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Home » \[ x^3 - 5x^2 + 6x - 4 = 0 \] - Groen Casting

\[ x^3 - 5x^2 + 6x - 4 = 0 \] - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We know $ an 60^\circ = \sqrt{3} $, so:

📌 an 120^\circ = -\sqrt{3}

📌 Final answer: $ oxed{-\sqrt{3}} $

📌 Question: In a triangle with side lengths 13, 14, and 15 units, find the length of the longest altitude.

📌 s = rac{13 + 14 + 15}{2} = 21

📌 Area $ A $ is:

📌 A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}

📌 = \sqrt{21 \cdot 8 \cdot 42} = \sqrt{7056} = 84

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= \sqrt{21 \cdot 8 \cdot 42} = \sqrt{7056} = 84 \text{ cm}^2
The shortest altitude corresponds to the longest side, which is 15 cm....
= \frac{1}{2} \cdot 15 \cdot h \Rightarrow 168 = 15h \Rightarrow h = \...
Thus, the shortest altitude is $ \boxed{11.2} $.Question: Find the vec...
Solution: Let $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$. Compute $\...
\mathbf{v} \times \mathbf{b} = \begin{vmatrix}
\end{vmatrix} = \langle 3v_2 - 2v_3, 3v_1 - v_3, 2v_1 - v_2 \rangle.
Set this equal to $\mathbf{c} - \mathbf{b} = \langle 3, 3, 3 \rangle$:
3v_2 - 2v_3 = 3 \\
3v_1 - v_3 = 3 \\

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