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
1. Slope = 7
2. x-intercept = 6/7 = 0.85714
3. y-intercept = 6/ - 1 = -6.00000
Rearrange:
Rearrange the equation by subtracting what is to the right if the equal sign from both sides of the equation:
7x-y- (6) = 0
Answer:
Step-by-step explanation:
Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.
Therefore, we can set up the following equation to find the new balance after 2 years:
If Carly had more DVDs than Rob then you would subtract her amount away from the total. 42-4=38
Answer:
1/4 * 1/8 = 1/32 inch
Step-by-step explanation:
1/4 * 1/8 = 1/32inch
