Circles

This lesson tells the basics about circles. I define what a circle is, radius, diameter, circumference and area.

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transcript:

Welcome to Your Tutor Online Video Podcast. In today’s lesson, we will learn some basics about circles including diameter, radius, circumference and area.

A circle has a center point. The actual circle has all the points that are the same distance away from that point. Imagine a string with one end attached to the point and a pencil at the other. If you pull the string tight and rotate it around the point we just drew, we will get a circle. This is how projector works.

The line we just drew is called a radius. I am going to use the letter R to represent it. The radius is the distance from the center to the edge of a circle. A line that passes through the circle from edge to edge and passes through the center is called the diameter. It is going to be represented by the letter D. Diameter is equal to two times the radius.

And pi. Pi is a special irrational number. This means we cannot read it as a fraction. It is used to help us find the measurements of circles. To get a little more technical, pi is the ratio of the circumference to the diameter of a circle. If you need a number close to pi, if your teacher wants you to give your answer in decimals or fraction. If you use 3.14 or 22 over 7, these two numbers are not exactly pi but they are close enough to get an idea of what the answer should be.

Now for some formulas. Circumference is a measure around the circle. It is a very similar to perimeter with polygons. Circumference is equal to pi times diameter. Area is a measurement of the region that the circle takes up. Area is equal to Pi R squared. The answer here will be units squared.

When it comes to solving problems with circles, you may be given circumference for us to find the radius or you might know the radius and we have to find the circumference. Either way you plug in what you note, the formulas that I had showed you and then solve for what you do not know and you have your answer.

We are just going to look at two examples for this lesson. Example 1, what is the circumference of a circle which has radius of 4 centimeters. From the formulas I gave you, we know this, circumference is equal to pi times diameter but we were given the radius. There is no problem. We know that diameter is equal to two times the radius or in this case, diameter is equal to 8 centimeters. We are going to take that number and plug it into our formula, and so we know circumference is equal to 8 pi centimeters.

When we have pi as per different answer, we want to rate the number first followed by pi. If your teacher wants you to give the answer as a decimal or fraction we will do 8 times 3.14 for decimals or 8 times 22 over 7 for fractions.

One more example, what is the radius of a circle whose area is 25 pi. Our formula for area is pi times r square. I am going to fill in what we do know. Area is 25 pi. We are looking for radius now. When to buy both sides by pi and they just both cancelled out, so now we have 25 is equal to r square. We can square root both sides. The square root of 25 is 5. We are going to do nor negative because we cannot have negative link for radius, so five is equal to the radius. That is the final answer.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com. If you need more help with this or other topics visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our podcast and itunes to get the latest videos.

I will see you next time. Thanks for watching. Class dismissed.

How to Convert Units of Measure

This video shows how to convert one unit of measure to another using a chart.

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transcript:

Welcome to Your Tutor Online Video Podcast. In today’s lesson, I will teach you how to convert any unit of measure to any number, as long as you know the conversion ratio.

I will speak for myself here and say, “I have a hard time remembering tons of different formulas in order to convert units whether to multiply or divide even if I do know the unit of measure.”

If you use the method I am about to show you, you will not be confused anymore and you will get the correct answer 100 percent of the time. Let us say we want to convert 25 centimeters to millimeters. Well, we know that there are 100 centimeters in 1 meter. We also know that there are 1000 millimeters in 1 meter.

But it is a little hard to figure out how to put those two together to go from centimeters to millimeters. No problem. First, let us set up a chart that looks something like this. It is going to have two rows and we are just going to draw one column for now. In very top left spot, we are going to put the number we want to convert 25 and also very important is we want to include the units 25 centimeters.

Now, we already know that there are 100 centimeters in 1 meter just like we said before and 1000 millimeters in 1 meter. If we go from centimeters to meters, then meters to millimeters we have our problem solved.

We are going to draw one more column for now. We are going to put our first conversion ratio into this column. To determine whether which number goes on top and which one goes on the bottom, we are going to look our original the centimeters and opposite the side is for the other centimeters that is going to go.

So centimeters are on top here, centimeters will go on the bottom down here. 100 is what the centimeters and 1 meter goes on top. We are going to repeat the process one more time to go from meters to millimeters and that goes in this last column. Meters is on top here, so we want to do the opposite to put meter on the bottom over here and 1000 millimeters goes on top.

To make sure that you set the chart up correctly, we are going to make sure that all the units cancel out except for the unit of measure we are converting to, so we are just going to treat this chart like we were multiplying fractions together. Anything in the numerator can cancel out anything in the denominator.

Centimeters is on top. Centimeters is on the bottom, so they cancel out. Meter and meter cancel out and we are left with millimeters. As long as the only unit we are left with is on top and it is not crossed out, we set up the chart correctly.

Now, it is just a simple multiplying fraction’s problem. Before you get started, you want to make sure that you cancelled out anything that you cancelled out. I see that there is 100 in the denominator and 100 in the numerator, so we will simplify that. Now, all we have is 25 times 10 is 250. Since the only unit that is not cancelled is millimeters, final answer is 250 millimeters.

I will show you just one more really use the example, how many pounds is 48 ounces? We are going to set up our chart. We are going to put 48 here, 48 ounces with the units. You might need to look it up. You can look it up in a dictionary if you need to ounces to pounds. We know you will found out that 16 ounces is equal to 1 pound.

Since we have this conversion, we are going to put 16 on the bottom so that the ounces will cancel out. We are going to pound on top. Now, we should see ounces cancelled out and this 48 divided by 16 which is equal to 3 pounds.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com. If you need more help with this or other topics visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our podcast and itunes to get the latest videos.

I will see you next time. Thanks for watching. Class dismissed.

How to Graph Equations with Slope Intercept Form

In this lesson we will learn about the slope intercept formula. We look at what slope and intercept mean as well as how to graph the equation.

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transcript

Welcome to Your Tutor Online video podcast. In this lesson we'll learn about slope intercept form of a line.

The slope intercept form of a line helps to graph equations. The formula is y = mx + p. x and y are just going to be points in the line. m is the slope. p is the intercept. Here is an example equation for a line. y = 2x + 3. You can tell what each part of the equation is based on its position in the formula. The slope is 2, because it's in the first spot. And the intercept is +3, because it's in the second place.

Let's look at slope. Slope means rise over run. Always think of it as a fraction. When slope is a whole number like in our example, it can be rewritten just with a denominator of 1. 2 over 1. The top number of the fraction is rise, and the bottom number of the fraction is run. We normally go up and to the right. If any part of the slope is negative, we'll go on an opposite direction. So let's start with this point. If we had a slope of 2 we go up 2 over 1, up 2 and over 1. Slope talks about how each point on the line is in relation to another.

Next let's look at y-intercept. It's the last number in the equation and just means where the line crosses the y-axis. For example, it's +3, so just put a dot at positive 3 on the y-axis and that's the line that goes up and down. And we know that this equation is some line that passes through that point. If the y-intercept is negative, we will just put the dot at the negative part on the y-axis.

Now that we know about the slope and the intercept individually, we need build up those two things together. We're still going to use our example y = 2x + 3. To graph this we're going to start with the y-intercept. It's going to go on the y-axis, the up and down line at +3, (one, two, three) and put a dot.

Now we're going to work with our slope. It's 2. Remember that means 2 over 1, rise 2, run 1, up 2, (one, two) over 1 and put our second dot. And we'll repeat the process one more time, (one two), and over 1. All three those points are on our line. Now I just want to connect them with a single line. And here is our line y = 2x +3.

I want to give you one more example before we finish today. And this equation involves negative numbers so you can see how to handle those on the graphing. y = -2/3x - 2. Again we're going to start with the y-intercept at -2 and go to -2 on the y-intercept and put a dot.

This time our slope is -2/3. So we're going to rise -2, just the same thing as going down and then run 3. So down 2, (one, two) and run 3. I'm still going to move to the right (one, two, three). Repeat the process one more time, down 2, (one, two). Run 3 (one, two, three). Three points should be enough, so I'll connect my dots. And there's our line.

One thing I forgot to show you in the last example is we need to add little arrows on either end of our line to show that it continues on forever.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com.

If you need more help with this or other topics, visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in the virtual classroom you just saw on this video. Be sure to subscribe to our podcast in iTunes to get the latest videos. I'll see you next time. Thanks for watching. Class dismissed.

Area of Polygons

This video gives formulas and examples for how to find the area of squares, rectangles, triangles, parallelograms, and trapezoids. The video also explains the difference between base and height.

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transcript:

Welcome to Your Tutor Online video podcast. In this lesson, we’re going to look at area for several different polygons. Area is a measurement of a region that a shape takes up. It’s measured in units squared. The easiest way to find area is just to count the number of squares that it takes up on graph paper. Look at the blue box I just drew and we can easily see the area by counting the boxes -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. So this square has an area of 12 units squared.

Sometimes we can’t just count the squares on graph paper because it’s unavailable, so we need to learn the following formulas for area. The first and the easiest shape we’re going to look at are squares and rectangles. Squares are rectangles so they have the same area formula. Area is equal to the length times the width. Or in other words, just one side times the other side.

Here’s a very easy example. We have a rectangle with a length of 7 inches and a width of 3 inches. 7 times 3 is 21. We’re going to write the same units that we see, inches, and then we’re going to put a little 2 up above the inches to show that’s inches squared. And that way, everybody knows we’re talking about the area and not just the length.

The next shape we’re going to look at is a triangle. The formula for the area of a triangle is area is equal to one-half times the base, times the height. The base is just going to be any of the sides of the triangle, and the height extends from that base to the opposite vertex at a perpendicular angle.

Let’s look at base and height a little more closely because I know it can be confusing.
First, for a right triangle, we’re just going to pick the two legs of the right triangle for your base and height. It doesn’t matter which one because multiplication can be done in any order.

For other triangles, it gets a little more confusing. I normally just choose the side that’s closest to me to be my base, and then the height is going to go from the base to the opposite vertex, down exactly at a 90° angle.

For the flask triangle, again, I’m going to choose the side closest to me for my base. The opposite vertex is all the way over here. Drop directly down from the vertex to my base. And notice here, the height is actually outside of the triangle, which is OK.

Let’s look at an example. Now, the hardest part of figuring out the area of a triangle is to know which one is your base, and which number is your height. So we have all these numbers here, our clue is with the right angle symbol. The right angle symbol is going to join together your base and your height. So we see this side, 4 centimeters, and this side, 3 centimeters, as our base and our height. Just to refresh your memory on the area, it’s equal to one-half base times the height. 4 times 3 is 12, times one-half, is equal to 6 centimeters cubed.

Parallelograms are easy if you understand the formula for triangles. The hardest part here, again, is to figure out what the height is. But we already know our clue is that right triangle symbol. The formula for area of a parallelogram is just base times height. We’re not going to multiply by one-half this time because a parallelogram is basically two of the same triangle put together. Since it’s so similar to a triangle, we’re not going to have an example for parallelogram. You should be able to handle plugging in the numbers into the formula.

The last polygon we’re going to look at in this lesson is the trapezoid. The formula for area of a trapezoid is one-half times the quantity base 1 plus base 2, times the height. In other words, we’re going to add the two bases together first, then divided by 2, then multiply it by the height. In a trapezoid, we have one pair of parallel sides. Those two parallel sides are our bases, base 1 and base 2. Again, we have the clue, for our height, it extends between the two bases at a perpendicular angle.

Let’s look at an example. Base 1 is 9 meters, base 2 is 7 meters. We know that because these two sides are parallel with each other. The height is 4 meters because it connects the two bases at a 90° angle. So I’m going to plug that into our formula here. One-half base 1 plus base 2, times the height which is 4. 9 plus 7 is 16. 16 divided by 2 is 8. 8 times 4 is 32. You’re going to keep the same units, meters, put the little 2 on top to show that it’s meters squared.

Sometimes you’ll have polygons with extra sides that you might not know what to do with. Well, if you can break that polygon up into smaller parts of shapes that you do know how to find the area for, you’ll be able to find the area of the whole thing. Here, we have a rectangle and two triangles. Find the area of the rectangle, the area of this triangle, and the area of this triangle. Add them all together and you have the area of the whole figure.

Let’s look at an example. If we add a line to this figure, we’ll break it up into two shapes – a rectangle and a trapezoid. The area of this rectangle is 8 times 4, which is 32, and the area of the trapezoid is the base plus the base, 12 plus 8 which is 20. 20 divided by 2 is 10, times the height -- 10 times 2 is 20. 32 plus 20 is 52. The units is feet squared.

If you have any suggestions for future lessons, email us at podcast@yourtutoronline.com. If you need more help with this or other topics, visit www.yourtutoronline.com to find the tutor, or just send an email to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our video podcast in iTunes to get the latest videos. I'll see you next time. Thanks for watching. Class dismissed.

Parallel Lines and Transversal

In this lesson we will learn about angle pairs in parallel lines. I cover corresponding, alternate interior, and same-side interior angles.

CORRECTION: I know, I know, I spelled "interirror" incorrectly in the video...twice. For the record it is "interior." I apologize, I'm a math guy and I am lost without spell check.

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transcript:

Welcome to Your Tutor Online video podcast. For today's lesson, we're going to look at parallel lines and angles that are formed when another line crosses them.

First, we need some definitions. Parallel lines are two lines which will never intersect or touch. They have the same slope. A transversal is a line that crosses two or more parallel lines. I numbered each of the angles formed by the transversal. We will use these numbers to refer to each angle. When we have parallel lines with a transversal, you can make conclusions about certain angle pairs. We will look at each of these pairs one at a time. The first angle pair is corresponding angles. It's easier if we look at each set of angles separately. Angles 1 through 4 is one set. And angles 5 through 8 is another.

Corresponding angles are in the same position in each group. Think of it in terms of which corner the angle is in. Angle 1 is in the top left corner of this set, so its corresponding angle is in the top left corner of the other set. So angle 1 and angle 5 are corresponding angles.

Corresponding angles are congruent. Meaning they have the same angle measure. For example, if you know that this angle is 37° and we know that its corresponding angle is also 37°. The angle we know about is in the top right corner, so the top right corner of the other group, (this one) is 37° also.

Next we'll look at alternate interior angles. There are two parts to this definition - alternate and interior. Let's look at interior part first. Interior means that the angle is in between the two parallel lines. In other words, inside this blue box I just drew, angles 3, 4, 5, and 6 are all interior angles.

Alternate means, to get to its pair, you need to cross the line and go to the other side. I'll start with angle 3. The alternate interior angle is 6. Because we crossed the line and go to the other side of the box. Alternate interior angles are also congruent.

For example, if you know this angle is 72°, then we know its alternate interior angle is also 72°. You crossed the line and go to the other side, so this angle is 72°.

The last angle pair we will look at in this lesson is same side interior angles. This is very similar to alternate interior angles, except they do not cross the line. The angles are still going to be in between two parallel lines, in other words, inside this blue box. Let's pick angle 4. The same side interior angle to angle 4 is angle 6 because it's the only angle you can get to without crossing any lines. Same side interior angles are supplementary which means they add up to 180°.

For example, if you know that this angle is 50°, then we can figure out the measure of its same side interior angle. This one is 130°, because 180 minus 50 is equal to 130. It's on the same side interior. That's the end of our lesson. If you need more help with this or other topics, visit www.yourtuturonline.com to find a tutor. yourtutoronline.com provides online tutoring services in a virtual classroom you just saw on this video. I'll see you next time. Thanks for watching. Class dismissed.

Box and Whiskers Plot

For our first video lesson, I thought we should do something visual. Let's try our hand at some graphing.

This lesson covers how to draw a box and whiskers plot given a set of data.

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transcript:

In this video I'm going to show you how to draw a box and whiskers plot. A box and whiskers plot helps to show you how a certain set of data is distributed among its points. I want to start with an example - 22, 23, 25, 27, 28 and 32. Check to see that the numbers are in order from least to greatest. And if they're not, you're going to have to rearrange them. For example we're lucky they are in order from least to greatest so we're ready for our next step.

We're looking for three specific points here. We're looking for our median, our lower quartile and upper quartile. The median just means the middle number. We'll find that first. To find the median, the middle number, let's count up all the numbers we have. One, two, three, four, five, six, we're going to divide that by two. Six divided by two is three. So we know the median is between the third and the fourth number. Right here.

When you have an even set of data, you have two middle numbers, 25 and 27 are both our middle number because there's two on either side of those. We need to find the average of those two middle numbers. The average of 25 and 27 is 26. If we had an odd set of numbers which we'll see in a second, we'd still divide however many numbers we have by two. And then round that number up.

For example, if we had one more number, say 34 in our set. We now have one, two, three, four, five, six, seven numbers. Seven divided by two is 3.5 - rounds up to four. So the fourth number would be the median in that case. One, two, three, four, 27.

And you can see three on the left of 27, three on the right of 27. It lets you know that 27 is your middle number. So let's just go ahead and get rid of 34 for now. We're going to find the lower quartile by finding the middle number of the first half of the numbers we have. That's why I do that line. It's a little helpful to separate the two halves of data. The middle number here is obviously 23. But you could still do the same processes before if you have a larger set of numbers.

Three numbers divided by two is 1.5, rounds up to two. So the second number is our lower quartile, 23. The upper quartile is found the same way as the lower quartile. Except you're going to look at the second half of data. In this case, 28 is the middle number.

All right. Now we have the basic information we need to draw our box and whiskers plot. And next we're actually going to draw the plot. To draw the box and whiskers plot, we want to draw a number line to represent data. The number line needs to be long enough to include the smallest number and biggest number.

We also want to make sure we draw the scale or else our box and whiskers plot isn't going to be an accurate representation of the data we have. I'm just going to go by 1's on this number line because we have such a small set of data.

But you could feel free to go by any scale you'd like which will help you represent the numbers as best as you can. As a refresher, our numbers were 22, 23, 24, 25, and so on all the way up to 32. We want to look back at our median, the lower quartile and the upper quartile and put a dot above the the number line at each of those places.

Our median was 26. So we have to put a dot up here at 26. Our lower quartile was 23, so another dot goes there. And the upper quartile was at 28. Twenty seven, 28. So a dot goes there. We have two more dots and those are just smallest number and the biggest number for the data. So 22 and 32.

Next we want to draw a vertical line that goes through our median, the lower quartile and the upper quartile. And this is going to be the basis of our box. So you're just going to connect those three lines in order to form a box. For the whiskers part, we're just going to draw a line out from the box to our biggest number and our smallest number. And that is your box and whiskers plot.

I hope this video was helpful. But if you need more help with this or other topics, visit www.yourtutoronline.com to find a tutor. Yourtutoronline.com provides online tutoring services in the virtual classroom you just saw on this video. Thanks for watching!