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
Your answer is B. 91 2/3 pi Units Squared
The slope is -2. this is because if you look at the graph it goes down 2 units and it goes right to the once so it’ll be -2/1 which equals -2.
Given
Rob is twice Joshua's age
Nick is 5 years older than Joshua.
sum of all their ages is 45.
Find the age of nick.
To proof
As given
Rob is twice Joshua's age
let Joshua's age = x
than Rob age = 2x
Nick is 5 years older than Joshua.
Nick age = 5 + x
sum of all their ages is 45
than the equation becomes
Joshua's age + Rob age + Nick age = 45
put the value
x + 2x + 5 + x = 45
4x = 40
x = 10
Joshua's age = 10 year
than Rob age = 20 year
Nick age = 5 + 10
= 15year
Hence proved
Answer:
x=-2
Step-by-step explanation:
Given points are (-2,2) and (-2,-3).
Now we need to find equation of the line passing through the given points.
So let's begin by finding slope
which is undefined. That means graph of the line must be vertical as you can see that in given points, x-value is not changing.
Equation of vertical line is given by x=k where k is the fixed value of x-coordinate.
x-coordinate is -2 in given points.
Hence final equation is x=-2.
