What is the mathematical representation of y varies directly as x and a square of Z and inversely as Y?

Answer: y = ( k × x ) / z2, where k is the constant of proportionality.

What happens to the value of Y if the value of x is doubled in a direct variation?

So, when x is doubled, y is quadrupled.

What does the statement y varies directly as x describe?

The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality.

What does the statement y varies inversely as x describe?

The statement “y varies inversely as x means that when x increases, ydecreases by the same factor. In other words, the expression xy is constant: xy = k.

What is y varies directly as x?

(Some textbooks describe direct variation by saying ” y varies directly as x “, ” y varies proportionally as x “, or ” y is directly proportional to x . “) This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

What equation must be satisfied if x varies directly with Y?

For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

What will happen to Y if y varies inversely as x and x is doubled?

y = c 1/x. Intuitively this means that if x doubles then y is reduced by 1/2 and if x triples then y is reduced by 1/3. For example if you are going on a 200 mile drive then the time it takes, y, is inversely proportional to your average speed, x. y = 200 1/x.

What do the statement z varies directly as x and inversely as Y means?

Explanation: when z varies directly proportional to x means a division. c=zx where c is a constant of proportionality. when z varies inversely proportional to x it means a product. zy=c.

What kind of variation is this y varies directly as x and inversely as z?

Joint Variation
A General Note: Joint Variation If x varies directly with y and inversely with z , we have x=kyz x = k y z .

How do you say that Y varies directly with X?

We say y varies directly with x (or as x , in some textbooks) if: for some constant k , called the constant of variation or constant of proportionality . (Some textbooks describe direct variation by saying ” y varies directly as x “, ” y varies proportionally as x “, or ” y is directly proportional to x .”)

What is the constant of variation when x = 2?

For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

What is the direct variation of X?

Direct Variation. The statement “y varies directly as x,” means that when x increases, y increases by the same factor. In other words, y and x always have the same ratio: where k is the constant of variation.

What happens to X and Y when x = 12?

This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same. The graph of the direct variation equation is a straight line through the origin. Given that y varies directly as x , with a constant of variation k = 1 3 , find y when x = 12 .