Answer:
1.92cm
Step-by-step explanation:
Circumference of a circle is computed using the formula:
Where:
r = radius
π = 3.14
Since the radius is the distance of the center of the circle from any point of the circle and the diameter is the measure of a straight line that goes across the center of the circle from one side to the other, radius is half of a diameter. So the diameter = 2r.
We can then use the diameter to solve for the circumference by using the formula"
So we just plug in what we know in the formula:
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
Answer is B. second one
A = 1/8, B = 5/16, C = 7/12, D = 5/6
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Answer:
The statement is true for every n between 0 and 77 and it is false for 
Step-by-step explanation:
First, observe that, for n=0 and n=1 the statement is true:
For n=0: 
For n=1: 
From this point we will assume that 
As we can see, 
and 
. Then,
Now, we will use the formula for the sum of the first 4th powers:
Therefore:
and, because 
,
Observe that, because 
and is an integer,
In concusion, the statement is true if and only if n is a non negative integer such that 
So, 78 is the smallest value of n that does not satisfy the inequality.
Note: If you compute 
for 77 and 78 you will obtain:
