Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
The answer to this question is
B. (x+7)²+(y-4)²=64
I hope this helps!!!!!!!
Turn 5% into a decimal which is 0.05, then multiply by 2.95 = 0.1475
round it off, which is 0.15
so $0.15 is the tax and if ur looking for the total price then add $2.95 to $0.15
Final Answer: 
Steps/Equations:
Question: 
Step 1: Move the negative sign to the left side.
Step 2: Multiply both sides by 
.
Step 3: Simplify 
to 
.
Step 4: Multiply both sides by 
.
~I hope I helped :)~
50/2.5=
20
Unit rate is 20 miles per gallon
