$$ 1 \leftarrow \begin{array}{l} ext { Solve the formula for } t ext {. } \ \qquad=3 \pi z t+3 \pi z^{2} \ t=\square\end{array} $$

Question

$$ 1 \leftarrow \begin{array}{l}	ext { Solve the formula for } t 	ext {. } \ \qquad=3 \pi z t+3 \pi z^{2} \ t=\square\end{array} $$

UpStudy AI · Accepted Answer

To solve the equation for $$ t $$:

$$
1 = 3\pi z t + 3\pi z^{2}
$$

**Step 1:** Subtract $$ 3\pi z^{2} $$ from both sides to isolate the term containing $$ t $$:

$$
1 - 3\pi z^{2} = 3\pi z t
$$

**Step 2:** Divide both sides by $$ 3\pi z $$ to solve for $$ t $$:

$$
t = \frac{1 - 3\pi z^{2}}{3\pi z}
$$

**Simplified Form:**

Alternatively, you can simplify the expression further:

$$
t = \frac{1}{3\pi z} - z
$$

**Final Solution:**

$$
t = \frac{1 - 3\pi z^{2}}{3\pi z}
$$
$$ t = \frac{1 - 3\pi z^{2}}{3\pi z} $$

\( 1 \leftarrow \begin{array}{l}\text { Solve the formula for } t \text {. } \\ \qquad=3 \pi z t+3 \pi z^{2} \\ t=\square\end{array} \)