-7.8
The rest can be solved as rational. Negative numbers are not rational.
The formulas:

Expand the expression:

Plug the values into the expression:
Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:

Where <em>k</em> is the constant of variation.
Inverse variation is in the form:

In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using <em>f</em> for frequency and <em>l</em> for length:

We can solve for the constant of variation. We know that the frequency <em>f</em> is 4.3 when the length is 0.65 meters long. Thus:

Solve for <em>k: </em>
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So, our equation becomes:

Then when the length is 0.5 meters, the frequency will be:

Answer:
The independent quantity in the situation is the length of the diameter.
Step-by-step explanation:
Consider a relationship between two variables.
Of the two variables one variable is dependent upon the other.
Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variable values are changed.
Independent variables are the variables that are being altered to see a proportionate change in the dependent variable.
In this case, it is provided that Grissom knows there is a relationship between the volume of the sphere and the length of its diameter.
With every sphere that Grissom draws, the volume of the sphere changes according to its diameter length.
That is the volume of the sphere depends upon the length of its diameter.
Thus, the independent quantity in the situation is the length of the diameter.
The number is no longer negative and changed in warm ness