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Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
If the ratios of the polynomial ax 3 +3bx 2 +3cx+d are in AP, Prove that 2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z
advantages and disadvantages of paasche and laspeyres indices
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
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how are polynomials be factored/?
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
the area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Given is a regular pentagon. Find the measure of angle LHIK.
5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does 1 hockey puck cost?
A concrete retaining wall is 120 feet long with ends shaped as given. How many cubic yards of concrete are required to construct the wall? a. 217.8 yd 3 b. 5,880 yd 3
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