Solve frac{(frac{sqrt{3}}{2})^2*30*a}{450frac{sqrt{3}}{2}*6}

$$\frac { ( \frac { \sqrt { 3 } } { 2 } ) ^ { 2 } \times 30 \cdot a } { 450 \frac { \sqrt { 3 } } { 2 } \times 6 }$$

Evaluate

$$\frac{\sqrt{3}a}{180}$$

Short Solution Steps

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{30\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}a}{6\times 450\times \frac{\sqrt{3}}{2}}$$

Express 30\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{30\left(\sqrt{3}\right)^{2}}{2^{2}}a}{6\times 450\times \frac{\sqrt{3}}{2}}$$

Express \frac{30\left(\sqrt{3}\right)^{2}}{2^{2}}a as a single fraction.

$$\frac{\frac{30\left(\sqrt{3}\right)^{2}a}{2^{2}}}{6\times 450\times \frac{\sqrt{3}}{2}}$$

Multiply 6 and 450 to get 2700.

$$\frac{\frac{30\left(\sqrt{3}\right)^{2}a}{2^{2}}}{2700\times \frac{\sqrt{3}}{2}}$$

Cancel out 2, the greatest common factor in 2700 and 2.

$$\frac{\frac{30\left(\sqrt{3}\right)^{2}a}{2^{2}}}{1350\sqrt{3}}$$

Express \frac{\frac{30\left(\sqrt{3}\right)^{2}a}{2^{2}}}{1350\sqrt{3}} as a single fraction.

$$\frac{30\left(\sqrt{3}\right)^{2}a}{2^{2}\times 1350\sqrt{3}}$$

Cancel out 30\sqrt{3} in both numerator and denominator.

$$\frac{\sqrt{3}a}{45\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{3}a}{45\times 4}$$

Multiply 45 and 4 to get 180.

$$\frac{\sqrt{3}a}{180}$$

Differentiate w.r.t. a

$$\frac{\sqrt{3}}{180} = 0.009622504486493762$$