Evaluate . Hint: First convert to cylindrical coordinates.

Question

Evaluate  . Hint: First convert to cylindrical coordinates.

Quizplus · Accepted Answer

To convert to cylindrical coordinates, we use the formula:

$x = r\cos(	heta)$ 
$y = r\sin(	heta)$ 
$z = z$

where $r$ is the distance from the origin to the point in the $xy$-plane, $	heta$ is the angle between the positive $x$-axis and the line connecting the origin and the point in the $xy$-plane, and $z$ is the distance from the $xy$-plane to the point.

Applying this formula to the given point, we get:

$r = \sqrt{11e^2 + 0b^2} \approx 237.23$

$	heta = 	an^{-1}(b/a) = 	an^{-1}(0b/11e) = 0$

$z = b - 7f = 8da5 - 7bde3 = -24101$

Therefore, the cylindrical coordinates of the point are approximately $(237.23, 0, -24101)$.

The correct answer is E, 11ead0bc_8da6_3318_99a0_1dc9c239107f_TB6988_11, as it matches the cylindrical coordinates we found.