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Answer:</h2>
D. (1m, 0.5m)
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Explanation:</h2>
The center of mass (or center of gravity) of a system of particles is the point where the weight acts when the individual particles are replaced by a single particle of equivalent mass. For the three masses, the coordinates of the center of mass C(x, y) is given by;
x = (m₁x₁ + m₂x₂ + m₃x₃) / M ----------------(i)
y = (m₁y₁ + m₂y₂ + m₃y₃) / M ----------------(ii)
Where;
M = sum of the masses
m₁ and x₁ = mass and position of first mass in the x direction.
m₂ and x₂ = mass and position of second mass in the x direction.
m₃ and x₃ = mass and position of third mass in the x direction.
y₁ , y₂ and y₃ = positions of the first, second and third masses respectively in the y direction.
From the question;
m₁ = 6kg
m₂ = 4kg
m₃ = 2kg
x₁ = 0m
x₂ = 3m
x₃ = 0m
y₁ = 0m
y₂ = 0m
y₃ = 3m
M = m₁ + m₂ + m₃ = 6 + 4 + 2 = 12kg
Substitute these values into equations (i) and (ii) as follows;
x = ((6x0) + (4x3) + (2x0)) / 12
x = 12 / 12
x = 1 m
y = (6x0) + (4x0) + (2x3)) / 12
y = 6 / 12
y = 0.5m
Therefore, the center of mass of the system is at (1m, 0.5m)
Answer:
The concentration of hydrogen ion at pH is equal to 2 :![= [H^+]=0.01 mol/L](https://tex.z-dn.net/?f=%3D%20%5BH%5E%2B%5D%3D0.01%20mol%2FL)
The concentration of hydrogen ion at pH is equal to 6 : ![[H^+]'=0.000001 mol/L](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%27%3D0.000001%20mol%2FL)
There are 0.009999 more moles of
ions in a solution at a pH = 2 than in a solution at a pH = 6.
Explanation:
The pH of the solution is the negative logarithm of hydrogen ion concentration in an aqueous solution.
![pH=-\log [H^+]](https://tex.z-dn.net/?f=pH%3D-%5Clog%20%5BH%5E%2B%5D)
The hydrogen ion concentration at pH is equal to 2 = [H^+]
![2=-\log [H^+]\\](https://tex.z-dn.net/?f=2%3D-%5Clog%20%5BH%5E%2B%5D%5C%5C)
![[H^+]=10^{-2}M= 0.01 M=0.01 mol/L](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%3D10%5E%7B-2%7DM%3D%200.01%20M%3D0.01%20mol%2FL)
The hydrogen ion concentration at pH is equal to 6 = [H^+]
![6=-\log [H^+]\\\\](https://tex.z-dn.net/?f=6%3D-%5Clog%20%5BH%5E%2B%5D%5C%5C%5C%5C)
![[H^+]=10^{-6}M= 0.000001 M= 0.000001 mol/L](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%3D10%5E%7B-6%7DM%3D%200.000001%20M%3D%200.000001%20mol%2FL)
Concentration of hydrogen ion at pH is equal to 2 =![[H^+]=0.01 mol/L](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%3D0.01%20mol%2FL)
Concentration of hydrogen ion at pH is equal to 6 = ![[H^+]'=0.000001 mol/L](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%27%3D0.000001%20mol%2FL)
The difference between hydrogen ion concentration at pH 2 and pH 6 :
![= [H^+]-[H^+]' = 0.01 mol/L- 0.000001 mol/L = 0.009999 mol/L](https://tex.z-dn.net/?f=%3D%20%5BH%5E%2B%5D-%5BH%5E%2B%5D%27%20%3D%200.01%20mol%2FL-%200.000001%20mol%2FL%20%3D%200.009999%20mol%2FL)
Moles of hydrogen ion in 0.009999 mol/L solution :

There are 0.009999 more moles of
ions in a solution at a pH = 2 than in a solution at a pH = 6.
To solve this problem we will apply the concepts related to the Doppler effect. The Doppler effect is the change in the perceived frequency of any wave movement when the emitter, or focus of waves, and the receiver, or observer, move relative to each other. Mathematically it can be described as

Here,
=frequency received by detector
=frequency of wave emitted by source
=velocity of detector
=velocity of source
v=velocity of sound wave
Replacing we have that,


Therefore the frequencty that will hear the passengers is 422Hz
1950 g This is the answer due to the kilograms of lead being distributed