Please help. given the units for four of the six variables, what must be the units of z and y?
a=m
t=s/K
h=N^4
x=m
z^a=xh cos(yt)
To determine the units of z and y, we can analyze the given equation:
z^a = xh * cos(yt)
Let's break down each term and identify the units:
Term 1: z^a
The variable z is raised to the power of a (m). To obtain the same units on both sides of the equation, z^(m), the units of z should be the m-th root of z^(a). Therefore, the units of z will be the square root of m.
Term 2: xh
From the given information, we know that x has the units of meters (m) and h has the units of N^4.
Term 3: cos(yt)
No units are specified for cos(yt) in the equation, which implies that the input must be dimensionless. Therefore, the product yt also needs to be dimensionless.
To achieve dimensionless units for yt, we need to ensure that the units of y and t cancel each other out. Given that the units of t are s/K and the units of yt should be dimensionless, the units of y must be K/s.
In summary, the units for z are the square root of m (√m) and the units for y are K/s.