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:
3.25 days
Step-by-step explanation:
Irri is traveling in a group of 8 cat warriors. Each cat needs 4 liters of milk per day to maintain good morale.
The total number of liters for the cat is calculated as:
8 × 4 liters of milk
= 32 liters of milk.
Another cat has enough milk to last for 2days.
= 4 liters of milk × 2 days
= 8 liters
Mirri has a supply of 96 liters of milk.
Total liters of milk = 96 liters + 8 liters
= 104 liters
Which equation can we use to find the total number of days the milk will last?
This is calculated as:
= 104 liters/32 liters
= 3.25 days
The correct answer is letter "<span>B. (3x – 2)(x + 3)."
</span>
This is how to factor the given polynomial:
<span>3x^2 + 7x – 6
(3x - 2) (x + 3)
It takes trial and error in order to get the final factor of a given polynomial. It has to be exact and correctly done.</span>
Answer:
Miguel start to swim when Ario has traveled 4.4 m.
Step-by-step explanation:
The total lenght of the pool is 25.
Since both of them standing 3 m from one side of the pool, then, the total distance both need to cover is
m= 22 m.
Assume that the distance traveled by Ario before Miguel start to swin is
. That means, the remaining distance to Ario (to cover the total size of the pool) is
.
Then, in acoordance to the problem, the ratio between these two distances must be equal to 1/4.
That is,
.
So, we need to obtain
from this equation. We must note that
, otherwise we have a zero in the denominator.
So, we rearrange the equation,
(Multiplying both sides of equation by (
).
Then,
.
Therefore,
m.
Answer:
45
Step-by-step explanation:
Use khan acedaemy