Solve 5/4f=5/sqrt{k-7}[v]

$$\frac { 5 } { 4 } f = \frac { 5 } { \sqrt { k - 7 } } [ v ]$$

Solve for f

$$f=\frac{4v}{\sqrt{k-7}}$$

$$k>7$$

Steps for Solving Linear Equation

Express \frac{5}{\sqrt{k-7}}v as a single fraction.

$$\frac{5}{4}f=\frac{5v}{\sqrt{k-7}}$$

Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{4}f}{\frac{5}{4}}=\frac{5v}{\frac{5}{4}\sqrt{k-7}}$$

Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.

$$f=\frac{5v}{\frac{5}{4}\sqrt{k-7}}$$

Divide \frac{5v}{\sqrt{k-7}} by \frac{5}{4} by multiplying \frac{5v}{\sqrt{k-7}} by the reciprocal of \frac{5}{4}.

$$f=\frac{4v}{\sqrt{k-7}}$$

Solve for k

$$\left\{\begin{matrix}k=16\times \left(\frac{v}{f}\right)^{2}+7\text{, }&\left(f>0\text{ and }v>0\right)\text{ or }\left(f<0\text{ and }v<0\right)\\k>7\text{, }&f=0\text{ and }v=0\end{matrix}\right.$$