Another triple integral.  We're integrating over the interior of the sphere

Let's do the outer integral over z.   z stays within the sphere so it goes from -2 to 2.
For the middle integral we have

x is the inner integral so at this point we conservatively say its zero.  That means y goes from  and
 and 
Similarly the inner integral x goes between 
So we rewrite the integral

Let's work on the inner one,

There's no z in the integrand, so we treat it as a constant. 

So the middle integral is
 
  
I gotta go so I'll stop here, sorry.
 
        
                    
             
        
        
        
Basically you need to make the denominator (whats on the bottom) the same, lets take the first one for example
2 3/4, lets put this all over 4 for the same denominator.
2=8/4, and then add this to 3/4 to get 11/4.
the second part will work the same way, 
start by making 1 into 8/8. add this to 1/8 to get 9/8
now we have to add 11/4 and 9/8. to do this, you have to find the smallest multiple between the two (for example: between 6 and 4 it would be 12, since 4*3= 12, and 2*6=12)
now, the smallest common multiple between 4 and 8 would just be 8
11/4= 22/8, since you multiply the bottom and top by the same amount so it still equals 11/4, but your denominator will now be 8.
now you can subtract. 22/8- 9/8= 13/8
final answer: 13/8
try the rest yourself since this is important for later math, hoped this helped :)
        
                    
             
        
        
        
let's use engineering notation for the sake of brevity.
1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.
1 million is then 1E6, six zeros.
we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

 
        
             
        
        
        
Answer:
Part 1) The vertex is the point (-83,-9)
Part 2) The focus is the point (-82.75,-9)
Part 3) The directrix is 
Step-by-step explanation:
step 1
Find the vertex
we know that
The equation of a horizontal parabola in the standard form is equal to

 where 
p≠ 0. 
(h,k) is the vertex
(h + p, k) is the focus
x=h-p is the directrix
In this problem we have

Convert to standard form



so
This is a horizontal parabola open to the right
(h,k) is the point (-83,-9)
so
The vertex is the point (-83,-9)
step 2
we have

<em>Find the value of p</em>


<em>Find the focus</em>
(h + p, k) is the focus
substitute
(-83+1/4,-9)
The focus is the point (-82.75,-9)
step 3
Find the directrix
The directrix of a horizontal parabola is 

substitute


 
        
             
        
        
        
Answer:
It should be 1/2 because they both have the same amount of wins and loses.