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systems analysis and design using matlab

MATLAB An Introduction With Applications 6th Edition Amos Gilat - Solutions

7. Define the variablesa, b,c, and d as:, , and , and then evaluate:a)b)
6. Define the variables x and z as x = 5.3, and z = 7.8, then evaluate:a)b)
5. Define the variable x as x = 9.75, then evaluate:a)b)c)
4. Calculate:a)b)
5 The values of the variables B, t, years, and months are displayed(since a semicolon was not typed at the end of the commands that calculates the values).28.5 ⋅ 33 – 1500 112 + 37.3------------------------------------------73⎝-- ⎠⎛ ⎞2⋅ 43 ⋅ 18 67(93 – 652)–
3. Calculate:a)b)>> format short g B =20011 t =16.374 years =16 months =
2. Calculate:a)b)
1. Calculate:a)b)
29. Create the following three matrices: 5 -3 7 A=1 0 -6 -4 8 9 [32-1 B=68-7 4 4 0 -9 8 3 C=17-5 3 36 (a) Calculate A + B and B+ A to show that addition of matrices is commu- tative. (b) Calculate 1*(B*C) and (4*B)*C to show that multiplication of matrices is associative. (c) Calculate 5(B+C) and
28. The monthly lease payment, Pmt, of a new car can be calculated by: Lov Fy (+12) Pmt= 1+1+1/12) 1/12 where Py and Fy are the present value and the future value (at the end of the lease) of the car, respectively. N is the duration of the lease in months, and i is the interest rate per year.
27. The Hazen Williams equation can be used to calculate the pressure drop, Pd (psi/ft of pipe) in pipes due to friction: P=4.520 / (Cd) where is the flow rate (gpm), C is a design coefficient determined by the type of pipe, and d is pipe diameter in inches. Consider a 3.5-in.-diameter steel pipe
26. Show that lim 5 sin(6x) 2-04x 7.5. Do this by first creating a vector x that has the elements 1.0, 0.1, 0.01, 0.001, and 0.0001. Then, create a new vector y in 5 sin(6x) which each element is determined from the elements of x by 4x Compare the elements of y with the value 7.5. Use format long
25. Show that lim sin(x-/3) Do this by first creating a vector x that 6 has the elements /3+0.01, and /3-0.1. /3-0.01, #/3-0.0001, x/3+0.0001. /3+0.1. Then, create a new vector y in which each cle- ment is determined from the elements of x by sin(x-x/3). Compare the ele- 4 cos x-1 ments of y with
24. The natural exponential function can be expressed by e*= mine e by calculating the sum of the series for: (a) n=5, (b) n=15, (c) n = 25 Deter- For each part create a vector n in which the first element is 0, the increment is 1, and the last term is 5, 15, or 25. Then use element-by-element
23. Use MATLAB to show that the sum of the infinite series to 6. Do this by computing the sum for (a) n=5, (b) n=15, (c) n=30 converges For each part, create a vector n in which the first element is 1, the increment is 1 and the last term is 5, 15, or 30. Then use element-by-element calcula- tions
22. Use MATLAB to show that the sum of the infinite series converges to /6. Do this by computing the sum for: (a) n=5, (b) n=50. (c) n=5000 For each part create a vector # in which the first element is 1, the increment is 1 and the last term is 5, 50, or 5,000. Then use element-by-element calcula-
21. The maximum distances and the maximum that a projectile shot at an angle 0 height are given by: where ssin = sin 29 and h sin 2g is the shooting velocity and g=9.81 m/s. Determine (0) and h(0) for 0-15, 25, 35, 45, 55, 65, 75 if vo=260m/s.
20. Define the vectors: a=71-4j+6k, b=-4+7j+5k, and 5i-6j+8k Use the vectors to verify the identity: a (bc) b(a c)-c(a+b) Using MATLAB's built-in functions cross and dot, calculate the value of the left and right sides of the identity.
19. The center of mass, (x, y, z), of n particles can be calculated by: E where x, y, and z; and m; are the coordinates and the mass of particle i, respectively. The coordinates and mass of six par- ticles are listed in the following table. Calculate the center of mass of the particles.Particle
18. The cross product of two vectors can be used for determining the angle between two vectors: Use MATLAB's built-in functions asind, cross, sqrt, and dot to find the angle (in degrees) between r =2.5i +8j-5k r-li+6j+3k. Recall that rrr. and
17. The area of a triangle ABC can be calculated by src/2, where IAB and C are vec- tors connecting the vertices A and B, and A and C, respectively. Determine the area of the triangle shown in the figure. Use the follow- ing steps in a script file to calculate the area. First, define the vectors
16. Definer and s as scalars r=1.610 and s=14.2, and, 1, x, and y as vectors = 2, 3, 4, 51, x=12, 4, 6, 8, 101, and y=13, 6, 9, 12, 15]. Then use these variables to calculate the following expressions using element-by- element calculations for the vectors. (a) =x+(-x) (b) R=(-)-(-0.5x)
15. Define x and y as the vectors x=10.5, 1, 1.5, 2, 2.51 and y=10.8, 1.6, 2.4, 3.2, 4.01. Then use them in the following expressions to calculate z using element-by-element calculations (a) = x+2xy (b)=xy-xy +8.5
14. Define the vector 15 4 3 2]. Then use the vector in a mathematical expression to create the following vectors: (a) a = 3+ 4+4 3+3 2+2 (c) c= (b) b=15' 4' 321 (d) d=
13. Define the vector [135 71. Then use the vector in a mathematical expression to create the following vectors: (a) a 13 9 15 21] (b) =[1925 49](c) c[111] (d) d = [6 6 66]
12. The following two vectors are defined in MATLAB: v=[3 -1 2], u=[6 4 -3] (d)d. ^2 By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB. (a) v.*u (b) v.^u (c) v*u*
11. The following vector is defined in MATLAB: d=[243] By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB. (a) d+d (b) d.^d (c)d. *d
10. The angle between two vectors u, xi+yj+zk and uxi+yj+ can be determined by cos 0= where u+y UU2 Given the vectors u =3.2i -6.8j+9k and u = -4i+2j+7k, determine the angle between them (in degrees) by writing one MATLAB command that uses element-by-element multiplication and the MATLAB built-in
9. A unit vector u, in the direction of the vector u=xi+yj+zk is given by uu/u where u is the length (magnitude) of the vector, given by u =x+ y+2. Given the vector u=4i +13j-7k, determine the unit vec- tor in the direction of u using the following steps: (a) Assign the vector to a variable u. (b)
8. The length lul (magnitude) of a vector uxi+yj-zk is given by Jul=x+ y+2. Given the vector u=-5.61+11j-14k, determine its length by writing one MATLAB command in which the vector is multiplied by itself using element-by-element operation and the MATLAB built-in functions sum and sqrt are used.
7. The remaining loan balance, B, of a fixed payment years mortgage after x years is given by: B= (1+21 where L is the loan amount, and r is the annual interest rate. Calculate the balance of a 30-year, $100,000 mortgage, with annual interest rate of 6% (use 0.06 in the equation) after 0, 5, 10,
6. A 70 lb-bag of rice is being pulled by a per- son by applying a force F at an angle e as shown. The force required to drag the bag is given by: F(0)=. sin cos where = 0.35 is the friction coefficient. (a) Determine F(0) for 85, 10, 15, 20, 25, 30, and 35. (b) Determine the angle 0 where Fis
5. The radius, r, of a sphere can be calculated from its volume, V, by: 3/31 The surface area of a sphere, S, is given by: S = 42 Determine the radius and surface area of spheres with volumes of 4,000, 3,500, 3,000, 2,500, 2,000, 1,500, and 1,000 in.. Display the results in a three-column table
4. For the function y=- calculate the value of y for the following values of x using element-by-element operations: 15, 25, 35, 45, 55, 65.
3. For the function y = (x+x/x+3)(1+2x)-x, calculate the value of y for the following values of x using element-by-element operations: -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2. 4sin x+6
2. For the function y=x'e, calculate the value of y for the following values of x using element-by-element operations: 1.5, 2, 2.5, 3, 3.5, 4.
1. For the function y = x-calculate the value of y for the following val- ues of x using element-by-element operations: 0, 1, 2, 3, 4, 5, 6, 7.
45. Use the eye, ones, and zeros commands to create the following arrays:Using the variables A, B, and C, write a command that creates the following matrix D:
44. Using the zeros, ones, and eye commands, create the following arrays by typing one command:(a) (b) (c)
43. By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB.V=[1:2:11;13:2:23]V(:,4:6)=V(:,1:3)V(3:4,:)=V V(:,[2:3 5:6])=[]
42. The following matrix is defined in MATLAB:T =2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB.(a) D=[T(1,1:4);T(3,2:5)](b) E=[T(:,4);
41. The following matrix is defined in MATLAB:S =1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB.(a) A=S(2,[2,4]) (b)
40. Create the following matrix K:K =0.25 0.5 0.75 1.0 1.25 1.5 1.75 2 4 6 8 10 12 14 25 30 35 40 45 50 55(a) Create a matrix Ga such that its first row includes the elements of the second column of K followed by the elements of the fifth column of K, the second row of Ga includes the first six
39. Create the following matrix G:G =0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 9 8 7 6 5 4 0 0.2 0.4 0.6 0.8 1.0 1.2 5 3 1 -1 -3 -5 -7(a) Create a matrix Ma from the first, third, and fourth rows and the first two and last two columns of matrix G.(b) Create a matrix Mb from the first three rows and the
38. Create the following matrix N:N =0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51(It can be done by typing: N=reshape(0:3:51,6,3)'.)By writing one command and using the colon to address range of elements(do not type individual elements explicitly), use the matrix N to:(a) Create a six-element
37. Create the following matrix M:M =1 7 13 19 25 3 9 15 21 27 5 11 17 23 29 By writing one command and using the colon to address range of elements(do not type individual elements explicitly), use the matrix M to:(a) Create a five-element row vector named Va that contains the elements of the third
36. Create the following vectors:u=[0 9 -5 6 3 -1 2] and w=[-2 3 7 -4 0 1 5]By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB.(a) A=[u(2:5);w([7 5]) u([6 7])](b) B=[w(4:7)', zeros(4,2),
35. Create the following vector:v=[5 0 -3 7 6 -1 2 8 4 9]By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB.(a) a=v([4 5:7 10]) (b) b=v([9, 1, 6:-2:2])'(c) c=[b' a']
34. By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB. In parts (b), (c), (d), (e), and (f) use the vector that was defined in part (a).(a) a=2:2:20 (b) b=a(4:8) (c) c=a(1:2:7)(d)
33. Create the following two row vectors:d=[6-1 4 0 -2 5], and e=[7 5 9 0 1 3].(a) Use the two vectors in a MATLAB command to create a matrix such that the first row consists of elements 2 through 4 of vectord, the second row consists of elements 3 through 5 of vectore, and the third row consists
32. Create the following three row vectors:a=[5 8 -1 0 2], b=[4 1 9 -2 3], and c=[-3 5 0 6 1].(a) Use the three vectors in a MATLAB command to create a matrix in which the rows are the vectorsc, b, anda, respectively.(b) Use the three vectors in a MATLAB command to create a matrix in which the
31. Create the following three row vectors:a=[5 8 -1 0 2], b=[4 1 9 -2 3], and c=[-3 5 0 6 1].(a) Use the three vectors in a MATLAB command to create a nine-element row vector consisting from the first three elements of the vectorsa, b, andc, respectively (i.e., 5 8 -1 4 1 9 -3 5 0).(b) Use the
30. Create the following matrix by typing one command. Do not type individual elements explicitly.G =1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1
29. Create the following matrix by typing one command. Do not type individual elements explicitly.F =0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2
28. Create the following matrix by typing one command. Do not type individual elements explicitly.E =0 0 0 0 8 0 0 0 0 7 0 0 0 0 6
27. Create the following matrix by typing one command. Do not type individual elements explicitly.D =1 1 1 1 1 1 1 1 1 1 1 1 8 6 4 2
26. Create the following matrix by typing one command. Do not type individual elements explicitly.C =6 8 6 8 6 8 6 8 6 8
25. Create the following vector by using the linspace command. Do not type individual elements explicitly.B =4 4 4 4 4 5 5 5 5
24. Create the following matrix by assigning vectors with constant spacing to the rows (use the linspace command for the third row). Do not type individual elements explicitly.A =1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 7.0000 6.0000 5.0000 4.0000 3.0000 2.0000 1.0000 2.0000 3.1667 4.3333
23. Create a nine-element row vector vF=5:7:61. Then create a vector (name it vFrev) that consist of the elements of vF in reverse order. Do it by using a vector to address the elements of VF. (Do not type the elements of vF vector explicitly.)
22. Create two row vectors vD=20:4:44 and vE=50:3:71. Then, create the following new vectors by assigning elements of vD and vE to the new vectors:(a) A vector (name it vDE) that contains the 2nd through the 5th elements of vD and the 4th through 7th elements of vE; i.e., vDE = 24 28 32 36 59 62 65
21. Create a row vector vC=2:3:38 that has 13 elements. Then, create the following new vectors by assigning elements of vC to the new vectors:(a) A vector (name it vCodd) that contains all the elements with odd index of vC; i.e., vCodd = 2 8 14 ... 38.(b) A vector (name it vCeven) that contains all
20. Create a row vector vA=1:3:34 that has 12 elements. Then, create a new nine-element vector vB from the elements of vA such that the first five elements are the first five elements of the vector vA, and the last four are the last four elements of the vector vA. Use the colon symbol to address a
19. Create a row vectors A=4:3:13 and a column vector B=[14:-2:6]’.Then only using the name of the vectors (A and B), create the following:(a) A row vector C that is made from the elements of B followed by the elements of A.(b) A column vector D that is made from the elements of A followed by the
18. Create two column vectors T=[5:5:25]’ and S=[27:2:33]’. Then, by only using the name of the vectors (T and S), create a column vector R that is made from the elements of T followed by the elements of S.
17. Create two row vectors v=41:-3:29 and w=17:4:37. Then, by only using the name of the vectors (v and w), create a row vector u that is made from the elements of w followed by the elements of v.
16. Use a single command to create a row vector (assign it to a variable named R) with 10 elements such that R =-4 -1 2 5 8 14 18 22 26 30 Do not type the vector elements explicitly.
15. Use a single command to create a row vector (assign it to a variable named q) with nine elements such that the last four elements are 8.1 and the rest of the elements are 0s. Do not type the vector elements explicitly.
14. Use a single command to create a row vector (assign it to a variable named P) with eight elements such that the last element is 5.9 and the rest of the elements are 0s. Do not type the vector elements explicitly.
13. Using the colon symbol, create a variable named Sevens that is a row vector of seven elements that are all the number 7.
12. Using the linspace command, create a row vector (assign it to a variable named Fours) with nine elements that are all 4.
11. Using the colon symbol, create a row vector (assign it to a variable named Time) in which the first element is 0, the spacing is 1, and the last element is 20.
10. Create a variable N that is a column vector with seven equally spaced elements in which the first element is 44 and the last element is 23. (A column vector can be created by the transpose of a row vector.)
9. Create a variable M that is a column vector in which the first element is 6.4, the elements increase with increments of 0.8, and the last element is 12. (A column vector can be created by the transpose of a row vector.)
8. Create a variable h that is a row vector with eight equally spaced elements in which the first element is 68 and the last element is 12.
7. Create a variable g that is a row vector in which the first element is 3 and the last element is 27, with an increment of 4 between the elements (3, 7, 11, … , 27).
6. Define the variables and , and then use them to create a column vector (assign it to a variable namedf) that has the following elements:d2,c, (c+d), cd, and d.
5. Define the variables and , and then use them to create a row vector (assign it to a variable namede) that has the following elements: x/y, x+y, xy, , y2, and x.
4. Create a variable d that is a column vector with the following elements:, 11.1, , , , and 0.116.
3. Create a variable c that is a column vector with the following elements:, , 28.5, 2.74/3, and e3.
2. Create a variable b that is a row vector with the following elements: ,, , 15.8, , and .
1. Create a variable a that is a row vector with the following elements: 9, 1, 32, 7/4, 0, , 0.8, and .
40. According to Newton's law of universal gravitation, the attraction force between two bodies is given by: F G where my and my are the masses of the bodies, r is the distance between the bodies, and G=6.67 10" N-m/kg is the universal gravitational constant. Determine how many times the attraction
39. Gosper's approximation for factorials is given by: =(2+) Use the formula for calculating 19!. Compare the result with the true value obtained with MATLAB's built-in function factorial by calculating the error (Error=(True Val-Approx Valy/TrueVal).
38. Use the Help Window to find a display format that displays the output as a ratio of integers. For example, the number 3.125 will be displayed as 25/8. Change the display to this format and execute the following operations: (a) 5/8+16/6 (b) 1/3-11/13 +2.72
37. The velocity v and the falling distance d as a function of time of a skydiver that experience the air resistance can be approximated by: kg where = 0.24 kg/m is a constant, m is the skydiver mass, g=9.81m/s is the acceleration due to gravity, and 7 is the time in seconds since the skydiver
36. Newton's law of cooling gives the temperature 7(1) of an object at time z in terms of To, its temperature at =0), and 7, the temperature of the sur- roundings.T(t)=T,+(T-T)e A police officer arrives at a crime scene in a hotel room at 9:18 PM, where he finds a dead body. He immediately measures
35. According to the Doppler effect of light, the perceived wavelength x, of a light source with a wavelength of, is given by: where e is the speed of light (about 300 x10 m/s) and v is the speed the observer moves toward the light source. Calculate the speed the observer has to move in order to
34. The amount of energy E (in joules) that is released by an earthquake is given by: E=1.741010 M where M is the magnitude of the earthquake on the Richter scale. (a) Determine the energy that was released from the Anchorage earthquake (1964, Alaska, USA), magnitude 9.2. (b) The energy released in
33. The greatest common divisor is the largest positive integer that divides the numbers without a remainder. For example, the greatest common divisor of 8 and 12 is 4. Use the MATLAB Help Window to find a MATLAB built-in function that determines the greatest common divisor of two numbers. Then use
32. Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modeled with the exponential function ()/(0), where r is time, f(0) is the amount of material at 1=0, f() is the amount of material at time 1, and k is a constant. Carbon-14 has a half-life of
31. The output voltage or in the circuit shown is given by (Millman's theorem): R R Vo RR R 1.11 36V, 28V, 1',=24V, Calculate Vout given R, 400, R, 2009, R, =600 2.
30. The equivalent resistance of two resistors R and R connected in parallel is given by Rea= RR R+R 2000 www The equivalent resistance of www 14052 Ra two resistors R and R, connected in series is given by R, R, +R. Determine the 80 www. www 2502 www equivalent resistance of the four resistors in
29. The number of combinations C of taking objects out of n objects is given by: 11-18) In the Powerball lottery game the player chooses five numbers from 1 through 59, and then the Powerball number from 1 through 35. Determine how many combinations are possible by calculating Csos Cast (Use the
28. The number of permutations P, of taking r objects out of n objects with- out repetition is given by: P= n! (-)! (a) Determine how many six-letter passwords can be formed from the 26 letters in the English alphabet if a letter can only be used once. (b) How many passwords can be formed if the
27. The monthly payment M of a mortgage P for n years with a fixed annual interest rate r can be calculated by the formula: M P- (1+)20-1 Determine the monthly payment of a 30-year $450,000 mortgage with inter- est rate of 4.2% (r=0.042). Define the variables P, r, and and then use them in the
26. The current in a series RCL circuit is given L 000 by: + WC where w=2rf. Calculate I for the circuit shown if the supply voltage is 80 = V. = 50 Hz, R=6L 400 x10 H, and C 4010 F.
25. The voltage difference Vab between points a and b in the Wheatstone bridge circuit is given by: e-d (c+I)(d+1), where c=R/R and d=R/R4. Calculate the Vab if = 15 V, R =119.8 R, 121.2 2 and R =119.3 2 R = 120.5
24. Change the display to format long g. Assign the number 7E8/13 to a variable, and then use the variable in a mathematical expression to calculate the following by typing one command: (a) Round the number to the nearest tenth. (b) Round the number to the nearest million.
23. A total of 777 people have to be transported using buses that have 46 seats and vans that have 12 seats. Calculate how many buses are needed if all the buses have to be full, and how many seats will remain empty in the vans if enough vans are used to transport all the people that did not fit

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