MMAN3200 Assignment.pdf

# 1 05ℎ 1 ℎ 2 1 0 05ℎ 1 ℎ 2 05ℎ 2 ℎ 3 2 0

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1 (?) − 0.5√ℎ 1 − ℎ 2 ? 1 = 0 0.5√ℎ 1 − ℎ 2 − 0.5√ℎ 2 − ℎ 3 ? 2 = 0 0.5√ℎ 2 − ℎ 3 − 0.5√ℎ 3 ? 3 = 0 Step2: ? 1 (?) − 0.5√ℎ 1 − ℎ 2 = 0 √ℎ 1 − ℎ 2 = √ℎ 2 − ℎ 3 √ℎ 2 − ℎ 3 = √ℎ 3 Substituting q1(t) = 0.5, 0.5 − 0.5√ℎ 3 = 0 3 = 1𝑚 2 = 2𝑚 1 = 3𝑚 Question3 According the Jacobin matrixes:

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𝑑𝑥(?) 𝑑? = 1 2 3 𝑓 1 = 𝑓 2 𝑓 3 = 𝑞 1 (?)−0.5√ℎ1−ℎ2 𝜋(4+4ℎ1+ℎ1 2 ) 0.5√ℎ1−ℎ2 −0.5√ℎ2−ℎ3 𝜋(4+4ℎ2+ℎ2 2 ) 0.5√ℎ2−ℎ3 −0.5√ℎ3 𝜋(4+4ℎ3+ℎ3 2 ) 𝜕𝑓 1 𝜕ℎ 1 = − 8 ∗ ?√ℎ 1 − ℎ 2 − 3ℎ 1 + 4ℎ 2 + 2 4𝜋(ℎ 1 + 2) 3 √ℎ 1 − ℎ 2 𝜕𝑓 1 𝜕ℎ 2 = 1 4𝜋(ℎ 1 2 + 4ℎ 1 + 4)√ℎ 1 − ℎ 2 𝜕𝑓 1 𝜕ℎ 3 = 0 𝜕𝑓 1 𝜕? = 1 𝜋(ℎ 1 2 + 4ℎ 1 + 4)√ℎ 1 − ℎ 2 𝜕𝑓 2 𝜕ℎ 1 = 1 4𝜋(ℎ 2 2 + 4ℎ 2 + 4)√ℎ 1 − ℎ 2 𝜕𝑓 2 𝜕ℎ 2 = √ℎ 2 − ℎ 3 (−3ℎ 2 − 4ℎ 1 − 2) + 3√ℎ 1 − ℎ 2 √ℎℎ 2 +(−4ℎ 3 −2) √ℎ 1 − ℎ 2 4𝜋 (ℎ 2 − 2)√ℎ 2 − ℎ 3 3 𝜕𝑓 2 𝜕ℎ 3 = 1 4𝜋(ℎ 2 2 + 4ℎ 2 + 4)√ℎ 2 − ℎ 3 𝜕𝑓 3 𝜕ℎ 1 = 0 𝜕𝑓 3 𝜕ℎ 2 = 1 4𝜋(ℎ 3 2 + 4ℎ 3 + 4)√ℎ 2 − ℎ 3 𝜕𝑓 3 𝜕ℎ 3 = (3√ℎ 3 + √ℎ 2 − ℎ 3 )ℎ 3 + (−4 ⋅ ℎ 2 − 2)√ℎ 3 − √ℎ 2 − ℎ 3 2 4𝜋√ℎ 2 − ℎ 3 √ℎ 3 (ℎ 3 + 2) 3 By applying the value of operation point h1=3m, h2=2m, h1=1m 𝜕𝑓 1 𝜕ℎ 1 = −0.00318 , 𝜕𝑓 1 𝜕ℎ 2 = 0.00318 , 𝜕𝑓 1 𝜕ℎ 3
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