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Discrete Mathematics Q&A Archive of March 23, 2025

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March 23 of 2025

Draw the graph of the function \( f(x)=\lceil 2 x]+1 \quad \) (take minimum 6 values) \begin{tabular}{|c|c|} \hline\( x \) & {\( [2 x\rceil+11 \)} \\ \hline-2 & -3 \\ -1.5 & -2 \\ -1 & -1 \\ -0.5 & 0 \\ 0 & 1 \\ 0.5 & 2 \\ 1 & 3 \\ 1.5 & 4 \\ 2 & 5 \\ \hline \end{tabular}
Type your answer into the boxes. The ratio of yellow balls to green balls in a bag is \( 4: 2 \) What fraction of the balls are yellow? \( \square \) \( \square \) Give your answer in its simplest form.
(d) \( \mathcal{L}^{-1}\left\{\frac{3}{2 s^{2}+7}\right\} \) [2]
2. Using \( \left[\begin{array}{lll}x_{1} & x_{2} & x_{3}\end{array}\right]=\left[\begin{array}{lll}1 & 3 & 5\end{array}\right] \) as the initial guess, the value of \( \left[\begin{array}{lll}x_{1} & x_{2} & x_{3}\end{array}\right] \) after three iterations in Gauss-Seidel method…
4. Using a computer with four significant digits with chopping, Gaussian elimination with partial pivoting solution to \[ \begin{array}{l} 0.0030 x_{1}+55.23 x_{2}=58.12 \\ 6.239 x_{1}-7.123 x_{2}=47.23 \end{array} \] is (A) \( x_{1}=26.66 ; x_{2}=1.051 \) (B) \( x_{1}=8.769 ; x_{2}=1.051…
Reflection questions: - How do these assets support learning? (5 Marks) - What strengths do they represent? (5 Marks)
\[ \begin{array}{l|l} { }^{-1}(x) & \text { ii) } f(x)=\frac{2 x-3}{x+4}, x \neq-4 \\ f^{-1} y g & f(x)=\frac{2 x-3}{x+4} \\ \text { etiap } & \begin{aligned} f(y) & =x \\ \frac{2 y-3}{y+4} & =x \\ 2 y-3 & =x(y+4) \\ 2 y-3 & =x y+4 x \\ 2 y-x y & = \end{aligned} \$ f^{-1(x)} \end{array} \] Date
ini \( f(x)=\frac{x+2}{x-2} \) biar \( y=f^{-1}(x) \) \[ \begin{aligned} f(y) & =x \\ \frac{y+2}{y-2} & =x \\ y+2 & =x(y-2) \\ y+2 & =x y-2 x \\ y-x y & =-2 x-2 \\ y(1-x) & =-2 x-2 \\ y & =\frac{-2 x-2}{1-x} \\ & =\frac{-2(x+1)}{(x-1)} \end{aligned} \]