The graph of the equation 2x=y^2 from A(0,0) to B(2,2) is rotated around the x axis. The surface area of the resulting solid is?
1 answer:
Write the given equation as
x = (1/2)y² or as y = √(2x)
Graph the given curve within the region (0,0) and (2,2) as shown in the figure below.
When the curve is rotated about the x-axis, an element of surface area is
dA = 2πy dx
The surface area of the resulting solid is
![A= 2\pi \int_{0}^{2} \sqrt{2x} dx = \frac{4 \sqrt{2} \pi}{3} [x^{3/2}]_{0}^{2} = \frac{16 \pi}{3}](https://tex.z-dn.net/?f=A%3D%202%5Cpi%20%5Cint_%7B0%7D%5E%7B2%7D%20%20%5Csqrt%7B2x%7D%20dx%20%3D%20%20%5Cfrac%7B4%20%5Csqrt%7B2%7D%20%5Cpi%7D%7B3%7D%20%5Bx%5E%7B3%2F2%7D%5D_%7B0%7D%5E%7B2%7D%20%3D%20%5Cfrac%7B16%20%5Cpi%7D%7B3%7D%20)
If the right end is considered, the extra area is π*(2²) = 4π
Answer:
The surface area of the rotated solid is (16π)/3.
If the right end is considered, it is an extra area of 4π.
x = (1/2)y² or as y = √(2x)
Graph the given curve within the region (0,0) and (2,2) as shown in the figure below.
When the curve is rotated about the x-axis, an element of surface area is
dA = 2πy dx
The surface area of the resulting solid is
If the right end is considered, the extra area is π*(2²) = 4π
Answer:
The surface area of the rotated solid is (16π)/3.
If the right end is considered, it is an extra area of 4π.
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Answer:
a i.) The mean for the security company is $ 1.47 million
a ii.) The median for the security company is $ 1.55 million
a iii.) The mean for the other companies is $ 1.96 million.
a iv.) The mean for the other companies is $ 2.0 million.
b) B. The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies.
c) B. Since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security company's employees.
Step-by-step explanation:
By mean, we sum all the observation and divide by the sample size (n). Where sample size is the number of observations.
Mathematically,
, where xi is the observations or values given.
By median, we mean middle number. So, we sort the values in ascending or descending order and take the value(s) in the middle. If the sample size is even, we take the 2 middle values and obtain the average.
See below, R programming codes for the solution.
##########...... R code
s = c(1.6,1.8,1.6,1.8,1.7,1.2,1.1,1.2,1.2,1.5)
c = c(1.5,2.1,1.9,2.2,1.9,1.7,2.1,2.2,2.2,1.8)
length(s)
mean(s); median(s)
mean(c);median(c)
t = (mean(s)-mean(c))/sqrt((var(s) + var(c))/length(s))
pnorm(t)
##############################################
For question C, we compute the test statistics, and obtain the p-value, see the last two lines of the R codes.
And since the p-value is less than level of significance, the test is significant. Thus, we conclude that:
<em>Since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security company's employees.</em>