Solve ((0.1*10^2+0.19*21^2+0.24*35^2+0.18*49^2+0.11*{73}^{2}*0.08*{102}^2+0.06*{122}^2+0.04*{146}^2)*{10}^6)div100894.8

$$((0.1 \times { 10 }^{ 2 } +0.19 \times { 21 }^{ 2 } +0.24 \times { 35 }^{ 2 } +0.18 \times { 49 }^{ 2 } +0.11 \times { 73 }^{ 2 } \times 0.08 \times { 102 }^{ 2 } +0.06 \times { 122 }^{ 2 } +0.04 \times { 146 }^{ 2 } ) \times { 10 }^{ 6 } ) \div 100894.8$$

Evaluate

$$\frac{1226158277000}{252237}\approx 4861135.666060094$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{\left(0.1\times 100+0.19\times 21^{2}+0.24\times 35^{2}+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.1 and 100 to get 10.

$$\frac{\left(10+0.19\times 21^{2}+0.24\times 35^{2}+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 21 to the power of 2 and get 441.

$$\frac{\left(10+0.19\times 441+0.24\times 35^{2}+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.19 and 441 to get 83.79.

$$\frac{\left(10+83.79+0.24\times 35^{2}+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Add 10 and 83.79 to get 93.79.

$$\frac{\left(93.79+0.24\times 35^{2}+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 35 to the power of 2 and get 1225.

$$\frac{\left(93.79+0.24\times 1225+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.24 and 1225 to get 294.

$$\frac{\left(93.79+294+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Add 93.79 and 294 to get 387.79.

$$\frac{\left(387.79+0.18\times 49^{2}+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{\left(387.79+0.18\times 2401+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.18 and 2401 to get 432.18.

$$\frac{\left(387.79+432.18+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Add 387.79 and 432.18 to get 819.97.

$$\frac{\left(819.97+0.11\times 73^{2}\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 73 to the power of 2 and get 5329.

$$\frac{\left(819.97+0.11\times 5329\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.11 and 5329 to get 586.19.

$$\frac{\left(819.97+586.19\times 0.08\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 586.19 and 0.08 to get 46.8952.

$$\frac{\left(819.97+46.8952\times 102^{2}+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 102 to the power of 2 and get 10404.

$$\frac{\left(819.97+46.8952\times 10404+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 46.8952 and 10404 to get 487897.6608.

$$\frac{\left(819.97+487897.6608+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Add 819.97 and 487897.6608 to get 488717.6308.

$$\frac{\left(488717.6308+0.06\times 122^{2}+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 122 to the power of 2 and get 14884.

$$\frac{\left(488717.6308+0.06\times 14884+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Multiply 0.06 and 14884 to get 893.04.

$$\frac{\left(488717.6308+893.04+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Add 488717.6308 and 893.04 to get 489610.6708.

$$\frac{\left(489610.6708+0.04\times 146^{2}\right)\times 10^{6}}{100894.8}$$

Calculate 146 to the power of 2 and get 21316.

$$\frac{\left(489610.6708+0.04\times 21316\right)\times 10^{6}}{100894.8}$$

Multiply 0.04 and 21316 to get 852.64.

$$\frac{\left(489610.6708+852.64\right)\times 10^{6}}{100894.8}$$

Add 489610.6708 and 852.64 to get 490463.3108.

$$\frac{490463.3108\times 10^{6}}{100894.8}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{490463.3108\times 1000000}{100894.8}$$

Multiply 490463.3108 and 1000000 to get 490463310800.

$$\frac{490463310800}{100894.8}$$

Expand \frac{490463310800}{100894.8} by multiplying both numerator and the denominator by 10.

$$\frac{4904633108000}{1008948}$$

Reduce the fraction \frac{4904633108000}{1008948} to lowest terms by extracting and canceling out 4.

$$\frac{1226158277000}{252237}$$

Factor

$$\frac{22783 \cdot 53819 \cdot 2 ^ {3} \cdot 5 ^ {3}}{3 \cdot 83 \cdot 1013} = 4861135\frac{168005}{252237} = 4861135.666060095$$