a. Write a function that models a combined variation situation with two independent variables, let one of the variables have direct variation with the dependent variable, and the other have an inverse variation
b. Let the independent variables be equal to 3 and 6, Find the value of the independent variable
c. let the dependent variable be 15, and one of the independent variables be 5. Find the value of other independent variable
d. let the independent variable that varies directly with the dependent variable be 2. Does the other independent variable increase, decrease, or remain constant when the dependent variable increases in value? Now let the other independent variable that varies inversely with the dependent variable be 4. Does the other independent variables increase, decrease, or remain constant when the dependent variable increases in value
e. let the dependent variable be 1. Does one of the independent variables increase, decrease, or remain constant when the other increases in value
a.
Let the dependent variable (y) be represented as a combined variation of two independent variables (x and z).
y = kxz
Where:
- x represents the independent variable that has direct variation with y
- z represents the independent variable that has inverse variation with y
- k is a constant of variation
b.
When x = 3 and z = 6:
y = k(3)(6) = 18k
c.
When y = 15 and x = 5:
15 = k(5)z
3 = z
d.
If x = 2:
y = k(2)z = 2kz
As y increases, z must decrease in order to keep the product constant. Therefore, the other independent variable, z, decreases when y increases.
If z = 4:
y = kx(4) = 4kx
As y increases, x must increase in order to keep the product constant. Therefore, the other independent variable, x, increases when y increases.
e.
When y = 1:
1 = kxz
Since k is a constant, if one of the independent variables (x or z) increases, the other must decrease proportionally in order to keep the product constant. Therefore, when one independent variable increases, the other must decrease, and vice versa.