e).
- Need To Answer All Questions B C D And E 1 (66.59 KiB) Viewed 65 times
Need to answer all questions : b) c) d) and e).
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Need to answer all questions : b) c) d) and e).
Need to answer all questions : b) c) d) and
e).
For this part of the assignment, it may help to draw a cross-section of the Earth at the equator. Suppose a long cable has been wound tightly around the equator exactly once, and then the length of the cable is extended by 1 metre. You may assume that the equator is a perfect circle of radius R = 6378 kilometres, and you may ignore the effects of gravity on the shape of the cable. The bulleted questions below will be relevant • If the cable were pinched at a point on the equator where a 5-metre tall giraffe is standing, and raised as high as possible, can the cable be lifted over the giraffe? • If the cable were instead pinched at a point on the equator where the 30-metre high Marco Zero monument in Macapa is located, and raised as high as possible, can the cable be lifted above the monument? • What is the maximum height that the pinched cable can be raised over the equator? The accuracy of some Taylor polynomials will be tested below. (b) Find two expressions for the length of the cable. Use these together with your Maclaurin polyno- mial for tan(b) to show that 03 The accompanying figure may be helpful. 2R 0.003) 1/3 R 27-2Q (C) Now use your answer from part (b) and your Maclaurin polynomial for sec() to find an approxi- mate answer to the bulleted questions above. (d) The recursion formula for a sequence produced by Newton's method to approximate a solution to the equation h(0) = 0 is given by Pn+= 0 hon) Derive a recursion formula for the sequence produced by Newton's method to approximate the exact value of . (e) Taking , to be the approximate value of ¢ from (b), use for some n> 1 to obtain more accurate values for both o and the maximum height of the raised cable. Hence comment on and explain the accuracy of your answers in (b). W )
e).
For this part of the assignment, it may help to draw a cross-section of the Earth at the equator. Suppose a long cable has been wound tightly around the equator exactly once, and then the length of the cable is extended by 1 metre. You may assume that the equator is a perfect circle of radius R = 6378 kilometres, and you may ignore the effects of gravity on the shape of the cable. The bulleted questions below will be relevant • If the cable were pinched at a point on the equator where a 5-metre tall giraffe is standing, and raised as high as possible, can the cable be lifted over the giraffe? • If the cable were instead pinched at a point on the equator where the 30-metre high Marco Zero monument in Macapa is located, and raised as high as possible, can the cable be lifted above the monument? • What is the maximum height that the pinched cable can be raised over the equator? The accuracy of some Taylor polynomials will be tested below. (b) Find two expressions for the length of the cable. Use these together with your Maclaurin polyno- mial for tan(b) to show that 03 The accompanying figure may be helpful. 2R 0.003) 1/3 R 27-2Q (C) Now use your answer from part (b) and your Maclaurin polynomial for sec() to find an approxi- mate answer to the bulleted questions above. (d) The recursion formula for a sequence produced by Newton's method to approximate a solution to the equation h(0) = 0 is given by Pn+= 0 hon) Derive a recursion formula for the sequence produced by Newton's method to approximate the exact value of . (e) Taking , to be the approximate value of ¢ from (b), use for some n> 1 to obtain more accurate values for both o and the maximum height of the raised cable. Hence comment on and explain the accuracy of your answers in (b). W )