Janelle and her best friend Carmen go shopping. the function p(t) = 5^4-3x^3 +2^2+24 represents how much money each girl spent b
2 answers:
<h2>Hello!</h2>
The answer is:
They spent $176 together.
<h2>Why?</h2>We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.
Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:
Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:
Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.
Calculating we have:
Hence, we have that they spent $176 together.
Have a nice day!
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Answer:
Step-by-step explanation:
divided by
is the same thing as multiplying
by
.
The equation we get is:
With this equation, we can factor each equation:
We can cancel out like terms since they would be dividing each other:
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