The Position Vector of a Particle Is R(t) $t = \frac { \pi } { 4 }$

question 50

Multiple Choice

The position vector of a particle is r(t) . Find the requested vector.
-The acceleration at $t = \frac { \pi } { 4 }$ for $r ( t ) = ( 2 \sin 2 t ) \mathbf { i } - ( 2 \cos 2 t ) \mathbf { j } + ( 5 \csc 2 t ) \mathbf { k }$

• A) \(a \left( \frac { \pi } { 4 } \right) = 8 i + 20 k\)
• B) \(a \left( \frac { \pi } { 4 } \right) = - 8 i + 20 k\)
• C) \(\left( \frac { \pi } { 4 } \right) = - 8 \mathbf { i } - 20 \mathbf { k }\)
• D) \(a \left( \frac { \pi } { 4 } \right) = 8 \mathbf { j } + 20 \mathbf { k }\)

Differentiate between the adequacy of consideration and the factors courts consider in evaluating it.

Understand the applications and limitations of the doctrine of promissory estoppel.

Distinguish between enforceable and non-enforceable promises based on the presence of consideration.

Recognize the legal implications of agreements lacking consideration, such as accord and satisfaction.

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Definitions:

Proteins

Large, complex molecules made up of amino acids that perform a variety of functions in the body, including structural support, catalysis of metabolic reactions, and transport.

Gastrointestinal Tract

The series of hollow organs joined in a long, twisting tube from the mouth to the anus, including organs like the stomach and intestines, involved in digesting food and absorbing nutrients.

Dipeptide

A molecule consisting of two amino acids joined by a single peptide bond.

Fatty Chyme

A semi-fluid mass of partly digested food enriched with fats, that moves from the stomach to the small intestine.