How can x^2=x^2+2x+9 be set up as a system of equations
1 answer:
Answer:
Step-by-step explanation:
1. As you can see, is equal to the other quadratic equation
.
2. Then, this would the same as write the quadratic equations as following:
3. And then set them equal to each other, as you can see below:
Substituting, you obtain:
3. Keeping the above on mind, you can set up the given equations as a system of equations as folllowing:
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