 bill. If the payment is less than the amount to be paid, an error message is displayed. If the payment is sufficient, the program calculates the change and lists the bills and/or the coins that make up the change, which has to be composed of the least number each of bills and coins. For example, if the amount to be paid is $2.33 and a $10 bill is entered as payment, then the change is one $5 bill, two $1 bills, two quarters, one dime, one nickel, and two pennies. Execute the program three times.

The concentration of a drug in the body C P can be modeled by the equation: Da k -kt -kt Cp = Va(ka:ke)(e -e ) where Da is the dosage administered (mg), Va is the volume of distribution (L), ka is the absorption rate constant (h-1), ke is the elimination rate constant (h-1), and tis the time (h) since the drug was administered. For a certain drug, the following quantities are given: Da = 150mg, Va =SOL, ka = 1.6 h-I' and ke = 0.4 h-1 (a) A single dose is administered at t = 0. Calculate and plot C P versus t for 10 hours. (b) A ftrst dose is administered at t = 0, and subsequently four more doses are administered at intervals of 4 hours (i.e., at t = 4, 8, 12, 16 ). Calculate and plot C P versus t for 24 hours.

One numerical method for calculating the cubic root of a number, VP is in iterations. The process starts by choosing a value x 1 as a first estimate of the solution. Using this value, a second, more accurate value x2 can be calculated with x2 = (Pixr + 2x1)/3 , which is then used for calculating a third, still more accurate value x3, and so on. The general equation for calculating the value of xi+ 1 from the value of xi is xi+ 1 = (Pix'f + 2xi)/3 . Write a MATLAB program that calculates the cubic root of a number. In the program use x 1 = P for the first estimate of the solution. Then, by using the general equation in a loop, calculate new, more accurate values. Stop the looping when the estimated relative errorE defined byE = lxi+ i-xil is smaller than 0.00001. Use the program to calculate: (a) V10o (b) 3Js31o1 (c) V19.35

Write a program in a script file that converts a measure of pressure given in units of either Pa, psi, atm. or torr to the equivalent quantity in different units specified by the user. The program asks the user to enter the amount of pressure, its cmrent units, and the desired new units. The output is the specification of pressure in the new units. Use the program to: (a) Convert 70 psi to Pa. (b) Convert 120 torr to atm.

In a oneional random walk, the position x of a walker is computed by: x1 = x1+s where s is a random number. Write a program that calculates the number of steps required for the walker to reach a boundary x = B. Use MATLAB's built-in function randn ( 1, 1) to calculates. Run the program 100 times (by using a loop) and calculate the average number of steps when B = 10.

The SieJp:inslci. triangle can be implemented in MAILAB by plotting points iteratively according to one of the following three rules that are selected randomly with equal probability. Rule 1: x,..1 = O.Sx,., Y+t = O.Sy,. Rule2: X11+1 = O.Sx,.+0.2S, Y11+1 = O.Sy11+(,J3)/4 Rule 3: x11+t = O.Sx11+0.S, Y11+1 = O.Sy. Write a program in a script file that calculates the x andy vectors and then plots y versus x as individual points (use plot (x, y, '"' ) ). Start with x1 = o and y1 = o. Run the program four times with 10, 100, 1,000, and 10,000 itemtions.

Cam is a mechanical device that transforms rotary motion into linear motion. The shape of the disc is designed to produce a specified displacement profile. A displacement profile is a plot of the displacement of the follower as a function of the angle of rotation of the cam. The motion of a certain cam is given by the following equations: y = 6[28-0.SsinO]ht for 0 9 7V2 y = 6 for n/292n/3 y = 6-3[1-0.scos(3(8-2))] for 2n/3S9S4n/3 y = 3 for 4n/3 e 3n /2 y = 3-t.s(8-!)2>Y for 3n/2SOS7n/4 y = 0.75-0.75(1-1-4)r for 71t/4SOS2n Write a MATLAB program that plots the displacement profile for one revolution. First create a 100 element vector fore, then by using a loop and conditional statements calculate the value of y for the corresponding values of e . Once y and e are known, plot y vs. e

The overall grade in a course is determined from the grades of 6 quizzes, 3 midterms, and a final exam, using the following scheme: Quizzes: Quizzes are graded on a scale from 0 to 10. The grade of the lowest quiz is dropped and the average of the 5 quizzes with the higher grades constitutes 30% ofthe course grade. Midterms and final exam: Midterms and fmal exams are graded on a scale from 0 to 100. If the average of the midterm scores is higher than the score on the fmal exam, the average of the midterms constitutes 50% of the course grade and the grade of the final exam constitutes 20% of the course grade. If the fmal grade is higher than the average of the midterms, the average of the midterms constitutes 20% of the course grade and the grade of the fmal exam constitutes 50% of the course grade. Write a computer program in a script file that determines the course grade for a student. The program first asks the user to enter the six quiz grades (in a vector), the three midterm grades (in a vector), and the grade of the fmal. Then the program calculates a numerical course grade (a number between 0 and 100). Finally, the program assigns a letter grade according to the following key: A for Grade 90 , B for 80 :5: Grade < 90 , C for 70 :5: Grade < 80 , D for 60 :5: Grade< 70, and E for a grade lower than 60. Execute the program for the following cases: (a) Quiz grades: 6, 10, 6, 8, 7, 8. Midterm grades: 82, 95, 89. Final exam: 81. (b) Quiz grades: 9, 5, 8, 8, 7, 6. Midterm grades: 78, 82, 75. Final exam: 81.

The handicap differential (HCD) for a round of golf is calculated from the formula: HCD = (Score- Course Rating) X 113 Course Slope The course rating and the slope are measures of how difficult a particular course is. A golfers handicap is calculated from a certain number N of their best (lowest) handicap scores according to the following table. # Rounds played N # Rounds played N 5-6 1 15-16 6 7-8 2 17 7 9-10 3 18 8 11-12 4 19 9 13-14 5 20 10 219 For example, if 13 rounds have been played, only the best five handicaps are used. A handicap cannot be computed for fewer than five rounds. If more than 20 rounds have been played, only the 20 most recent results are used. Once the lowest N handicap differentials have been identified, they are averaged and then rounded down to the nearest tenth. The result is the player's handicap. Write a program in a script file that calculates a person's handicap. The program asks the user to enter the golfers record in a three columns matrix where the first column is the course rating, the second is the course slope, and the third is the player's score. Each row corresponds to one round. The program displays the person's handicap. Execute the program for players with the following records. (a) Rating Slope Score 71.6 122 85 72.8 118 87 69.7 103 83 70.3 115 81 70.9 116 79 72.3 117 91 71.6 122 89 70.3 115 83 72.8 118 92 70.9 109 80 73.1 132 94 68.2 115 78 74.2 135 103 71.9 121 84 (b) Rating Slope Score 72.2 119 71 71.6 122 73 74.0 139 78 68.2 125 69 70.2 130 74 69.6 109 69 66.6 111 74