Answer:
The plot of the function production rate m(t) (in kg/min) against time t (in min) is attached to this answer.
The production rate function M(t) is:
![m(t)=[H(t)\cdot10+H(t-20)\cdot5-H(t-80)\cdot14+H(t-81)\cdot9]kg/min](https://tex.z-dn.net/?f=m%28t%29%3D%5BH%28t%29%5Ccdot10%2BH%28t-20%29%5Ccdot5-H%28t-80%29%5Ccdot14%2BH%28t-81%29%5Ccdot9%5Dkg%2Fmin)
(1)
The Laplace transform of this function is:
![\displaystyle m(s)=[\frac{10+5e^{-20s}-14e^{-80s}+9e^{-81s}}{s}]kg/min](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%28s%29%3D%5B%5Cfrac%7B10%2B5e%5E%7B-20s%7D-14e%5E%7B-80s%7D%2B9e%5E%7B-81s%7D%7D%7Bs%7D%5Dkg%2Fmin)
(2)
Explanation:
The function of the production rate can be considered as constant functions by parts in the domain of time. To make it a continuous function, we can use the function Heaviside (as seen in equation (1)). To join all the constant functions, we consider at which time the step for each one of them appears and sum each function multiply by the function Heaviside.
For the Laplace transform we use the following rules:
![\mathcal{L}[f(x)+g(x)]=\mathcal{L}[f(x)]+\mathcal{L}[g(x)]=F(s)+G(s)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bf%28x%29%2Bg%28x%29%5D%3D%5Cmathcal%7BL%7D%5Bf%28x%29%5D%2B%5Cmathcal%7BL%7D%5Bg%28x%29%5D%3DF%28s%29%2BG%28s%29)
(3)
![\mathcal{L}[aH(x-b)]=\displaystyle\frac{ae^{-bs}}{s}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5BaH%28x-b%29%5D%3D%5Cdisplaystyle%5Cfrac%7Bae%5E%7B-bs%7D%7D%7Bs%7D)
(4)
Answer:
Mogul executives takes samples of n=8 eagletrons at a time.
They found that the average is 3.25 mph.
For n = 8,
D4 =1.864(table value)
D3=0.136(table value)
The upper and lower control limits are found as
UCL =1.864 ×3.25= 6.058
LCL = 0.136 ×3.25= 0.442
Answer: 1. sadly yes, some people are treated unfairly for crimes people yet have commited. 2. no 3. yes
Explanation:
i did this last year
Answer:
El conocer la función del sistema nervioso permite comprender la estructura del cuerpo. Puesto que, toda acción que se se realice en ella dependerá del sistema nervioso para que sea eficaz
Answer: Fracture will not occur since Kc (32.2 MPa√m) ∠ KIc (35 MPa√m).
Explanation:
in this question we are asked to determine if an aircraft will fracture for a given fracture toughness.
let us begin,
from the question we have that;
stress = 325 MPa
fracture toughness (KIc) = 35 MPa√m
the max internal crack length = 1.0 m
using the formula;
Y = KIc/σ√(πα) ---------------(1)
solving for Y we have;
Y = 35 (MPa√m) / 250 (MPa) √(π × 2×10⁻3/2m)
Y = 2.50
so to calculate the fracture roughness;
Kc = Y × σ√(πα) = 2.5 × 3.25√(π × 1×10⁻³/2) = 32.2 MPa√m
Kc = 32.2 MPa√m
From our results we can say that fracture will not occur since Kc (32.2 MPa√m) is less than KIc (35 MPa√m) of the material.
cheers i hope this helps!!!!
