The following equation can be used to compute values of y as a function of x: y=be¯ªsin(bx) (0.0012x¹ −0.15x³ +0.075x² +2.5x) where a and b are parameters. (a) Write Python code to compute a vector y for a = 2, b = 5, and x as a vector with values from 0 to π/2 in increments Ax= π/40. (b) Compute the vector z = y² with element-by-element-wise operations. (c) Combine x, y, and zinto a 3-column matrix W.(Hint use np. hstack function) (d) Generate a plot of y and z versus x. Include a title, axis labels, and a legend. For the y versus x curve, format a solid blue line. For the z versus x curve, choose a magenta dashed line. Include grid lines.

(Computation) Among other applications, Pascal’s triangle (see Figure 7.22) provides a means of determining the number of possible combinations of n things taken r at a time. For example, the number of possible combinations of five people (n = 5) taken two at a time (r=2)is10. Each row of the triangle begins and ends with 1. Every other element in a row is the sum of the element directly above it with the element to the left of the one above it. That is, element[n][r]=element[n1][r]+element[n1][r1] Using this information, write and test a C++ program to create the first 11 rows of a twodimensional array representing Pascal’s triangle. For any given value of n less than 11 and r less than or equal to n, the program should display the correct element. Use your program to determine in how many ways a committee of 8 can be selected from a group of 10 people

(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.

(Data processing) Your professor has asked you to write a C++ program that determines grades at the end of the semester. For each student, identified by an integer number between 1 and 60, four exam grades must be kept, and two final grade averages must be computed. The first grade average is simply the average of all four grades. The second grade average is computed by weighting the four grades as follows: The first grade gets a weight of 0.2, the second grade gets a weight of 0.3, the third grade gets a weight of 0.3, and the fourth grade gets a weight of 0.2. That is, the final grade is computed as follows: 0.2grade1+0.3grade2+0.3grade3+0.2grade4 Using this information, construct a 60-by-7 two-dimensional array, in which the first column is used for the student number, the next four columns for the grades, and the last two columns for the computed final grades. The program’s output should be a display of the data in the completed array. For testing purposes, the professor has provided the following data:

(Practice) State whether the following are valid function names and if so, whether they’re mnemonic names that convey some idea of the function’s purpose. If they are invalid names, state why. powerdensity m1234 newamp 1234 abcd total tangent absval computed b34a 34ab volts$ a2B3 while minVal sine $sine cosine speed netdistance sum return stack

(Practice) Write a C++ program that adds equivalent elements of the two-dimensional arrays named first and second. Both arrays should have two rows and three columns. For example, element [1][2] of the resulting array should be the sum of first [1][2]andsecond[1][2]. The first and second arrays should be initialized as follows: first second 16 18 23 24 52 77 54 9111 16 19 59

(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

(Numerical) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is A=s(sa)(sb)(sc) where s=(a+b+c)2 Write, test, and execute a function that accepts the values of a, b, and c as parameters from a calling function, and then calculates the values of sand[s(sa)(sb)(sc)]. If this quantity is positive, the function calculates A. If the quantity is negative, a, b, and c do not form a triangle, and the function should set A=1. The value of A should be returned by the function.

(Practice) Write array declarations, including initializers, for the following: a. A list of 10 integer voltages: 89, 75, 82, 93, 78, 95, 81, 88, 77, and 82 b. A list of five double-precision slopes: 11.62, 13.98, 18.45, 12.68, and 14.76 c. A list of 100 double-precision distances; the first six distances are 6.29, 6.95, 7.25, 7.35, 7.40, and 7.42 d. A list of 64 double-precision temperatures; the first 10 temperatures are 78.2, 69.6, 68.5, 83.9, 55.4, 67.0, 49.8, 58.3, 62.5, and 71.6 e. A list of 15 character codes; the first seven codes are f, j, m, q, t, w, and z

(Statistical) In many statistical analysis programs, data values considerably outside the range of the majority of values are simply dropped from consideration. Using this information, write a C++ program that accepts up to 10 floating-point values from a user and determines and displays the average and standard deviation of the input values. All values more than four standard deviations away from the computed average are to be displayed and dropped from any further calculation, and a new average and standard deviation should be computed and displayed.