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
Answer:
Step-by-step explanation:
refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;
The factorial of an integer n is evaluated as;
Using this concept, the above expression can now be simplified as follows;
Therefore, the permutations of 5 items taken 3 at a time is 60.
The next expression, 
refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;
Therefore, the combinations of 6 items taken 4 at a time is 15.
The final step is to evaluate the product;
Y = -3/4x + 6
you write in the y=mx+c form!
m= the slope
c = the y-intercept. (it is the second number of the coordinates)
Answer:
D.
Step-by-step explanation:
2 is it's length while in the perinthesis is x for its length plus the width which is doubled, explained by the x.
5.24 x 5 = $26.2
5 Muffins would cost $26.2
