SKETCH THE REGION ENCLOSED BY THE GIVEN CURVES:
Y=|10X|, Y=X^2-11
To sketch the region enclosed by the given curves, we first need to find the points where the two curves intersect.
Setting the two equations equal to each other, we have:
|10X| = X^2 - 11
Next, we need to solve this equation for X. Since the absolute value function can be positive or negative, we need to consider both cases separately.
1. For positive values of 10X:
10X = X^2 - 11
X^2 - 10X - 11 = 0
By solving this quadratic equation, we get two values for X, let's call them X1 and X2.
2. For negative values of 10X:
-10X = X^2 - 11
X^2 + 10X - 11 = 0
Again, by solving this quadratic equation, we get two values for X, let's call them X3 and X4.
Now that we have the X-values of the intersection points, we can determine the corresponding Y-values by substituting these X-values into either of the original equations.
For Y = |10X|:
- Substitute X1 and X2 separately to get Y1 and Y2.
For Y = X^2 - 11:
- Substitute X3 and X4 separately to get Y3 and Y4.
Now we have four points: (X1, Y1), (X2, Y2), (X3, Y3), and (X4, Y4).
To sketch the region enclosed by the given curves, plot these points on the coordinate plane. Then sketch the curves Y = |10X| and Y = X^2 - 11. The region enclosed by these curves is the area enclosed by the curves and the x-axis between the intersections.