Solve the formula for the indicated variable. $$ H=\frac{N^{3}}{c d}-\frac{S^{3}}{d} \text { for } N^{3} $$ $$ N^{3}=\square $$

Question

UpStudy AI · Accepted Answer

To solve the formula

$$
H = \frac{N^{3}}{c d} - \frac{S^{3}}{d}
$$

for $$ N^{3} $$, we will first isolate the term containing $$ N^{3} $$.

1. Start by adding $$ \frac{S^{3}}{d} $$ to both sides:

$$
H + \frac{S^{3}}{d} = \frac{N^{3}}{c d}
$$

2. Next, multiply both sides by $$ c d $$ to eliminate the fraction:

$$
(H + \frac{S^{3}}{d}) \cdot c d = N^{3}
$$

3. Distributing $$ c d $$ on the left side gives:

$$
N^{3} = c d H + S^{3} c
$$

Thus, the solution for $$ N^{3} $$ is:

$$
N^{3} = c d H + S^{3} c
$$
$$ N^{3} = c d H + S^{3} c $$

Solve the formula for the indicated variable. \[ H=\frac{N^{3}}{c d}-\frac{S^{3}}{d} \text { for } N^{3} \] \( N^{3}=\square \)