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Answer
La suma \( \sum F_x \) es aproximadamente **-0.274**.
Solution
Para calcular la suma \( \sum F_x \):
\[
\sum F_x = 0 \cdot \sin(0°) + 0.8 \cdot \sin(-20°)
\]
Sabemos que:
\[
\sin(0°) = 0
\]
\[
\sin(-20°) = -\sin(20°) \approx -0.3420
\]
Sustituyendo estos valores en la expresión:
\[
\sum F_x = 0 \cdot 0 + 0.8 \cdot (-0.3420) = -0.2736
\]
Por lo tanto, la suma \( \sum F_x \) es aproximadamente **-0.274**.
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Simplify this solution Bonus Knowledge
Did you know that the sine function plays a crucial role in physics, particularly in vector resolution? When you break down forces, the sine helps to determine the vertical components, showcasing the elegance of trigonometry in understanding forces in equilibrium. It's like a dance of numbers that keeps everything balanced! Also, when tackling equations like this one, a common mistake is neglecting to pay attention to the angle's direction and sign. Ensure you carefully assess the quadrants and how sine values can be negative or positive depending on the angle—this is essential for accurate solutions! It’s like making sure every dance partner is in sync!
