↧↧↧ Detailed Video Solution to the Problem ↧↧↧We need to find the area of the region bounded by |x + y| < 20 and 0 < y < 20Plotting | x + y | < 20Let's simplifying | x + y | < 20 before plotting it
Using
|A| < k => -k < A < k=> | x + y | < 20 can be simplified as
-20 < x + y < 20
Now, | x + y | < 20 can be plotted by plotting two regions
x + y > -20 and x + y < 20 and taking the intersection of them.
Attachment:
Image.jpg [ 70.79 KiB | Viewed 3962 times ]
To do this first we will plot x + y = -20 and consider the area to the top of the line (as we have x+y > -20) as show in the attached image as Orange line
(HINT: put x = 0 and get y = -20 and y = 0 and x = -20 and plot the line)
Then we will plot x + y = 20 and consider the area to the bottom of the line (as we have x+y < 20) as show in the attached image as Green line
(HINT: put x = 0 and get y = 20 and y = 0 and x = 20 and plot the line)
Plotting 0 < y < 20We need to plot 0 < y < 20, this means y lies between 0 and 20
y =0 is x-axis (blue horizontal line in the image)
y = 20 passes through (0,20) and is parallel to x-axis (white line)
So, 0 < y < 20 is area between these two lines
Finally, |x + y| < 20 and 0 < y < 20 is the yellow shaded region in the image below.
This is a parallelogram with base 40 [ distance between (-20,0) and (20,0) ] and height 20.
So, Area = Base * Height = 40 * 20 = 800,
So,
Answer will be BHope it helps!
Watch the following video to learn Basics of Absolute ValuesLearn About How to Solve Inequalities and Absolute Values Together Here