To determine the domain of the function [tex]\( H(w) = \frac{70}{w} \)[/tex], we need to identify the values of [tex]\( w \)[/tex] that make the function valid (i.e., [tex]\( H(w) \)[/tex] is defined).
The function [tex]\( H(w) = \frac{70}{w} \)[/tex] is a rational function, which is defined for all values of [tex]\( w \)[/tex] except those that make the denominator zero. Specifically, the function will be undefined if the denominator [tex]\( w \)[/tex] is zero, since division by zero is undefined in mathematics. Therefore, [tex]\( w \)[/tex] cannot be zero.
Thus, the function is defined for every other real number except zero. This means [tex]\( w \)[/tex] can be any positive or negative value, as long as it is not zero. However, negative widths do not make sense in the context of a physical rectangle's dimensions, given the height [tex]\( H(w) \)[/tex] relates to the width [tex]\( w \)[/tex] of a rectangle with a specified area.
In practical scenarios, we are only interested in positive values for width [tex]\( w \)[/tex] because a width, being a measurement in geometry, should be greater than zero.
Therefore, the domain of the function [tex]\( H(w) = \frac{70}{w} \)[/tex] in this context is all positive real numbers:
[tex]\[ w > 0 \][/tex]
Hence, the correct answer is:
C. [tex]\( w > 0 \)[/tex]
