Write a Set of Parametric Equations for the Surface of Revolution

question 77

Multiple Choice

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function $y = x ^ { \frac { 3 } { 7 } } , 0 \leq x \leq 4$ about the $x$ -axis.

• A) \(x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ { \frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi\)
• B)\(x = u , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ {\frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi\)
• C)\(x = u , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , 0 \leq u \leq 4 , v \geq 0\)
• D)\(x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , u \geq 4,0 \leq v \leq 2 \pi\)
• E)\(x = v , y = v ^ { \frac { 3 } { 7 } } \cos u , z = v ^ { \frac { 3 } { 7 } } \sin u , u \geq 4 , v \geq 0\)

---

Definitions:

Compounded Annually

The process of calculating interest on both the initial principle and the accumulated interest of previous periods on a yearly basis.

Beginning of the Year

Refers to the start date of a calendar or fiscal year.

Pay Today

The requirement or action of making a payment at the current date, commonly used in the context of purchasing or settling debts.

Cloture

A legislative procedure used to end a filibuster in the Senate, requiring a supermajority vote to close debate on a bill or nomination and proceed to a vote.