A Chlorine Solution Is Poured Over the Surface of a Rectangular

question 42

Short Answer

A chlorine solution is poured over the surface of a rectangular swimming pool that is 20 meters long, 10 meters wide and 2 meters deep everywhere.Before the circulating pumps in the pool are turned on, it is discovered that the density of the chlorine solution at a height h meters above the bottom of the pool is given by $\rho$ (h)= 100h grams/m^3. In other words, the chlorine solution has distributed itself so that its density increases linearly from the bottom of the pool.Write a Riemann sum that approximates the total mass of chlorine solution in the pool, convert it into a definite integral, and evaluate it to find the total mass of the chlorine solution in the pool.Give your answer in kg.

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Definitions:

Right Ventricle

One of the four chambers of the heart, responsible for pumping oxygen-depleted blood to the lungs.

Pulmonary Semilunar

Referring to the pulmonary semilunar valve, one of the heart's valves that prevents blood from flowing back into the right ventricle from the pulmonary artery.

Tricuspid

Referring to a valve in the heart that lies between the right atrium and the right ventricle, ensuring the flow of blood in one direction.

Pericardium

The thin, sac-like membrane surrounding the heart, providing protection and contributing to its function.