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Chapter 11: Q9. (page 673)

Solve. Assume that yvaries inversely as x.

Ify=8whenx=4finding xwhen y=2.

Short Answer

Expert verified

When y=2,x=16.

Step by step solution

01

Step 1. State the concept. 

Relationship of the form xy=kor y=kxwhere x,y鈮�0for some nonzero constant kis known as inverse variation i.e., yvaries inversely as x.

Product Rule for Inverse Variations 鈥� If x1,y1 and x2,y2 are solutions of an inverse variation, then x1y1=x2y2.

02

Step 2. Apply Product rule for Inverse Variations. 

To find ywhen y=2, substitute 4 for x1, 8 for y1, and 2 for y2into the equation x1y1=x2y2.

x1y1=x2y24脳8=x22

03

Step 3. Simplify for x2.

Further, simplify by dividing both sides by 2.

4脳8=x2232=2x2x2=322x2=16

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

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