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Home » \(8x = 32\) â \(x = rac328 = 4\). - Groen Casting

\(8x = 32\) â \(x = rac328 = 4\). - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. Calculate its area using Heron's formula.

📌 Semi-perimeter (s) = (13 + 14 + 15) / 2 = 21 cm.

📌 Area = √[s(s - a)(s - b)(s - c)].

📌 Area = √[21(21 - 13)(21 - 14)(21 - 15)] = √[21 * 8 * 7 * 6].

📌 Area = √[7056] = 84 cm².

📌 A cylindrical tank has a height of 10 m and a base radius of 3 m. What is the volume of the tank (use π = 3.14)?

📌 Volume formula: V = πr²h.

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\mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = \mathbf{a} \times \...
Using the identity $ \mathbf{a} \times (\mathbf{v} \times \mathbf{a})...
\|\mathbf{a}\|^2 \mathbf{v} = \mathbf{a} \times \mathbf{b}
Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $
Now compute $ \mathbf{a} \times \mathbf{b} $:
\mathbf{a} \times \mathbf{b} = \begin{vmatrix}
& -2 & 1 \\
\end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \c...
= \mathbf{i}(2 + 6) - \mathbf{j}(1 - 3) + \mathbf{k}(-2 - 2) = \langle...
14\mathbf{v} = \langle 8, 2, -4 \rangle \quad \Rightarrow \quad \mathb...

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