Math Answers

Obtain a solution of the wave equation
∂^2u(x,t)/∂t^2=16(∂^2u(x,t)/∂x^2)

for 0≤ x ≤ π and t > ,0 and the following boundary and initial conditions:
u(0,t)=u(π,t)=0,
u(x,0)=x(π-x) and ∂u(x,0)/∂t=0

George Penny will receive $31,250 for the next 12 years as a payment for a slogan he coined. Currently a 11 percent discount rate is appropriate and i want to calculate PV

X be a non-empty set and let R be an equivalence relation on X. For each x ∈ X, define
[x]={y∈X suchthatxRy}
to be the equivalence class of x. Here x R y means (x, y) ∈ R.
SupposethatA=[x]andB=[y]. ProvethatifA∩B̸=∅,thenA=B.

Question one

Prove by induction that the following statements are true for all integers n
a) 12x2+22x3+…..+n2(n+1)= n(n+1)(n+2)(3n+1)/12
b)4007n-1 is divisible by 2003

Question five

For each of the following sentences, write the sentence in logical notation , negate the sentence , and say whether the sentence or its negation is true.
a) Given any integer, there is a larger integer.

Obtain the curl of the following vector field :
A=(eˆr+rcosθeˆθ+reˆφ)

Reduce the following PDE to a set of three ODEs by the method of separation of
variables (1/r)(∂/∂r)(r(∂V/∂r)+(1/r^2)(∂^2V/∂θ^2)+(∂^2V/∂z^2)+(k^2)V=0

Obtain a solution of the wave equation
∂^2u(x,t)/∂t^2=16(∂^2u(x,t)/∂x^2)

for 0≤ x ≤ π and t > ,0 and the following boundary and initial conditions:
u(0,t)=u(π,t)=0,
u(x,0)=x(π-x) and ∂u(x,0)/∂t=0

(1) Solve sin x cos x = 0.

(2) Solve 2 sin2 x − sin x − 1 = 0.

(3) Solve cos x + cos 2x = 0.

(4) Solve 2 cos x + sec x = 3.

(5) Solve sec x − 1 = tan x.