Solve for k 40=k(30)^2

$40 = k {(30)}^{2}$

Step 1

Rewrite the equation as $k \cdot 30^{2} = 40$ .

$k \cdot 30^{2} = 40$

Step 2

Divide each term in $(k \cdot 30^{2}) = 40$ by $30^{2}$ and simplify.

Divide each term in $(k \cdot 30^{2}) = 40$ by $30^{2}$ .

$\frac{(k \cdot 30^{2})}{30^{2}} = \frac{40}{30^{2}}$

Simplify the left side.

Cancel the common factor of $30^{2}$ .

Cancel the common factor.

$\frac{k \cdot 30^{2}}{30^{2}} = \frac{40}{30^{2}}$

Divide $k$ by $1$ .

$k = \frac{40}{30^{2}}$

Simplify the right side.

Raise $30$ to the power of $2$ .

$k = \frac{40}{900}$

Cancel the common factor of $40$ and $900$ .

Factor $20$ out of $40$ .

$k = \frac{20 (2)}{900}$

Cancel the common factors.

Factor $20$ out of $900$ .

$k = \frac{20 \cdot 2}{20 \cdot 45}$

Cancel the common factor.

$k = \frac{20 \cdot 2}{20 \cdot 45}$

Rewrite the expression.

$k = \frac{2}{45}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = \frac{2}{45}$

Decimal Form:

$k = 0.0\overline{4}$