$$ 100=6 \int_{0.325}^{x_{2}} \frac{d x}{0.00488} $$ what is the value of $$ x_{2} $$ ?

Question

UpStudy AI · Accepted Answer

To solve for $$ x_{2} $$ in the equation:

$$
100 = 6 \int_{0.325}^{x_{2}} \frac{dx}{0.00488}
$$

Let's follow these steps:

1. **Evaluate the Integral:**

$$
\int \frac{dx}{0.00488} = \frac{x}{0.00488} + C
$$

So,

$$
\int_{0.325}^{x_{2}} \frac{dx}{0.00488} = \frac{x_{2}}{0.00488} - \frac{0.325}{0.00488}
$$

2. **Substitute Back into the Equation:**

$$
100 = 6 \left( \frac{x_{2}}{0.00488} - \frac{0.325}{0.00488} \right)
$$

3. **Simplify the Equation:**

Divide both sides by 6:

$$
\frac{100}{6} = \frac{x_{2}}{0.00488} - \frac{0.325}{0.00488}
$$

$$
16.\overline{6} = \frac{x_{2} - 0.325}{0.00488}
$$

4. **Solve for $$ x_{2} $$:**

Multiply both sides by $$ 0.00488 $$:

$$
16.\overline{6} \times 0.00488 = x_{2} - 0.325
$$

$$
0.081333\ldots = x_{2} - 0.325
$$

Add $$ 0.325 $$ to both sides:

$$
x_{2} = 0.325 + 0.081333\ldots = 0.406333\ldots
$$

5. **Final Answer:**

$$
x_{2} \approx 0.4063
$$

**Therefore, the value of $$ x_{2} $$ is approximately 0.4063.**
$$ x_{2} \approx 0.4063 $$

\( 100=6 \int_{0.325}^{x_{2}} \frac{d x}{0.00488} \) what is the value of \( x_{2} \) ?