Q. An inverse variation includes the points (16,1) and (4,n). Find n. Write and solve an inverse variation equation to find the answer.n=____
Identify general form: Given that there is an inverse variation between two variables.Identify the general form of inverse variation.In inverse variation, one variable is directly proportional to the inverse of the other.Inverse variation: y=xk
Find constant of variation: We know that the point (16,1) lies on the inverse variation curve.Use this point to find the constant of variation k.Substitute 16 for x and 1 for y in y=k/x.1=k/16
Solve for k: Solve the equation to find the value of k.To isolate k, multiply both sides by 16.1×16=(16k)×1616=k
Write equation with k: We have found that k=16. Write the inverse variation equation using the value of k. Substitute k=16 into y=xk. y=x16
Find n when x=4: We need to find n when x=4. Substitute 4 for x in the inverse variation equation y=x16. n=416
Find n when x=4: We need to find n when x=4. Substitute 4 for x in the inverse variation equation y=x16. n=416 Calculate the value of n. n=416x=40
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