Question: top-left: A fraction with $x$ in the numerator and $2110$ in the denominator, equal to a fraction with $8.73$ in the numerator and $360$ in the denominator.arc length
1. **State the problem:**
We are given the equation $$\frac{x}{2110} = \frac{8.73}{360}$$ and need to solve for $x$.
2. **Formula and rules:**
This is a proportion equation where two fractions are equal. To solve for $x$, we use cross multiplication:
$$x \times 360 = 8.73 \times 2110$$
3. **Cross multiply:**
$$360x = 8.73 \times 2110$$
Calculate the right side:
$$8.73 \times 2110 = 18420.3$$
So,
$$360x = 18420.3$$
4. **Solve for $x$ by dividing both sides by 360:**
$$x = \frac{18420.3}{360}$$
Show cancellation:
$$x = \frac{\cancel{18420.3}}{\cancel{360}}$$
5. **Calculate the division:**
$$x = 51.1675$$
6. **Answer:**
The value of $x$ is approximately $51.17$ (rounded to two decimal places).