Chapter 11: Q3. (page 671)

If $y$ varies inversely as $x$ and $y = 4$ when $x = - 8$ find $y$ when $x = - 4$ .

Short Answer

Expert verified

When $x = - 4, y = 8$ .

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 $x = - 4$ , substitute $- 8$ for $x_{1}$ , 4 for $y_{1}$ , and $- 4$ for $x_{2}$ into the equation $x_{1} y_{1} = x_{2} y_{2}$ .

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

Step 3. Simplify for y2.

Further, simplify by dividing both sides by $- 4$ .

$(- 8) (4) = (- 4) y_{2} - 32 = - 4 y_{2} y_{2} = \frac{- 32}{- 4} y_{2} = 8$

Therefore, $y = 8$ , when $x = - 4$ .

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If $y$ varies inversely as $x$ and $y = 4$ when $x = - 8$ find $y$ when $x = - 4$ .

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Apply Product rule for Inverse Variations.

Step 3. Simplify for y2.

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If yvaries inversely as xand y=4whenx=−8find ywhenx=−4.

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Apply Product rule for Inverse Variations.

Step 3. Simplify for y2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

If $y$ varies inversely as $x$ and $y = 4$ when $x = - 8$ find $y$ when $x = - 4$ .