Find the length S of the spiral (t cos(t), t sin(t)) for 0 ≤ t ≤ 3π. (Round your answer to three decimal places.) S =

The arc length is

where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,

so the line element is

So we have

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol