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Find the area of the region determined by the inequalities \(y \ge |x|\) and \(y \leq -|x+1| + 4.\)

 May 16, 2020
 #1
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Graphing would be one way to find out which areas are covered by the inequalities.

 May 16, 2020
 #2
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I tried to graph it, but it's telling me my answer is wrong and I would like to see if anyone has an algebraic way of solving it. (or an explanation for the graphing method).

Guest May 16, 2020
 #3
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Graphing  is definitely WAY easier  than an algebraic method

 

This shows  that  we really have the area of a simple region  (a rectangle)

 

https://www.desmos.com/calculator/xood3yofrf

 

One dimension of the rectangle  is   sqrt [( 1.5^2 + 1.5^2]  = 1.5sqrt (2)

 

And the other  is    sqrt [ 2.5^2 + 2.5^2]  = 2.5sqrt(2)

 

The area is   ( 1.5) (2.5) sqrt (2) * sqrt (2)  =  3.75 * 2  =    7

 

 

cool cool cool

 May 16, 2020

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