Which graph shows the solution to the system of linear inequalities?
2 answers:
Answer:
- See below
Step-by-step explanation:
<u>Given system:</u>
- y ≥ 2x + 1
- y ≤ 2x – 2
The solution is the common area shaded by the inequalities.
The lines are parallel because of same slope.
Both lines are solid because of equal sign in both inequalities.
The first inequality has a y-intercept of 1 and shaded area is to the left of the line since the value of y is greater as x increases.
The second inequality has a y-intercept of -2 and shaded area is to the right of the line since the value of y is greater as x increases.
The matching graph is the second picture (or attached below) and there is no solution.
You might be interested in
The two parabolas intersect for
and so the base of each solid is the set
The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, . But since -2 ≤ x ≤ 2, this reduces to
.
a. Square cross sections will contribute a volume of
where ∆x is the thickness of the section. Then the volume would be
where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of
We end up with the same integral as before except for the leading constant:
Using the result of part (a), the volume is
c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is
and using the result of part (a) again, the volume is