Determine the Angle $\theta$ Through Which the Axes Are Rotated $24 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 32$

question 3

Multiple Choice

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places.​ $24 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 32$ ​

• A) \(\theta = 78.87 ^ { \circ }\)
• B) \(\theta = 79.87 ^ { \circ }\)
• C) \(\theta = 81.87 ^ { \circ }\)
• D) \(\theta = 77.87 ^ { \circ }\)
• E) \(\theta = 80.87 ^ { \circ }\)

---

Definitions:

Universal Generalization

A form of logical inference where a general statement is made about all members of a set based on sufficient evidence or instances.

Existential Instantiation

A logical operation that infers the existence of at least one individual satisfying a particular property from a general statement.

Universal Instantiation

A logical rule of inference that allows one to deduce a particular instance from a universal statement, essentially moving from a general statement to a specific example.

Existential Generalization

A logical inference rule stating that if something is true for some member of a domain, then it is true that there exists something in that domain for which the proposition holds.