Solve overline 49; C = ((sqrt(3))/5) ^ 2 D | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$49 : C = ( \frac { \sqrt { 3 } } { 5 } ) ^ { 2 } : D$$

Solve for C

$C=\frac{1225D}{3}$
$D\neq 0$

Steps for Solving Linear Equation

Variable $C$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $CD$, the least common multiple of $C,D$.

$$D\times 49=C\times \left(\frac{\sqrt{3}}{5}\right)^{2}$$

To raise $\frac{\sqrt{3}}{5}$ to a power, raise both numerator and denominator to the power and then divide.

$$D\times 49=C\times \frac{\left(\sqrt{3}\right)^{2}}{5^{2}}$$

Express $C\times \frac{\left(\sqrt{3}\right)^{2}}{5^{2}}$ as a single fraction.

$$D\times 49=\frac{C\left(\sqrt{3}\right)^{2}}{5^{2}}$$

The square of $\sqrt{3}$ is $3$.

$$D\times 49=\frac{C\times 3}{5^{2}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$D\times 49=\frac{C\times 3}{25}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{C\times 3}{25}=D\times 49$$

Multiply both sides of the equation by $25$.

$$C\times 3=25D\times 49$$

Multiply $25$ and $49$ to get $1225$.

$$C\times 3=1225D$$

The equation is in standard form.

$$3C=1225D$$

Divide both sides by $3$.

$$\frac{3C}{3}=\frac{1225D}{3}$$

Dividing by $3$ undoes the multiplication by $3$.

$$C=\frac{1225D}{3}$$

Variable $C$ cannot be equal to $0$.

$$C=\frac{1225D}{3}\text{, }C\neq 0$$

Solve for D

$D=\frac{3C}{1225}$
$C\neq 0$

Steps for Solving Linear Equation

Variable $D$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $CD$, the least common multiple of $C,D$.

$$D\times 49=C\times \left(\frac{\sqrt{3}}{5}\right)^{2}$$

To raise $\frac{\sqrt{3}}{5}$ to a power, raise both numerator and denominator to the power and then divide.

$$D\times 49=C\times \frac{\left(\sqrt{3}\right)^{2}}{5^{2}}$$

Express $C\times \frac{\left(\sqrt{3}\right)^{2}}{5^{2}}$ as a single fraction.

$$D\times 49=\frac{C\left(\sqrt{3}\right)^{2}}{5^{2}}$$

The square of $\sqrt{3}$ is $3$.

$$D\times 49=\frac{C\times 3}{5^{2}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$D\times 49=\frac{C\times 3}{25}$$

Multiply both sides of the equation by $25$.

$$25D\times 49=C\times 3$$

Multiply $25$ and $49$ to get $1225$.

$$1225D=C\times 3$$

The equation is in standard form.

$$1225D=3C$$

Divide both sides by $1225$.

$$\frac{1225D}{1225}=\frac{3C}{1225}$$

Dividing by $1225$ undoes the multiplication by $1225$.

$$D=\frac{3C}{1225}$$

Variable $D$ cannot be equal to $0$.

$$D=\frac{3C}{1225}\text{, }D\neq 0$$