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If x varies inversely as y 3 - 1 and is equal to 7 when y = 2, find x when y = 6.
21549тАЛ
21649тАЛ
21650тАЛ
21551тАЛ
21549тАЛ
Calculate k once using the given values (x=7, y=2), then plug the new y=6 into the derived equation x=k/(y3тИТ1).
x varies inversely as y┬│ - 1, and x = 7 when y = 2. Find x when y = 6.
xтИЭy3тИТ11тАЛтЯ╣x=y3тИТ1kтАЛ
Calculate k once using the given values (x=7, y=2), then plug the new y=6 into the derived equation x=k/(y3тИТ1).
Students often forget to subtract 1 from the cube of y or confuse direct and inverse variation.
Establish the relationship
Since x varies inversely as y┬│ - 1, we write the relation as x = k / (y┬│ - 1), where k is a constant.
x=y3тИТ1kтАЛ
Determine the constant k
Substitute x = 7 and y = 2 into the equation: 7 = k / (2┬│ - 1). This simplifies to 7 = k / (8 - 1), which means 7 = k / 7.
k=7├Ч7=49
Solve for x when y = 6
Using k = 49 and y = 6, substitute into the formula: x = 49 / (6┬│ - 1). Since 6┬│ = 216, we get x = 49 / (216 - 1).
x=21549тАЛ
A is correct because substituting y = 6 into the derived equation x=49/(y3тИТ1) yields 49/215.
This concept is a foundational part of 'Proportionality' in Quantitative Aptitude, often appearing in speed-distance and work-time problems.
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