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Question: Solve. Assume that y varies inversely as x.

Ify=7whenx=6finding ywhenx=-21.

Short Answer

Expert verified

When x=21,y=2.

Step by step solution

01

Step 1. State the concept. 

Relationship of the form xy=kor y=kxwhere x,y0for some nonzero constant kis known as inverse variation i.e., yvaries inversely as x.

Product Rule for Inverse Variations – 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=21, substitute 6 for x1, 7 for y1, and -21for x2into the equation x1y1=x2y2.

x1y1=x2y26×7=21y2

03

Step 3. Simplify for y2.

Further, simplify by dividing both sides by -21.

6×7=21y2

42=21y2y2=4221y2=2

Therefore, y=2, when x=21.

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