Find the Exact Mass of a Thin Wire in the Shape

question 26

Multiple Choice

Find the exact mass of a thin wire in the shape of the helix $x = 2 \sin ( t ) , y = 2 \cos ( t ) , z = 3 t , 0 \leq t \leq 2 \pi$ if the density is 5 .

• A) \(4 \sqrt { 13 }\)
• B) \(8 \sqrt { 10 } \pi ^ { 2 }\)
• C) \(10 \sqrt { 13 }\)
• D) \(10 \sqrt { 13 } \pi\)
• E) \(\sqrt { 13 } \pi\)

---

Definitions:

Capacitive Reactance

The opposition that a capacitor offers to alternating current (AC), which decreases as the frequency of the AC increases, calculated as 1/(2πfC) where f is the frequency and C is the capacitance.

Series Connection

A circuit configuration in which components are connected end-to-end, providing a single path for current flow.

Frequency Source

A device or circuit component that generates an oscillating electrical signal of a specific frequency.

Capacitive Reactance

The opposition to change in voltage across a capacitor, inversely proportional to the frequency of the applied AC signal and the capacitor's capacitance.