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A detailed tutorial on how to identify disconnected graphs. Step by step tutorial including several examples of disconnected graphs for reference.

A disconnected graph is a graph where not every single vertex is connected to all other vertices. Typically, graphs will have paths from all vertices, but if there is not a direct path from each and every vertex, then it is considered to be a disconnected graph. Some common shapes that are seen that are disconnected graphs are stars, rectangles, and hexagons. The opposite of a disconnected graph is a connected graph.

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A detailed tutorial on how to identify connected graphs. Step by step tutorial including several examples of connected graphs for reference.

A connected graph is a graph where every single vertex is connected to every other vertex. This does not mean to simply have a clear path from one vertex to another – it means there needs to be a direct path, or an edge, between two vertices. A triangle is a commonly seen shape that is a connected graph. The opposite of a connected graph is a disconnected graph.

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A detailed tutorial on what aspect ratio is. Step by step tutorial including several examples of how to find the aspect ratio for reference.

The aspect ratio can only be used when referring to a shape, typically a square type of shape, such as a square, rhombus, rectangle, or parallelogram. The aspect ratio is used very often for describing measurements. It is the ratio of the longer dimension to the shorter dimension – that is, the length to the width. In a 3D shape, the depth – which is the second measurement of width – is added to the end of this measurement.

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A detailed tutorial on what composite figures are. Step by step tutorial including several examples of how to identify composite figures for reference.

A composite figure is any figure that can be split into more than one shape. Hardly any regular shapes are considered to be composite shapes. The only one is a regular trapezoid – it can be split into three shapes, two triangles and a rectangle. You could technically consider a rectangle to be a composite figure – you can split it into squares or smaller rectangles – but since it doesn’t need to be split into different shapes to solve for area, then it is not considered a composite figure.

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A detailed tutorial on how to use area models. Step by step tutorial including several examples of how to use area models for reference.

An area model is used to help mutliply and divide integers. It is called an area model because of the way it is set up – it looks like you are solving for area when the model is used correctly. These models are typically composed of many small one by one squares, although different sizes can be used in order to make mulitplication and division earlier. Area models are used to provide a visual representation of the multiplication and division algorithms.

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A detailed tutorial on how to use algebra tiles. Step by step tutorial including several examples of how to use algebra tiles for reference.

Algebra tiles are a visual expression of polynomials and polynomial equations. Each tile is meant to represent a different polynomial. A large square tile represents the squared variable, a smaller square tile represents a single number, with no variable, and a rectangle represents the single variable. The tiles are red and green. Green represents positive monomials, and red represents negative monomials. Tiles can be combined to create equations, or the same tiles can be combined to express the coefficient. Addition and subtraction can be performed by adding and removing tiles.

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A detailed tutorial on using the midpoint rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the midpoint rule for reference.

The midpoint rule, also known as the rectangle method, is the easiest way of solving error bounds. The region under the graph of a function is sectioned off into rectangles of equal width. You then must find the areas of these rectangles. Then all the areas are added together to find the approximation of the integral. The formula for this is:

The least complicated form of the midpoint rule is expressed as:

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Description

This video gives a specific example for how to find the surface area of a pyramid, and also provides one of the basic formulas. The problem is completely worked through in the video to raise students understanding of the subject matter.

Overview

The surface area is the area of each side, or face, of the shape added together. For a pyramid, this typically means the rectangle or square that is the base, and the four triangles that make up the sides of the pyramid. There are more complicated versions of a pyramid, ones that have different shapes on the bottom and a different number of triangles, but the most common shape to see is a simple pyramid. First, solve for the areas of the triangles. The area formula for a triangle is A = (1/2) * b * h. If the shape on the bottom is a square, all the triangles have the same area and you will only need to multiply your answer by 4. If the shape is a rectangle or a more complicated shape, it is entirely possible that the triangles have different areas, and you may want to solve for area more than once. Then you need to find the area of the base. Depending on what your base is there will be a different area formula. Once you have all the areas, add them together to get the surface area of your pyramid.

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Description

This video explains how to find the volume of a cylinder. It shows the different parts of a cylinder and says what parts need to be used to find the surface area and why. Examples are provided in the video.

Overview

The surface area is the area of each side, or face, of the shape added together. A cylinder as three faces – the base, which has two faces of equal area, and the middle section of the cylinder, which is actually a rectangle  that has been wrapped into a round shape. However, because not all the dimensions of the rectangle are typically given in a manner easy to understand, there is a formula that can be used to solve for the surface area of a cylinder.

SA = 2 * (pi * r^2) + (2 * pi * r) * h

The first part of the formula represents the area of the two circles that form the base. The second part of the formula represents the circumference of the base (which is equal to the width of the rectangle) and the height of the cylinder (which represents the length of the rectangle).

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Description

This video displays how to find the surface area of a rectangular prism. The different parts of a rectangular prism are explained in detail. One sample problem is worked through in the video to show how to correctly apply the formula.

Overview

The surface area is the area of each side, or face, of the shape added together. Rectangular prisms have 6 sides, which consist of 3 pairs. This makes solving for a rectangular prism’s surface area a bit easier. In order to solve for the surface area, you need to solve for the area of each face seperately, first. All the faces of a rectangular prism are rectangles, so the area can be found using this formula: A = l * w. You only have to solve for this three times – the matching face (found exactly opposite of the one you solved for) will have the same area, so just multiply your result by 2. After doing this three times, add them all together. Your result is the surface area.