Remember
∛(ab)=(∛a)(∛b)
also
i¹=i
i²=-1
i³=-i
i⁴=1
so
∛-2i=(∛2)(∛-i)=(∛2)(i)=i∛2
<span>c. This budget can be modified by reducing the amount spent on food and clothes, thereby reducing overall expenses to have the maximum amount of money for fixed expenses and maintaining a positive actual net income.
You can't reduce fixed expenses. These are expenses that are constant every month like rent expense, utility payments, and cell phone plan. The only expenses you can reduce are food and clothes. These expenses are called variable expenses meaning the amount of these expenses varies. Thus, it can be manipulated. </span>
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)
For more information about differential equation, visit
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