If anyone knows the answer to these, that would be great!! And label like for example 1) b...thanks in advance!

Consider the initial value function y given by

Nuetrik [128]

Answer:

y(s) = $\frac{5s-53}{s^{2} - 10s + 26}$

we will compare the denominator to the form $(s-a)^{2} +\beta ^{2}$

$s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}$

comparing coefficients of terms in s

$s^{2} :$ 1

s: -2a = -10

a = -2/-10

a = 1/5

constant: $a^{2}+\beta ^{2} = 26$

$(\frac{1}{5} )^{2} + \beta ^{2} = 26\\\\\beta^{2} = 26 - \frac{1}{10} \\\\\beta =\sqrt{26 - \frac{1}{10}} =5.09$

hence the first answers are:

a = 1/5 = 0.2

β = 5.09

Given that y(s) = $A(s-a)+B((s-a)^{2} +\beta ^{2} )$

we insert the values of a and β

$\\5s-53$ = $A(s-0.2)+B((s-0.2)^{2} + 5.09^{2} )$

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

the constants are

a = 0.2

β = 5.09

A = 5.4

B = -2

Step-by-step explanation:

since the denominator has a complex root we compare with the standard form $s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}$
Expand and compare coefficients to obtain the values of a and β 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...

3 0

3 years ago

Please take a look at the picture. Please write your answer with an explanation.

g100num [7]

Answer:

Step-by-step explanation:

<h3>Given question:</h3>

To simplify - 

$14 + 16 \div {2}^{3} - (12 + {3}^{2} ) \div 7 + 2 \times ( - 5)$

<h3>Solution:</h3>

According to PEMDAS rule,

[First parenthesis]

$= 14 + 16 \div {2}^{3} - (12 + 9 ) \div 7 + 2 \times ( - 5)$

$= 14 + 16 \div {2}^{3} - 21 \div 7 + 2 \times ( - 5)$

[Then exponents]

$= 14 + 16 \div 8 - 21 \div 7 + 2 \times ( - 5)$

[Then multiplication]

= 14 + 16 ÷ 8 - 21 ÷ 7 - 10

[Then division]

= 14 + 2 - 3 - 10

[Then addition]

= 16 - 13

[Then subtraction]

= 3 (Ans)

8 0

3 years ago

Name at least two independent variables that could result in a change in the price of a basket of apples.

Novay_Z [31]

Answer:

In an experimental study looking at classical music exposure and reading ability in children, the researcher divided the children into two groups (Groups A and B

5 0

3 years ago

Plz help im an idiot

MrMuchimi

Answer:

3.)138

4.) 149

Step-by-step explanation:

you add the two inside measures together.

5 0

3 years ago

Read 2 more answers

Trigonometry need help on this one

morpeh [17]

Answer:

Step-by-step explanation:

you have a right triangle, more precisely is a isosceles right triangle, as you have one angle= 45⁰, the other angle is also= 45⁰

In this triangle the hypotenuse, c, is

c=9 $\sqrt{2}$ = 12.72

7 0

3 years ago