Answer:
y(s) = ![\frac{5s-53}{s^{2} - 10s + 26}](https://tex.z-dn.net/?f=%5Cfrac%7B5s-53%7D%7Bs%5E%7B2%7D%20-%2010s%20%20%2B%2026%7D)
we will compare the denominator to the form ![(s-a)^{2} +\beta ^{2}](https://tex.z-dn.net/?f=%28s-a%29%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D)
![s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}](https://tex.z-dn.net/?f=s%5E%7B2%7D%20-10s%2B26%20%3D%20%28s-a%29%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D%20%3D%20s%5E%7B2%7D%20-2as%20%2Ba%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D)
comparing coefficients of terms in s
1
s: -2a = -10
a = -2/-10
a = 1/5
constant: ![a^{2}+\beta ^{2} = 26](https://tex.z-dn.net/?f=a%5E%7B2%7D%2B%5Cbeta%20%5E%7B2%7D%20%3D%2026)
![(\frac{1}{5} )^{2} + \beta ^{2} = 26\\\\\beta^{2} = 26 - \frac{1}{10} \\\\\beta =\sqrt{26 - \frac{1}{10}} =5.09](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B5%7D%20%29%5E%7B2%7D%20%2B%20%5Cbeta%20%5E%7B2%7D%20%3D%2026%5C%5C%5C%5C%5Cbeta%5E%7B2%7D%20%3D%2026%20-%20%5Cfrac%7B1%7D%7B10%7D%20%5C%5C%5C%5C%5Cbeta%20%3D%5Csqrt%7B26%20-%20%5Cfrac%7B1%7D%7B10%7D%7D%20%3D5.09)
hence the first answers are:
a = 1/5 = 0.2
β = 5.09
Given that y(s) = ![A(s-a)+B((s-a)^{2} +\beta ^{2} )](https://tex.z-dn.net/?f=A%28s-a%29%2BB%28%28s-a%29%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D%20%29)
we insert the values of a and β
= ![A(s-0.2)+B((s-0.2)^{2} + 5.09^{2} )](https://tex.z-dn.net/?f=A%28s-0.2%29%2BB%28%28s-0.2%29%5E%7B2%7D%20%2B%205.09%5E%7B2%7D%20%29)
to obtain the constants A and B we equate the numerators and we substituting s = 0.2 on both side to eliminate A
5(0.2)-53 = A(0.2-0.2) + B((0.2-0.2)²+5.09²)
-52 = B(26)
B = -52/26 = -2
to get A lets substitute s=0.4
5(0.4)-53 = A(0.4-0.2) + (-2)((0.4 - 0.2)²+5.09²)
-51 = 0.2A - 52.08
0.2A = -51 + 52.08
A = -1.08/0.2 = 5.4
<em>the constants are</em>
<em>a = 0.2</em>
<em>β = 5.09</em>
<em>A = 5.4</em>
<em>B = -2</em>
<em></em>
Step-by-step explanation:
- since the denominator has a complex root we compare with the standard form
![s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}](https://tex.z-dn.net/?f=s%5E%7B2%7D%20-10s%2B26%20%3D%20%28s-a%29%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D%20%3D%20s%5E%7B2%7D%20-2as%20%2Ba%5E%7B2%7D%20%2B%5Cbeta%20%5E%7B2%7D)
- Expand and compare coefficients to obtain the values of a and <em>β </em>as shown above
- substitute the values gotten into the function
- Now assume any value for 's' but the assumption should be guided to eliminate an unknown, just as we've use s=0.2 above to eliminate A
- after obtaining the first constant, substitute the value back into the function and obtain the second just as we've shown clearly above
Thanks...
Answer:
B (-1,0), (3,0)
Step-by-step explanation:
Quadratic Formula
B) 4/9 is correct
Mark with crown!
Answer:
5t + 2
General Formulas and Concepts:
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define Expression</u>
4t - 18 - t + 2t + 20
<u>Step 2: Simplify</u>
- Combine like terms (t): 5t - 18 + 20
- Combine like terms (Z): 5t + 2
The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.
<h3>What is a quote?</h3>
Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.
Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.
You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.
In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.
Learn more about quote on:
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