2 years ago

3n^2=6-17n I need Vertex form please.

Mathematics

1 answer:

nasty-shy [4]2 years ago

8 0

Answer:

3( n + $\frac{17}{6}$ )² - $\frac{361}{12}$ = 0

Step-by-step explanation:

3n² = 6 - 17n ⇔ 3n² + 17n - 6 = 0

3( n² + 2 × $\frac{17}{6}$ n + ( $\frac{17}{6}$ )² - ( $\frac{17}{6}$ )² - 2 ) = 0

3( n + $\frac{17}{6}$ )² - 3 × $\frac{289}{36}$ - 6 = 0

3( n + $\frac{17}{6}$ )² - $\frac{361}{12}$ = 0

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2 years ago

K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

spin [16.1K]

I suppose <em>K</em> is the matrix

$K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}$

To compute det(<em>K</em>), you can use a simple cofactor expansion along the first row:

$\det(K) = 14\times\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)\times\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0\times\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14\times(8\times5-(-1)\times(-2)) + 13\times(3\times5-(-1)\times(-10)) + 0 \\\\ \det(K) = 14\times38 + 13\times5 = \boxed{597}$