The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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Answer:
The fourth of twenty is 5
Step-by-step explanation:
The 4th of twenty implies that we divide the number twenty into 4 place, let's us divide it 4
20/4= 5
This problem bothers on on division of numbers and it requires proper understanding of words/terms associated with it.
Answer:
Sample Response: Perform the transformations from right to left. First, rotate the triangle 90 degrees. Negate the y-coordinate and then switch the coordinates to get (–1, 0). Next, perform the translation up by adding 0 to the x-coordinate and 2 to the y-coordinate to get (–1, 2). Finally, reflect this point over the y-axis by negating the x-coordinate to get (1, 2).
Step-by-step explanation:
Since it is a right angle you would subtract 57 from 90 because both angles added together are 90°. 90-57= 33°
