For the inverse variation equation [tex]xy=k[/tex], what is the constant of variation, [tex]k[/tex], when [tex]x=7[/tex] and [tex]y=3[/tex]?
Answer (2)
The constant of variation k when x = 7 and y = 3 is 21 . This is found by substituting the values into the equation x y = k and calculating the product. Thus, k = 7 ⋅ 3 = 21 .
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Substitute the given values x = 7 and y = 3 into the inverse variation equation x y = k .
Calculate the product of x and y to find k .
Perform the multiplication: k = 7"."3 = 21 .
The constant of variation is 21 .
Explanation
Understanding the Problem We are given the inverse variation equation x y = k , where k is the constant of variation. We are also given that x = 7 and y = 3 . Our goal is to find the value of k .
Substituting Values To find the constant of variation k , we substitute the given values of x and y into the equation x y = k . So we have k = x y = 7"."3
Calculating k Now, we perform the multiplication: k = 7"."3 = 21
Final Answer Therefore, the constant of variation is 21.
Examples
Inverse variation is a relationship where one variable decreases as the other increases proportionally. For example, imagine you're organizing a pizza party. The number of slices each person gets varies inversely with the number of guests. If you have a fixed number of pizza slices (say, 24), then as the number of guests increases, the number of slices per guest decreases. If 6 people attend, each gets 4 slices. If 12 people attend, each gets 2 slices. This concept is useful in resource allocation, understanding rates, and many other real-world scenarios where quantities are inversely related.
