What classes do you have to take in college for be a system software engineer

Please answer fast. With full step by step solution.

lina2011 [118]

Let f(z) = (4z ² + 2z) / (2z ² - 3z + 1).

First, carry out the division:

f(z) = 2 + (8z - 2) / (2z ² - 3z + 1)

Observe that

2z ² - 3z + 1 = (2z - 1) (z - 1)

so you can separate the rational part of f(z) into partial fractions. We have

(8z - 2) / (2z ² - 3z + 1) = a / (2z - 1) + b / (z - 1)

8z - 2 = a (z - 1) + b (2z - 1)

8z - 2 = (a + 2b) z - (a + b)

so that a + 2b = 8 and a + b = 2, yielding a = -4 and b = 6.

So we have

f(z) = 2 - 4 / (2z - 1) + 6 / (z - 1)

or

f(z) = 2 - (2/z) (1 / (1 - 1/(2z))) + (6/z) (1 / (1 - 1/z))

Recall that for |z| < 1, we have

$\displaystyle\frac1{1-z}=\sum_{n=0}^\infty z^n$

Replace z with 1/z to get

$\displaystyle\frac1{1-\frac1z}=\sum_{n=0}^\infty z^{-n}$

so that by substitution, we can write

$\displaystyle f(z) = 2 - \frac2z \sum_{n=0}^\infty (2z)^{-n} + \frac6z \sum_{n=0}^\infty z^{-n}$

Now condense f(z) into one series:

$\displaystyle f(z) = 2 - \sum_{n=0}^\infty 2^{-n+1} z^{-(n+1)} + 6 \sum_{n=0}^\infty z^{-n-1}$

$\displaystyle f(z) = 2 - \sum_{n=0}^\infty \left(6+2^{-n+1}\right) z^{-(n+1)}$

$\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{-(n-1)+1}\right) z^{-n}$

$\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{2-n}\right) z^{-n}$

So, the inverse Z transform of f(z) is $\boxed{6+2^{2-n}}$ .

4 0

3 years ago

An electric water heater held at 120° F is kept in a 60°F room. When purchased, its insulation is equivalent to R-5. An owner pu

Trava [24]

Answer:

Total saving would be of 36.917 $\yr

Explanation:

Given Data:

$T_{heater} = 120$ Degree F

$T_{room} = 60$ Degree F

A = 30 ft^2

$\eta = 100$ %

Heat loss before previous final value $= \frac{A \Delta T}{R}$

$=\frac{30\times *(120-60)}{5}$

= 360 Btu/hr

Heat loss after new value $= \frac{30\times \times (120-60)}{15} = 120 Btu/hr$

saving would be $= 360 - 120 Btu/hr \times kw hr/ 3412 Btu\times 24 hr/day \times 365 day/year$

= 616.1782 kw hr/yr

$cost = 616.1782 \times 0.06$ $

= 36.917 $\yr

6 0

4 years ago

The difference between a thermocouple and a thermistor is the A. technology inside. B. thermocouple measures temperatures at the

Zepler [3.9K]

Answer: B. thermocouple measures temperatures at the tip and the thermistor at the dimple.

Explanation:

A thermistor is a temperature-sensitive resistor, whilst a thermocouple generates a voltage proportional to the temperature. Thermocouples can work at much higher temperatures than thermistors. They are commonly used for temperature control in heating systems.

8 0

3 years ago

A market research survey has 15 questions and will be sent to 500 people. What is the total cost to conduct survey if it has a $

Dimas [21]

Answer:

$39,500

Explanation:

In order to find the total cost, we proceed as follows:

1)

First, the base fee is:

$b=\$1000$

2)

Then we calculate the total number of questions: we have 15 questions per survey, and a total of 500 surveys (for 500 people), therefore the total number of questions is

$Q=15\cdot 500 =7500$