## Electrical Problem Algebra 2

Maybe just a comment. So that comes in a later video. Its imaginary part comes from L and C.

They have a choice. That the voltage is the current times the resistance. This is to find. Capacitance those are the three elements of a simple linear constant coefficient problem associated with one loop.

It will become a minus, so I was thinking if I put the I up there.

That would be L times I double prime. The real part is R. So I have L. But I know that I should see the mass, the damping, and the stiffness there.

Believe me, all these ideas are so important. Those are the three terms that come– times W, the unknown. The linear algebra is the question. So an analog computer actually solved the equation by creating the model and measuring the answer. Again, this is an RLC loop that everybody has to understand, as in electrical engineering.

And we saw our differential equation will have that unknown I of t, rather than my usual y. And of course, we find it right away. So all that squared. So we have essentially successfully solved a second order constant coefficient single equation for the current. And in the capacitance, which is building up charge, the integral of the current comes in.

I have found that linear algebra is a useful tool in The first step in solving this problem is to write the sum of voltages around each loop. fresh-air-purifiers.com gives great strategies on practice algebra 2 problems, electricians, multiplication and rational and other math subjects.

## What You Need To Know Before Taking The Test

The most common issue I hear from people who have just completed taking the test is, I really wish I had brushed up on my math skills. Now those individuals may have to wait another 6 months to a year before they can test again.

So make sure you brush up on your math before you sign up for the aptitude test.

**The IBEW aptitude test consists of two parts math / mechanical and reading.**

## Example: Graph The Line Illustrating Speed

To graph this line, we need the y-intercept and the slope to write the equation. The slope was 5 miles per hour and since the starting point was at , the y-intercept is 0. So our final function is y=5x.

**Distance and time graph:** The graph of y=5x. The two variables are time and distance . The rate the runner runs is 5 miles per hour. Using the graph, predictions can be made assuming that his average speed remains the same.

With this new function, we can now answer some more questions.

- How many miles did he run after the first half hour? Using the equation, if x=\frac, solve for y. If y=5x, then y=5=2.5 miles.
- If he kept running at the same pace for a total of 3 hours, how many miles will he have run? If x=3, solve for y. If y=5x, then y=5=15 miles.

There are many such applications for linear equations. Anything that involves a constant rate of change can be nicely represented with a line with the slope. Indeed, so long as you have just two points, if you know the function is linear, you can graph it and begin asking questions! Just make sure what youre asking and graphing makes sense. For instance, in the marathon example, the domain is really only x\geq0, since it doesnt make sense to go into negative time and lose miles!

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## Rate Word Problems: Work And Time

If it takes Felicia 4 hours to paint a room and her daughter Katy 12 hours to paint the same room, then working together, they could paint the room in 3 hours. The equation used to solve problems of this type is one of reciprocals. It is derived as follows:

For this problem:

To make this into a solvable equation, find the total time needed for Felicia and Katy to paint the room. This time is the sum of the rates of Felicia and Katy, or:

Example 9.10.1

Karl can clean a room in 3 hours. If his little sister Kyra helps, they can clean it in 2.4 hours. How long would it take Kyra to do the job alone?

The equation to solve is:

Example 9.10.2

Doug takes twice as long as Becky to complete a project. Together they can complete the project in 10 hours. How long will it take each of them to complete the project alone?

The equation to solve is:

This means that Beckys rate is .

Since Dougs rate is twice Beckys, the time for Doug is .

Example 9.10.3

Joey can build a large shed in 10 days less than Cosmo can. If they built it together, it would take them 12 days. How long would it take each of them working alone?

Cosmo can build the large shed in either 30 days or 4 days. Joey, therefore, can build the shed in 20 days or 6 days .

The solution is Cosmo takes 30 days to build and Joey takes 20 days.

Example 9.10.4

Clark can complete a job in one hour less than his apprentice. Together, they do the job in 1 hour and 12 minutes. How long would it take each of them working alone?

## Sample Ibew Apprenticeship Reading Comprehension

Reading comprehension measures your ability to retain information. Its simple to read a paragraph but understanding the context can be tricky.

Here is a sample of what youre likely to see on the exam:*The timing of New Years Day has changed with customs and calendars. The Mayan civilization, on what is now called the Yucatan peninsula of Mexico, celebrated the New Year on one of the two days when the noonday sun is directly overhead.*

*In the equatorial regions of the earth, between the Tropics of Cancer and Capricorn, the sun is in this position twice a year, once on its passage southward, and once on its passage northward. At the early Mayan city of Izapa in the southern Yucatan, the overhead date for the sun on its southward passage was August 13.*

*The Mayans celebrated this as the date for the beginning of the New Year. Later at the more northerly Mayan site at Edzna, the corresponding overhead date is July 26. Analyses of Mayan pictorial calendars indicate that they celebrated the New Year on August 13 prior to 150 AD, and on July 26 after that year.*

*This change has been explained by archaeological dating showing that 150 AD was the time that the Mayans moved the hub of their civilization from the southern to the northern site.*

**Questions:**

1. According to the passage, the sun at Edzna was directly overhead at noon on:A. July 26 onlyC. July 26 and one other dateD. August 13 and one other date

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## Ibew Njatc Aptitude Practice Test Questions

Algebra and Functions portion has 33 questions with a 46 minute time limit. Reading Comprehension has 36 questions with a 51 minute time limit. With only 33 questions there is little room for error. You need to be prepared so you can limit wrong answers.

**Algebra Sample:**1. Consider the following formula: A = B + 3

If B equals 5 and C equals 2, what is the value of A?A.7

4.Consider the following formula: a = 1/2 b 4

Which of the following statements is true for this formula?A. When the value of b is less than 8, a is negative.B. When the value of b is greater than 8, a is negative.C. When the value of b is less than 8, a is positive.D. When the value of b is greater than 4, a is positive.

If you need to brush up on your math skills then you may want to check out **Khan Academys Algebra 1 course**. This is a FREE course!

Also, check with your local community college to see if Algebra courses are offered.

## Types Of Angles Worksheet

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## Chapter 1 Matter And Measurements Text Problems

**Chapter 2 matter and change worksheet answers**. Protons have a positive charge and neutrons carry no charge. A horizontal row of elements in the periodic table is called an period. The book uses slightly different rounding rules.

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Answer Key

## What Is An Aptitude Test

Aptitude tests are one of the most commonly used assessments in measuring a candidates suitability for a role.

The IBEW wants to ensure that their candidates have a solid ability to comprehend written text, basic algebra, and have some mechanical aptitude.

The aptitude test primarily applies to the Inside Wireman and the Limited Energy Technician apprenticeship programs.

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## Example: Write The Least Squares Fit Line And Then Graph The Line That Best Fits The Data

For n=8 points: ,,,,,, and .

**Example Points:** The points are graphed in a scatterplot fashion.

First, find the slope and y-intercept that best approximate this data, using the equations from the prior section:

To find the slope, calculate:

\displaystyle \begin \sum_^x_y_& =0+0+1+4+3+10+15+24\\& =57 \end \displaystyle \begin \sum_^x_& =-1+0+1+2+3+4+5+6\\& =20 \end\displaystyle \begin \sum_^y_& =0+0+1+2+1+2.5+3+4\\& =13.5 \end

\displaystyle m=\frac^x_y_-\frac\sum_^x_\sum_^y_}^-\frac^}

4. Calculate the numerator: The product of the xand y-coordinatesminus one-eighth the product of the sum of the x-coordinates and the sum of the y-coordinates:

\displaystyle \sum_^x_y_-\frac\sum_^x_\sum_^y_

The numerator in the slope equation is:

\displaystyle 57-\frac=23.25

5. Calculate the denominator: Thesum of the squares of the x-coordinates minus one-eighth the sum of the x-coordinates squared:

\displaystyle \sum_^-\frac^

\displaystyle \begin \sum_^& =1+0+1+4+9+16+25+36\\& =92 \end

The denominator is 92-\frac^=92-50=42 and the slope is the quotient of the numerator and denominator: \frac\approx0.554.

Now for the y-intercept, one-eighth times the average of the x-coordinates: \bar=\frac=2.5 and one-eighth times the average of the y-coordinates: \bar=\frac=1.6875.

Therefore b=\frac \sum_^ y_ – m \frac \sum_^ x_ \\:

\displaystyle b\approx1.6875-0.554=0.3025.

## Example: Renting A Moving Van

A rental company charges a flat fee of $30 and an additional $0.25 per mile to rent a moving van. Write a linear equation to approximate the cost y in terms of x, the number of miles driven. How much would a 75 mile trip cost?

Using the slope-intercept form of a linear equation, with the total cost labeled y and the miles labeled x :

\displaystyle y=mx+b

The total cost is equal to the rate per mile times the number of miles driven plus the cost for the flat fee:

\displaystyle y=0.25x+30

To calculate the cost of a 75 mile trip, substitute 75 for x into the equation:

\displaystyle \begin y& =0.25x+30\\ & =0.25+30\\ & =18.75+30\\ & =48.75 \end

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## Outliers And Least Square Regression

If we have a point that is far away from the approximating line, then it will skew the results and make the line much worse. For instance, lets say in our original example, instead of the point we have .

Using the same calculations as above with the new point, the results are:m\approx0.0536 and b\approx2.3035, to get the new equation y=0.0536x+2.3035.

Looking at the points and line in the new figure below, this new line does not fit the data well, due to the outlier . Indeed, trying to fit linear models to data that is quadratic, cubic, or anything non-linear, or data with many outliers or errors can result in bad approximations.

Outlier Approximated Line: Here is the approximated line given the new outlier point at .

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