The area of the surface is 144.708
The equation of the given surface is,
z=g(x,y)=xy
Solving the partial derivatives,
∂g∂x=y,∂g∂y=x
Substituting to the formula
S=∬√1+( ∂g∂x)2+(∂g∂y)2dA
Thus,
S=∬√1+(y)2+(x)2dAS=∬√1+x2+y2dA
The region in the XY-plane is defined by the intervals 0≤θ≤2π,0≤r≤4
Converting the integral into polar coordinates,
S=∫2π0∫40√1+r2rdrdθ
Integrating with respect to r
S=∫2π0[13(1+r2)32]40dθ
S=∫2π0(17√173−13)dθ
Integrating with respect to θ
S=(17√173−13)[θ]2π0
S≈144.708
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Answer: 
Step-by-step explanation:
The missing figure is attached.
The volume of an oblique cylinders and the volume of a right cylinder can be found with this formula:
Where "r" is the radius and "h" is the height.
The volume of an oblique cone and the volume of a right cone can be found with this formula:
Where "r" is the radius and "h" is the height.
According to the information given in the exercise, you know that the volume of the cylinder and also the radius of the cylinder and the cone ,are the following:

Therefore, in order to find the volume of the cone, you only need to multiply the volume of the cylinder by
.
Then, you get:

Answer:
(b)0.56
(c)0.38
Step-by-step explanation:
(a)
P(Ben Pass) =0.8
Therefore: P(Ben fails)=1-0.8 =0.2
P(Tom Pass) =0.7
Therefore: P(Tom fails)=1-0.7 =0.3
See attached for the completed tree diagram
(b)Probability that both will pass
P(both will pass)=P(Ben pass and Tom pass)
=P(Ben pass) X P(Tom pass)
=0.8 X 0.7
=0.56
(c)The probability that only one of them will pass
Since either Tom or Ben can pass, we have:
P(only one of them will pass)
=P(Ben pass and Tom fails OR Ben Fails and Tom Pass)
=P(Ben pass and Tom fails)+P(Ben Fails and Tom Pass)
=(0.8 X 0.3) + (0.2 X 0.7)
=0.24 + 0.14
=0.38
Answer:
Step-by-step explanation:
Neutron: has mass and no charge
Protons: has mass and a positive charge
Answer:
x ≥ 0
Step-by-step explanation:
The absolute value of x+8 equals itself, thus x must be a real number (0 or any positive number).