7 : 21
which can be simplified to 1 : 3 as both sides are divisible by 7
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:
4 has 8 halves.
Step-by-step explanation:
To find the answer, we already know that 2 halves make up 1. So, multiply 2 by 4 to get 8 halves. Therefore, the answer is 8 halves.
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When you illustrate the problem, it would look like the diagram shown in the picture. There are pictures, each with a length of 6 inches, that are placed all around the perimeter. To solve the number of pictures, the solution is as follows:
Size of picture = 6 inches * 1 ft/12 inches = 0.5 ft/picture
Pictures along the length = 7 ft * 1 picture/0.5 ft = 14 pictures
Pictures along the width = 4 ft * 1 picture/0.5 ft = 8 pictures
Since perimeter is 2L + 2W, the total number of pictures is:
Total pictures = 2(14) + 2(8) = 44 pictures