An article reported that, in a study of

2022-04-27

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 239 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.)

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asked 2022-04-25

Heat transfer between two fluids through a sandwiched solid (coupled problem):
Two fluids (th, tc) flow opposite to each other on either side of a solid (T), while exchanging heat among themselves. In such a scenario, the conduction in the solid is governed by:
x[0,1],y[0,1]
1) dTdx2+μbh(thT)νbc(Ttc)=0
with boundary condition as T(0)=T(1)=0
The fluids are governed by the following equations:
2) dthdx+bh(thT)=0
3) dtcdx+bc(Ttc)=0
The hot fluid initiates at x=0 and the cold fluid starts from x=1.
The boundary conditions are th(x=0)=1 and tc(x=1)=0
Equation (1), (2) and (3) form a coupled system of ordinary differential equations.
It is pretty evident that using (2) and (3), Equation (1) can be re-written as:
4) d2Tdx2μdthdx+νdtcdx=0
However, I have not been able to proceed further.
Some parameter values are
bc=12.38, bh=25.32, μ=1.143, ν=1, κ=2.16

asked 2022-04-23

How to solve homogenous differential equation (x+y)2 dx=xy dy?
First i find value of dydx=(x+y)2xy     (i)
let y=vx
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I tried to solve using equation (i) and (ii) but I am stuck.
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If n = 20 and p = 0.70, then P(X < 2)  is

asked 2022-03-31
  1. f(x) = 12 xe6x
asked 2022-03-25

How a solving a nonlinear PDE with Self-similar Solution?
I want to solve the problem :
ut=|u|2p(2uξ2+(1p)2uη2)
We search for a self-similarity solution, the general form of which is as follows
u(x,y,t)=f(ξ),  with  ξ=d(x2+y2)na(t)
from which we obtain
αξ=(1p)(2n)2p+2((12n(1p)+2n12n)(ddfdξ)2p+ξ(ddfdξ)2p1dd2fdξ2)
Now, I am very confused on how to solve the above equation and find the exact solution of f(ξ), thereby finding the exact solution of u(x,y,t). So my question is, does anyone know how to solve this ordinary differential equation?

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In 2008, the population of a district was 36,700. With a continuous annual growth rate of approximately 2%, what will the population be in 2028 according to the exponential growth function?

asked 2022-04-03

Solving a systemof eqns by given initial conditions
x(t)=2x+8y
y(t)=x2y
Which has the I.C. X(0)=(6,2). So I take that it means this:
6=2x+8y
2=x2y
and then it is solved as any other system? We get eigenvector (1,12), but since the eigenvalues of the system are two, ±2i, we have to find the second generalized eigenvector.
(2-2i8-1-2-2i)(112)=(6-2i-2-i)
So the second vector would be (62i,2i). Using the general solutions for the system, we get
y(t)=e2it(1,12)+e2it(62i,2i)
Would this be correct, or did I misinterpret the initial conditions?