Chapter 11: Q5. (page 699)

Assume that $y$ varies inversely as $x$ .
If $y = 3$ when $x = 2$ , find $y$ when $x = 4$ .

Short Answer

Expert verified

When $x = 4$ then $y = \frac{3}{2}$ .

Step by step solution

Step 1. Define an inverse variation equation.

The inverse variation equation of two variables $x$ and $y$ is given by

$x y = k$

Where, $k$ is called the constant of variation.

Step 2. Define the product rule for inverse variation.

If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are solutions of an inverse variation, then the equation $x_{1} y_{1} = x_{2} y_{2}$ is called the product rule for inverse variation.

Step 3. Calculate y when x=4 and if y=3 when x=2.

Assume that $y$ varies inversely as $x$ .

Then the product rule for inverse variation is given by

$x_{1} y_{1} = x_{2} y_{2}$

Substitute $x_{1} = 2, y_{1} = 3$ and $x_{2} = 4$ in $x_{1} y_{1} = x_{2} y_{2}$ .

localid="1650904035932" $\begin{array}{l} 2 (3) = 4 (y_{2}) \\ 6 = 4 y_{2} \\ y_{2} = \frac{6}{4} \\ y_{2} = \frac{3}{2} \end{array}$

Therefore when localid="1650904026878" $x = 4$ then localid="1650904022237" $y = \frac{3}{2}$ .

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Assume that $y$ varies inversely as $x$ .
If $y = 3$ when $x = 2$ , find $y$ when $x = 4$ .

Short Answer

Step by step solution

Step 1. Define an inverse variation equation.

Step 2. Define the product rule for inverse variation.

Step 3. Calculate y when x=4 and if y=3 when x=2.

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Assume thaty varies inversely as x.Ify=3 when x=2, findy when x=4.

Short Answer

Step by step solution

Step 1. Define an inverse variation equation.

Step 2. Define the product rule for inverse variation.

Step 3. Calculate y when x=4 and if y=3 when x=2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Geometry

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Assume that $y$ varies inversely as $x$ .
If $y = 3$ when $x = 2$ , find $y$ when $x = 4$ .