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Find the area of a semi-circle whose radius is 7cm. [Take π = 22/7]
Mathematics
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- If and , find .
Calculate $4P$.
$$ 4P = 4 \begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 4 \times 4 \\ 4 \times 3 \end{pmatrix} = \begin{pmatrix} 16 \\ 12 \end{pmatrix} $$Calculate $2Q$.
$$ 2Q = 2 \begin{pmatrix} 2 \\ -1 \end{pmatrix} = \begin{pmatrix} 2 \times 2 \\ 2 \times -1 \end{pmatrix} = \begin{pmatrix} 4 \\ -2 \end{pmatrix} $$Subtract $2Q$ from $4P$.
$$ 4P - 2Q = \begin{pmatrix} 16 \\ 12 \end{pmatrix} - \begin{pmatrix} 4 \\ -2 \end{pmatrix} $$ $$ 4P - 2Q = \begin{pmatrix} 16 - 4 \\ 12 - (-2) \end{pmatrix} $$ $$ 4P - 2Q = \begin{pmatrix} 12 \\ 12 + 2 \end{pmatrix} $$ $$ 4P - 2Q = \begin{pmatrix} 12 \\ 14 \end{pmatrix} $$ The calculated result is $\begin{pmatrix} 12 \\ 14 \end{pmatrix}$. This answer is not among the given options.28. Given that vector and , find the value of x if .
If two vectors are equal, their corresponding components must be equal.
$$ \begin{pmatrix} -5 \\ 12 \end{pmatrix} = \begin{pmatrix} 10x \\ 12 \end{pmatrix} $$Equate the x-components.
$$ -5 = 10x $$Solve for x.
$$ x = \frac{-5}{10} $$ $$ x = -\frac{1}{2} $$ The value of x is $\boxed{\text{B. } -\frac{1}{2}}$.
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