Solve 4+176*sin(35^circ)*3.92-1/2*9.81*3.92^2

$$4 + 176 \times \sin ( 35 ^ { \circ } ) \times 3.92 - \frac { 1 } { 2 } \times 9.81 \times 3.92 ^ { 2 }$$

Evaluate

$$324.34966296731365632$$

Solution Steps

Evaluate trigonometric functions in the problem

$$4 + 176 \cdot 0.573576436351046 \cdot 3.92 - \frac{1}{2} \cdot 9.81 \cdot 3.92 ^ {2}$$

Multiply 176 and 0.573576436351046 to get 100.949452797784096.

$$4+100.949452797784096\times 3.92-\frac{1}{2}\times 9.81\times 3.92^{2}$$

Multiply 100.949452797784096 and 3.92 to get 395.72185496731365632.

$$4+395.72185496731365632-\frac{1}{2}\times 9.81\times 3.92^{2}$$

Add 4 and 395.72185496731365632 to get 399.72185496731365632.

$$399.72185496731365632-\frac{1}{2}\times 9.81\times 3.92^{2}$$

Convert decimal number 9.81 to fraction \frac{981}{100}.

$$399.72185496731365632-\frac{1}{2}\times \frac{981}{100}\times 3.92^{2}$$

Multiply \frac{1}{2} times \frac{981}{100} by multiplying numerator times numerator and denominator times denominator.

$$399.72185496731365632-\frac{1\times 981}{2\times 100}\times 3.92^{2}$$

Do the multiplications in the fraction \frac{1\times 981}{2\times 100}.

$$399.72185496731365632-\frac{981}{200}\times 3.92^{2}$$

Calculate 3.92 to the power of 2 and get 15.3664.

$$399.72185496731365632-\frac{981}{200}\times 15.3664$$

Convert decimal number 15.3664 to fraction \frac{153664}{10000}. Reduce the fraction \frac{153664}{10000} to lowest terms by extracting and canceling out 16.

$$399.72185496731365632-\frac{981}{200}\times \frac{9604}{625}$$

Multiply \frac{981}{200} times \frac{9604}{625} by multiplying numerator times numerator and denominator times denominator.

$$399.72185496731365632-\frac{981\times 9604}{200\times 625}$$

Do the multiplications in the fraction \frac{981\times 9604}{200\times 625}.

$$399.72185496731365632-\frac{9421524}{125000}$$

Reduce the fraction \frac{9421524}{125000} to lowest terms by extracting and canceling out 4.

$$399.72185496731365632-\frac{2355381}{31250}$$

Convert decimal number 399.72185496731365632 to fraction \frac{312282699193213794}{10000000000}. Reduce the fraction \frac{312282699193213794}{10000000000} to lowest terms by extracting and canceling out 2.

$$\frac{156141349596606897}{390625000000000}-\frac{2355381}{31250}$$

Least common multiple of 390625000000000 and 31250 is 390625000000000. Convert \frac{156141349596606897}{390625000000000} and \frac{2355381}{31250} to fractions with denominator 390625000000000.

$$\frac{156141349596606897}{390625000000000}-\frac{29442262500000000}{390625000000000}$$

Since \frac{156141349596606897}{390625000000000} and \frac{29442262500000000}{390625000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{156141349596606897-29442262500000000}{390625000000000}$$

Subtract 29442262500000000 from 156141349596606897 to get 126699087096606897.

$$\frac{126699087096606897}{390625000000000}$$

Factor

$$\frac{23 \cdot 163 \cdot 3319 \cdot 5279 \cdot 23813 \cdot 3 ^ {4}}{2 ^ {9} \cdot 5 ^ {17}} = 324\frac{136587096606896}{390625000000000} = 324.34966296731363$$