Polar form: (r,θ)
Using these formulas:
x²+y²=r²
tan(θ)=y/x
We have the point (1,1) in cartesian coordinates. We need to find r and θ to get it in polar form.
r²=1²+1²
r²=2
r=±√2
tan(θ)=1/1
tan(θ)=1
θ=π/4 radians or 45 degrees
Polar coordinates: (√2,π/4)
Those answer choices look strange. Are you sure these are the right answer choices?
It would take 60 days to add 30 million new accounts
The other person is correct the answer is C
I got 110 because 35+35=70 and 180-70=110. I added 35 to 35 because it says that AB=AD, so they should make congruent angles. So add the 35+35 and work from there.
The tangent to 
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces 
and 
at that point.
Let 
. Then is the level curve 
. Recall that the gradient vector is perpendicular to level curves; we have
so that the gradient of 
at (1, 1, 1) is
For the surface , we have
so that 
. We can obtain a vector normal to by taking the cross product of the partial derivatives of 
, and evaluating that product for 
:
Now take the cross product of the two normal vectors to and :
The direction of vector (24, 8, -8) is the direction of the tangent line to at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by 
. Then adding (1, 1, 1) shifts this line to the point of tangency on . So the tangent line has equation
