Answer:
0.234
Explanation:
True stress is ratio of instantaneous load acting on instantaneous cross-sectional area
σ = k × (ε)^n
σ = true stress
ε = true strain
k = strength coefficient
n = strain hardening exponent
ε = ( σ / k) ^1/n
take log of both side
log ε =
( log σ - log k)
n = ( log σ - log k) / log ε
n = (log 578 - log 860) / log 0.20 = 0.247
the new ε = ( 600 / 860)^( 1 / 0.247) = 0.234
Answer:
25 mm = 0.984252 inches
Explanation:
Millimeter and inches are both units of distance. The conversion of millimeter into inches is shown below:
<u>1 mm = 1/25.4 inches</u>
From the question, we have to convert 25 mm into inches
Thus,
<u>25 mm = (1/25.4)*25 inches</u>
So,
![25 mm=\frac{25}{25.4} inches](https://tex.z-dn.net/?f=25%20mm%3D%5Cfrac%7B25%7D%7B25.4%7D%20inches)
Thus, solving we get:
<u>25 mm = 0.984252 inches</u>
Answer:
a) ![F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Clambda%20%5Cint_0%5E%7B%5Cinfty%7D%20e%5E%7B-%5Clambda%20x%7D%20dx%3D%20-e%5E%7B-%5Clambda%20x%7D%20%5CBig%7C_0%5E%7B%5Cinfty%7D%20%3D%201-%20e%5E%7B-%5Clambda%20x%7D%20%5C)
b) ![P(10 < X](https://tex.z-dn.net/?f=P%2810%20%3C%20X%3C20%29%3De%5E%7B-0.1%2A10%7D%20-e%5E%7B-0.1%2A20%7D%3D0.368-0.135%3D0.233)
Explanation:
Previous concepts
The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution".
Part a
Let X the random variable of interest. We know on this case that ![X\sim Exp(\lambda)](https://tex.z-dn.net/?f=X%5Csim%20Exp%28%5Clambda%29)
And we know the probability denisty function for x given by:
![f(x) = \lambda e^{-\lambda x} , x\geq 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Clambda%20e%5E%7B-%5Clambda%20x%7D%20%2C%20x%5Cgeq%200)
In order to find the cdf we need to do the following integral:
![F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Clambda%20%5Cint_0%5E%7B%5Cinfty%7D%20e%5E%7B-%5Clambda%20x%7D%20dx%3D%20-e%5E%7B-%5Clambda%20x%7D%20%5CBig%7C_0%5E%7B%5Cinfty%7D%20%3D%201-%20e%5E%7B-%5Clambda%20x%7D%20%5C)
Part b
Assuming that
, then the density function is given by:
![f(x) = 0.1 e^{-0.1 x} dx , x\geq 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%200.1%20e%5E%7B-0.1%20x%7D%20dx%20%2C%20x%5Cgeq%200)
And for this case we want this probability:
![P(10 < X](https://tex.z-dn.net/?f=P%2810%20%3C%20X%3C20%29%20%3D%20%5Cint_%7B10%7D%5E%7B20%7D%200.1%20e%5E%7B-0.1%20x%7D%20dx%20%3D%20-e%5E%7B-0.1%20x%7D%20%5CBig%7C_%7B10%7D%5E%7B20%7D)
And evaluating the integral we got:
![P(10 < X](https://tex.z-dn.net/?f=P%2810%20%3C%20X%3C20%29%3De%5E%7B-0.1%2A10%7D%20-e%5E%7B-0.1%2A20%7D%3D0.368-0.135%3D0.233)
The magnetic force on a free moving charge is perpendicular to both the velocity of the charge and the magnetic field with direction given by the right hand rule. The force is given by the charge times the vector product of velocity and magnetic field.
Answer:
116.3 electrons
Explanation:
Data provided in the question:
Time, t = 2.55 ps = 2.55 × 10⁻¹² s
Current, i = 7.3 μA = 7.3 × 10⁻⁶ A
Now,
we know,
Charge, Q = it
thus,
Q = (7.3 × 10⁻⁶) × (2.55 × 10⁻¹²)
or
Q = 18.615 × 10⁻¹⁸ C
Also,
We know
Charge of 1 electron, q = 1.6 × 10⁻¹⁹ C
Therefore,
Number of electrons past a fixed point = Q ÷ q
= [ 18.615 × 10⁻¹⁸ ] ÷ [ 1.6 × 10⁻¹⁹ ]
= 116.3 electrons