How did the supreme court rule in case vs. cherokees

I'm going to assume you mean the Cherokee Nation v. Georgia U.S Court Case.

In the case, the Supreme Court ruled the Cherokee Nation was not fully  considered to be a foreign nation, and, therefore, the Supreme Court lacked the jurisdiction, which is the official power to make legal decisions, to hear the claims of the Cherokees. The Court then dismissed the case.

levels of production can be increased by technology while holding labor and capital constant, because increased technology makes the production process more efficient. subsequently, the lras curve is almost a vertical line, that can shift to the right, with an increase in technology.

the relationship between the lras curve and the ppc is that both can make the economy could grow. the ppc achieves that when it shifts outward because of more resources or technological advances while the lras curve shifts if more resources are developed or if there are technological advances.

the lras curve is a vertical line at an output level that represents the number of goods and services a nation can produce over a sustained period using all of its productive resources as efficiently as possible with all of the current technology available to it.

the production possibilities frontier (ppf) is a graphical device that is used for economic analysis of production decisions because the ppf measures the maximum possible combinations of two goods that an economy is capable of producing with its currently available resources and technology.