Find the Surface Area of the Surface S $\mathrm { S }$

question 147

Multiple Choice

Find the surface area of the surface S.
- $\mathrm { S }$ is the portion of the surface $10 \sqrt { 7 } x + 10 y ^ { 2 } - 20 \ln y - 30 z = 0$ that lies above the rectangle $0 \leq x \leq 1$ and $1 \leq y \leq 7$ in the $x - y$ plane.

• A) \(\frac { 2 } { 3 } [ 24 + \ln 7 ]\)
• B) \(\frac { 1 } { 15 } [ 24 + \ln 7 ]\)
• C) \(\frac { 20 } { 3 } [ 24 + \ln 7 ]\)
• D) \(\frac { 4 } { 3 } [ 24 + \ln 7 ]\)

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Definitions:

500 mL

A volume measurement often referencing the typical amount of blood pumped by the left ventricle of the heart in one minute, or the capacity of a standard drink bottle.

Tubular Load

Amount of a substance per minute that crosses the filtration membrane into Bowman’s capsule.

Afferent Arteriole

A small artery that carries blood toward the glomeruli of the kidney, playing a key role in the regulation of blood pressure.

Filtration Membrane

A selectively permeable barrier that separates substances in a mixture based on size or other characteristics, widely used in biological and chemical processes.