Advanced Math

Problem 1: Given the following data for the results of Test 1 for course MATH2100 (a) Create the histogram for the number of observation and relative frequency for the above data. (b) Create the cumulative frequency. (c) Find the mode, mean, median and standard deviation for the above. (d) Use Microsoft Excel and MatLab and check your results.

EXPERT ANSWER First of all insert the values in MSExcel and add one relative frequency column, and insert a graph (histogram)

Let f(x) = e* -2- x, and starting with (-2.4,-1.6]. Write one C++ program that does the following: a. C. Find the roots of f(x) = 0 accurate to 3 x 10′ using the Bisection Method. b. Print all approximated roots Cn. Print the number of iterations needed to reach given accuracy using Bisection Method. d. Find the roots of f(x) = 0 accurate to 4.5 x 10 using the False Position Method. e. Print all intervals (a, b). f. Print the number of iterations needed to reach given accuracy using False Position Method. Note: given accuracy is 8 Active Wind

EXPERT ANSWER C++ code:- #include <iostream> #include <cmath> using namespace std; #define EP 0.01 // An example function whose solution is determined using // Bisection Method. The function is exp(x)-2-x double solution(double x) { return exp(x)- 2-x; } // Prints root of solution(x) with error in EPSILON void bisection(double a, double b) { if (solution(a) …

Let f(x) = e* -2- x, and starting with (-2.4,-1.6]. Write one C++ program that does the following: a. C. Find the roots of f(x) = 0 accurate to 3 x 10′ using the Bisection Method. b. Print all approximated roots Cn. Print the number of iterations needed to reach given accuracy using Bisection Method. d. Find the roots of f(x) = 0 accurate to 4.5 x 10 using the False Position Method. e. Print all intervals (a, b). f. Print the number of iterations needed to reach given accuracy using False Position Method. Note: given accuracy is 8 Active Wind Read More »

In Example 4.29 we deduced the equipotence [0, 1] ≈ (0, 1) by invoking the Schr¨oder–Bernstein theorem, but we didn’t actually construct a bijection [0, 1] → (0, 1). (a) Verify that the function h given by the following scheme is such a bijection:

How do you prove surjection for the middle function? EXPERT ANSWER Answer :- Bijective. Alternatively, f is bijective if it is a one-to-one correspondence between those sets, in other words both injective and surjective. Example: The function f(x) = x2 from the set of positive real numbers to positive real numbers is both injective and surjective. Thus it is also bijective.

Consider the following problem: Minimize Z= 5×1 + 722 subject to 201 + 3×2 > 147 3×1 + 4×2 > 210 i + 22 > 63 x1 > 0, x2 > 0. (1) 2) (3) (a) Let M +0. Let Z = -2. Let e; and a; be the excess and artificial variables for the constraint i (i = 1,2,3). Construct the initial big-M simplex tableau in canonical form. (b) Identify X5,X, C, A, b and Zo of the matrix equation for the initial simplex tableau. (c) A basis for the problem is given by 12 IB= ei 21 Construct the corresponding big-M simplex tableau by the fundamental insight. (d) Find the optimal solution for (x1, x2) and the associated optimal value for Z. (Note: You may use either tabular form or matrix form of the big-M simplex method.)

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A homicide victim is found at 6: 00 PM in an office building that is maintained at 72 degree F. When the victim was found, his body temperature was at 85 degree F. Three hours later at 9: 00 PM, his body temperature was recorded at 78 degree F. Assume the temperature of the body at the time of death is the normal human body temperature of98.6 degree F. The governing equation for the temperature theta of the body is d theta/dt = – k(theta – theta_) where, theta = temperature of the body, F, theta_ = ambient temperature, F, t = time, hours, k constant based on thermal properties of the body and air. Estimate the time of death.

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A linear spring-mass-damper system is illustrated in the figure below. w(t) k m f(t) 1 5 This dynamic system is governed by the following ordinary differential equation; dt? d’w dw m +5 + kw=f(t) dt where w denotes the position of the mass from its equilibrium position, f(t)is the forcing function, and m, 5, and k denote the mass, damping, and stiffness coefficients, respectively. For a spring system with mass m = 1, damping coefficient 5 = 2, spring constant k = 5 and the forcing function f(t)=4ecos 2t initial conditions given as w(0)=1 and w'(O)=0. 1. Obtain the analytical solution via method of undetermined coefficient method. 2. Obtain the analytical solution via method of variation of parameters.

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