Could you please help me with the following question?
Find the variation equation for the variation statement.
31. z varies jointly as y and the cube of x; z=96 when x=2 and y=6 (I don't understand this one. My answer choices are: a.y=2x^3y,b.y=2xy^3, c.y=-2x^3y, or d. y=-2xy^3)
Could you please help me with the following question?
Find the variation equation for the variation statement.
31. z varies jointly as y and the cube of x; z=96 when x=2 and y=6 (I don't understand this one. My answer choices are: a.y=2x^3y,b.y=2xy^3, c.y=-2x^3y, or d. y=-2xy^3)
To find the variation equation, we need to understand the concept of joint variation. In a joint variation, a variable varies directly with two or more other variables, raised to some powers.
In this case, we are told that "z varies jointly as y and the cube of x." This means that z is directly proportional to both y and the cube (third power) of x. Mathematically, we can write this as:
z = k * x^3 * y
Here, k represents the constant of variation.
To find the value of k, we can use the given information. It states that z is equal to 96 when x is 2 and y is 6. Substituting these values into the variation equation, we get:
96 = k * (2^3) * 6
96 = k * 8 * 6
96 = k * 48
Now, we can solve for k by dividing both sides of the equation by 48:
k = 96 / 48
k = 2
Substituting the value of k back into the variation equation, we get:
z = 2 * x^3 * y
Comparing this equation to the answer choices, we see that the correct answer is (a) y = 2x^3y.
So, the variation equation for the given variation statement is y = 2x^3y.