Answer:
Yes the frequency of the angular simple harmonic motion (SHM) of the balance wheel increases three times if the dimensions of the balance wheel reduced to one-third of original dimensions.
Explanation:
Considering the complete question attached in figure below.
Time period for balance wheel is:
![T=2\pi\sqrt{\frac{I}{K}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%5Csqrt%7B%5Cfrac%7BI%7D%7BK%7D%7D)
![I=mR^{2}](https://tex.z-dn.net/?f=I%3DmR%5E%7B2%7D)
m = mass of balance wheel
R = radius of balance wheel.
Angular frequency is related to Time period as:
![\omega=\frac{2\pi}{T}\\\omega=\sqrt{\frac{K}{I}} \\\omega=\sqrt{\frac{K}{mR^{2}}](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B2%5Cpi%7D%7BT%7D%5C%5C%5Comega%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BI%7D%7D%20%5C%5C%5Comega%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR%5E%7B2%7D%7D)
As dimensions of new balance wheel are one-third of their original values
![R_{new}=\frac{R}{3}](https://tex.z-dn.net/?f=R_%7Bnew%7D%3D%5Cfrac%7BR%7D%7B3%7D)
![\omega_{new}=\sqrt{\frac{K}{mR_{new}^{2}}}\\\\\omega_{new}=\sqrt{\frac{K}{m(\frac{R}{3})^{2}}}\\\\\omega_{new}={3}\sqrt{\frac{K}{mR^{2}}}\\\\\omega_{new}={3}\omega](https://tex.z-dn.net/?f=%5Comega_%7Bnew%7D%3D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR_%7Bnew%7D%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%5Csqrt%7B%5Cfrac%7BK%7D%7Bm%28%5Cfrac%7BR%7D%7B3%7D%29%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%7B3%7D%5Csqrt%7B%5Cfrac%7BK%7D%7BmR%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Comega_%7Bnew%7D%3D%7B3%7D%5Comega)
Answer:
a)![P(6)=0.25](https://tex.z-dn.net/?f=P%286%29%3D0.25)
b)![p(x](https://tex.z-dn.net/?f=p%28x%3Cg%29%3D0.9537)
c)![p(x\geq3)=0.9878](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D0.9878)
d)![\sigma=\sqrt{2.4}=1.5492](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B2.4%7D%3D1.5492)
Explanation:
From the question we are told that:
Population percentage ![p_\%=\60%](https://tex.z-dn.net/?f=p_%5C%25%3D%5C60%25)
Sample size ![n=10](https://tex.z-dn.net/?f=n%3D10)
Let x =customers ask for water
Let y =customers dose not ask for water with their meal
Generally the equation for y is mathematically given by
![y=1-p_\%\\y=1-0.60\\y=0.40](https://tex.z-dn.net/?f=y%3D1-p_%5C%25%5C%5Cy%3D1-0.60%5C%5Cy%3D0.40)
Generally the equation for pmf p(x) is mathematically given by
![P(x)=10C_x (0..6)^x(0.4)^{10-x}](https://tex.z-dn.net/?f=P%28x%29%3D10C_x%20%280..6%29%5Ex%280.4%29%5E%7B10-x%7D)
a)
Generally the probability that exactly 6 ask for water is mathematically given by
![P(x)6=10C_6 (0..6)^6(0.4)^{10-6}](https://tex.z-dn.net/?f=P%28x%296%3D10C_6%20%280..6%29%5E6%280.4%29%5E%7B10-6%7D)
![P(6)=0.25](https://tex.z-dn.net/?f=P%286%29%3D0.25)
b)
Generally the probability that less than 9 ask for water with meal is mathematically given by
![p(xg)](https://tex.z-dn.net/?f=p%28x%3Cg%29%3D1-p%28x%3Eg%29)
![p(x](https://tex.z-dn.net/?f=p%28x%3Cg%29%3D1%28p%289%29%29%2Bp%2810%29)
![p(x](https://tex.z-dn.net/?f=p%28x%3Cg%29%3D1-%2810_C_9%20%280..6%29%5E9%280.4%29%5E%7B10-9%7D%2B10_C_10%20%280..6%29%5E10%280.4%29%5E%7B10-10%7D%29%5C%5Cp%28x%3Cg%29%3D1-0.0463)
![p(x](https://tex.z-dn.net/?f=p%28x%3Cg%29%3D0.9537)
c)
Generally the probability that at least 3 ask for water with meal is mathematically given by
![p(x\geq3)=1-p(x](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D1-p%28x%3C3%29)
![p(x\geq3)=1-[p(0)+p(1)+p(2)]](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D1-%5Bp%280%29%2Bp%281%29%2Bp%282%29%5D)
![p(x\geq3)=1-[0.00001+0.0015+0.0106]](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D1-%5B0.00001%2B0.0015%2B0.0106%5D)
![p(x\geq3)=1-[0.0122]](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D1-%5B0.0122%5D)
![p(x\geq3)=0.9878](https://tex.z-dn.net/?f=p%28x%5Cgeq3%29%3D0.9878)
d)
Generally the mean and standard deviation of sample size is mathematically given by
Mean
![\=x=np=10(0.6)=6](https://tex.z-dn.net/?f=%5C%3Dx%3Dnp%3D10%280.6%29%3D6)
Standard deviation
![v(x)=npq=10(0.6)(0.4)=2.4](https://tex.z-dn.net/?f=v%28x%29%3Dnpq%3D10%280.6%29%280.4%29%3D2.4)
![\sigma=\sqrt{2.4}=1.5492](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B2.4%7D%3D1.5492)
<span>Pitch and frequency are more or less the same thing - high pitch = high frequency.
The freqency of vibration of a string f = 1/length (L) so as length decreases the frequency increases.</span>
<span> The boiling point of water at sea level is 100 °C. At higher altitudes, the boiling point of water will be.....
a) higher, because the altitude is greater.
b) lower, because temperatures are lower.
c) the same, because water always boils at 100 °C.
d) higher, because there are fewer water molecules in the air.
==> e) lower, because the atmospheric pressure is lower.
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Water boils at a lower temperature on top of a mountain because there is less air pressure on the molecules.
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I hope this is helpful. </span>