- x = 0 \Rightarrow x = 5
Related Articles
- Question: Find the value of $x$ such that the vectors $\begin{pmatrix} 2 \\ x \\ -3 \end{pmatrix}$ and $\begin{pmatrix} 4 \\ -1 \\ 1 \end{pmatrix}$ are orthogonal.
- Two vectors are orthogonal if their dot product is zero. Compute the dot product:
- \begin{pmatrix} 2 \\ x \\ -3 \end{pmatrix} \cdot \begin{pmatrix} 4 \\ -1 \\ 1 \end{pmatrix} = 2 \cdot 4 + x \cdot (-1) + (-3) \cdot 1 = 8 - x - 3 = 5 - x
- Question: A hydrologist is minimizing the energy cost of pumping water through an aquifer modeled by the function $f(x) = 2x^2 - 8x + 11$. Find the minimum value of $f(x)$.
- This is a quadratic function in the form $f(x) = ax^2 + bx + c$, with $a = 2 > 0$, so the parabola opens upward and has a minimum at the vertex.
- The x-coordinate of the vertex
