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Chapter 1: Problem 4

Suppose that \(u=1\) and \(v=3\). Evaluate the following expressions asing MATLAB. a. \(\frac{4 u}{3 v}\) b. \(\frac{2 v^{-2}}{(u+v)^{2}}\) c. \(\frac{v^{3}}{v^{3}-u^{3}}\) d. \(\frac{4}{3} \pi v^{2}\)

Short Answer

Expert verified
The short answers for the given expressions are: a. \(\frac{4 u}{3 v} = \frac{4}{9}\) b. \(\frac{2 v^{-2}}{(u+v)^{2}} = \frac{2}{225}\) c. \(\frac{v^{3}}{v^{3}-u^{3}} = 1.5\) d. \(\frac{4}{3} \pi v^{2} = 12\pi\)

Step by step solution

01

Define the given values

First, we need to define the given values for u and v using Matlab code. We can do this with the following code: u = 1; v = 3;
02

Compute expression a

Now, we'll compute the first expression: \(\frac{4 u}{3 v}\) using Matlab code. We can do this with the following code: expression_a = 4*u/(3*v);
03

Compute expression b

Next, we'll compute the second expression: \(\frac{2 v^{-2}}{(u+v)^{2}}\) using Matlab code. We can do this with the following code: expression_b = 2*v^(-2)/((u+v)^2);
04

Compute expression c

Now, we'll compute the third expression: \(\frac{v^{3}}{v^{3}-u^{3}}\) using Matlab code. We can do this with the following code: expression_c = v^3/(v^3-u^3);
05

Compute expression d

Finally, we'll compute the fourth expression: \(\frac{4}{3} \pi v^{2}\) using Matlab code. We can do this with the following code: expression_d = (4/3)*pi*v^2;
06

Display the results

Now that we have computed all the expressions, we can display the results using Matlab's "disp" function. We can do this with the following code: disp('Expression a:'), disp(expression_a); disp('Expression b:'), disp(expression_b); disp('Expression c:'), disp(expression_c); disp('Expression d:'), disp(expression_d);

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Most popular questions from this chapter

The following MATLAB statements plot the function \(y(x)=2 e^{-02 x}\) for the range \(0 \leq x \leq 10\). \(x=0: 0.1: 10 ;\) \(y=2 * \exp (-0.2 \cdot x) ;\) \(p 10 t(x, y):\) Use the MATLAB Edit Window to create a new empty M-file, type these statements into the file, and save the file with the name teat. 1 .m. Then, execute the program by typing the name test 1 in the Command Window. What result do you get?

Get help on the MATLAB function exp using: (a) The "help exp" command typed in the Command Window, and \((b)\) the Help Browser.

Assume that \(a, b, c\), and \(d\) are defined as follows, and calculate the results of the following operations if they are legal. If an operation is illegal, explain why it is illegal. $$ \begin{array}{ll} a=\left[\begin{array}{rr} 2 & -2 \\ -1 & 2 \end{array}\right] & b=\left[\begin{array}{rr} 1 & -1 \\ 0 & 2 \end{array}\right] \\ c=\left[\begin{array}{r} 1 \\ -2 \end{array}\right] & d=\text { eye }(2) \end{array} $$ a. result \(=a+b\); b. result \(=a=d_{i}\) c. result \(=a\). * \(d\); d. result \(=a \cdot c\); c. reault \(=a . * c\) ? f. result \(=a \backslash b\) : g. result \(=a .1 \mathrm{~b}\) : h. result \(=a . A b\);

Solve the following system of simultaneous equations for \(x\). \(-2.0 x_{1}+5.0 x_{2}+1.0 x_{3}+3.0 x_{4}+4.0 x_{5}-1.0 x_{6}=0.0\) \(2.0 x_{1}-1.0 x_{2}-5.0 x_{3}-2.0 x_{4}+6.0 x_{5}+4.0 x_{6}=1.0\) \(-1.0 x_{1}+6.0 x_{2}-4.0 x_{3}-5.0 x_{4}+3.0 x_{5}-1.0 x_{6}=-6.0\) \(4.0 x_{1}+3.0 x_{2}-6.0 x_{3}-5.0 x_{4}-2.0 x_{5}-2.0 x_{6}=10.0\) \(-3.0 x_{1}+6.0 x_{2}+4.0 x_{3}+2.0 x_{4}-6.0 x_{5}+4.0 x_{6}=-6.0\) \(2.0 x_{1}+4.0 x_{2}+4.0 x_{3}+4.0 x_{4}+5.0 x_{5}-4.0 x_{6}=-2.0\)

Determine the size and contents of the following arrays. Note that the later arrays may depend on the definitions of arrays defined earlier in this exercise. a. \(a=1: 2: 5\); b. \(b=\left\\{a^{+} a^{*} a^{*}\right\\}\) c. \(c=b(1: 2: 3,1: 2: 3)\); d. \(d=a+b(2,:)=\) c. \(w=\) [zeros \((1,3)\) ones \((3,1), 3: 5^{*}\) ? f. \(b([1] 3], 2)=b([3,1], 2)=\)
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