Find the equation of variation in which y varies jointly as x and z and y=8, x=4 and z=2
if a varies directly with b, then it means
a = k*b
If y varies jointly as x & z, then it means y = k * x * z
So, if 8 = k * 4 * 2
Then k = 1, and y = x*z
To find the equation of variation in which y varies jointly as x and z, we can write it as:
y = k * x * z
Here, k is the constant of variation.
Given that y = 8, x = 4, and z = 2, we can substitute these values into the equation:
8 = k * 4 * 2
Simplifying the equation, we have:
8 = 8k
Dividing both sides of the equation by 8, we find:
k = 1
Therefore, the equation of variation in which y varies jointly as x and z is:
y = x * z
To find the equation of variation, we need to determine the constant of variation. In this case, the problem states that y varies jointly as x and z. This means that y is directly proportional to both x and z.
To find the constant of variation, we can set up a proportion using the given values:
y = kxz
Substituting the given values:
8 = k * 4 * 2
Simplifying:
8 = 8k
Solving for k:
k = 1
Now that we have the constant of variation, we can write the equation of variation as:
y = xz
So, the equation of variation is y = xz.