Lila knows that 316 means “3 divided by 16.” She uses this to find the decimal equivalent for 316. Enter a digit into each box t
o continue her work.
1 answer:
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Answer:
Step-by-step explanation:
let's start by separating the fraction into two new smaller fractions
.
First,<em> s(s^2+s+1)</em> must be factorized the most, and it is already. Every factor will become the denominator of a new fraction.
Where <em>A</em>, <em>B</em> and <em>C</em> are unknown constants. The numerator of <em>s</em> is a constant <em>A</em>, because <em>s</em> is linear, the numerator of <em>s^2+s+1</em> is a linear expression <em>Bs+C</em> because <em>s^2+s+1</em> is a quadratic expression.
Multiply both sides by the complete denominator:
Simplify, reorganize and compare every coefficient both sides:
Solving the system, we find <em>A=1</em>, <em>B=-1</em>, <em>C=0</em>. Now:
Then, we can solve the inverse Laplace transform with simplified expressions:
The first inverse Laplace transform has the formula:
For:
We have the formulas:
We have to factorize the denominator:
It means that:
So <em>a=-1/2</em> and <em>b=(√3)/2</em>. Then:
Finally: