Solve 51*2*712/445^2+51*98*sin(35pi/180)+51*98*cos(35pi/180)*04

$$51 \times 2 \times \frac{ 712 }{ { 445 }^{ 2 } } +51 \times 98 \times \sin ( \frac{ 35 \pi }{ 180 } ) +51 \times 98 \times \cos ( \frac{ 35 \pi }{ 180 } ) \times 04$$

Evaluate

$$\frac{63793014392636245953}{22250000000000000}\approx 2867.101770456$$

Solution Steps

Evaluate trigonometric functions in the problem

$$51 \cdot 2 \cdot \frac{712}{{(445)} ^ {2}} + 51 \cdot 98 \cdot 0.573576436351046 + 51 \cdot 98 \cdot 0.8191520442889918 \cdot 0 \cdot 4$$

Multiply 51 and 2 to get 102. Multiply 51 and 98 to get 4998. Multiply 51 and 98 to get 4998.

$$102\times \frac{712}{445^{2}}+4998\times 0.573576436351046+4998\times 0.8191520442889918\times 0\times 4$$

Calculate 445 to the power of 2 and get 198025.

$$102\times \frac{712}{198025}+4998\times 0.573576436351046+4998\times 0.8191520442889918\times 0\times 4$$

Reduce the fraction \frac{712}{198025} to lowest terms by extracting and canceling out 89.

$$102\times \frac{8}{2225}+4998\times 0.573576436351046+4998\times 0.8191520442889918\times 0\times 4$$

Express 102\times \frac{8}{2225} as a single fraction.

$$\frac{102\times 8}{2225}+4998\times 0.573576436351046+4998\times 0.8191520442889918\times 0\times 4$$

Multiply 102 and 8 to get 816.

$$\frac{816}{2225}+4998\times 0.573576436351046+4998\times 0.8191520442889918\times 0\times 4$$

Multiply 4998 and 0.573576436351046 to get 2866.735028882527908.

$$\frac{816}{2225}+2866.735028882527908+4998\times 0.8191520442889918\times 0\times 4$$

Convert decimal number 2866.735028882527908 to fraction \frac{716683757220631977}{10000000000}. Reduce the fraction \frac{716683757220631977}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{816}{2225}+\frac{716683757220631977}{250000000000000}+4998\times 0.8191520442889918\times 0\times 4$$

Least common multiple of 2225 and 250000000000000 is 22250000000000000. Convert \frac{816}{2225} and \frac{716683757220631977}{250000000000000} to fractions with denominator 22250000000000000.

$$\frac{8160000000000000}{22250000000000000}+\frac{63784854392636245953}{22250000000000000}+4998\times 0.8191520442889918\times 0\times 4$$

Since \frac{8160000000000000}{22250000000000000} and \frac{63784854392636245953}{22250000000000000} have the same denominator, add them by adding their numerators.

$$\frac{8160000000000000+63784854392636245953}{22250000000000000}+4998\times 0.8191520442889918\times 0\times 4$$

Add 8160000000000000 and 63784854392636245953 to get 63793014392636245953.

$$\frac{63793014392636245953}{22250000000000000}+4998\times 0.8191520442889918\times 0\times 4$$

Multiply 4998 and 0.8191520442889918 to get 4094.1219173563810164.

$$\frac{63793014392636245953}{22250000000000000}+4094.1219173563810164\times 0\times 4$$

Multiply 4094.1219173563810164 and 0 to get 0.

$$\frac{63793014392636245953}{22250000000000000}+0\times 4$$

Multiply 0 and 4 to get 0.

$$\frac{63793014392636245953}{22250000000000000}+0$$

Add \frac{63793014392636245953}{22250000000000000} and 0 to get \frac{63793014392636245953}{22250000000000000}.

$$\frac{63793014392636245953}{22250000000000000}$$

Factor

$$\frac{17 \cdot 29 \cdot 197 \cdot 479 \cdot 152363856263 \cdot 3 ^ {2}}{89 \cdot 2 ^ {13} \cdot 5 ^ {15}} = 2867\frac{2264392636243968}{22250000000000000} = 2867.1017704555616$$