Solve for k 110=k(50)^2

$110 = k {(50)}^{2}$

Step 1

Rewrite the equation as $k \cdot 50^{2} = 110$ .

$k \cdot 50^{2} = 110$

Step 2

Divide each term in $(k \cdot 50^{2}) = 110$ by $50^{2}$ and simplify.

Divide each term in $(k \cdot 50^{2}) = 110$ by $50^{2}$ .

$\frac{(k \cdot 50^{2})}{50^{2}} = \frac{110}{50^{2}}$

Simplify the left side.

Cancel the common factor of $50^{2}$ .

Cancel the common factor.

$\frac{k \cdot 50^{2}}{50^{2}} = \frac{110}{50^{2}}$

Divide $k$ by $1$ .

$k = \frac{110}{50^{2}}$

Simplify the right side.

Raise $50$ to the power of $2$ .

$k = \frac{110}{2500}$

Cancel the common factor of $110$ and $2500$ .

Factor $10$ out of $110$ .

$k = \frac{10 (11)}{2500}$

Cancel the common factors.

Factor $10$ out of $2500$ .

$k = \frac{10 \cdot 11}{10 \cdot 250}$

Cancel the common factor.

$k = \frac{10 \cdot 11}{10 \cdot 250}$

Rewrite the expression.

$k = \frac{11}{250}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = \frac{11}{250}$

Decimal Form:

$k = 0.044$