Answer:
A) The maximum error in the calculated surface area: ![25cm^2](https://tex.z-dn.net/?f=25cm%5E2)
Relative error: ![0.013](https://tex.z-dn.net/?f=0.013)
B) The maximum error in the calculated volume: ![162cm^2](https://tex.z-dn.net/?f=162cm%5E2)
Relative error: ![0.019](https://tex.z-dn.net/?f=0.019)
Step-by-step explanation:
A) The formula for the surface area is:
![A=4\pi r^2](https://tex.z-dn.net/?f=A%3D4%5Cpi%20r%5E2)
The measured value is the circumference which is equal to:
![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
then the radius is:
![r=\frac{C}{2\pi}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7BC%7D%7B2%5Cpi%7D)
Substituting in the formula of the surface:
![A=4\pi(\frac{C}{2\pi})^2\\A=4\pi(\frac{C^2}{4\pi^2})\\A=\frac{C^2}{\pi}](https://tex.z-dn.net/?f=A%3D4%5Cpi%28%5Cfrac%7BC%7D%7B2%5Cpi%7D%29%5E2%5C%5CA%3D4%5Cpi%28%5Cfrac%7BC%5E2%7D%7B4%5Cpi%5E2%7D%29%5C%5CA%3D%5Cfrac%7BC%5E2%7D%7B%5Cpi%7D)
Using the formula to calculate the error:
![dy=f'(x)dx](https://tex.z-dn.net/?f=dy%3Df%27%28x%29dx)
Where
is the variable measured and
is a function of
(
).
![dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC](https://tex.z-dn.net/?f=dA%3Df%27%28C%29dC%5C%5CdA%3D%5Cfrac%7B2C%5E%7B%282-1%29%7D%7D%7B%5Cpi%7DdC%5C%5CdA%3D%5Cfrac%7B2C%7D%7B%5Cpi%7DdC)
We have C=80cm and dC=0.5cm
![dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2](https://tex.z-dn.net/?f=dA%3D%5Cfrac%7B2C%7D%7B%5Cpi%7DdC%5C%5CdA%3D%5Cfrac%7B2%2880%29%7D%7B%5Cpi%7D%280.5%29%5C%5CdA%3D%5Cfrac%7B160%7D%7B%5Cpi%7D%280.5%29%5C%5CdA%3D50.9296%280.5%29%5C%5CdA%3D25.4648%5Capprox25cm%5E2)
The relative error is the maximum error divide by the total area. The total area is: ![A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7BC%5E2%7D%7B%5Cpi%7D%3D%5Cfrac%7B%2880%29%5E2%7D%7B%5Cpi%7D%3D%5Cfrac%7B6400%7D%7B%5Cpi%7D%3D2037.1833cm%5E2)
![\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7BA%7D%3D%5Cfrac%7B25.4648%7D%7B2037.1833%7D%20%3D0.0125%5Capprox0.013)
B) The formula for the volume is:
![V=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
Using ![r=\frac{C}{2\pi}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7BC%7D%7B2%5Cpi%7D)
![V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3%5C%5CV%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7BC%7D%7B2%5Cpi%7D%29%5E3%5C%5CV%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7BC%5E3%7D%7B8%5Cpi%5E3%7D%29%5C%5CV%3D%5Cfrac%7B1%7D%7B3%7D%28%5Cfrac%7BC%5E3%7D%7B2%5Cpi%5E2%7D%29%5C%5CV%3D%5Cfrac%7BC%5E3%7D%7B6%5Cpi%5E2%7D)
The maximum error is:
![dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2](https://tex.z-dn.net/?f=dV%3D%5Cfrac%7B3C%5E%7B3-1%7D%7D%7B6%5Cpi%5E2%7DdC%5C%5CdV%3D%5Cfrac%7BC%5E%7B2%7D%7D%7B2%5Cpi%5E2%7DdC%5C%5CdV%3D%5Cfrac%7B%2880%29%5E%7B2%7D%7D%7B2%5Cpi%5E2%7D%280.5%29%5C%5CdV%3D%5Cfrac%7B6400%7D%7B2%5Cpi%5E2%7D%280.5%29%5C%5CdV%3D%5Cfrac%7B6400%7D%7B2%5Cpi%5E2%7D%280.5%29%5C%5CdV%3D%28324.2278%29%280.5%29%5C%5CdV%3D162.1139%5Capprox162cm%5E2)
The calculated volume is:
![V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BC%5E3%7D%7B6%5Cpi%5E2%7D%5C%5CV%3D%5Cfrac%7B%2880%29%5E3%7D%7B6%5Cpi%5E2%7D%5C%5CV%3D%5Cfrac%7B512000%7D%7B6%5Cpi%5E2%7D%5C%5CV%3D8646.0743)
The relative error is:
![\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7BV%7D%3D%5Cfrac%7B162.1139%7D%7B8646.0743%7D%3D0.0188%5Capprox0.019)
Answer:
could be wrong. but I belive its B
Step-by-step explanation:
7 X 2 = 14 x pi (3.14) = gives us 43.96. since its 4 tall. you would muiliply 43.96 x 4. it would give you 175.84.
here is the formula because I want you to understand this.
R = radius
D = 2 x radius
Pi = 3.14
C = circumference
C = Pi x (radius x 2)
The answer is the square root of 45
20 is the numerical coefficient of m^2.
Answer:
B. School C
Step-by-step explanation:
Having a U-shaped distribution means that the school would have the least number in the middle value/values and the most at the ends.
School C exhibits this trend because it has the most on the outermost ranges (82 for between 1.5 and 2, and 78 for between 3.5 and 4.0), as well as the least number for the middle value (26 for 2.5-3.0
The numbers inbetween also follow the trend, as you can see if you read down the column of school C, the numbers decrease as you get to 2.5-3.0 and increase again to 4.0
Hope this helped!