Express statement as an equation. Use the given information to find the constant proportionality
z varies inversely as t. If t � 3, then z � 5.
since zt=k is constant,
k=3*5 = 15, and we have
zt = 15
To express a statement as an equation, we can use the notation "y varies inversely as x" as the equation y = k/x, where k represents the constant of proportionality.
In this case, the given information states that z varies inversely as t. So, we can write the equation as z = k/t.
To find the constant proportionality (k), we need to use the additional information provided. The statement says that if t = 3, then z = 5.
Substituting these values into the equation, we have 5 = k/3.
To solve for k, we multiply both sides of the equation by 3: 5 * 3 = k.
Therefore, the constant proportionality (k) is 15.
The final equation that expresses the given information is z = 15/t.