While shopping for clothes, Consuelo spent $3 less than twice what Brenda spent. Consuelo spent $73. How much did Brenda spe
1 answer:
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Answer:
C) 75 + 50x = 25 + 70x
Step-by-step explanation:
ABC Tech:
$50 an hour. So,for x hours= 50 * x = 50x
Service charge = 75 + 50x
Tech Squad:
$70 an hour. So,for x hours= 70 * x = 70x
Service charge = 25 + 70x
C) 75 + 50x = 25 + 70x
50x - 70x = 25 - 75
-20x = -50
x = -50/-20
x =5/2 = 2hours
Take the homogeneous part and find the roots to the characteristic equation:
This means the characteristic solution is
.
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form
. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.
With
and 
, you're looking for a particular solution of the form 
. The functions 
satisfy
where
is the Wronskian determinant of the two characteristic solutions.
So you have
So you end up with a solution
but since
is already accounted for in the characteristic solution, the particular solution is then
so that the general solution is
This means the characteristic solution is
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form
With
where
So you have
So you end up with a solution
but since
so that the general solution is