How much toilet paper is left on the roll? The volume of a cylinder with length...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
How much toilet paper is left on the roll? The volume of a cylinder with length and radius r is given by the formula: Пер2 You've got some time on your hands, so you carefully measure your toilet roll and discover its dimensions to the nearest mm: • length = 94 mm, • radius of the inner cardboard cylinder r = 26 mm, and • radius of the outer cylinder R = 57 mm. The volume of toilet paper on the roll is thus given by the formula: According to your measurements, the volume of toilet paper is (to the nearest cubic mm): V (94, 26, 57) = mm³. However, since your initial measurements were only accurate to the nearest mm, the true volume of toilet paper may be different. V(l,r, R) = πl(R² -p²). The total differential approximation can be used to estimate how the measured volume V (94, 26, 57) differs from the true value of V (l, r, R) as: Əl ᏭᏙ ᎧᏙ V(l,r, R) V(94, 26, 57) + (94, 26, 57) (94) + (94, 26, 57) (r - 26) + Əl Ꮩ OR (94, 26, 57) (R-57) We calculate the partial derivatives (to the nearest integer): av -(94, 26, 57) = 数字 (94, 26, 57) ** Ər av (94, 26, 57) * ƏR Since we measured l, r and R to the nearest mm, ᎧᏙ Ər av Əl |l94|< 0.5, |r – 26| < 0.5 and R — 57| < 0.5. Using the integer approximations above together with the triangle inequality, |V (l, r, R) – V (94, 26, 57)| ≤ (94, 26, 57)||(l — 94)| + | (94, 26, 57)||(r - 26)| + av Ər And so our measured volume V (94, 26, 57) differs from the true volume by |V (l,r, R) – V (94, 26, 57)| < To two decimal places, this represents an approximate error of no more than mm³. |V(l,r, R)-V(94,26,57)| V (94,26,57) Are you satisfied with this level of precision? (this part is not worth marks) O No, we need more precise measurements. O Yes, this level of precision is sufficient for my needs. O Better go buy some more toilet paper to account for this potentially significant error. <3.76%. av OR {(94, 26, 57)||(R - 57)| How much toilet paper is left on the roll? The volume of a cylinder with length and radius r is given by the formula: Пер2 You've got some time on your hands, so you carefully measure your toilet roll and discover its dimensions to the nearest mm: • length = 94 mm, • radius of the inner cardboard cylinder r = 26 mm, and • radius of the outer cylinder R = 57 mm. The volume of toilet paper on the roll is thus given by the formula: According to your measurements, the volume of toilet paper is (to the nearest cubic mm): V (94, 26, 57) = mm³. However, since your initial measurements were only accurate to the nearest mm, the true volume of toilet paper may be different. V(l,r, R) = πl(R² -p²). The total differential approximation can be used to estimate how the measured volume V (94, 26, 57) differs from the true value of V (l, r, R) as: Əl ᏭᏙ ᎧᏙ V(l,r, R) V(94, 26, 57) + (94, 26, 57) (94) + (94, 26, 57) (r - 26) + Əl Ꮩ OR (94, 26, 57) (R-57) We calculate the partial derivatives (to the nearest integer): av -(94, 26, 57) = 数字 (94, 26, 57) ** Ər av (94, 26, 57) * ƏR Since we measured l, r and R to the nearest mm, ᎧᏙ Ər av Əl |l94|< 0.5, |r – 26| < 0.5 and R — 57| < 0.5. Using the integer approximations above together with the triangle inequality, |V (l, r, R) – V (94, 26, 57)| ≤ (94, 26, 57)||(l — 94)| + | (94, 26, 57)||(r - 26)| + av Ər And so our measured volume V (94, 26, 57) differs from the true volume by |V (l,r, R) – V (94, 26, 57)| < To two decimal places, this represents an approximate error of no more than mm³. |V(l,r, R)-V(94,26,57)| V (94,26,57) Are you satisfied with this level of precision? (this part is not worth marks) O No, we need more precise measurements. O Yes, this level of precision is sufficient for my needs. O Better go buy some more toilet paper to account for this potentially significant error. <3.76%. av OR {(94, 26, 57)||(R - 57)|
Expert Answer:
Answer rating: 100% (QA)
The image shows a problem statement dealing with the volume of toilet paper left on a roll The volume V of a cylinder with length and radius r is give... View the full answer
Related Book For
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler
Posted Date:
Students also viewed these mathematics questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Question A satellite is to be constructed in the shape of a cylinder with a hemisphere at each end. The radius of the cylinder is r metres and its height is h metres (see diagram below). The outer...
-
A tree is a perfect cylinder with radius 0.5 m no matter what the height (the volume of a cylinder with height h and radius r is hr2). Find the volumes of the above two cartoon trees (drawing a...
-
Why do we need Normalization? How many forms of Normalization exist? What is the minimum normal form required? Describe each normal form List Normalization conversion process
-
Would a court be likely to give Chevron deference to the SECs interpretation of the law on insider trading? Why or why not? Assume that the Securities and Exchange Commission (SEC) has a rule that it...
-
A sound wave has a speed of 3 8 0 meter / second in some gas. There is a source of waves with a frequency of 6 7 0 hertz, the source is not moving. There is an observer moving towards the source, the...
-
For the saponification of ethyl acetate with sodium hydroxide in a tubular reactor with fully developed laminar flow at \(75^{\circ} \mathrm{C}\), use COMSOL to account for radial diffusion. Estimate...
-
Toyland Corporation, an S corporation, uses the calendar year as its tax year. Bob, Alice, and Carter own 60, 30, and 10 shares, respectively, of the Toyland stock. Carters basis for his stock is...
-
Can be any store Napa auto, , kohls, gamestop. Use the stores don't have no info on them to anwser questions below Approximately how many different items are carried in inventory? . What method of...
-
1. Fill the missing values in the table and show the calculations. 2. Provide a detailed description of the Fresnel Zone and how it is affecting the condition of the link between the two sites. 3....
-
The following information are relevant to determine the proper amount to be reported on Son Gokus December 31, 2025 financial statements: Accounts payable: The unadjusted balance of accounts payable...
-
Interest payments on bonds are tax deductible dividend payments are not. For the above sentence, insert any necessary semicolons, commas, or colons. Count the number of marks you add. Write that...
-
Using the questions in Figure 2.4, write a brief analysis of the audience for each of the following communication tasks. What kind of reaction should you expect from the primary reader and any...
-
The following cover letter accompanies Annalise Ortez-Villas rsum (Radical Rewrite 13.1). Like this applicants rsum, the cover letter needs major revision. Your Task. Analyze each section of the...
-
First _____________ must _____________ to their payment obligations; then the office staff can admit them to see a doctor. a. patients, assent b. patients, ascent c. patience, assent For the above...
-
a. Although Gianna will give him some tough competition, Rashad is confident hell get the promotion. b. The work ethic in America is not dead it is deeply ingrained in most people. c. Leila thought...
-
Michael is 45 years old and wants to retire when he turns 65. Based on this cash flow,Michael tells you he can save $350 a month, every month, for the next 20 years. If Michael can earn a rate of...
-
Draw and label the E and Z isomers for each of the following compounds: 1. CH3CH2CH==CHCH3 2. 3. 4. CH,CH2C CHCH2CH Cl CH3CH2CH2CH2 CH CH2CCCH2CI CHCH3 CH3 HOCH CH CCC CH O-CH C(CH
-
xt+1 = xt / a + xt where a is a positive parameter. What happens to this system if a = 0? Find all non-negative equilibria of the above mathematically elegant discrete-time dynamical systems.
-
yt + 1 = -1.2yt with y0 = 2.0. When will the value exceed 100?
-
An intriguing species of worm spends its time wandering around in search of food. Two percent of the plate is covered with food. A point containing food contains worms with probability 0.1. A point...
-
List differences between the temptation pattern described here and the traditional pattern.
-
What are the capabilities required to achieve temptation? Describe each of them.
-
Draw and describe the class diagram for stable temptation pattern?
Study smarter with the SolutionInn App