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sqrt(1^2 + 1^2 ) = sqrt(2)sqrt(sqrt(2)^2 + 1^2 ) = sqrt(3)
sqrt(sqrt(3)^2 + 1^2 ) = sqrt(4)
sqrt(sqrt(4)^2 + 1^2 ) = sqrt(5)
sqrt(sqrt(5)^2 + 1^2 ) = sqrt(6)
sqrt(sqrt(6)^2 + 1^2 ) = sqrt(7)
sqrt(sqrt(7)^2 + 1^2 ) = sqrt(8)
sqrt(sqrt(8)^2 + 1^2 ) = sqrt(9)
sqrt(sqrt(9)^2 + 1^2 ) = sqrt(10)
sqrt(sqrt(10)^2 + 1^2 ) = sqrt(11)
sqrt(sqrt(11)^2 + 1^2 ) = sqrt(12)
sqrt(sqrt(12)^2 + 1^2 ) = sqrt(13)
sqrt(sqrt(13)^2 + 1^2 ) = sqrt(14)
sqrt(sqrt(14)^2 + 1^2 ) = sqrt(15)
sqrt(sqrt(15)^2 + 1^2 ) = sqrt(16)
sqrt(sqrt(16)^2 + 1^2 ) = sqrt(17)
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What is consistent and dependent?
The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.
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