Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.
equal to zero
less than 2
equal to 6
greater than 11
Y = 6x = 11
X = 11/6 = 1 5/6. Less than 2.
To determine the value of X when Y is 11, we need to use the concept of direct variation. In direct variation, when two variables, such as X and Y, are directly proportional, their relation can be expressed as Y = kX, where k is the constant of variation.
Given that Y varies directly with X and has a constant rate of change of 6, we can write the equation as:
Y = 6X
Now, let's substitute the value of Y as 11 into the equation and solve for X:
11 = 6X
To isolate X, divide both sides of the equation by 6:
11/6 = X
Therefore, the value of X could be greater than 11/6. Therefore, the answer is "greater than 11".
To solve this problem, we need to use the concept of direct variation. In a direct variation relationship, if the variable Y is directly proportional to the variable X, it means that as X increases or decreases, Y will do the same proportionally.
In this case, we are given that Y varies directly with X and has a constant rate of change of 6. This means that for every unit increase in X, Y will increase by a constant factor of 6.
To find the value of X when Y is 11, we need to set up the equation:
Y = kX
where k is the constant of variation.
Given that the rate of change is 6, we have:
11 = 6X
Now we can solve for X by dividing both sides of the equation by 6:
11/6 = X
The value of X could be equal to 11/6, which is approximately 1.83.
Therefore, the value of X could be less than 2.