Maximum Allowable Percent Error
Contents |
Help Suggestions Send Feedback Answers Home All Categories Arts & Humanities Beauty & Style Business & Finance Cars & Transportation Computers & Internet Consumer Electronics Dining Out Education & Reference Entertainment & Music Environment Family how to calculate percent error in volume & Relationships Food & Drink Games & Recreation Health Home maximum allowable error statistics & Garden Local Businesses News & Events Pets Politics & Government Pregnancy & Parenting use differentials to estimate the maximum error in the calculated volume. Science & Mathematics Social Science Society & Culture Sports Travel Yahoo Products International Argentina Australia Brazil Canada France Germany India Indonesia Italy Malaysia Mexico New error and approximation in numerical methods Zealand Philippines Quebec Singapore Taiwan Hong Kong Spain Thailand UK & Ireland Vietnam Espanol About About Answers Community Guidelines Leaderboard Knowledge Partners Points & Levels Blog Safety Tips Science & Mathematics Mathematics Next Percent Error In calculating area? Can anyone please help me with this problem? The measurement of
Approximation And Errors In Maths
the circumference of a circle is found to be 56 inches, with a possible error of 1.2 inches. Approximate the percent error in computing the area of the circle. Estimate the maximum allowable percent error in measuring the circumference if the... show more Can anyone please help me with this problem? The measurement of the circumference of a circle is found to be 56 inches, with a possible error of 1.2 inches. Approximate the percent error in computing the area of the circle. Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area can not exceed 3% Thanks in advance. Follow 2 answers 2 Report Abuse Are you sure you want to delete this answer? Yes No Sorry, something has gone wrong. Trending Now Atlanta Falcons Barack Obama Leigh-Anne Pinnock Emma Stone Alaska Airlines Cheap Airline Tickets Chuc
3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade High School 9th Grade 10th Grade 11th Grade 12th Grade College Adult Education Post a New QuestionCurrent Questions Homework Help: Calculus (check my work) Posted by Lindsay on Tuesday, December 17, 2013 at 6:52pm. The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of
Errors And Approximations In Maths Pdf
0.9 centimeter. Approximate the percent error in computing the area of the circle. MY ANSWER 8.83% Calculus (check my error in volume of cylinder work) - Lindsay, Tuesday, December 17, 2013 at 6:55pm Also, it says to estimate the maximum allowable percent error in measuring the circumference if the error in computing the calculus relative error area cannot exceed 3%. How do I do this? Calculus (check my work) - Damon, Tuesday, December 17, 2013 at 7:02pm C = 2 pi r = 64 so r = 64/(2pi) = 10.19 dC/dr = 2 pi so dC = 2 pi dr .64 = 2 pi https://answers.yahoo.com/question/index?qid=20100331230622AAFnNFu dr so dr = .10186 A = pi r^2 = pi (10.19)^2 = 325.95 dA/dr = 2 pi r (of course:) dA = 2 pi r dr dA = 2 pi (10.19)(.10186) dA = 6.52 percent error = (6.52/325.95)100 = 2% Calculus (check my work) - Damon, Tuesday, December 17, 2013 at 7:11pm part 2 (dA/A)100 = 3 (2 pi r dr /pi r^2)100 = 3 or dr/r = .015 but dr = dC/(2pi) so dC/2 pi r = .015 or dC/C = .015 so 1.5 % error in C gives 3% error in A Calculus (check http://www.jiskha.com/display.cgi?id=1387324329 my work) - Lindsay, Tuesday, December 17, 2013 at 7:14pm Okay, I really don't understand how you did any of that. What's the point of half of it? I tried to do some of what you did, but I got different numbers for my answers. Calculus (check my work) - Damon, Tuesday, December 17, 2013 at 7:18pm I made that a lot harder than it needed to be but follow it and you will be able to shorten it. Calculus (check my work) - Damon, Tuesday, December 17, 2013 at 7:26pm well, let me do the second part slowly C = 2 pi r dC = 2 pi dr so dC/(2 pi r) = dr/r or dC/C = dr/r which any architect will tell you dA = C dr dA/A = C dr/A dA/A = C dr/(pir^2) dA/A = 2 pi r dr/(pi r^2) dA/A = (2)dr/r SO dr/r = (1/2) dA/A Important if dA/A = 3% then dr/r = half that or 1.5 % Calculus (check my work) - Lindsay, Tuesday, December 17, 2013 at 7:27pm You realize I'm a terrible Calculus student? I don't understand the concepts that the other students can pick up on right away. I don't really get why you did any of what you did, and there aren't any examples like this one in our book for me to look back on. arithmetic error in first part - Damon, Tuesday, December 17, 2013 at 7:38pm C = 2 pi r = 64 so r = 64/(2pi) = 10.19 dC/dr = 2 pi so dC = 2 pi dr .9 = 2 pi dr (used .64 by mistake) so dr = .1433 A = pi r^2 = pi (10.19)^2 = 325.95 dA
(eg, area of the square) is calculated as a function of x, say y = f(x), then any error involved in the measurement of x produces an error in the calculated value of y as well. Suppose the error in x is Dx, http://pkving4math2tor2.tripod.com/5_app_of_the_der_part_2/5_03_02_appr_of_e_in_mea.html which we use the differential dx to denote, ie, dx = Dx. See Fig. 1. Then the corresponding error in y is Dy = f(x + dx) – f(x), and the corresponding differential of f at x is dy = f '(x)dx. We have Dy = dy + E(x). For the same reason as in the previous section (Section 5.3.1), we can, for small dx, approximate Dy by dy: Dy » dy. Fig. 1 Dy » dy. Go To Problems & error in Solutions Return To Top Of Page 2. Types Of Errors The errors dx = Dx and dy » Dy are absolute errors. The ratio |dx/x| is called the relative error of x, and 100|dx/x| the percentage error or percent of error of x. In general, the relative error of a quantity Q with absolute error h is the error in Q expressed as a fraction of Q and is |h/Q|, and the percentage error or percent of error of Q is error in volume the error in Q expressed as a percentage of Q and is 100|h/Q|. Return To Top Of Page Problems & Solutions 1. The radius of a sphere is measured to be 5 m ± 10 cm. Find the approximate percentage error of the calculated volume of the sphere. (The volume V of a sphere of radius r is V = (4/3)pr3.) Solution Let r and V be the radius and volume of the sphere, respectively. The absolute error of the radius is dr = 10 cm = 0.1 m. The absolute error of the volume V = (4/3)pr3 is DV » dV = 4pr2 dr, and its relative error is DV/V » dV/V = 4pr2 dr/(4/3)pr3 = 3 dr/r = 3(0.1)/5 = 0.06. Thus, the percentage error of the volume is approximately 6%. Return To Top Of Page 2. It is desired that the computed area of a circle is with at most 2% error by measuring its radius. Estimate the maximum allowable percent of error that may be made in measuring the radius. Solution Let r and A = pr2 be the radius and area of the circle, respectively. The maximum percent of error of the area is 2 = 100(DA/A) » 100(dA/A) = 100(2pr dr/pr2) = 100(2 dr/r). Hence, the maximum allowable percent of error that may be made in measuring the radius is 100 dr/r » 2/2 = 1%. Return To Top Of Page Return To Contents