Chapter 11: Q11. (page 728)

Solve. Assume that $y$ varies inversely as $x$ .
If $y = 4$ when $x = 1$ , find $x$ when $y = 12$ .

Short Answer

Expert verified

When $y = 12$ , $x = \frac{1}{3}$ .

Step by step solution

Step 1. Product rule for inverse variation.

If $(a_{1}, b_{1})$ and $(a_{2}, b_{2})$ are solutions of an inverse variation, then the products $a_{1} b_{1}$ and $a_{2} b_{2}$ are equal.

Step 2. Apply product rule.

Apply product rule for inverse variation.

$\begin{matrix} x_{1} y_{1} = x_{2} y_{2} \\ (1) (4) = x (12) \end{matrix}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{matrix} \frac{4}{12} = \frac{12 x}{12} \\ x = \frac{1}{3} \end{matrix}$

Therefore, when $y = 12$ , $x = \frac{1}{3}$ .

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Solve. Assume that $y$ varies inversely as $x$ .
If $y = 4$ when $x = 1$ , find $x$ when $y = 12$ .

Short Answer

Step by step solution

Step 1. Product rule for inverse variation.

Step 2. Apply product rule.

Step 3. Simplify.

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Solve. Assume thaty varies inversely as x.Ify=4 when x=1, findx when y=12.

Short Answer

Step by step solution

Step 1. Product rule for inverse variation.

Step 2. Apply product rule.

Step 3. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve. Assume that $y$ varies inversely as $x$ .
If $y = 4$ when $x = 1$ , find $x$ when $y = 12$ .