Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y + z = 12.

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

which suggests we could use

with , and we get from the equation of the plane,

Now use the arc length formula:

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: