Someone pls help me with 7 and 8, thank you so much!!
1 answer:
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Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is:
To find the number of terms in the arithmetic sequence, we need to use the formula
where
is the nth number, 
is the first number, n is the number of terms and d is the difference of the two consecutive numbers.
7373 = 1313 + (n - 1)(303)
7373 = 1313 + 303n - 303
7373 = 1010 + 303n
7373 - 1010 = 303n
6363 = 303n
6363 ÷ 303 = n
n = 21
Therefore, there are 21 terms in the arithmetic sequence given.
where
7373 = 1313 + (n - 1)(303)
7373 = 1313 + 303n - 303
7373 = 1010 + 303n
7373 - 1010 = 303n
6363 = 303n
6363 ÷ 303 = n
n = 21
Therefore, there are 21 terms in the arithmetic sequence given.