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Home » e.R.I.S. Explained: The Revolutionary Method Revolutionizing Health Today! - Carbonext

e.R.I.S. Explained: The Revolutionary Method Revolutionizing Health Today! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Contradiction. Hence, no such vector $\mathbf{w}$ exists.

📌 oxed{ ext{No solution exists}}

📌 Question: A museum curator is restoring a triangular panel from a historical instrument, where the triangle has vertices at $A = (1, 3, -2)$, $B = (4, 1, 1)$, and $C = (2, -1, 3)$. Find the point $P$ on the line through $A$ and $B$ that is closest to point $C$.

📌 Solution: The line through $A$ and $B$ is parametrized as:

📌 \mathbf{r}(t) = \mathbf{A} + t(\mathbf{B} - \mathbf{A}) = \langle 1, 3, -2

📌 angle + t\langle 3, -2, 3

📌 angle = \langle 1 + 3t, 3 - 2t, -2 + 3t

📌 Let $P = \mathbf{r}(t)$. The vector $\overrightarrow{CP} = \mathbf{r}(t) - \mathbf{C} = \langle 1 + 3t - 2, 3 - 2t + 1, -2 + 3t - 3

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So, \( (x+1)(x-1) = 2^3 = 8 \).
Then \( x^2 - 1 = 8 \).
\( x^2 = 9 \), so \( x = \pm 3 \).
Since \( x-1 > 0 \), \( x > 1 \), thus \( x = 3 \).
The function \( f(x) = rac{2x^2 - 3x + 1}{x - 1} \) has a removable d...
Factor numerator: \( 2x^2 - 3x + 1 = (2x - 1)(x - 1) \).
So \( f(x) = rac{(2x - 1)(x - 1)}{x - 1} = 2x - 1 \) for \( x
Removing discontinuity, \( f(1) = 2(1) - 1 = 1 \).
A sequence is defined recursively by \( a_1 = 2 \), \( a_{2} = 3 \), a...
\( a_3 = a_2 + 2a_1 = 3 + 2(2) = 7 \)

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