Calculate the Flow in the Field F Along the Path

question 12

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = - \frac { z y } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { z x } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } j + \frac { z ^ { 3 } } { 3 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k } , C$ is the curve $r ( t ) = 4 \cos 6 t i + 4 \sin 6 t j + 3 t k , 0 \leq t$ $\leq 1$

• A) \(\frac { 61 } { 9 }\)
• B) 21
• C) \(\frac { 61 } { 3 }\)
• D) 0

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Definitions:

Mons Pubis

The mons pubis is a rounded mound of fatty tissue covering the pubic bone, usually more prominent in women, and becomes covered in hair during puberty.

Perineum

The area between the anus and the genitals, consisting of both muscular and fibrous tissue.

Spermatogenesis

The process by which spermatozoa are produced from male primordial germ cells by way of mitosis and meiosis.

Oogenesis

Oogenesis is the process by which the female gametes, or ova, are produced in the ovaries through a series of differentiation and maturation stages.