Compute the Length of the Given Vector $p ( t ) = 3 t + 4$

question 5

Multiple Choice

Compute the length of the given vector.
- $p ( t ) = 3 t + 4$ and $q ( t ) = 4 t - 5$ , where $t _ { 0 } = 0 , t _ { 1 } = 1 , t _ { 2 } = 2$

• A) \(\| \mathrm { p } \| = \sqrt { 153 } ; \| \mathrm { q } \| = \sqrt { 195 }\)
• B) \(\| \mathrm { p } \| = \sqrt { 165 } ; \| \mathrm { q } \| = \sqrt { 35 }\)
• C) \(\| \mathrm { p } \| = \sqrt { 165 } ; \| \mathrm { q } \| = \sqrt { 145 }\)
• D) \(\| \mathrm { p } \| = \sqrt { - 133 } ; \| \mathrm { q } \| = \sqrt { 15 }\)

Recognize the structural and functional distinctions between gap junctions in animals and plasmodesmata in plants.

Understand the principle of consideration in contract law.

Differentiate between valid and invalid consideration.

Recognize the role of promissory estoppel in the absence of formal consideration.

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Definitions:

Fixed Costs

Costs that do not change in total amount with a change in business activity level, such as rent or salaries.

Short Run

The short run in economics is a period during which at least one input, like plant size, is fixed and cannot be changed.

Monopolistically Competitive

A market structure where many firms sell products that are similar but not identical, allowing for some degree of market power and price setting.

Fixed Costs

Expenses that do not vary with the level of production or sales, such as rent or salaries.