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Home » The sum of the first n natural numbers is 210. Find n. - Aurero

The sum of the first n natural numbers is 210. Find n. - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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\|\vec{d}(t)\|^2 = (4 - 8t + 4t^2) + (1 + 2t + t^2) + (25 + 10t + t^2)...
Take derivative and set to 0:
\frac{d}{dt}(6t^2 + 4t + 30) = 12t + 4 = 0 \Rightarrow t = -\frac{1}{3...
Substitute $t = -\frac{1}{3}$ into $\vec{r}(t)$:
\vec{r}\left(-\frac{1}{3}\right) = \begin{pmatrix} 1 + 2(-\frac{1}{3})...
Thus, the closest point is:
\boxed{\begin{pmatrix} \frac{1}{3} \\ -\frac{1}{3} \\ -\frac{8}{3} \en...
Question: Find the value of $x$ such that the vectors $\begin{pmatrix}...
Two vectors are orthogonal if their dot product is zero. Compute the d...
\begin{pmatrix} 2 \\ x \\ -3 \end{pmatrix} \cdot \begin{pmatrix} 4 \\...

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