A worker pushes a box across the floor. Which option correctly describes what happens, based on Newton's third law of motion?
A. The box pushes back against the worker with less force.
B. The box pushes back against the worker with an equal force.
C. The box pushes back against the worker with a greater force.
Answer (3)
The equation is − 0.25 x 2 − x + 2 = 0 The coordinates are ( 2 a − b ; 4 a − Δ ) Δ = b 2 − 4 a c = 1 + 2 = 3 The coordinates, thus, are ( − 0.5 1 ; − 1 − 1 ) = ( − 2 ; 1 )
The coordinates of the focus of the given parabola -0.25x² = y - 2 are (0, 1), after rearranging the equation into standard form and calculating the focus using the formula related to the vertex form of a parabola.
To determine the coordinates of the focus of the given parabola -0.25x² = y - 2, we first rewrite the equation in the standard form of a parabola. Starting with the given equation, we add 2 to both sides to get y = -0.25x² + 2. This is in the form of y = a(x - h)² + k, where the vertex (h, k) is at (0, 2), because h = 0 and k = 2 in this equation. Given that the parabola opens downwards (a negative coefficient for x²), the focus is below the vertex.
In the standard form y = a(x - h)² + k, the focus is at (h, k + p), where p = 1/(4a). For our equation, a = -0.25 and the focus is (0, 2 + p). We find p by calculating 1/(4a), thus p = -1.
Therefore, the focus is at (0, 2 - 1), which simplifies to (0, 1).
The coordinates of the focus of the parabola − 0.25 x 2 = y − 2 are (0, 1), found by first rearranging the equation to identify the vertex and then calculating the focus using the formula involving p . Therefore, the correct answer is option B.
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