The pressure in a chemical reaction chamber at time t minutes is given by p(t) = 60 arctan(2 + 3t2) kilopascals. (a) Find p'(2). Include the correct units (b) Give a complete sentence interpretation of your answer to part (a) in the context of this problem

The pressure in a chemical reaction chamber at time t minutes is given by p(t) = 60 arctan(2 + 3t2) kilopascals. (a) Find p'(2). Include the correct units (b) Give a complete sentence interpretation of your answer to part (a) in the context of this problem

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter19: Temperature, Thermal Expansion And Gas Laws

Section: Chapter Questions

Problem 71PQ

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Concept explainers

Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

Question

The pressure in a chemical reaction chamber at time t minutes is given by p(t) = 60 arctan(2 + 3t²) kilopascals.

(a) Find p'(2). Include the correct units

(b) Give a complete sentence interpretation of your answer to part (a) in the context of this problem.

Study of body parts and their functions. In this combined field of study, anatomy refers to studying the body structure of organisms, whereas physiology refers to their function.

Expert Solution

Part (a)

$p (t) = 60 \tan^{- 1} (2 + 3 t^{2}) p' (t) = 60 \times \frac{6 t}{1 + {(2 + 3 t^{2})}^{2}} p' (t) = \frac{360 t}{5 + 12 t^{2} + 9 t^{4}} kPa / \min$

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