Answer:
Step-by-step explanation:
The given system is:
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
We could solve the first equation for 
and replace the second with that.
Let's do that.
Subtract 
on both sides:
So we are replacing the second in the second equation with 
which gives us:
Now recall the first equation we arranged so that was the subject. I'm referring to .
We can now find given that using the equation .
Let's do that.
with :
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with 
:
is a true equation so the "solution" looks promising still.
with :
is also true so the solution has been verified since both equations render true for that point.
Answer:
The wedge cut from the first octant ⟹ z ≥ 0 and y ≥ 0 ⟹ 12−3y^2 ≥ 0 ⟹ 0 ≤ y ≤ 2
0 ≤ y ≤ 2 and x = 2-y ⟹ 0 ≤ x ≤ 2
V = ∫∫∫ dzdydx
dz has changed from zero to 12−3y^2
dy has changed from zero to 2-x
dx has changed from zero to 2
V = ∫∫∫ dzdydx = ∫∫ (12−3y^2) dydx = ∫ 12(2-x)-(2-x)^3 dx =
24(2)-6(2)^2+(2-2)^4/4 -(2-0)^4/4 = 20
Step-by-step explanation:
Well we set the perimeter to 120 feet.
This means that 2x+2y=120
Now we know the area of a rectangle is xy so we have to solve for both x and y in the perimeter equation.
2x=120-2y
x=60-y
2y=120-2x
y=60-x
Now we plug these values into our area equation A=xy to get:
A=(60-y)(60-x)
