Determine whether the equation represents direct, inverse,joint,or combined variation.
y=31x/wz If it is combined, please explain to me.
direct: y = kx
inverse: y=k/x
so, y varies directly with x, and inversely with w and z
To determine whether the equation represents direct, inverse, joint, or combined variation, let's examine the equation y = 31x/wz.
Direct variation occurs when one variable is directly proportional to another, meaning as one variable increases, the other also increases. The equation for direct variation is y = kx, where k is the constant of variation.
Inverse variation occurs when one variable is inversely proportional to another, meaning as one variable increases, the other decreases. The equation for inverse variation is y = k / x, where k is the constant of variation.
Joint variation occurs when one variable varies jointly with two or more other variables. The equation for joint variation is y = kxz.
Combined variation occurs when an equation contains elements of both direct and inverse variations. In the given equation y = 31x/wz, we can observe that the variable y is directly proportional to x and inversely proportional to wz. Therefore, this equation represents combined variation since it combines direct and inverse variations.
In summary, the equation y = 31x/wz represents combined variation because it includes elements of both direct and inverse variations.
To determine whether the equation represents direct, inverse, joint, or combined variation, we need to examine its structure and the relationship between the variables involved.
In this case, the equation is given as y = 31x/wz. To analyze the variation, let's compare the equation to the standard forms of direct, inverse, and joint variations:
1. Direct Variation: The equation y = kx represents direct variation, where k is a constant. In this case, we don't have the equation in this form because the variables w and z appear in the denominator.
2. Inverse Variation: The equation y = k/x represents inverse variation, where k is a constant. Again, the equation is not in this form because there are additional variables (w and z) involved.
3. Joint Variation: The equation y = kxz represents joint variation, where k is a constant. Although the equation has similar variables to this form, the presence of the division sign (/) indicates we do not have a joint variation.
4. Combined Variation: Combined variation occurs when an equation contains both direct and inverse variations. It is characterized by the presence of multiple variables in both the numerator and denominator. In this case, the equation y = 31x/wz qualifies as combined variation.
To explain the concept of combined variation, we consider the relationship between the variables involved. In this equation, the value of y is directly proportional to both x and 31, and inversely proportional to both w and z.
To work with combined variation, we would need to fix the values of three variables while observing the effect of changing the remaining variable. For example, we could fix the values of x, w, and z, and then vary the value of 31 to see how it affects y. Similarly, we could fix the values of x, 31, and z, and vary the value of w to observe the impact on y.
In conclusion, the equation y = 31x/wz represents combined variation, where y is directly proportional to both x and 31, and inversely proportional to both w and z.