Користувач:Vogand/Геометричні моменти трикутників

́O (4; 3,8)
A (0; 0)
B (5,090; 4,0)
Маса: 68

$AO={\sqrt {4^{2}+3,8^{2}}}={\sqrt {16+14,44}}\approx {\sqrt {2\times 10^{1}+14}}={\sqrt {2\times 10^{1}+1,4\times 10^{1}}}={\sqrt {3,4\times 10^{1}}}\approx {\sqrt {3\times 10^{1}}}=2{\sqrt {10}}\approx 2\times 3,2=6,4\approx 6$
$BO={\sqrt {5,090^{2}+4,0^{2}}}={\sqrt {25,9081+16}}\approx {\sqrt {25,91+16}}={\sqrt {41,91}}\approx {\sqrt {42}}\approx 6,5$
$AB={\sqrt {(4-5,090)^{2}+(3,8-4,0)^{2}}}={\sqrt {(-1,090)^{2}+(-0,2)^{2}}}\approx {\sqrt {(-1)^{2}+(-0,2)^{2}}}={\sqrt {1+0,04}}={\sqrt {1,04}}\approx {\sqrt {1}}=1$
$p=6+6,5+1=12,5+1\approx 13+1=14$
$S={\sqrt {{\frac {14}{2}}({\frac {14}{2}}-6)({\frac {14}{2}}-6,5)({\frac {14}{2}}-1)}}={\sqrt {7(7-6)(7-6,5)(7-1)}}={\sqrt {7\times 1\times 0,5\times 6}}\approx {\sqrt {7\times 1\times 1\times 6}}={\sqrt {7\times 6}}={\sqrt {42}}\approx {\sqrt {4\times 10^{1}}}=2{\sqrt {10}}\approx 2\times 3,2=6,4=6$
$M=68\times 6=408\approx 4\times 10^{2}$
$R={\frac {4\times 10^{2}}{6^{2}+6,5^{2}}}={\frac {4\times 10^{2}}{36+42,25}}\approx {\frac {4\times 10^{2}}{4\times 10^{1}+42}}={\frac {4\times 10^{2}}{3\times 10^{1}+4,2\times 10^{1}}}={\frac {4\times 10^{2}}{7,2\times 10^{1}}}\approx {\frac {4\times 10^{2}}{7\times 10^{1}}}\approx 0,6\times 10^{1}=6$
$M(1)=6\times 4\times 10^{1}=24\times 10^{1}\approx 2\times 10^{1}\times 10^{1}=2\times 10^{2}$
$M(2)=6\times 42=252\approx 3\times 10^{2}$
${\frac {2\times 10^{2}}{3\times 10^{2}}}={\frac {2}{3}}\approx 0,7$