If x varies directly as y and y varies inversely as the square of z. How is x varies with z?
x = ay
y = b/z^1/2
so
x = ab/z^1/2
a, b and ab are constants, so x varies inversely with the square root of z.
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To determine how x varies with z, we need to examine the relationships provided. If x varies directly as y and y varies inversely as the square of z, we can combine these two relationships to find the relationship between x and z.
First, let's write out the given relationships in the form of equations:
x = ky (direct relationship)
y = k/z^2 (inverse relationship)
Here, k is a constant of proportionality.
To find the relationship between x and z, we need to express y in terms of x and z. Let's solve the equations to eliminate the k:
From the second equation:
k = y * z^2
Substituting this value of k into the first equation:
x = (y * z^2) * y
Simplifying further:
x = y^2 * z^2
Thus, we can conclude that x varies directly with the square of z.