Find the Principal Unit Normal Vector N for the Curve $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

question 14

Multiple Choice

Find the principal unit normal vector N for the curve r(t) .
- $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

• A) \(\mathbf { N } = - \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } + \frac { t } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)
• B) \(\mathbf { N } = \frac { 1 } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• C) \(\mathbf { N } = - \frac { 1 } { \sqrt { t ^ { 2 } + 1 } } \mathbf { j } + \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• D) \(\mathbf { N } = \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \left( \mathrm { t } ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)

Understand the relationship between market prices, average variable cost (AVC), and average total cost (ATC).

Explain the significance of economic profits, normal profits, and losses to firm behavior and industry entry or exit.

Relate changes in input prices to shifts in a firm's marginal cost curve and industry supply curve.

Illustrate the concept of marginal cost and its relevance to firm production decisions.

---

Definitions:

Standardization

The process of implementing and developing technical standards to ensure uniformity and consistency across different products, services, or procedures.

Cross-Functional Collaboration

A process where team members from various departments or specialties work together towards a common goal.

Hierarchical Relationships

The relational structure in organizations based on levels of authority and responsibility, defining roles, and how communication and power flow.

Simple Structure

A structure within an organization that features minimal compartmentalization, broad ranges of control, a central point of authority, and little to no formal procedures.