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Chapter 11: Q11. (page 673)

Solve. Assume that y varies inversely as x.

Ify=鈭�5whenx=9finding ywhenx=6.

Short Answer

Expert verified

When x=6,y=鈭�7.5.

Step by step solution

01

Step 1. State the concept. 

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

Product Rule for Inverse Variations 鈥� If x1,y1and x2,y2are solutions of an inverse variation, then x1y1=x2y2.

02

Step 2. Apply Product rule for Inverse Variations. 

To find y when x=6, substitute 9 for x1, -5for y1, and 6 for role="math" localid="1648106415441" x2into the equation x1y1=x2y2.

x1y1=x2y29脳鈭�5=6y2

03

Step 3. Simplify for y2.

Further, simplify by dividing both sides by 6.

9脳鈭�5=6y2

鈭�45=6y2y2=鈭�456y2=鈭�7.5

Therefore, y=鈭�7.5, when x=6.

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