Answer:
L[f(t)=s/(1+s^2)]
Step-by-step explanation:
The Laplace Transform is given by the integral:
![L[f(t)]=\int_0^\infty e^{-st}\ f(t)dt](https://tex.z-dn.net/?f=L%5Bf%28t%29%5D%3D%5Cint_0%5E%5Cinfty%20e%5E%7B-st%7D%5C%20f%28t%29dt)
by replacing f(t)=cost we get
![\int_0^{\infty} e^{-st}costdt=[e^{-s(\infty)}sin(\infty)-1sin(0)]-s\int_{0}^{\infty}e^{-st}sintdt\\\\=0+s[-e^{-s(\infty)}cos(\infty)+e^{s(0)}cost(0)-s\int_0^{\infty}e^{-st}costdt]\\\\=0+s[0+1-s\int_0^{\infty}e^{-st}costdt]=s-s^2\int_0^{\infty}e^{-st}costdt\\\\(1+s^2)\int_0^{\infty}e^{-st}costdt=s\\\\\int_0^{\infty}e^{-st}costdt=\frac{s}{1+s^2}](https://tex.z-dn.net/?f=%5Cint_0%5E%7B%5Cinfty%7D%20e%5E%7B-st%7Dcostdt%3D%5Be%5E%7B-s%28%5Cinfty%29%7Dsin%28%5Cinfty%29-1sin%280%29%5D-s%5Cint_%7B0%7D%5E%7B%5Cinfty%7De%5E%7B-st%7Dsintdt%5C%5C%5C%5C%3D0%2Bs%5B-e%5E%7B-s%28%5Cinfty%29%7Dcos%28%5Cinfty%29%2Be%5E%7Bs%280%29%7Dcost%280%29-s%5Cint_0%5E%7B%5Cinfty%7De%5E%7B-st%7Dcostdt%5D%5C%5C%5C%5C%3D0%2Bs%5B0%2B1-s%5Cint_0%5E%7B%5Cinfty%7De%5E%7B-st%7Dcostdt%5D%3Ds-s%5E2%5Cint_0%5E%7B%5Cinfty%7De%5E%7B-st%7Dcostdt%5C%5C%5C%5C%281%2Bs%5E2%29%5Cint_0%5E%7B%5Cinfty%7De%5E%7B-st%7Dcostdt%3Ds%5C%5C%5C%5C%5Cint_0%5E%7B%5Cinfty%7De%5E%7B-st%7Dcostdt%3D%5Cfrac%7Bs%7D%7B1%2Bs%5E2%7D)
hope this helps!!
<h2>
<em>Answer</em><em>:</em></h2><h3>
<em>1</em><em>4</em><em> </em><em>ways</em><em>.</em></h3>
<em>Please</em><em> </em><em>see</em><em> the</em><em> attached</em><em> picture</em><em> for</em><em> full</em><em> solution</em><em>.</em><em>.</em>
<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>
<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em><em>.</em>
7n +6= 4n -9
7n-4n= -6 -9
3n = -15
n = -15/3
n = -5
Answer:
A; y- 4 = -2(x + 1)
Step-by-step explanation:
Here, we want to find the equation of the given line
The general form
is ;
y = mx + c
c is the y-intercept which is 2
So we have
y = mx + 2
The x-intercept where y = 0 is 1
Thus;
0 = m(1) + 2
0 = m + 2
m = -2
So the equation of the line is
y = -2x + 2
We can rewrite this in the point-slope form as:
y - 4 = -2(x + 1)
Answer:
All real numbers
Step-by-step explanation: