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Home » Now, the ratio of the volume of the nanoparticle to the volume of the carrier is: - Leaselab

Now, the ratio of the volume of the nanoparticle to the volume of the carrier is: - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \mathbf{v} \cdot \mathbf{d} = 4 \cdot 3 + 6 \cdot 1 = 12 + 6 = 18

📌 \mathbf{d} \cdot \mathbf{d} = 3^2 + 1^2 = 9 + 1 = 10

📌 Projection scalar:

📌 t = rac{18}{10} = 1.8

📌 Add \(t\mathbf{d}\) to \(\mathbf{r}_0\):

📌 egin{pmatrix} 1 \ -2 \end{pmatrix} + 1.8 egin{pmatrix} 3 \ 1 \end{pmatrix} = egin{pmatrix} 1 + 5.4 \ -2 + 1.8 \end{pmatrix} = egin{pmatrix} 6.4 \ -0.2 \end{pmatrix}

📌 Thus, the closest point on the bridge to the water source is \(oxed{egin{pmatrix} 6.4 \ -0.2 \end{pmatrix}}\).

📌 An online STEM student is exploring complex numbers and discovers the expression \((\cos rac{\pi}{6} + i \sin rac{\pi}{6})^6\). Compute this value and express it in the form \(a + bi\).

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