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Matlab An Introduction with Applications 5th edition Amos Gilat - Solutions

Make a plot of a circle with its center at (4.2, 2.7) and radius of 7.5.
A parametric equation is given by x = sin(t)cos(t), y = 1 .5cos(t) Plot the function for –π < t
Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) 12 – 4 < 5 × 3 (b) y = 8/4 > 6 × 3 – 42 > -3 (c) y = -3 < (8 - 12) + 2 × (5 > 1 8/6 -4) (d) (∽5 + ∽0) × 6 == 3 + 3 × –O
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
The reciprocal Fibonacci constant Î¨ is defined by the infinite sum: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 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,
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: 2/π = √2/2 . √2 + √2/2 . √2/ + √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
Write a program that generates a vector with 20 random elements between -10 and 10 and then finds the sum of the 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
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
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 finds 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
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 × (c+0061∽=a/b-b)==(a+c)∽=b
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
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 finds 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
The Taylor series expansion for cos(x) is: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
Write a MATLAB program in a script file that finds 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] × INTEN + RHR where AGE is the person's age, RHR the resting heart rate, and INTEN the fitness level
Body Mass Index (BMJ) is a measure of obesity. In standard units, it is calculated by the formulaBMI = 703/W/H2where W is weight in pounds, and His height in inches. The obesity classification is:Write a program in a script file that calculates the BMI of a person. The program asks the person to
Write a program in a script file that calculates the cost of shipping a package according to the following price schedule: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
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
The concentration of a drug in the body CP can be modeled by the equation:Cp = DG/Vd (ka/ke – ka)(e–ket – e–ket)where DG is the dosage administered (mg), Vd is the volume of distribution (L), ka is the absorption rate constant (h-1), ke is the elimination rate constant (h-1), and t is the
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) ∽ ∽μ (b) v = = ∽μ(c) u = = abs(v)(d) v >= u + v
One numerical method for calculating the cubic root of a number, 3√P is in iterations. The process starts by choosing a value x1 as a first estimate of the solution. Using this value, a second, more accurate value x2 can be calculated with x2 = (P/x21 + 2x1)/3, which is then used for calculating
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 current units, and the desired new units. The
In a one-dimensioni random walk, the position x of a walker is computed by: xj = xj + 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
The Sierpinski 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: xn+1 = 0.5xn, yn+1 = 0.5yn.Rule2: xn+1 = 0.5xn + 0.25, yn+1 = 0.5yn + (√3)/4Rule 3: xn+1 = 0.5xn + 1 + 0.5,
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
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% of
The handicap differential (HCD) for a round of golf is calculated from the formula:HCD = (Score- Course Rating)/Course Slope Ã— 113The 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
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) ∽5-3 (c) -2&2>318/3 (d) -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 precipitations (in) for Boston and Seattle during 2012 are given in the vectors below (data 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
Write a program in a script file that finds 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
Write a user-defined MATLAB function for the following math function: y(x) = (- 0.2x3 + 7x2)e-0.3x The input to the function is x and the output is y. Write the function such that x can be a vector (use element-by-element operations). (a) Use the function to calculate y(-1.5) and y(5). (b) Use the
Write a user-defined function that calculates grade point average (GPA) on a scale of 0 to 4, where A = 4, A- = 3.7, B+ = 3.3, B = 3, B- = 2.7, C+ = 2.3, C = 2, C- = 1.7, D+ = 1.3 D = 1, and E = 0. For the function name and arguments, use av = GPA ( g 1 h). The input argument g is a vector whose
The factorial n! of a positive number (integer) is defined by n! = n·(n-1)·(n-2)·. ..· 3·2·1, where 0! = 1. Write a user-defined function that calculates the factorial n! of a number. For function name and arguments, use y=fact (x), where the input argument x is the number whose factorial is
Write a user-defined MATLAB function that determines the angle that forms by the intersection of two lines. For the function name and arguments, use th=anglines (A,B,C). The input arguments to the function are vectors with the coordinates of the points A, B, and C, as shown in the figure, which can
Write a user-defined MATLAB function that determines the unit vector in the direction of the line that connects two points (A and B) in space. For the function name and arguments, use n = unitvec (A, B). The inputs to the function are two vectors A and B, each with the Cartesian coordinates of the
Write a user-defined MATLAB function that determines the cross product of two vectors. For the function name and arguments, use w = crosspro (u,v). The input arguments to the function are the two vectors, which can be two-or three-dimensional. The output w is the result (a vector). Use the function
The area of a triangle ABC can be calculated by: A= 1/2 AB x AC where AB is the vector from point A to point B and AC is the vector from point A to point C. Write a user-defined MATLAB function that determines the area of a triangle given its vertices' coordinates. For the function name and
Write a user-defined MATLAB function that determines the circumference of a triangle when the coordinates of the vertices are given. For the function name and arguments, use [cr] = cirtriangle (A, B, C). The input arguments A, B, C are vectors with the coordinates of the vertices, and the output
Write a user-defined function that plots a circle given the coordinates of the center and a point on the circle. For the function name and arguments, use circle PC (c, p). The input argument c is a two-element vector with the x and y coordinates of the center and the input argument p is a
Write a user-defined MATLAB function that converts integers written in decimal form to binary form. Name the function b=Bina (d), where the input argument d is the integer to be converted and the output argument b is a vector with 1 s and Os that represents the number in binary form. The largest
Write a user-defined function that plots a triangle and the circle that circumscribes the triangle, given the coordinates of its vertices. For the function name and arguments, use TriCirc (A, B, C). The input arguments are vectors with the x and y coordinates of the vertices, respectively. This
Write a user-defined MATLAB function for the following math function: r(θ) = 4cos(4sinθ) The input to the function is θ (in radians) and the output is r. Write the function such that e can be a vector. (a) Use the function to calculate r(π/6) and r(5π/6). (b) Use the function to plot (polar
Write a user-defined function that plots an ellipse with axes that are parallel to the x and y axes, given the coordinates of its center and the length of the axes. For the function name and arguments, use ellipseplot (xc, yc, a,b). The input arguments xc and yc are the coordinates X of the center,
In polar coordinates a two-dimensional vector is given by its radius and angle (r, e). Write a user-defined MATLAB function that adds two vectors that are given in polar coordinates. For the function name and arguments, use[r th] = AddVecPol (rl, thl, r2, th2),where the input arguments are (r1,
Write a user-defined function that finds all the prime numbers between two numbers m and n. Name the function pr=prime (m, n), where the input arguments m and n are positive integers and the output argument pr is a vector with the prime numbers. If m > n is entered when the function is called, the
The geometric mean GM of a set of n positive numbers x1, x2, ... , xn is defined by:GM =(x1. X2 . ... . xn)1/nWrite a user-defined function that calculates the geometric mean of a set of numbers. For function name and arguments use GM=Geomean (x) , where the input argument xis a vector of numbers
Write a user-defined function that determines the polar coordinates of a point from the Cartesian coordinates in a two-dimensional plane. For the function name and arguments, use [th rad] = CartToPolar (x, y). The input arguments are the x and y coordinates of the point, and the output arguments
Write a user-defined function that determines the mode of a set of data (the value in the set that occurs most often). For the function name and arguments, use m=mostfrq (x). The input to the function is a vector x of any length with values, and the output m is a two-element vector in which the
Write a user-defined function that sorts the elements of a vector from the largest to the smallest. For the function name and arguments, use y=downsort (x). The input to the function is a vector x of any length, and the output y is a vector in which the elements of x are arranged in a descending
Write a user-defined function that sorts the elements of a matrix. For the function name and arguments, use B = matrixsort (A), where A is any size (m x n) matrix and B is a matrix of the same size with the elements of A rearranged in descending order row after row with the (1,1) element the
Write a user-defined function that fmds the largest element of a matrix. For the function name and arguments, use [Em, rc] = matrixmax (A), where A is any size matrix. The output argument Em is the value of the largest element, and rc is a two-element vector with the address of the largest element
Write a user-defined MATLAB function that calculates the determinant of a 3 Ã— 3 matrix by using the formula:For the function name and arguments, use d3 = det3by3 (A), where the input argument A is the matrix and the output argument d3 is the value of the determinant. Write the code of det3by3
The fuel consumption of an airplane is measured in gal/mi (gallon per mile) or in L/km (liter per kilometers). Write a MATLAB user-defined function that converts fuel efficiency consumption from gal/mi to L/km. For the function name and arguments, use Lkm = Lkm To Galm(gmi). The input argument gmi
A two-dimensional state of stress at a point in a loaded material in the direction defmed by the x-y coordinate system is defined by three components of stress Ïƒxx Ïƒyy, and Ï„xy. The stresses at the point in the direction defined by the x'- y' coordinate systems are calculated by the
The dew point temperature Td and the relative humidity RH can be calculated (approximately) from the dry-bulb T and wet-bulb Tw temperatures by (www.wikipedia.org):where the temperatures are in degrees Celsius, RH is in %, and Psta is the barometric pressure in units of millibars.Write a
In a lottery the player has to select several numbers out of a list. Write a user-defined function that generates a list of n integers that are uniformly distributed between the numbers a and b. All the selected numbers on the list must be different. For function name and arguments, use x = lotto
The Taylor's series expansion for cosx about x = 0 is given by:where x is in radians. Write a user-defined function that determines cosx using Taylor's series expansion. For function name and arguments, use y = cosTay (x), where the input argument x is the angle in degrees and the output argument y
Write a user-defined function that determines the coordinate yc of the centroid of the U-shaped cross-sectional area shown in the figure. For the function name and arguments, use yc = centroidU (w, h, t, d), where the input arguments w, h, t, and d, are the dimensions shown in the figure and the
The area moment of inertia Ixo of a rectangle about the axis x0 passing through its centroid is Ixo = 1/12 bh3. The moment of inertia about an axis x that is parallel to x0 is given by Ix = Ixo + Ad2x, where A is the area of the rectangle, and dx is the distance between the two axes.Write a MATLAB
In a low-pass RL filter (a filter that passes signals with low frequencies), the ratio of the magnitudes of the voltages is given by:where Ï‰ is the frequency of the input signal.Write a user-defined MATLAB function that calculates the magnitude ratio. For the function name and arguments, use RV
A circuit that filters out a certain frequency is shown in the figure. In this filter, the ratio of the magnitudes of the voltages is given by:where Ï‰ is the frequency of the input signal.Write a user-defined MATLAB function that calculates the magnitude ratio. For the function name and
The first derivative df(x)/dx of a function f(x) at a point x = x0 can be approximated with the two-point central difference formula: df(x)/dx = f(x0 + h)-f(x0 - h)/2h where h is a small number relative to x0. Write a user-defined function (see Section 7.9) that calculates the derivative of a math
The new coordinates (X,, Y,) of a point in the x-y plane that is rotated about the z axis at an angle e (positive is clockwise) are given by Xr, = X0cosθ- Y0sinθ Yr, = X0sinθ + Y0cosθ where (X0, Y0) are the coordinates of the point before the rotation. Write a user-defined function that
Tables of materials properties list density, in units of kg/m3, when the international system of units (SI) is used and list specific weight, in units of lb/in3, when the U.S. customary system of units are used. Write a user-defined MATLAB function that converts density to specific weight. For the
In lottery the player has to guess correctly r numbers that are drawn out of n numbers. The probability, P, of guessing m numbers out of the r numbers can be calculated by the expression: p = Cr,mC(n-r),(r-m)/Cn,r where Cx,y = x!/y!(x – y)!. Write a user-defined MATLAB function that calculates P.
Write a user-defined MATLAB function that converts speed given in units of knots (one knot is one nautical mile per hour) to speed in units of feet per second. For the function name and arguments, use fps = ktsTOfps (kts). The input argument k t s is the speed in knots, and the output argument fp s
The body surface area (BSA) in m2 of a person (used for determining dosage of medications) can be calculated by the formula (DuBois formula): BSA = 0.007184w0.425H0.75 in which w is the mass in kg and H is the height in em. Write a MATLAB user-defined function that calculates the body surface area.
The fuel tank shown in the figure in shaped as a frustum of cone with r = 20 in., and H = 2r.Write a user-defined function (for the function name and arguments, use V = Volfuel (y)) that gives the volume of fuel in the tank (in gallons) as a function of the height y (measured from the bottom). Use
The surface area S of a ring in shape of a torus with an inner radius r and a diameter d is given by: S = π2(2r + d)d The ring is to be plated with a thin layer of coating. The weight of the coating W can be calculated approximately as W = γSt, where y is the specific weight of the coating
The windchill temperature Twc is the perceived air temperature felt by the body on exposed skin due to the flow of air. For temperatures below 50°F and wind speed higher than 3 mph, it is calculated by: Twc = C1 + C2TA + C3V0.16 + C4TAV0.16 where TA is the air temperature in degrees F, V is the
Plot the polynomial y = 0.lx5 - 0.2x4 -x3 + 5x2 - 41.5x + 235 in the domain -6 < x < 6 . First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
An aluminum fuel tank has a cylindrical middle section and a semi-spherical ends. The outside diameter is 10 in., and the length of the cylindrical section is 24 in. The wall-thickness of the cylindrical section is t, and the wall-thickness of the semispherical ends is 1.5t. Determine t if the tank
A 20 ft-long rod is cut into 12 pieces, which are welded together to form the frame of a rectangular box. The length of the box's base is 15 in. longer than its width.(a) Create a polynomial expression for the volume V in terms ofx.(b) Make a plot of V versus x.(c) Determine the x that maximizes
A rectangular piece of cardboard, 40 in. long by in. wide is used for making a rectangular box (open top) by cutting out squares of x by x from the corners and folding up the sides.(a) Create a polynomial expression for the volume Vin terms of x.(b) Make a plot of V versus x.(c) Determine x if the
Write a user-defined function that adds or subtracts two polynomials of any order. Name the function p=polyadd (pl, p2, operation). The first two input arguments pl and p2 are the vectors of the coefficients of the two polynomials. (If the two polynomials are not of the same order, the function
Write a user-defined function that multiplies two polynomials. Name the function p=polymul t (pl1, p2). The two input arguments pl and p2 are vectors of the coefficients of the two polynomials. The output argument p is the resulting polynomial. Use the function to multiply the following
Write a user-defined function that calculates the maximum (or minimum) of a quadratic equation of the form: f(x) = ax2 + bx + c Name the function [x, y, w] = maxormin (a, b, c). The input arguments are the coefficients a, b, and c. The output arguments are x, the coordinate of the maximum (or
A cone with base radius r and vertex in contact with the surface of a sphere is constructed inside a sphere, as shown in the figure. The radius of the sphere is R = 9 in.(a) Create a polynomial expression for the volume V of the cone in terms of h.(b) Make a plot of V versus h for 9 (c) Using the
Consider the parabola y = 1.5(x - 3)2 + 1 and the point P(3, 5.5) .(a) Create a polynomial expression for the distance d from point P to an arbitrary point Q on the parabola.(b) Make a plot of d versus x for 3 (c) Determine the coordinates of Q if d = 28.(d) Determine the coordinates of Q that
The following data is given:(a) Use linear least-squares regression to determine the coefficients m and b in the function y = mx + b that best fits the data.(b) Make a plot that shows the function and the data points.
The boiling temperature of water TB at various altitudes his given in the following table. Determine a linear equation in the form TB = mh + b that best fits the data. Use the equation for calculating the boiling temperature at 5,000 m. Make a plot of the points and the equation.
Plot the polynomial y = 0.008x4 - 1.8x2 -5.4x + 54 in the domain -14 < x < 16. First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
The U.S. population in selected years between 1815 and 1965 is listed in the table below. Determine a quadratic equation in the form P = a2t2 + at1 + a0, where t is the number of years after 1800 and P is the population in millions, that best fits the data. Use the equation to estimate the
The number of bacteria NB measured at different times t is given in the following table. Determine an exponential function in the form NB = Neat that best fits the data. Use the equation to estimate the number of bacteria after 4.5 hr. Make a plot of the points and the equation.
Growth data of a sunflower plant is given in the following table:The data can be modeled with a function in the form H = C/(1 + Ae-Bt) (logistic equation), where H is the height, C is a maximum value for H, A and B are constants, and t is the number of weeks. By using the method described in
Use the growth data from Problem 22 for the following: (a) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the height in week 6. (b) Fit the data with linear and spline interpolations and use each interpolation to estimate the height in week 6. In each part make a
The following points are given:(a) Fit the data with a first-order polynomial. Make a plot of the points and the polynomial.(b) Fit the data with a second-order polynomial. Make a plot of the points and the polynomial.(c) Fit the data with a third-order polynomial. Make a plot of the points and the
The standard air density, D (average of measurements made), at different heights, h, from sea level up to a height of 33 km is given below.(a) Make the following four plots of the data points (density as a function of height): (1) both axes with linear scale; (2) h with log axis, D with linear
Write a user-defined function that fits data points to a power function of the form y = bxm. Name the function [b, m] = powerfit (x,y), where the input arguments x and y are vectors with the coordinates of the data points, and the output arguments b and m are the constants of the fitted exponential
Viscosity is a property of gases and fluids that characterizes their resistance to flow. For most materials viscosity is highly sensitive to temperature. For gases, the variation of viscosity with temperature is frequently modeled by an equation of the formÎ¼ = CT3/2/T + Swhere Î¼ is the
Measurements of the fuel efficiency of a car FE at various speeds v are shown in the table.(a) Curve-fit the data with a second-order polynomial. Use the polynomial to estimate the fuel efficiency at 60 mi/h. Make a plot of the points and the polynomial.(b) Curve-fit the data with a third-order
The relationship between two variables P and t is known to be:p = mt/b + tThe following data points are givenDetermine the constants m and b by curve-fitting the equation to the data points. Make a plot of P versus t. In the plot show the data points with markers and the curve-fitted equation with

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