Solve 0.56.5^2/0.866+(0.5*9.8cot(30))/2cos(30)

$$\frac{ \frac{ 0.5 { 6.5 }^{ 2 } }{ 0.866 } +(0.5 \cdot 9.8 \cot ( 30 ) ) }{ 2 \cos ( 30 ) }$$

Evaluate

$$\frac{21125\sqrt{3}}{2598}+4.9\approx 18.983746463$$

Solution Steps

Calculate 6.5 to the power of 2 and get 42.25.

$$\frac{\frac{0.5\times 42.25}{0.866}+0.5\times 9.8\cot(30)}{2\cos(30)}$$

Multiply 0.5 and 42.25 to get 21.125.

$$\frac{\frac{21.125}{0.866}+0.5\times 9.8\cot(30)}{2\cos(30)}$$

Expand \frac{21.125}{0.866} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{21125}{866}+0.5\times 9.8\cot(30)}{2\cos(30)}$$

Multiply 0.5 and 9.8 to get 4.9.

$$\frac{\frac{21125}{866}+4.9\cot(30)}{2\cos(30)}$$

Get the value of \cot(30) from trigonometric values table.

$$\frac{\frac{21125}{866}+4.9\sqrt{3}}{2\cos(30)}$$

Get the value of \cos(30) from trigonometric values table.

$$\frac{\frac{21125}{866}+4.9\sqrt{3}}{2\times \frac{\sqrt{3}}{2}}$$

Cancel out 2 and 2.

$$\frac{\frac{21125}{866}+4.9\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\frac{21125}{866}+4.9\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\frac{21125}{866}+4.9\sqrt{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\frac{21125}{866}+4.9\sqrt{3}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply \frac{21125}{866}+4.9\sqrt{3} by \sqrt{3}.

$$\frac{\frac{21125}{866}\sqrt{3}+4.9\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{21125}{866}\sqrt{3}+4.9\times 3}{3}$$

Multiply 4.9 and 3 to get 14.7.

$$\frac{\frac{21125}{866}\sqrt{3}+14.7}{3}$$