In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where $$ x $$ is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). $$ P(x)=\frac{11 x}{1-x} \quad 0 \leq x

Question

In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where $$ x $$ is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). $$ P(x)=\frac{11 x}{1-x} \quad 0 \leq x<1 $$ A. The $$ x $$-intercept(s) is (are) $$ x=0 $$. (Simplify your answer. Use a comma to separate answers as needed.) answer box to complete your choice. B. There are no $$ x $$-intercepts. Find the $$ y $$-intercept(s) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $$ y $$-intercept(s) is (are) $$ y=\square $$ (Simplify your answer. Use a comma to separate answers as needed.) B. There are no $$ y $$-intercepts.

UpStudy AI · Accepted Answer

Let's analyze the function $$ P(x) = \frac{11x}{1-x} $$ step by step to answer parts (A) through (E).

### Part A: Finding the $$ x $$-intercept(s)

The $$ x $$-intercept occurs when $$ P(x) = 0 $$. To find the $$ x $$-intercept, we set the function equal to zero:

$$
\frac{11x}{1-x} = 0
$$

For a fraction to equal zero, the numerator must be zero (as long as the denominator is not zero). Therefore, we set the numerator equal to zero:

$$
11x = 0
$$

Solving for $$ x $$:

$$
x = 0
$$

Thus, the $$ x $$-intercept is:

$$
\text{The } x\text{-intercept(s) is (are) } x = 0.
$$

### Part B: Finding the $$ y $$-intercept(s)

The $$ y $$-intercept occurs when $$ x = 0 $$. We can find the $$ y $$-intercept by substituting $$ x = 0 $$ into the function $$ P(x) $$:

$$
P(0) = \frac{11(0)}{1-0} = \frac{0}{1} = 0
$$

Thus, the $$ y $$-intercept is:

$$
\text{The } y\text{-intercept(s) is (are) } y = 0.
$$

### Summary of Answers

- **Part A:** The $$ x $$-intercept(s) is (are) $$ x = 0 $$.
- **Part B:** The $$ y $$-intercept(s) is (are) $$ y = 0 $$.
- **Part A:** The $$ x $$-intercept is $$ x = 0 $$. - **Part B:** The $$ y $$-intercept is $$ y = 0 $$.

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