If $\mathbf { r } ( t ) = \left( t , t ^ { 5 } , t ^ { \imath } \right\rangle$

question 31

Multiple Choice

If $\mathbf { r } ( t ) = \left( t , t ^ { 5 } , t ^ { \imath } \right\rangle$ , find $\mathbf { r } ^ { tt } ( t )$

• A) \(\left( 0,42 t ^ { 4 } , 20 t ^ { 2 } \right\rangle\)
• B) \(\left( 0,42 t ^ { 5 } , 20 t ^ { 3 } \right)\)
• C) \(\left( 0,20 t ^ { 3 } , 42 t ^ { 5 } \right)\)
• D) \(\left\langle 1,5 t ^ { 6 } , 7 t ^ { 8 } \right\}\)
• E) \(\left( 0,20 t ^ { 2 } , 42 t ^ { 4 } \right)\)

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Definitions:

Elements

Substances that cannot be broken down into substances with different properties; composed of only one type of atom.

Reservoir

Location in a biogeochemical cycle where a chemical or resource is stored for long periods of time and is typically unavailable to living organisms.

Biotic Factor

Any living component that affects another organism or shapes the ecosystem, including animals, plants, and microorganisms.

Ecosystem

An ecosystem is a community of living organisms in conjunction with the nonliving components of their environment, interacting as a system through nutrient cycles and energy flows.