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
Cos = adjacent over hypotenuse
cos33 = b/170
170cos33 = b
b = 142.574 inches
Answer:
-p5q2 - p3q5 + 2p3 + 2pq2 + 2q3
____________________________
p3q2
Step-by-step explanation:
2
Simplify ——
q2
Equation at the end of step 1 :
(p+q) 2
(((2•—————)-(q3))+——)-p2
(p3) q2
Step 2 :
p + q
Simplify —————
p3 (p + q) 2
(((2 • ———————) - q3) + ——) - p2
p3 q2
Step 3 : 2 • (p + q) 2
((——————————— - q3) + ——) - p2
p3 q2 q3 q3 • p3
q3 = —— = ———————
1 p3
Answer:
Fabric used by each each player for headband is 16.51 inches and fabric used for wristband is 1.99 inches
Step-by-step explanation:
In first case it is given that there are players and 2 coaches
So total number = 44+2 = 46
It is given that 759.46 inches of fabric is used on headbands for 44 players and 2 coaches
So fabric used by each player 
Now in second 87.64 inches fabric is used for 44 players
So fabric used by each players 
So fabric used by wristband is 1.99 inches
Answer:
36 units
If OP is parallel to LN then we have, Substituting the respective values we obtain, Therefore option D is correct, y=36 units make OP||LN.