Rotation about the origin
Step-by-step explanation:
y=6+4x, as equation (iii)
=> -5x-(6+4x)=21
=> -5x-6-4x=21
=> -5x-4x-6=21
=> -9x-6=21
=> -9x=21+6
=> -9x=27
x= -3, by dividing both sides by -9
So, by inserting x in the first equation,
=> -4(-3)+y=6
=> 12+y=6
=> y=6-12
=> y= -6.
Therefore, x= -3 and y= -6
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:
the CEO earns about <em><u>31045.5</u></em> in a given month
