Answer:
11.28 ft
Step-by-step explanation:
The volume of a cylinder can be written as;
Volume V1 = πr^2 h
The volume of an hemisphere can be written as;
Volume V2 = (2/3)πr^3
The total volume of the silo is;
V = V1 + V2
V = πr^2 h + (2/3)πr^3
Given;
Volume of silo V= 15000 ft^3
Height of cylinder part h = 30 ft
Substituting the values;
V = πr^2 h + (2/3)πr^3
15000 = 30πr^2 + (2/3)πr^3
15000/π = 30r^2 + (2/3)r^3
2r^3 + 90r^2 - (15000×3/π) = 0
Solving the equation, we have;
r = 11.28 ft or -15.61 ft or -40.67 ft
Since the radius cannot be negative;
Radius r = 11.28 ft
We can compute the integral directly: we have
Then the integral is
You could also take advantage of Stokes' theorem, which says the line integral of a vector field 
along a closed curve 
is equal to the surface integral of the curl of over any surface 
that has as its boundary.
In this case, the underlying field is
which has curl
We can parameterize by
with 
and 
.
Note that when viewed from above, has negative orientation (a particle traveling on this path moves in a clockwise direction). Take the normal vector to to be pointing downward, given by
Then the integral is
Both integrals are kind of tedious to compute, but personally I prefer the latter method. Either way, you end up with a value of 
.
Answer:
The correct option is d.
Step-by-step explanation:
The given equations are
.... (1)
.... (2)
In equation 2, multiply both sides by 2.
.... (3)
Now add equation (1) and (3).
Divide both sides by 5.
Put this value in equation (2).
Therefore the solution of the system of equation is (2.4,0.2) and the system has only one solution. Option d is correct.
Answer:
77
Step-by-step explanation:
the dog ate half so there is only the other half left and there is 43 cards left
1 half + 1 half = 1 whole so 43 + 43 = 86
86 is the total after he bought 9 new cards
86 - 9 = 77
