Solve 3.14*0.05*(30/2-2)/3((30/2)^2+30*2/2+2^2)

$$\frac { 3.14 \times 0.05 \times ( \frac { 30 } { 2 } - 2 ) } { 3 } ( ( \frac { 30 } { 2 } ) ^ { 2 } + \frac { 30 \times 2 } { 2 } + 2 ^ { 2 } )$$

Evaluate

$$\frac{528619}{3000}\approx 176.206333333$$

Solution Steps

Multiply 3.14 and 0.05 to get 0.157.

$$\frac{0.157\left(\frac{30}{2}-2\right)}{3}\left(\left(\frac{30}{2}\right)^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Divide 30 by 2 to get 15.

$$\frac{0.157\left(15-2\right)}{3}\left(\left(\frac{30}{2}\right)^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Subtract 2 from 15 to get 13.

$$\frac{0.157\times 13}{3}\left(\left(\frac{30}{2}\right)^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Multiply 0.157 and 13 to get 2.041.

$$\frac{2.041}{3}\left(\left(\frac{30}{2}\right)^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Expand \frac{2.041}{3} by multiplying both numerator and the denominator by 1000.

$$\frac{2041}{3000}\left(\left(\frac{30}{2}\right)^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Divide 30 by 2 to get 15.

$$\frac{2041}{3000}\left(15^{2}+\frac{30\times 2}{2}+2^{2}\right)$$

Calculate 15 to the power of 2 and get 225.

$$\frac{2041}{3000}\left(225+\frac{30\times 2}{2}+2^{2}\right)$$

Cancel out 2 and 2.

$$\frac{2041}{3000}\left(225+30+2^{2}\right)$$

Add 225 and 30 to get 255.

$$\frac{2041}{3000}\left(255+2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2041}{3000}\left(255+4\right)$$

Add 255 and 4 to get 259.

$$\frac{2041}{3000}\times 259$$

Multiply \frac{2041}{3000} and 259 to get \frac{528619}{3000}.

$$\frac{528619}{3000}$$

Factor

$$\frac{7 \cdot 13 \cdot 37 \cdot 157}{3 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 176\frac{619}{3000} = 176.20633333333333$$