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

Guest May 16, 2020

#1**0 **

Graphing would be one way to find out which areas are covered by the inequalities.

Guest May 16, 2020

#3**+1 **

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

CPhill May 16, 2020