Q. Assume that y varies inversely with x. If y=3 when x=4, find y when x=1. Write and solve an inverse variation equation to find the answer.y= _____
Understand relationship: Understand the relationship between y and x. Since y varies inversely with x, the relationship can be described by the equation y=xk, where k is the constant of variation.
Find constant of variation: Use the given values to find the constant of variation k. We are given that y=3 when x=4. Substitute these values into the inverse variation equation to find k. 3=4k
Solve for k: Solve for k.To find k, multiply both sides of the equation by 4.3×4=k12=k
Write variation equation: Write the inverse variation equation with the found value of k. Now that we know k=12, we can write the equation as y=x12.
Find y for x=1: Find y when x=1. Substitute x=1 into the equation y=x12. y=112y=12
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