Answer:
Option 3: take base-4 log each side
In case of multiple answers:
Options 3,4 & 5
Step-by-step explanation:
4^(x+3) = 18
Apply log4 both sides to being the power down
You can take log with any other base too.
In case of multiple answers, options 4 and 5 are also valid
Answer:
C.
Step-by-step explanation:
......................
sin(x) = ⁴/₅
sin⁻¹[sin(x)] = sin⁻¹(⁴/₅)
x ≈ 53.13
cos(90 - x) = cos(90)cos(x) + sin(90)sin(x)
cos(90 - 53.13) = cos(90)cos(53.13) + sin(90)sin(53.13)
cos(36.87) = 0cos(53.13) + sin(53.13)
cos(36.87) = sin(53.13)
cos(36.87) = cos(90 - 53.13)
cos(36.87) = cos(36.87)
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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