The linear function y = 3 · w - 1 represents the number of sea shells found in each week.
The speed of the driven gear is 180 rounds per minute.
How to use direct and inverse relationships to analyze situations
In the first problem we have an example of linear progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the linear function y = 3 · w - 1, a kind of direct relationship.
In the second problem, we must an inverse relationship to determine the speed of the driven gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:
[tex]\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}[/tex]
If we know that [tex]v_{2} = 60\,rpm[/tex], [tex]N_{2} = 60[/tex] and [tex]N_{1} = 20[/tex], then the speed of the driven gear is:
[tex]v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}[/tex]
[tex]v_{1} = 60\,rpm \times \frac{60}{20}[/tex]
[tex]v_{1} = 180\,rpm[/tex]
The speed of the driven gear is 180 rounds per minute.
To learn more on inverse relationships: https://brainly.com/question/4147411
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