The Graph of the Following Curve Is Given $$r = 3 + 15 \sin 6 \theta$$

question 28

Multiple Choice

The graph of the following curve is given. Find the area that it encloses.
$$r = 3 + 15 \sin 6 \theta$$

• A) \(A = \frac { 27 \sqrt { 5 } } { 2 }\)
• B) \(A = \frac { 81 } { 2 } \pi\)
• C) \(A = 18 \pi\)
• D) \(A = \pi + \frac { 27 \sqrt { 5 } } { 2 }\)
• E) \(A = 18 \pi + \frac { 81 } { 2 }\)

---

Definitions:

Average Total Cost Curve

A graphical representation showing how the average total cost of production changes as the quantity of output changes.

Long-Run Equilibrium

A state in which all factors of production and costs are variable, allowing firms to make adjustments and leading to a situation where economic profit equals zero.

Just Tangent To

A condition where two curves meet at only one point without intersecting, often used in the context of optimizing problems.