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Let z0 = a + ic, z1 = b + id, z2 = -id, and z = [z0 + z1]. Let z0 be the apex of the wedge with one ray passing through z1 and the other passing through z2, and with z in its interior. Suppose φ is a harmonic function in the wedge that contains z, z1, z2, and z0, taking the value -0.5 on the ray passing through z1 and the value 1.5 on the ray passing through z2. What, to 3 decimal places, is the value of φ at z?
(Hint: if you can't figure out how to get the right quadrants for your angles, try breaking them into pieces - referencing each piece separately to the nearest axis, +y or -y or -x - so that each piece is between 0 and 90 degrees; then sum them up.)
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
Parents put $1000 into a saving account at birth of their children. If the account earns interest at 7% p.a compounded yearly, how much money will be in the account when their chil
With the help of energy bands explain how conduction takes place in semiconductors. Semiconductors: Substances as carbon, germanium and silicon that electrical conductivity l
simple problems on partial derivatives
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How do i perform mann''s test for the weibull distribution
''A three phase cage induction motor running at full load draws a stator current of 60A at a power factor of 0.8 lagging from a 415v, 50hz supply. Under the following conditions th
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
Answer the following set of simultaneous equations using elimination or substitution method. a) x-y +z= 10 b) 3x+y+2z=34 c) -5x+2y-z=-14
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