Due to the symmetry of the paraboloid about the <em>z</em>-axis, you can treat this is a surface of revolution. Consider the curve , with , and revolve it about the <em>y</em>-axis. The area of the resulting surface is then
But perhaps you'd like the surface integral treatment. Parameterize the surface by
with and , where the third component follows from
Take the normal vector to the surface to be
The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:
Then the area of the surface is
which reduces to the integral used in the surface-of-revolution setup.
Answer:
the angle between the vectors and is
Step-by-step explanation:
Given -
, ,
If two vector and are inclined at an angle
vector parallelogram method
64 = 16 + 36 + 48
<span>The car will stop in 140.625 ft
</span>
Answer:
$1,800 is the correct answer.
Answer:
Below.
Step-by-step explanation:
sin-1 1/2 = 30 degrees in the first quadrant.
As the sin is negative in Quadrants 3 and 4,
sin01 -1/2
= 210, 330 degrees, in the range 0-360 degrees