a.
To calculate: An expression for the efficiency ratio
The efficiency ratio
Given information:
The surface area for a cylinder:
The volume for a cylinder:
Concept used:
Algebraically simplifying the equations
Calculation:
The surface area for a cylinder:
The volume for a cylinder:
Now, For the efficiency ratio
Conclusion:
b.
To calculate: The efficiency ratio for each can list in the table.
The efficiency ratio:
For soup can =
For coffee can =
For paint can =
Given information:
The surface area for a cylinder:
The volume for a cylinder:
Soup can | Coffee can | Paint can | |
Height, | |||
Radius, |
Formula used:
The efficiency ratio:
Calculation:
According to given table:
Apply the formula for efficiency ratio:
The efficiency ratio:
Soup can | Coffee can | Paint can | |
Height, | |||
Radius, |
The efficiency ratio for soup can:
The efficiency ratio for soup can:
The efficiency ratio for soup can:
Conclusion:
The efficiency ratio:
For soup can =
For coffee can =
For paint can =
c.
To calculate: According to efficiency, rank the three cans. Explain your ranking.
According to efficiency, rank the cans: Paint, coffee, soup
The lower the ratio, the more efficient it is, because then it takes less material (surface area) per (volume).
Given information:
The surface area for a cylinder:
The volume for a cylinder:
Concept used:
The efficiency ratio:
Calculation:
Apply the efficiency ratio:
The efficiency ratio:
For soup can =
For coffee can =
For paint can =
According to efficiency, rank the cans:
Paint, coffee, soup
The lower the ratio, the more efficient it is, because then it takes less material (surface area) per (volume).
Conclusion:
Chapter 5 Solutions
EBK ALGEBRA 2
- Thank you.arrow_forwardThank you.arrow_forwardLet V, W, and Y be vector spaces. Suppose dim(V) dim(W) = dim(Y) = 2. = Let ("beta") be an ordered basis for V. Let ("gamma") be an ordered basis for W. Let ("zeta") be an ordered basis for Y. Suppose S is a linear transformation from V to W and that T is a linear trans- formation from W to Y. Remember that ToS is the function from V to Y defined by (TOS)(v) = T(S(v)). (a) Prove that To S is a linear transformation. (b) Prove that ° [T • S] = [T]{[S]}.arrow_forward
- Let W={(0, a, 0) | a Є R}. (a) List four elements from W. (b) Determine whether W is a subspace of R³, and prove that your answer is correct.arrow_forwardFor this problem, refer to the network as shown in Figure 1, answer the following questions. B A C FIGURE 1. For Problem (7). Let x₁ be the number of users at website A. Let x2 be the number of users at website B. Let x3 be the number of users at website C. Assume that there are a total of 900 users at these three websites. This gives us the following system of linear equations: x1 = x2 + 1x3 x2 = x1 + x3 x3 = x2 = 900 x1 + x2 + x3 = (a) Put this system into a standard form (with all variables on the left side and with the constants on the right), and convert that system into an augmented matrix, and then... (b) Use elementary row operations to put the augmented matrix into reduced row echelon form, and then... (c) Write down the solution space for this system of equations, and then... (d) Identify which website(s) would be ranked most highly by PageRank.arrow_forward4 2 Let C = -6 -3 (a) Find det(C). (b) Use your answer for (a) to determine whether C is invertible.arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education