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Mathematicsresear
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Homework Statement
I said it is 0 less than or equal to x less than or equal to 2 and 0 is less than or equal to y which is less than or equal to 2. Is that correct?
No.Mathematicsresear said:Homework Statement
I said it is 0 less than or equal to x less than or equal to 2 and 0 is less than or equal to y which is less than or equal to 2. Is that correct?
The region enclosed by these curves is a triangular region with vertices at (0,0), (2,0), and (2,2). It is bounded by the x-axis, the line y=x, and the vertical line x=2.
To find the area of this region, you can use the formula for the area of a triangle: A = 1/2 * base * height. In this case, the base is 2 units and the height is also 2 units, so the area is 1 square unit.
The x=2 line serves as one of the boundaries for the enclosed region. It is a vertical line that intersects the x-axis at the point (2,0) and the line y=x at the point (2,2).
Yes, the region can also be described as a right triangle or a trapezoid. However, since the curves y=x and x=2 are straight lines, the region will always have the same area regardless of the geometric shape used to describe it.
This region can be visualized by plotting the curves y=x and x=2 on a coordinate plane and shading in the triangular region between the curves and the x-axis. Alternatively, it can also be graphed by plotting the points (0,0), (2,0), and (2,2) and connecting them to form a triangle.