P varies inversely with x. If P = 14 when x = 16, find the value of P when x = 21.
Understand the Problem
The question is asking to find the value of P when x is 21, given that P varies inversely with x. This means P can be calculated using the formula P = k/x, where k is the constant of variation. We will first find k using the initial conditions and then calculate P for x = 21.
Answer
$P = \frac{k}{21}$, where $k$ is determined from initial conditions.
Answer for screen readers
The final answer would depend on the specific value of $k$ determined from the initial conditions.
Steps to Solve
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Identify the inverse relationship Since P varies inversely with x, we can represent this relationship as: $$ P = \frac{k}{x} $$ where $k$ is a constant.
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Find the constant of variation (k) If we have specific values for P and x, we can substitute those values into the equation to find $k$. For example, if we know $P_0$ when $x_0$ is given: $$ k = P_0 \cdot x_0 $$
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Substitute given value into the equation Now that we have determined $k$, we need to find $P$ when $x = 21$. We will substitute 21 into the equation: $$ P = \frac{k}{21} $$
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Calculate P Once we have $k$, we can compute the value of P by performing the calculation: $$ P = \frac{k}{21} $$
The final answer would depend on the specific value of $k$ determined from the initial conditions.
More Information
Knowing that P varies inversely with x means that as x increases, P decreases, and vice versa. The constant k determines the relationship's strength.
Tips
- Forgetting to find the constant $k$ before substituting for P.
- Incorrectly substituting values for x and P without confirming their relationship.
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