$\text { Find } \mathbf { r } ^ { t } ( t ) \text { given the following vector function. }$

question 73

Multiple Choice

$\text { Find } \mathbf { r } ^ { t } ( t ) \text { given the following vector function. }$ $\mathbf { r } ( t ) = - 5 t ^ { 4 } \mathbf { i } - 4 t ^ { 5 } \mathbf { j } + 6 t ^ { 3 } \mathbf { k }$

• A) \(\mathbf { r } ^ { t } ( t ) = - 5 t ^ { 3 } \mathbf { i } - 4 t ^ { 4 } \mathbf { j } + 6 t ^ { 2 } \mathbf { k }\)
• B) \(\mathbf { r } ^ { t } ( t ) = - 5 t ^ { 3 } \mathbf { i } - 4 t ^ { 2 } \mathbf { j } + 6 t ^ { 4 } \mathbf { k }\)
• C) \(\mathbf { r } ^ { t } ( t ) = - 20 t ^ { 3 } \mathbf { i } + 4 t ^ { 4 } \mathbf { j } + 6 t ^ { 2 } \mathbf { k }\)
• D) \(\mathbf { r } ^ { t} ( t ) = - 20 t ^ { \mathbf { 4 } } \mathbf { i } - 20 t ^ { 5 } \mathbf { j } + 18 t ^ { 3 } \mathbf { k }\)
• E) \(\mathbf { r } ^ { t } ( t ) = - 20 t ^ { 3 } \mathbf { i } - 20 t ^ { 4 } \mathbf { j } + 18 t ^ { 2 } \mathbf { k }\)

---

Definitions:

Environmental Problems

Issues affecting the natural world, often caused or exacerbated by human activity, including pollution, climate change, and biodiversity loss.

Democracies

A system of government in which power is vested in the people, who rule either directly or through freely elected representatives.

Good Leader

An individual who possesses the ability to inspire and guide a group towards achieving a common goal, effectively managing resources and people.

International Efforts

Collaborative actions taken by countries around the world to address global challenges, such as climate change, poverty, and peacekeeping.