A subway ride for a student costs $1.25. A monthly pass costs $35.Write an inequality that represents the number of times, x , y
2 answers:
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Answer:
1) y=3
2)x =38
3)m = 3
4)h=21
Step-by-step explanation:
Here are some equations given from which we have to find the values of the variables by using the simple techniques of mathematics. We will start From the very first to the last part
1)
The given equation is
y+2 = 5
We have to find y, we have to eliminate 2 from LHS
y + 2 = 5
Subtracting 2 from both sides
∵(to balance out the equation we do the operations on both side of equation)
y + 2 - 2 = 5 -2
y + 0 = 3
y = 3
2)
The given equation is
x - 18 = 20
we have to find value of x for this
adding 18 on both sides of the equation
x - 18 + 18 =20 + 18
x - 0 = 38
x = 38
3)
The given equation is
6m = 18
we have to find value of m for this
dividing 6 on both sides of the equation
∴18 = 6*3
Cancelling out 6 we get
m = 3
4)
The given equation is
To find the value of h
for this multiplying 3 on both sides of the equation
it becomes
h=21
Answer:
Step-by-step explanation:
Solution:-
- Given is the 2nd order linear ODE as follows:
- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:
- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:
Where,
are linearly independent functions of parameter ( t )
- To determine [ ], we will employ the use of wronskian ( W ).
- The functions [ ] are defined as:
Where,
F(t): Non-homogeneous part of the ODE
W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions
- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:
- Now we will evaluate function. Using the relation given for u1(t) we have:
- Similarly for the function u2(t):
- We can now express the particular solution ( yp ) in the form expressed initially:
Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.
- The general solution is the superposition of complementary and particular solution as follows: