Solve 53s/sqrt{1-(0.52^2)}

$$\frac { 53 s } { \sqrt { 1 - ( 0.52 ^ { 2 } ) } }$$

Evaluate

$$\frac{1325\sqrt{114}s}{228}$$

Solution Steps

Calculate 0.52 to the power of 2 and get 0.2704.

$$\frac{53s}{\sqrt{1-0.2704}}$$

Subtract 0.2704 from 1 to get 0.7296.

$$\frac{53s}{\sqrt{0.7296}}$$

Rationalize the denominator of \frac{53s}{\sqrt{0.7296}} by multiplying numerator and denominator by \sqrt{0.7296}.

$$\frac{53s\sqrt{0.7296}}{\left(\sqrt{0.7296}\right)^{2}}$$

The square of \sqrt{0.7296} is 0.7296.

$$\frac{53s\sqrt{0.7296}}{0.7296}$$

Divide 53s\sqrt{0.7296} by 0.7296 to get \frac{33125}{456}s\sqrt{0.7296}.

$$\frac{33125}{456}s\sqrt{0.7296}$$

Differentiate w.r.t. s

$$\frac{1325 \sqrt{114}}{228} = 62.04881001728723$$