Answer:
The quotient is 3x-8
Step-by-step explanation:
(6x^2-x-40)÷ (5 + 2x)
The above equation can be written as
(6x^2-x-40)÷ (2x + 5)
The division is shown in the figure below.
The quotient is 3x-8
Answer:

Step-by-step explanation:
y′′ + 4y′ − 21y = 0
The auxiliary equation is given by
m² + 4m - 21 = 0
We solve this using the quadratic formula. So

So, the solution of the equation is

where m₁ = 3 and m₂ = -7.
So,

Also,

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,


Substituting A into (1) above, we have

Substituting B into A, we have

Substituting A and B into y, we have

So the solution to the differential equation is

Answer:
First Integer = n = 45
Second Integer = n+1 = 45 + 1 = 46
And Third Integer = n+ 2 = 45 +2 = 47
Step-by-step explanation:
Let First integer = n
Second Integer = n+1
Third Integer = n+2
According to the question given (If the first of three consecutive integers is subtracted from 138, the result is the sum of the second and third) the equation will be:
138 - n = (n+1) + (n+2)
Solving the equation:
138 - n = n+1+n+2
138 - n = 2n+3
138 - 3 =2n +n
135 = 3n
135/3 = n
=> n= 45
So, First Integer = n = 45
Second Integer = n+1 = 45 + 1 = 46
And Third Integer = n+ 2 = 45 +2 = 47