a cylindrical tank is initially filled with water to a depth of 16 feet. a valve in the bottom is...
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![Page 1: A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water](https://reader036.vdocuments.mx/reader036/viewer/2022082418/5697bfd81a28abf838caf026/html5/thumbnails/1.jpg)
A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water in the tank decreases at a rate proportional to the square root of the depth. Write a differential equation that expresses this relationship.
![Page 2: A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water](https://reader036.vdocuments.mx/reader036/viewer/2022082418/5697bfd81a28abf838caf026/html5/thumbnails/2.jpg)
A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water in the tank decreases at a rate proportional to the square root of the depth; that is Solve the following differential Equation
where k is a constant. Find the solution of the differential equation in terms of k.
hkdtdh
![Page 3: A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water](https://reader036.vdocuments.mx/reader036/viewer/2022082418/5697bfd81a28abf838caf026/html5/thumbnails/3.jpg)
After the valve is opened, the water falls to a depth of 12.25 feet in 8 hours. Find the value of k with 0< k < 1.
How many hours after the valve was first opened will the tank be completely empty?