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Chapter 5: Problem 75
Define fluid pressure.
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A cone of height \(H\) with a base of radius \(r\) is cut by a plane parallel to and \(h\) units above the base. Find the volume of the solid (frustum of a cone) below the plane.
In Exercises \(13-26,\) sketch the region bounded by the graphs of the algebraic functions and find the area of the region. $$ y=\frac{1}{2} x^{3}+2, y=x+1, x=0, x=2 $$
The level of sound \(\beta\) (in decibels) with an intensity of \(I\) is $$\beta(I)=10 \log _{10} \frac{I}{I_{0}}$$ where \(I_{0}\) is an intensity of \(10^{-16}\) watt per square centimeter, corresponding roughly to the faintest sound that can be heard. Determine \(\beta(I)\) for the following. (a) \(I=10^{-14}\) watt per square centimeter (whisper) (b) \(I=10^{-9}\) watt per square centimeter (busy street corner) (c) \(I=10^{-6.5}\) watt per square centimeter (air hammer) (d) \(I=10^{-4}\) watt per square centimeter (threshold of pain)
The region bounded by \(y=\sqrt{x}, y=0, x=0,\) and \(x=4\) is revolved about the \(x\) -axis. (a) Find the value of \(x\) in the interval [0,4] that divides the solid into two parts of equal volume. (b) Find the values of \(x\) in the interval [0,4] that divide the solid into three parts of equal volume.
Sketch the region bounded by the graphs of the algebraic functions and find the area of the region. $$ g(x)=\frac{4}{2-x}, \quad y=4, \quad x=0 $$
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