Answer:
1
Step-by-step explanation:
4÷1=4 4×1=4 4+1 = 5 5-1 = 4
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
Its length would be 9 ft so 9 x 8 is 72.
Answer:
a. Vertex = (2.5,-12.25)
b. y-intercept = (0,-6)
c. x-intercept = (6,0) ; (-1,0)
Step-by-step explanation:
a.
Your equation is written as:
The easiest way to find the vertex is writing the equation this way:
Being the vertex (h,k)
So first complete the square
Vertex : (2.5,-12.25)
b.
To find the y-intercept you need to replace the equation when x = 0 and get y
c.
To find the x-intercept you need to replace the equation when y = 0 and get x
