Solve 1/4*3.14*8.85*79*1.6^2/7.68*1.6*(1+1/sin75^circ)

$$\frac { 1 } { 4 \times 3.14 \times 8.85 } \times \frac { 79 \times 1.6 ^ { 2 } } { 7.68 \times 1.6 } \times ( 1 + \frac { 1 } { \sin 75 ^ { \circ } } )$$

Evaluate

$$\frac{6182648896370875625}{20516264550379810692}\approx 0.301353537$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{4 \cdot 3.14 \cdot 8.85} \cdot \frac{79 \cdot 1.6 ^ {2}}{7.68 \cdot 1.6} \cdot {(1 + \frac{1}{0.9659258262890683})}$$

Multiply 4 and 3.14 to get 12.56.

$$\frac{1}{12.56\times 8.85}\times \frac{79\times 1.6^{2}}{7.68\times 1.6}\left(1+\frac{1}{0.9659258262890683}\right)$$

Multiply 12.56 and 8.85 to get 111.156.

$$\frac{1}{111.156}\times \frac{79\times 1.6^{2}}{7.68\times 1.6}\left(1+\frac{1}{0.9659258262890683}\right)$$

Expand \frac{1}{111.156} by multiplying both numerator and the denominator by 1000.

$$\frac{1000}{111156}\times \frac{79\times 1.6^{2}}{7.68\times 1.6}\left(1+\frac{1}{0.9659258262890683}\right)$$

Reduce the fraction \frac{1000}{111156} to lowest terms by extracting and canceling out 4.

$$\frac{250}{27789}\times \frac{79\times 1.6^{2}}{7.68\times 1.6}\left(1+\frac{1}{0.9659258262890683}\right)$$

Cancel out 1.6 in both numerator and denominator.

$$\frac{250}{27789}\times \frac{1.6\times 79}{7.68}\left(1+\frac{1}{0.9659258262890683}\right)$$

Multiply 1.6 and 79 to get 126.4.

$$\frac{250}{27789}\times \frac{126.4}{7.68}\left(1+\frac{1}{0.9659258262890683}\right)$$

Expand \frac{126.4}{7.68} by multiplying both numerator and the denominator by 100.

$$\frac{250}{27789}\times \frac{12640}{768}\left(1+\frac{1}{0.9659258262890683}\right)$$

Reduce the fraction \frac{12640}{768} to lowest terms by extracting and canceling out 32.

$$\frac{250}{27789}\times \frac{395}{24}\left(1+\frac{1}{0.9659258262890683}\right)$$

Multiply \frac{250}{27789} times \frac{395}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{250\times 395}{27789\times 24}\left(1+\frac{1}{0.9659258262890683}\right)$$

Do the multiplications in the fraction \frac{250\times 395}{27789\times 24}.

$$\frac{98750}{666936}\left(1+\frac{1}{0.9659258262890683}\right)$$

Reduce the fraction \frac{98750}{666936} to lowest terms by extracting and canceling out 2.

$$\frac{49375}{333468}\left(1+\frac{1}{0.9659258262890683}\right)$$

Expand \frac{1}{0.9659258262890683} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{49375}{333468}\left(1+\frac{10000000000000000}{9659258262890683}\right)$$

Convert 1 to fraction \frac{9659258262890683}{9659258262890683}.

$$\frac{49375}{333468}\left(\frac{9659258262890683}{9659258262890683}+\frac{10000000000000000}{9659258262890683}\right)$$

Since \frac{9659258262890683}{9659258262890683} and \frac{10000000000000000}{9659258262890683} have the same denominator, add them by adding their numerators.

$$\frac{49375}{333468}\times \frac{9659258262890683+10000000000000000}{9659258262890683}$$

Add 9659258262890683 and 10000000000000000 to get 19659258262890683.

$$\frac{49375}{333468}\times \frac{19659258262890683}{9659258262890683}$$

Multiply \frac{49375}{333468} times \frac{19659258262890683}{9659258262890683} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49375\times 19659258262890683}{333468\times 9659258262890683}$$

Do the multiplications in the fraction \frac{49375\times 19659258262890683}{333468\times 9659258262890683}.

$$\frac{970675876730227473125}{3221053534409630278644}$$

Reduce the fraction \frac{970675876730227473125}{3221053534409630278644} to lowest terms by extracting and canceling out 157.

$$\frac{6182648896370875625}{20516264550379810692}$$

Factor

$$\frac{79 \cdot 6277 \cdot 19948734347 \cdot 5 ^ {4}}{43 \cdot 59 \cdot 3656111 \cdot 61440671 \cdot 2 ^ {2} \cdot 3 ^ {2}} = 0.3013535373941363$$