Question

Sketch the region that is common to the graphs of x ≥ 2,

Answer 1

a. Find the graph of their common region in the attachment

b. The area of the common region of the graphs is 8 units²

a. How to sketch the region common to the graphs?

Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.

• The graph of x ≥ 2 is the region right of the line x = 2.

• The graph of y ≥ 0 is the region above the line y = 0 or x-axis.

• To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.

So, the graph of x + y ≤ 6 is the region below the line y = - x + 6

From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)

Find the graph of their common region in the attachment

b. The area of the common region

From the graph, we see that the common region is a right angled triangle with

• height = 4 units and
• base = 4 units

So, its area = 1/2 × height × base

= 1/2 × 4 units × 4 units

= 1/2 × 16 units²

= 8 units²

So, the area of the common region of the graphs is 8 units²

Learn more about region common to graphs here:

brainly.com/question/27932405

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