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Home » The solutions are $ \boxed{2 + \sqrt7} $ and $ \boxed{2 - \sqrt7} $. - Get link 4share

The solutions are $ \boxed{2 + \sqrt7} $ and $ \boxed{2 - \sqrt7} $. - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The area where the device is **not** operational is the difference:

📌 A_{\text{non-operational}} = 36\pi - 9\pi = 27\pi \text{ cm}^2

📌 Thus, the area is $\boxed{27\pi}$ square centimeters.

📌 Question: An entomologist models the flight path of a pollinating insect as a triangle with side lengths $13$, $14$, and $15$ meters. What is the length of the longest altitude of this triangle?

📌 Solution: First, compute the area of the triangle using Heron’s formula. The semi-perimeter is:

📌 Area $A$ is:

📌 = \sqrt{7056} = 84 \text{ m}^2

📌 The altitude corresponding to a side is $ h = \frac{2A}{\text{side}} $. The longest altitude corresponds to the shortest side, which is 13 m:

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\mathbf{u} \cdot \mathbf{u} = 4,\quad \|\mathbf{v}\|^2 = 9,\quad \|\ma...
\mathbf{u} \cdot \mathbf{v} = 1,\quad \mathbf{v} \cdot \mathbf{w} = 6.
Assume all vectors lie in a 3D subspace. Express \(\mathbf{u}\) and \(...
Let us apply the inequality:
but refine using vector decomposition. Decompose \(\mathbf{w}\) into c...
\mathbf{w} = \mathbf{w}_\parallel + \mathbf{w}_\perp, \quad \mathbf{w}...
\|\mathbf{w}_\perp\|^2 = \|\mathbf{w}\|^2 - \|\mathbf{w}_\parallel\|^2...
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