Which of the following equations is an example of inverse variation?
A. d = c/2
B. m = 5s
C. a = 10/b
D. (kr)/5 = 1
Answer (2)
The equation representing inverse variation is C. a = 10/b , where as b increases, a decreases, indicating an inverse relationship. The other options do not exhibit this property. In inverse variation, the product of the two variables remains constant.
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Inverse variation is a mathematical relationship where one variable decreases as another variable increases. It occurs when the product of the two variables is constant. The general form of an inverse variation is given by the equation:
y = x k
where k is a constant, y is the dependent variable, and x is the independent variable.
Let's analyze the equations given:
A. d = 2 c
This equation shows a direct variation between d and c since d is directly proportional to c divided by a constant.
B. m = 5 s
This equation shows a direct variation because m is directly proportional to s with a constant multiplier of 5.
C. a = b 10
This equation is an example of inverse variation because a and b multiply to a constant value of 10 ( a × b = 10 ). As b increases, a decreases.
D. 5 k r = 1
Rewriting this equation, we get k r = 5 , which is an example of inverse variation between k and r since their product is a constant (5), but the original form doesn't show a direct inverse relation like option C does.
Thus, the correct answer is C. a = b 10 because it directly shows inverse variation in the classic form.
