Answer:
Projected area= Diameter of the bolt* thickness.
Explanation:
Between a plate and the body of a bolt, the projected area is equal to the product of the bolt _Diameter of the bolt______ and the plate ___thickness____.
Projected area= Diameter of the bolt* thickness.
Projected area is a 2-dimensional area measurement of a 3-dimensional body by projecting its surface on an arbitrary plane
Answer:
Approximate height of the building is 23213 meters.
Explanation:
Let the height of the building be represented by h.
0.02 radians = 0.02 × 
= 0.02 x (180/
)
0.02 radians = 1.146°
10.5 km = 10500 m
Applying the trigonometric function, we have;
Tan θ = 
So that,
Tan 1.146° = 
⇒ h = Tan 1.146° x 10500
= 2.21074 x 10500
= 23212.77
h = 23213 m
The approximate height of the building is 23213 m.
Answer:
The distance is 
Explanation:
From the question we are told that
The distance from the conversation is 
The intensity of the sound at your position is 
The intensity at the sound at the new position is 
Generally the intensity in decibel is is mathematically represented as
![\beta = 10dB log_{10}[\frac{d}{d_o} ]](https://tex.z-dn.net/?f=%5Cbeta%20%20%3D%20%2010dB%20log_%7B10%7D%5B%5Cfrac%7Bd%7D%7Bd_o%7D%20%5D)
The intensity is also mathematically represented as

So
![\beta = 10dB * log_{10}[\frac{P}{A* d_o} ]](https://tex.z-dn.net/?f=%5Cbeta%20%20%3D%20%2010dB%20%2A%20%20log_%7B10%7D%5B%5Cfrac%7BP%7D%7BA%2A%20d_o%7D%20%5D)
=> ![\frac{\beta}{10} = log_{10} [\frac{P}{A (l_o)} ]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cbeta%7D%7B10%7D%20%20%3D%20%20log_%7B10%7D%20%5B%5Cfrac%7BP%7D%7BA%20%28l_o%29%7D%20%5D)
From the logarithm definition
=> 
=> ![P = A (d_o ) [10^{\frac{\beta }{ 10} } ]](https://tex.z-dn.net/?f=P%20%3D%20%20A%20%28d_o%20%29%20%5B10%5E%7B%5Cfrac%7B%5Cbeta%20%7D%7B%2010%7D%20%7D%20%5D)
Here P is the power of the sound wave
and A is the cross-sectional area of the sound wave which is generally in spherical form
Now the power of the sound wave at the first position is mathematically represented as
![P_1 = A_1 (d_o ) [10^{\frac{\beta_1 }{ 10} } ]](https://tex.z-dn.net/?f=P_1%20%3D%20%20A_1%20%28d_o%20%29%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_1%20%7D%7B%2010%7D%20%7D%20%5D)
Now the power of the sound wave at the second position is mathematically represented as
![P_2 = A_2 (d_o ) [10^{\frac{\beta_2 }{ 10} } ]](https://tex.z-dn.net/?f=P_2%20%3D%20%20A_2%20%28d_o%20%29%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_2%20%7D%7B%2010%7D%20%7D%20%5D)
Generally power of the wave is constant at both positions so
![A_1 (d_o ) [10^{\frac{\beta_1 }{ 10} } ] = A_2 (d_o ) [10^{\frac{\beta_2 }{ 10} } ]](https://tex.z-dn.net/?f=A_1%20%28d_o%20%29%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_1%20%7D%7B%2010%7D%20%7D%20%5D%20%20%3D%20A_2%20%28d_o%20%29%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_2%20%7D%7B%2010%7D%20%7D%20%5D)
![4 \pi r_1 ^2 [10^{\frac{\beta_1 }{ 10} } ] = 4 \pi r_2 ^2 [10^{\frac{\beta_2 }{ 10} } ]](https://tex.z-dn.net/?f=4%20%5Cpi%20r_1%20%5E2%20%20%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_1%20%7D%7B%2010%7D%20%7D%20%5D%20%20%3D%204%20%5Cpi%20r_2%20%5E2%20%20%20%5B10%5E%7B%5Cfrac%7B%5Cbeta_2%20%7D%7B%2010%7D%20%7D%20%5D)
![r_2 = \sqrt{r_1 ^2 [\frac{10^{\frac{\beta_1}{10} }}{ 10^{\frac{\beta_2}{10} }} ]}](https://tex.z-dn.net/?f=r_2%20%3D%20%20%5Csqrt%7Br_1%20%5E2%20%5B%5Cfrac%7B10%5E%7B%5Cfrac%7B%5Cbeta_1%7D%7B10%7D%20%7D%7D%7B%2010%5E%7B%5Cfrac%7B%5Cbeta_2%7D%7B10%7D%20%7D%7D%20%5D%7D)
substituting value
![r_2 = \sqrt{ 24^2 [\frac{10^{\frac{ 40}{10} }}{10^{\frac{80}{10} }} ]}](https://tex.z-dn.net/?f=r_2%20%3D%20%20%20%5Csqrt%7B%2024%5E2%20%5B%5Cfrac%7B10%5E%7B%5Cfrac%7B%2040%7D%7B10%7D%20%7D%7D%7B10%5E%7B%5Cfrac%7B80%7D%7B10%7D%20%7D%7D%20%5D%7D)
