Applied Mathematics Banga

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Running head : Mathematics 1 Applied Mathematics Name Institution Date
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Mathematics 2 QUESTION 1 Part (a) 45a+15b=15……1 15a+5b=10…….2 45a+15b=15……3 3(15a+5b=10)….4 Subtracting equations 3 and 4 gives 0+0=5 which is false? Therefore it is not solvable Part (b) It is clear from the equalities that the answers are not true. Given this case, we cannot use the Cauchy Schwarz inequality. For instance: ∑ x 2 ≠45.This include values from 1 to 5 QUESTION 2
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Mathematics 3
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Mathematics 4
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Mathematics 5 Part (b) C(x, y) = (cx, CY) a (cx) +b (cy) =c acx+bcy=c a+b=1
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Mathematics 6 Since c changes to 1, the vector becomes a unit vector Part (c) We multiply (a, b) by -1 This gives (-a,-b) (x,y) is defined as ax by=c Hence (-a,-b) =(x, y) which is the negative of each other. They are therefore perpendicular to each other. QUESTION 3 Part (a) To know how much water flows out at the bottom during the given time interval, we set t=0 Hence, h=h (0).This gives h=1 Part (b) h=h (t) v=√2gh v=√2gh(t) dv/dt=d/dt(√2gh(t)) Therefore the height changes according to the differential equation d/dt(√2gh(t)
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