Question 1
Question 2
Question 3
Question 4
Answer to question 1
consider the equation
Step 2
d2xdt2+x-y=0d2ydt2+y-x=0x=0 , x'(0)=-5 , y(0)=0 , y'(0)=1Taking the Laplace Transform of the given system x fieldssx1=-0 Sx2=0 of equivalently Sx1+x-y=0 sx2+y-x=-5solving this algebric system using cramers rule x1s=1x-y1y-x s x-y 2 y-xTaking the inverse Laplace transform of x1s and x2sX1=e2t-4te2tX2=e2t+4te2t
Answer to question 2
We will use a graphing calculator to graph the region
This graph properly shows the area between the given curves.
Then we find where do y=1/x and y=1/x2 meet
We set them equal and solve for x
For both functions, x can not be 0. So x=1
So we have to integrate from 1 to 8
Answer to question 3
Answer to question 4
Step 1: Concept
f(x+a)…….left by a units
f(x)-a…… down by a units
-f(x)……reflection across x axis
Step 2: Solution
Because of minus sign with the function, reflection across x axis.
Because of +6 inside the function, left 6 units.
Because of -5 with the function, down by 5 units
Option d