Center of gravity

The mass points are distributed in space as specified by coordinates and weight. Find the center of gravity of the mass points system:

A₁ [1; -20; 3] m₁ = 46 kg
A₂ [-20; 2; 9] m₂ = 81 kg
A₃ [9; -2; -10] m₃ = 59 kg
A₄ [3; 18; -14] m₄ = 91 kg
A₅ [6; -12; -19] m₅ = 48 kg
A₆ [5; 4; -18] m₆ = 72 kg
A₇ [-14; 3; 19] m₇ = 21 kg

Correct answer:

x₀ =  -0.9952
y₀ =  1.2847
z₀ =  -6.7129

Step-by-step explanation:

$$\begin{gathered} x_1=1;y_1=-20;z_1=3 \\ {m}_1=46 \\ {x}_2=-20;y_2=2;z_2=9 \\ {m}_2=81 \\ {x}_3=9;y_3=-2;z_3=-10 \\ {m}_3=59 \\ {x}_4=3;y_4=18;z_4=-14 \\ {m}_4=91 \\ {x}_5=6;y_5=-12;z_5=-19 \\ {m}_5=48 \\ {x}_6=5;y_6=4;z_6=-18 \\ {m}_6=72 \\ {x}_7=-14;y_7=3;z_7=19 \\ {m}_7=21 \\ m=m_1+m_2+m_3+m_4+m_5+m_6+m_7=46+81+59+91+48+72+21=418 \\ {M}_x=m_1\cdot x_1+m_2\cdot x_2+m_3\cdot x_3+m_4\cdot x_4+m_5\cdot x_5+m_6\cdot x_6+m_7\cdot x_7=46\cdot 1+81\cdot (-20)+59\cdot 9+91\cdot 3+48\cdot 6+72\cdot 5+21\cdot (-14)=-416 \\ {M}_y=m_1\cdot y_1+m_2\cdot y_2+m_3\cdot y_3+m_4\cdot y_4+m_5\cdot y_5+m_6\cdot y_6+m_7\cdot y_7=46\cdot (-20)+81\cdot 2+59\cdot (-2)+91\cdot 18+48\cdot (-12)+72\cdot 4+21\cdot 3=537 \\ {M}_z=m_1\cdot z_1+m_2\cdot z_2+m_3\cdot z_3+m_4\cdot z_4+m_5\cdot z_5+m_6\cdot z_6+m_7\cdot z_7=46\cdot 3+81\cdot 9+59\cdot (-10)+91\cdot (-14)+48\cdot (-19)+72\cdot (-18)+21\cdot 19=-2806 \\ {x}_0=\frac{M_x}{m}=\frac{(-416)}{418}=-\frac{208}{209}=-0.9952 \end{gathered}$$

$y_0=\frac{M_y}{m}=\frac{537}{418}=1\frac{119}{418}=1.2847$

$z_0=\frac{M_z}{m}=\frac{(-2806)}{418}=-\frac{1403}{209}=-6\frac{149}{209}=-6.7129$

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