Let the Position Function of a Particle Be $\mathbf { r } ( t ) = \langle 3 \sin 2 t , 2 \cos 2 t , - \sin 4 t \rangle$

question 56

Multiple Choice

Let the position function of a particle be $\mathbf { r } ( t ) = \langle 3 \sin 2 t , 2 \cos 2 t , - \sin 4 t \rangle$ . Find the speed of the particle when $t = \frac { \pi } { 4 }$ .

• A)1
• B)4
• C)3
• D) \(4 \sqrt { 2 }\)
• E) \(\sqrt { 8 }\)
• F) \(\sqrt { 10 }\)
• G) \(\sqrt { 13 }\)
• H) \(\sqrt { 14 }\)

Apply fraction operations to solve real-world problems including division and multiplication.

Translate mixed numbers to improper fractions and vice versa for computation.

Compute scaled quantities for recipes or mixes based on different serving sizes.

Understand and apply concepts of area and length conversion to real-world problems.

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Definitions:

Adenylyl Cyclase

Enzyme responsible for catalyzing the conversion of ATP to cyclic AMP (cAMP).

Protein Kinase

An enzyme that modifies other proteins by chemically adding phosphate groups, playing a crucial role in cellular signaling and function.

Endoplasmic Reticulum

A membranous network within cells that is involved in protein and lipid synthesis, transport, and detoxification processes, existing in two forms: rough and smooth.

Calcium Ions

Positively charged calcium atoms (Ca2+) that play essential roles in biological processes like bone formation, muscle contraction, and blood clotting.