Answer:
Greater than/equal to 9
Step-by-step explanation:
-⅓m《-3
3《⅓m
3×3《m
9《m
m》9
'Commutative' means you can work it in the other direction without changing it.
But 1/2 is not the same number as 2/1 . So I guess division is NOT commutative.
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
When you create the number line, put 0 in the middle. Basically you put all the numbers you got from least to greatest on the number.
Since -3/2 is less than 0, it will go to the left of 0.
Since 3/2 and 5/2 are greater than 0, it will go to the right of 0.
Remember to use sub points of 1.
Best of Luck!
