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!!
Yield is given by:
current yield=(annual cash flow)/(market price)
annual cashflow(coupon)= 2.9/100×4750=137.75
market price of the bond= $3940
thus the yield will be given by:
137.75/3940
=0.03496
Answer:
The value of 
is -16.
Step-by-step explanation:
We need to evaluate for x = -1, y = 5 and let us assume that z = 1
It can be simply done by putting the values of x,y and z in the given expression.
We know that the value of 4² = 16
So,
So, the value of is -16.
Answer:
x= 72°
reason: this is because it is a corresponding angle. Corresponding angles are equal to another
Answer:
p(chocolate chip) = 2/7
p(oatmeal) = 7/27
Step-by-step explanation:
probability = favorable outcomes/total outcomes
First, add up all the cookies in the bag.
8 + 6 + 7 + 7 = 28
Next find the probability of selecting a chocolate chip cookie. Since there are 8 chocolate chip cookies and 28 cookies in the bag, create a fraction.
p(chocolate chip) = 8/28
reduce by 4
p(chocolate chip) = 2/7
Now that the cookie was eaten that will reduce the number of chocolate chip cookies to 7 and the overall number of cookies to 27.
There are 7 oatmeal cookies and 27 total cookies, so create the fraction.
p(oatmeal) = 7/27
