Solve 5.1*2*7.12/4.45^2+5.1*9.8*sin(35pi/180)+5.1*9.8*cos(35pi/180)*0.4

$$5.1 \times 2 \times \frac{ 7.12 }{ { 4.45 }^{ 2 } } +5.1 \times 9.8 \times \sin ( \frac{ 35 \pi }{ 180 } ) +5.1 \times 9.8 \times \cos ( \frac{ 35 \pi }{ 180 } ) \times 0.4$$

Evaluate

$$\frac{1354781743213850462487}{27812500000000000000}\approx 48.711253689$$

Solution Steps

Evaluate trigonometric functions in the problem

$$5.1 \cdot 2 \cdot \frac{7.12}{{(4.45)} ^ {2}} + 5.1 \cdot 9.8 \cdot 0.573576436351046 + 5.1 \cdot 9.8 \cdot 0.8191520442889918 \cdot 0.4$$

Multiply 5.1 and 2 to get 10.2.

$$10.2\times \frac{7.12}{4.45^{2}}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Calculate 4.45 to the power of 2 and get 19.8025.

$$10.2\times \frac{7.12}{19.8025}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Expand \frac{7.12}{19.8025} by multiplying both numerator and the denominator by 10000.

$$10.2\times \frac{71200}{198025}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Reduce the fraction \frac{71200}{198025} to lowest terms by extracting and canceling out 2225.

$$10.2\times \frac{32}{89}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Convert decimal number 10.2 to fraction \frac{102}{10}. Reduce the fraction \frac{102}{10} to lowest terms by extracting and canceling out 2.

$$\frac{51}{5}\times \frac{32}{89}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Multiply \frac{51}{5} times \frac{32}{89} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51\times 32}{5\times 89}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Do the multiplications in the fraction \frac{51\times 32}{5\times 89}.

$$\frac{1632}{445}+5.1\times 9.8\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Multiply 5.1 and 9.8 to get 49.98.

$$\frac{1632}{445}+49.98\times 0.573576436351046+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Multiply 49.98 and 0.573576436351046 to get 28.66735028882527908.

$$\frac{1632}{445}+28.66735028882527908+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Convert decimal number 28.66735028882527908 to fraction \frac{716683757220631977}{10000000000}. Reduce the fraction \frac{716683757220631977}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1632}{445}+\frac{716683757220631977}{25000000000000000}+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Least common multiple of 445 and 25000000000000000 is 2225000000000000000. Convert \frac{1632}{445} and \frac{716683757220631977}{25000000000000000} to fractions with denominator 2225000000000000000.

$$\frac{8160000000000000000}{2225000000000000000}+\frac{63784854392636245953}{2225000000000000000}+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Since \frac{8160000000000000000}{2225000000000000000} and \frac{63784854392636245953}{2225000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{8160000000000000000+63784854392636245953}{2225000000000000000}+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Add 8160000000000000000 and 63784854392636245953 to get 71944854392636245953.

$$\frac{71944854392636245953}{2225000000000000000}+5.1\times 9.8\times 0.8191520442889918\times 0.4$$

Multiply 5.1 and 9.8 to get 49.98.

$$\frac{71944854392636245953}{2225000000000000000}+49.98\times 0.8191520442889918\times 0.4$$

Multiply 49.98 and 0.8191520442889918 to get 40.941219173563810164.

$$\frac{71944854392636245953}{2225000000000000000}+40.941219173563810164\times 0.4$$

Multiply 40.941219173563810164 and 0.4 to get 16.3764876694255240656.

$$\frac{71944854392636245953}{2225000000000000000}+16.3764876694255240656$$

Convert decimal number 16.3764876694255240656 to fraction \frac{10235304793390952541}{10000000000}. Reduce the fraction \frac{10235304793390952541}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{71944854392636245953}{2225000000000000000}+\frac{10235304793390952541}{625000000000000000}$$

Least common multiple of 2225000000000000000 and 625000000000000000 is 55625000000000000000. Convert \frac{71944854392636245953}{2225000000000000000} and \frac{10235304793390952541}{625000000000000000} to fractions with denominator 55625000000000000000.

$$\frac{1798621359815906148825}{55625000000000000000}+\frac{910942126611794776149}{55625000000000000000}$$

Since \frac{1798621359815906148825}{55625000000000000000} and \frac{910942126611794776149}{55625000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{1798621359815906148825+910942126611794776149}{55625000000000000000}$$

Add 1798621359815906148825 and 910942126611794776149 to get 2709563486427700924974.

$$\frac{2709563486427700924974}{55625000000000000000}$$

Reduce the fraction \frac{2709563486427700924974}{55625000000000000000} to lowest terms by extracting and canceling out 2.

$$\frac{1354781743213850462487}{27812500000000000000}$$

Factor

$$\frac{3 \cdot 17 \cdot 227 \cdot 3557 \cdot 45599 \cdot 721496317}{89 \cdot 2 ^ {14} \cdot 5 ^ {19}} = 48\frac{1.9781743213850396 \times 10^{19}}{2.78125 \times 10^{19}} = 48.71125368858788$$