Find the radius of a cylindrical container
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A packaging design team has determined that a cost-efficient way of manufacturing cylindrical containers for their products is to have the volume, V, in cubic centimeters, modeled by: V(x) = 9pix^3 + 51pix^2 + 88pix + 48pi. The height, h, in centimeters, of each cylinder is a linear function given by h(x) = x + 3.
Divide the polynomial 9pix^3 + 51pix^2 + 88pix + 48pi by x + 3. Interpret the meaning of the quotient in terms of this context. Determine an expression for the radius in terms of x.
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Solution Summary
The solution consists of details of finding the radius of base of a cylindrical container.
Solution Preview
It is easy to factor V(x) out as follows.
V(x) = 9pix^3 + 51pix^2 + 88pix + 48pi
=pi * [ 9x^3 + 51x^2 + ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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