Let $x ^ { 3 } y + y ^ { 3 } z + z ^ { 3 } x = 4$

question 240

Multiple Choice

Let $x ^ { 3 } y + y ^ { 3 } z + z ^ { 3 } x = 4$ , find $\frac { \delta z } { \delta x }$ .

• A) \(\frac { 3 x ^ { 2 } y + z ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• B) \(- \frac { 3 y ^ { 2 } z + x ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• C) \(\frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 y ^ { 2 } z + x ^ { 3 } }\)
• D) \(- \frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 x ^ { 2 } y + z ^ { 3 } }\)
• E) \(- \frac { 3 x ^ { 2 } y + z ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• F) \(\frac { 3 y ^ { 2 } z + x ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• G) \(- \frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 y ^ { 2 } z + x ^ { 3 } }\)
• H) \(\frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 x ^ { 2 } y + z ^ { 3 } }\)

Distinguish between situations where numerals or words are used for numbers according to standard English conventions.

Identify and classify different types of adjectives and adverbs in sentences.

Understand the concept of dangling modifiers and identify sentences free of such errors.

Correctly identify parts of speech, such as articles, gerunds, and infinitives, in given contexts.

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Definitions:

Defect

A flaw or imperfection in a product, process, or system that fails to meet specified criteria.

Proportion

A statistical measure that indicates the fraction of the total that possesses a certain attribute or characteristic.

Relative Risk

A measure in epidemiology that quantifies the risk of a certain event happening in one group compared to its occurrence in another group.

Defective

Pertaining to a product or item that fails to meet the quality or performance standards, often due to manufacturing errors or flaws.