Precalculus Examples

$F = q v B$ , $F = \frac{m v^{2}}{r}$

Step 1

Solve the equation for $m$ .

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Rewrite the equation as $\frac{m v^{2}}{r} = q v B$ .

$\frac{m v^{2}}{r} = q v B$

$F = q v B$

Multiply both sides by $r$ .

$\frac{m v^{2}}{r} \cdot r = q v B r$

$F = q v B$

Simplify the left side.

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Cancel the common factor of $r$ .

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Cancel the common factor.

$\frac{m v^{2}}{r} \cdot r = q v B r$

$F = q v B$

Rewrite the expression.

$m v^{2} = q v B r$

$F = q v B$

$m v^{2} = q v B r$

$F = q v B$

$m v^{2} = q v B r$

$F = q v B$

Divide each term in $m v^{2} = q v B r$ by $v^{2}$ and simplify.

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Divide each term in $m v^{2} = q v B r$ by $v^{2}$ .

$\frac{m v^{2}}{v^{2}} = \frac{q v B r}{v^{2}}$

$F = q v B$

Simplify the left side.

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Cancel the common factor of $v^{2}$ .

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Cancel the common factor.

$\frac{m v^{2}}{v^{2}} = \frac{q v B r}{v^{2}}$

$F = q v B$

Divide $m$ by $1$ .

$m = \frac{q v B r}{v^{2}}$

$F = q v B$

$m = \frac{q v B r}{v^{2}}$

$F = q v B$

$m = \frac{q v B r}{v^{2}}$

$F = q v B$

Simplify the right side.

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Cancel the common factor of $v$ and $v^{2}$ .

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Factor $v$ out of $q v B r$ .

$m = \frac{v (q B r)}{v^{2}}$

$F = q v B$

Cancel the common factors.

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Factor $v$ out of $v^{2}$ .

$m = \frac{v (q B r)}{v \cdot v}$

$F = q v B$

Cancel the common factor.

$m = \frac{v (q B r)}{v \cdot v}$

$F = q v B$

Rewrite the expression.

$m = \frac{q B r}{v}$

$F = q v B$

$m = \frac{q B r}{v}$

$F = q v B$

$m = \frac{q B r}{v}$

$F = q v B$

$m = \frac{q B r}{v}$

$F = q v B$

$m = \frac{q B r}{v}$

$F = q v B$

$m = \frac{q B r}{v}$

$F = q v B$

Step 2

Solve the equation for $q$ .

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Rewrite the equation as $q v B = F$ .

$q v B = F$

$m = \frac{q B r}{v}$

Divide each term in $q v B = F$ by $v B$ and simplify.

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Divide each term in $q v B = F$ by $v B$ .

$\frac{q v B}{v B} = \frac{F}{v B}$

$m = \frac{q B r}{v}$

Simplify the left side.

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Cancel the common factor of $v$ .

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Cancel the common factor.

$\frac{q v B}{v B} = \frac{F}{v B}$

$m = \frac{q B r}{v}$

Rewrite the expression.

$\frac{q B}{B} = \frac{F}{v B}$

$m = \frac{q B r}{v}$

$\frac{q B}{B} = \frac{F}{v B}$

$m = \frac{q B r}{v}$

Cancel the common factor of $B$ .

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Cancel the common factor.

$\frac{q B}{B} = \frac{F}{v B}$

$m = \frac{q B r}{v}$

Divide $q$ by $1$ .

$q = \frac{F}{v B}$

$m = \frac{q B r}{v}$

$q = \frac{F}{v B}$

$m = \frac{q B r}{v}$

$q = \frac{F}{v B}$

$m = \frac{q B r}{v}$

$q = \frac{F}{v B}$

$m = \frac{q B r}{v}$

$q = \frac{F}{v B}$

$m = \frac{q B r}{v}$

Step 3

Solve the equation for $v$ .

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Since $v$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(\frac{q B r}{v}) \cdot \frac{v^{2}}{r} = q v B$

$q = \frac{F}{v B}$

Simplify $(\frac{q B r}{v}) \cdot \frac{v^{2}}{r}$ .

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Rewrite.

$0 + 0 + (\frac{q B r}{v}) \cdot \frac{v^{2}}{r} = q v B$

$q = \frac{F}{v B}$

Simplify by adding zeros.

$(\frac{q B r}{v}) \cdot \frac{v^{2}}{r} = q v B$

$q = \frac{F}{v B}$

Combine.

$\frac{q B r v^{2}}{v r} = q v B$

$q = \frac{F}{v B}$

Cancel the common factor of $r$ .

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Cancel the common factor.

$\frac{q B r v^{2}}{v r} = q v B$

$q = \frac{F}{v B}$

Rewrite the expression.

$\frac{q B v^{2}}{v} = q v B$

$q = \frac{F}{v B}$

$\frac{q B v^{2}}{v} = q v B$

$q = \frac{F}{v B}$

Cancel the common factor of $v^{2}$ and $v$ .

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Factor $v$ out of $q B v^{2}$ .

$\frac{v (q B v)}{v} = q v B$

$q = \frac{F}{v B}$

Cancel the common factors.

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Raise $v$ to the power of $1$ .

$\frac{v (q B v)}{v} = q v B$

$q = \frac{F}{v B}$

Factor $v$ out of $v^{1}$ .

$\frac{v (q B v)}{v \cdot 1} = q v B$

$q = \frac{F}{v B}$

Cancel the common factor.

$\frac{v (q B v)}{v \cdot 1} = q v B$

$q = \frac{F}{v B}$

Rewrite the expression.

$\frac{q B v}{1} = q v B$

$q = \frac{F}{v B}$

Divide $q B v$ by $1$ .

$q B v = q v B$

$q = \frac{F}{v B}$

$q B v = q v B$

$q = \frac{F}{v B}$

$q B v = q v B$

$q = \frac{F}{v B}$

$q B v = q v B$

$q = \frac{F}{v B}$

Move all terms containing $v$ to the left side of the equation.

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Subtract $q v B$ from both sides of the equation.

$q B v - q v B = 0$

$q = \frac{F}{v B}$

Combine the opposite terms in $q B v - q v B$ .

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Reorder the factors in the terms $q B v$ and $- q v B$ .

$B q v - B q v = 0$

$q = \frac{F}{v B}$

Subtract $B q v$ from $B q v$ .

$0 = 0$

$q = \frac{F}{v B}$

$0 = 0$

$q = \frac{F}{v B}$

$0 = 0$

$q = \frac{F}{v B}$

Since $0 = 0$ , the equation will always be true.

Always true

$q = \frac{F}{v B}$

Always true

$q = \frac{F}{v B}$

Step 4

Solve the equation for $B$ .

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Rewrite the equation as $(\frac{F}{v B}) \cdot (v B) = F$ .

$(\frac{F}{v B}) \cdot (v B) = F$

Always true

Cancel the common factor of $v B$ .

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Cancel the common factor.

$\frac{F}{v B} \cdot (v B) = F$

Always true

Rewrite the expression.

$F = F$

Always true

$F = F$

Always true

The variable $B$ got canceled.

All real numbers

Always true

All real numbers

Always true

Step 5

The simplified system is the arbitrary solution of the original system of equations.

All real $n u (\frac{q B r}{v}) \cdot (b e r s)$

Always true