Solve 100k/sqrt{3400*0.85}

$$\frac{ 100k }{ \sqrt{ 3 } 400 \cdot 0.85 }$$

Evaluate

$$\frac{5\sqrt{3}k}{51}$$

Solution Steps

Cancel out 100 in both numerator and denominator.

$$\frac{k}{0.85\times 4\sqrt{3}}$$

Multiply 0.85 and 4 to get 3.4.

$$\frac{k}{3.4\sqrt{3}}$$

Rationalize the denominator of \frac{k}{3.4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{k\sqrt{3}}{3.4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{k\sqrt{3}}{3.4\times 3}$$

Multiply 3.4 and 3 to get 10.2.

$$\frac{k\sqrt{3}}{10.2}$$

Differentiate w.r.t. k

$$\frac{5 \sqrt{3}}{51} = 0.16980890270283108$$