Chapter 8.2, Problem 53E

A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a. Compute the area of the piece to be cut. Round the answer to the nearest square millimeter. b. After cutting the piece, determine the percentage of the plate that will be wasted.

Consider the image attached of the graphs of y = (1/2)x + 5 (what the red line represents) and y = |x| (what the blue line represents) in the same coordinate system. Also consider the image attached of the x and y values of the coordinates in which both of the graphs intersect. What is the area of the region bounded by both of the graphs? The answer to this question should be a mathematical expression (instead of a number) in square units.

A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line parallel to the x-axis passing through P(x, y) is equal to x + y. Find the equation of the curve.