Answer:
The volume of the solid is 
Step-by-step explanation:
In this case, the washer method seems to be easier and thus, it is the one I will use.
Since the rotation is around the y-axis we need to change de dependency of our variables to have 
. Thus, our functions with 
as independent variable are:
For the washer method, we need to find the area function, which is given by:
![A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]](https://tex.z-dn.net/?f=A%3D%5Cpi%5Ccdot%20%5B%28%5Crm%7Bouter%5C%20radius%29%5E2%20-%28%5Crm%7Binner%5C%20radius%29%5E2%20%5D)
By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function 
and the inner one by 
. Thus, the area function is:
![A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)](https://tex.z-dn.net/?f=A%28y%29%3D%5Cpi%5Ccdot%20%5B%28%5Csqrt%7By%7D%20%29%5E2-%28y%5E2%29%5E2%5D%5C%5CA%28y%29%3D%5Cpi%5Ccdot%20%28y-y%5E4%29)
Now we just need to integrate. The integration limits are easy to find by just solving the equation 
, which has two solutions 
and 
. These are then, our integration limits.
Answer:
When given 2 sides of a triangle, the third side must be:
Greater than the difference of the other 2 sides AND
less than the sum of the other 2 sides.
So side "x" must be greater than
(8 -5) and less than (8 +5) or
3 < "x" < 13
Source: http://www.1728.org/trianinq.htm
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Pythagorean Theorem
a²+b²=c²
(c² is the hypotenuse)
a² + 40² = 41²
a² + 1,600 = 1,681
subtract 1681-1600 in order to isolate a², which is the missing leg we are trying to find
a² = 81 in order to find our answer, we isolate a by squaring both sides
√a² = √81
a = 9
Our answer is 9.
Answer:
CFD = 180
EFD= 152
180-152= 28
CFE= 28
Step-by-step explanation:
Step-by-step explanation:
Co-prime numbers are numbers that only have 1 as a common factor.
For example, 35 = 1×5×7, and 39 = 1×3×13. So 35 and 39 are co-prime.
Write the prime factorization of each number:
17 = 1×17
25 = 1×5²
35 = 1×5×7
43 = 1×43
55 = 1×5×11
119 = 1×7×17
187 = 1×11×17
43 is co-prime with all of these, so we will not use it.
If we start with 35 in the upper left, and 187 in the lower right, then we can also rule out 17 and 25, since these are co-prime with either 35 or 187.
So that leaves 55 and 119 as the other two numbers. They can go in any order, as long as they are diagonal from each other.
![\left[\begin{array}{cc}35&55\\119&187\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D35%2655%5C%5C119%26187%5Cend%7Barray%7D%5Cright%5D)
