Answer:
16 people
Step-by-step explanation:
While waiting in line to open james notices that his friend Carlos is ahead of him and that there are only 5 ahead of him.
- This means that carlo is the 6th person in line.
If there is a total of 38 people in line and 15 of those are behind james
- This means that james is the 23rd person in line
how many are between james and carlos
- This is the difference between the 6th position and 23rd position
There are 16 positions between 6 and 23. Hence that's the number of people between them
Answer: You have to use the distributive property of multiplication. You're answer would be 21x+6y.
Step-by-step explanation: 3(7x+2y) You have to take each individual number in the parentheses by three. That will get you 21x+6y.
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