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Lawrence A.
Tutor for 7 years, Retired engineer and college professor
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MATLAB
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Question:

Write a short Matlab code to obtain the sum of the first 10 terms of the series $$S = 1 +\frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \, ... \,$$ Evaluate the sum for x = 2.

Lawrence A.

function testSum() clc n = input('Enter number of terms to use [10] '); if isempty(n); n=10; end x = input('Enter x [2] '); if isempty(x); x=2; end % Note that 0,1,2, ... (n-1) equals n terms. S=0; for j=0:n-1 S = S + 1/x^j; end fprintf(1,'Number of terms = %d\n',n); fprintf(1,'Sum of series = %8.4f\n',S); end ------------------------------------------------- Matlab output: Enter number of terms to use [10] Enter x [2] Number of terms = 10 Sum of series = 1.9980

Pre-Calculus
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Question:

It s known that the following polynomial has a zero at x=1. f(x) = $$x^3 - 2x^2 + 3x -2$$ Use synthetic division to factorize the polynomial.

Lawrence A.

Because x=1 is a zero, a factor of the polynomial is (x-1). Perform synthetic division. Explanation 1 | 1 -2 3 -2 Write the coefficients of the polynomial. 1 -1 2 This line will be filled with math operations. ------------------ 1 -1 2 0 Therefore f(x) = (x-1)($$x^2 -x+2$$). Answer: $$f(x)=(x-1)(x^2-x+2)$$

Numerical Analysis
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Question:

Mary’s score on a test was 25% higher than Jim’s score. The sum of Mary’s and Jim’s scores was 153. Determine Mary’s score

Lawrence A.

Let x = Mary’s score, and y = Jim’s score. Because Mary's score was 25% higher than Jim's score, therefore x = y +(25/100)y = y + (1/4)y = (5/4)y. That is, x = (5/4)y. Multiply each side by 4 to obtain 4x = 5y (1) The sum of the two scores is 153, therefore x + y = 153 (2) Rewrite equation (2) as y = 153 - x (3) Substitute equation (3) into equation (1). 4x = 5(153 - x) = 765 - 5x Add 5x to each side. 9x = 765 x = 765/9 = 85 Answer: Mary’s score was 85.

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