Assuming That the Equations Define X and Y Implicitly as Differentiable

question 362

Multiple Choice

Assuming that the equations define x and y implicitly as differentiable functions x = f(t) , y = g(t) , find the slope of the curve x = f(t) , y = g(t) at the given value of t.
- $$x = t \sin t + t , y \cos t + y = 2 t , t = \frac { \pi } { 2 }$$

• A) \(\frac { 2 + \pi } { 2 }\)
• B) \(\frac { 2 } { 2 + \pi }\)
• C) \(2 + \pi\)
• D) \(- \frac { 2 } { 2 + \pi }\)

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Definitions:

Explanandum

The term explanatory in nature, referring to a statement or phenomenon that needs to be explained.

Hypothesis

A suggested theory put forward with minimal evidence as an initial step for more in-depth inquiry.

Proposition

An announcement or avowal that presents an evaluation or sentiment.

Hypothesis

A supposition or proposed explanation made on the foundation of limited information, aimed at further examination.