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3 years ago

What are the rules for setting up an integral of rotation?

1 answer:

3 0

Setting up an integral of rotation is used as a method of of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is similar to finding the area, but there is one additional component of rotating the area around a line of symmetry.

<span>First the solid of revolution should be defined. The general function is y=f(x), on an interval [a,b].</span>

Then the curve is rotated about a given axis to get the surface of the solid of revolution. That is the integral of the function.

<span>It all depends of the function f(x), which must be known in order to calculate the integral.</span>

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4 years ago

The sound intensity from a jack hammer breaking concrete is 2.0W/m2 at a distance of 2.0 m from the point of impact. This is suf

kupik [55]

Answer:

(a) $I_{1}=3.2*10^{-3}W/m^{2}$

(b) $\beta =95dB$

Explanation:

Given data

Distance r₁=50 m

Distance r₂=2 m

Intensity I₂=2.0 W/m²

To find

(a) The Sound Intensity I₁

(b) The Sound Intensity level β

Solution

For (a) the Sound Intensity I₁

$\frac{I_{1} }{I_{2}}=\frac{(r_{2})^{2} }{(r_{1})^{2} }\\I_{1} =I_{2}(\frac{(r_{2})^{2} }{(r_{1})^{2} })\\I_{1}=(2.0W/m^{2} )(\frac{(2m)^{2} }{(50m)^{2} })\\I_{1}=3.2*10^{-3}W/m^{2}$

For (b) the Sound Intensity level β

The Sound Intensity level β is calculated as follow

$\beta =(10dB)log_{10}(\frac{I}{I_{o} } )\\\beta =(10dB)log_{10}(\frac{3.2*10^{-3}W/m^{2} }{1.0*10^{-12} W/m^{2} } )\\\beta =95dB$

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3 years ago