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Part 1) What value of & is given? 5 Hint: We need to keep the volume V(r) (i.e. the output values) within 5 mm³ of 3,375 mm³. Part j) What is the corresponding value of d? 0.01011 X Hint: Calculate the distance between the radius you found in part a) and each boundary you found in part b); d is the smallest of the two distances. (Keep in mind that that distance is positive. 2009

Part 1) What value of & is given? 5 Hint: We need to keep the volume V(r) (i.e. the output values) within 5 mm³ of 3,375 mm³. Part j) What is the corresponding value of d? 0.01011 X Hint: Calculate the distance between the radius you found in part a) and each boundary you found in part b); d is the smallest of the two distances. (Keep in mind that that distance is positive. 2009

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part 1) What value of ɛ is given? 5 Hint: We need to keep the volume V(r) (i.e. the output values) within 5 mm³ of 3,375 mm³. Part j) What is the corresponding value of d? 0.01011 Hint: Calculate the distance between the radius you found in part a) and each boundary you found in part b); d is the smallest of the two distances. (Keep in mind that that distance is positive. Submit Question ◆ Previous E □ % X 5 f6 A 6 f7 & fg * 8 [] ( 9 Jo O f11 112 +
Transcribed Image Text:Part 1) What value of ɛ is given? 5 Hint: We need to keep the volume V(r) (i.e. the output values) within 5 mm³ of 3,375 mm³. Part j) What is the corresponding value of d? 0.01011 Hint: Calculate the distance between the radius you found in part a) and each boundary you found in part b); d is the smallest of the two distances. (Keep in mind that that distance is positive. Submit Question ◆ Previous E □ % X 5 f6 A 6 f7 & fg * 8 [] ( 9 Jo O f11 112 +
n m ✔ A manufacturing company produces classroom furniture for an online distributor. For a particular desk, multiple predrilled circular holes will fit the same size pin. To fit the pin, the volume of the hole should be 3,375 mm, and the depth of the hole should be equal to its radius. Consequently, the volume of the hole is given by V(r) = TT³ where r is the radius. Part a) What is the exact radius that will produce a volume of 3,375 mm³¹? 4 3375 TL $ 3 Hint: To determine the radius, substitute the volume 3,375 mm³ into V(r) = ³ and solve for r. k Part b) If the volume is allowed to vary from 3,375 mm³ by at most 5 mm³, what range of measurement is allowable for the radius 'r of the hole? (If necessary, round to 5 decimal places.) mm <r < 10.24681 10.23670 3 3 Hint: Since the volume can vary from 3,375 mm by at most 5 mm³, we know that the minimum allowable volume is 3,370 and the maximum allowable volume is 3,380. To find the left and right boundaries for the radius r, substitute the minimum volume and then the maximum volume into V(r)= r and solve for r. Or, you could use graphing technology to find the boundaries on r. Here again, is the e, & definition of a limit. lim f(x) = L if for each => 0 there exists >0 such that 2-a Previous B 15 % 5 閑 ** ^ 6 G f7 & 7 18 Tal * mm 8 fg 9 fio yo 0 f1 f12 + 11 Next > insert prt sc
Transcribed Image Text:n m ✔ A manufacturing company produces classroom furniture for an online distributor. For a particular desk, multiple predrilled circular holes will fit the same size pin. To fit the pin, the volume of the hole should be 3,375 mm, and the depth of the hole should be equal to its radius. Consequently, the volume of the hole is given by V(r) = TT³ where r is the radius. Part a) What is the exact radius that will produce a volume of 3,375 mm³¹? 4 3375 TL $ 3 Hint: To determine the radius, substitute the volume 3,375 mm³ into V(r) = ³ and solve for r. k Part b) If the volume is allowed to vary from 3,375 mm³ by at most 5 mm³, what range of measurement is allowable for the radius 'r of the hole? (If necessary, round to 5 decimal places.) mm <r < 10.24681 10.23670 3 3 Hint: Since the volume can vary from 3,375 mm by at most 5 mm³, we know that the minimum allowable volume is 3,370 and the maximum allowable volume is 3,380. To find the left and right boundaries for the radius r, substitute the minimum volume and then the maximum volume into V(r)= r and solve for r. Or, you could use graphing technology to find the boundaries on r. Here again, is the e, & definition of a limit. lim f(x) = L if for each => 0 there exists >0 such that 2-a Previous B 15 % 5 閑 ** ^ 6 G f7 & 7 18 Tal * mm 8 fg 9 fio yo 0 f1 f12 + 11 Next > insert prt sc
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