Unit vector along the direction v = <3,1,-4> is :
So, unit vector opposing the 
is :
so, vector of magnitude 3 units in opposite direction from v is :
Hence, this is the required solution.
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Step-by-step explanation:
The top square is 8. The long rectangle 19.5. The bottom rectangle is 3.
Answer: dr/dt = 9/(24pi) cm per minute
9/(24pi) is approximately equal to 0.119366
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Work Shown:
Given info
dS/dt = 18 cm^2/min is the rate of change of the surface area
r = 6 cm is the radius, from the fact that the diameter is 12 cm
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Use the surface area equation given, apply the derivative, plug in the given values and then isolate dr/dt which represents the rate of change for the radius
S = 4*pi*r^2
dS/dt = 2*4*pi*r*dr/dt
dS/dt = 8*pi*r*dr/dt
18 = 8*pi*6*dr/dt
18 = 48*pi*dr/dt
48pi*dr/dt = 18
dr/dt = 18/(48pi)
dr/dt = (9*2)/(24*2pi)
dr/dt = 9/(24pi)
The units are cm per minute, which can be written as cm/min.
3.2 gallons of paint is needed since 2640 divided by 825 = 3.2
