I think pencil and paper would be the best method
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:
a= (1,4)
b=(4,2)
c=(2,6)
d=(2,-1)
Step-by-step explanation:
All I did was looked at the regions the points began and ended. I'm not 100% this is correct but I hope I helped!
Answer:
54
Step-by-step explanation:
Angles in a triangle add to 180° and we can see a right angle so
x = 180 - ( 90 + 36 )
x = 180 - 126
x = 54
Answer:
Step-by-step explanation:
Two lines are perpendicular if the first line has a slope of 
and the second line has a slope of 
.
With this information, we first need to figure out what the slope of the line is that we're given, and then we can determine what the slope of the line we're trying to find is:
We now know that 
for the first line, which means that the slope of the second line is 
. With this, we have the following equation for our new line:
where 
is the Y-intercept that we now need to determine with the coordinates given in the problem statement, 
:
Finally, we can create our line:
