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Home » Gleichungen setzen**: \(2l + 2w = 36\), \(l = 2w\) - Nelissen Grade advocaten

Gleichungen setzen**: \(2l + 2w = 36\), \(l = 2w\) - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Substitute \( p = 2 \), \( q = 2 \) into (1):

📌 + 2 + r = 10 \implies r = 6

📌 Thus, \( p = 2 \), \( q = 2 \), \( r = 6 \).

📌 \boxed{p = 2, \, q = 2, \, r = 6}

📌 \]Question: A tech entrepreneur in Athens designs a drone navigation system where the drone's path is represented by unit vectors $\mathbf{u}$ and $\mathbf{v}$ with an angle $\theta$ between them. If $\mathbf{u} \cdot \mathbf{v} = \frac{\sqrt{3}}{2}$, find $\theta$.

📌 Solution: The dot product of two unit vectors is $\mathbf{u} \cdot \mathbf{v} = \cos\theta$. Given $\cos\theta = \frac{\sqrt{3}}{2}$, the angle $\theta$ satisfies $\theta = \arccos\left(\frac{\sqrt{3}}{2}\right)$. This corresponds to $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians. However, since cosine is positive in both the first and fourth quadrants, but angles between vectors are typically taken in $[0, \pi]$, the solution is $\boxed{\dfrac{\pi}{6}}$.

📌 Question: A biochemistry technician measures the angle between two molecular bonds modeled as vectors $\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}$. Compute $\cos\theta$ where $\theta$ is the angle between them.

📌 Solution: The cosine of the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is given by $\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|}$. Compute the dot product: $\mathbf{a} \cdot \mathbf{b} = (1)(0) + (0)(1) + (1)(1) = 1$. The magnitudes are $\|\mathbf{a}\| = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{2}$ and $\|\mathbf{b}\| = \sqrt{0^2 + 1^2 + 1^2} = \sqrt{2}$. Thus, $\cos\theta = \frac{1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$. The final answer is $\boxed{\dfrac{1}{2}}$.

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Ratio = 225 / 0 → still undefined.
But since KE = (1/2)mv², and v = 15 > 0, ratio is undefined.
Thus, to fix: change to same mass or use relative comparison.
A science educator demonstrates that a 1000-kg car at 20 m/s has kinet...
Car KE = 0.5 × 1000 × 400 = 200,000 J
Boulder KE = 0.5 × 2 × 10,000 = 10,000 J
Ratio = 200,000 : 10,000 = 20:1 → but question asks for ratio of car’s...
So: car KE / boulder KE = 200,000 / 10,000 = 20
Then ratio = 20:1 → but format wants single number.
So ratio is 20.

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