Find a Vector Function That Represents the Curve of Intersection $x ^ { 2 } + y ^ { 2 } = 4$

question 54

Multiple Choice

Find a vector function that represents the curve of intersection of the two surfaces:
The circular cylinder $x ^ { 2 } + y ^ { 2 } = 4$ and the parabolic cylinder $z = x y$ .

• A) \(\mathbf { r } ( t ) = 4 \cos t \mathbf { i } + 4 t \mathbf { j } + 4 \cos ^ { 2 } t \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = 2 \cos ( t ) \mathbf { i } + 2 \sin ( t ) \mathbf { j } - \sin ( t ) \cos ( t ) \mathbf { k }\)
• C) \(\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } - 4 \cos 2 t \mathbf { k }\)
• D) \(\mathbf { r } ( t ) = \cos ( t ) \mathbf { i } + \sin ( t ) \mathbf { j } + 4 \sin ( t ) \cos ( t ) \mathbf { k }\)
• E) \(\mathbf { r } ( t ) = 2 \cos ( t ) \mathbf { i } + 2 \sin ( t ) \mathbf { j } + 4 \sin ( t ) \cos ( t ) \mathbf { k }\)

Recognize the conditions under which a chi-square test of independence is valid.

Determine appropriate statistical tests for analyzing the relationship between two qualitative variables.

Comprehend the concept of expected frequency in the context of contingency tables.

Apply chi-square tests to real-world research scenarios to assess independence between variables.

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