Chapter 11: Q9. (page 673)

Solve. Assume that $y$ varies inversely as $x$ .
If $y = 8$ when $x = 4$ finding $x$ when $y = 2$ .

Short Answer

Expert verified

When $y = 2, x = 16$ .

Step by step solution

Step 1. State the concept.

Relationship of the form $x y = k$ or $y = \frac{k}{x}$ where $x, y \neq 0$ for some nonzero constant $k$ is known as inverse variation i.e., $y$ varies inversely as $x$ .

Product Rule for Inverse Variations – If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are solutions of an inverse variation, then $x_{1} y_{1} = x_{2} y_{2}$ .

Step 2. Apply Product rule for Inverse Variations.

To find $y$ when $y = 2$ , substitute 4 for $x_{1}$ , 8 for $y_{1}$ , and 2 for $y_{2}$ into the equation $x_{1} y_{1} = x_{2} y_{2}$ .

$x_{1} y_{1} = x_{2} y_{2} (4) \times 8 = x_{2} (2)$

Step 3. Simplify for x2.

Further, simplify by dividing both sides by 2.

$(4) \times 8 = x_{2} (2) 32 = 2 x_{2} x_{2} = \frac{32}{2} x_{2} = 16$

Therefore, $x = 16$ , when $y = 2 .$ .

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Solve. Assume that $y$ varies inversely as $x$ .
If $y = 8$ when $x = 4$ finding $x$ when $y = 2$ .

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Apply Product rule for Inverse Variations.

Step 3. Simplify for x2.

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Solve. Assume that yvaries inversely as x. Ify=8whenx=4finding xwhen y=2.

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Apply Product rule for Inverse Variations.

Step 3. Simplify for x2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve. Assume that $y$ varies inversely as $x$ .
If $y = 8$ when $x = 4$ finding $x$ when $y = 2$ .