B. Negative exponent flip from denominator to numerator and numerator to denominator.
B is the second option.
Given:
Consider the given gallons are 
gallons.
To find:
The number of quarts in gallons.
Solution:
We know that,
1 gallons = 4 quarts
Using this conversion, we get
Therefore, there are 33 quarts in gallons.
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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Answer:
y=[-2]x[+][5]
Step-by-step explanation:
m= -2
Using the point (1,3) Find the value of b
3= -2(1)+b
3= -2+b
+2 +2
---------
5=b
y= -2x+5
