Solve v/sqrt{tvarepsilon^2}=0.9

$$\frac { v } { \sqrt { t \varepsilon ^ { 2 } } } = 0.9$$

Solve for v (complex solution)

$$v=\frac{9\sqrt{t\epsilon ^{2}}}{10}$$

$$t\neq 0\text{ and }\epsilon \neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{\sqrt{t\epsilon ^{2}}}v=0.9$$

Divide both sides by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{t\epsilon ^{2}}}v\sqrt{t\epsilon ^{2}}}{1}=\frac{0.9\sqrt{t\epsilon ^{2}}}{1}$$

Dividing by \left(\sqrt{t\epsilon ^{2}}\right)^{-1} undoes the multiplication by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$v=\frac{0.9\sqrt{t\epsilon ^{2}}}{1}$$

Divide 0.9 by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$v=\frac{9\sqrt{t\epsilon ^{2}}}{10}$$

Solve for v

$$v=\frac{9\sqrt{t}|\epsilon |}{10}$$

$$t>0\text{ and }\epsilon \neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{\sqrt{t\epsilon ^{2}}}v=0.9$$

Divide both sides by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{t\epsilon ^{2}}}v\sqrt{t\epsilon ^{2}}}{1}=\frac{0.9\sqrt{t\epsilon ^{2}}}{1}$$

Dividing by \left(\sqrt{t\epsilon ^{2}}\right)^{-1} undoes the multiplication by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$v=\frac{0.9\sqrt{t\epsilon ^{2}}}{1}$$

Divide 0.9 by \left(\sqrt{t\epsilon ^{2}}\right)^{-1}.

$$v=\frac{9\sqrt{t}|\epsilon |}{10}$$

Solve for t (complex solution)

$$t=\frac{100\times \left(\frac{v}{\epsilon }\right)^{2}}{81}$$

$$v\neq 0\text{ and }\epsilon \neq 0\text{ and }|\frac{arg(v^{2})}{2}-arg(v)|<\pi$$

Solve for t

$$t=\frac{100\times \left(\frac{v}{\epsilon }\right)^{2}}{81}$$

$$\epsilon \neq 0\text{ and }v>0$$