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What is an application of vector analysis?

If a plane is trying to fly to an airstrip 50 miles north of its current location, and it is travelling at 100 mph, a person might assume the plane would arrive in 30 minutes if the pilot pointed the plane due north. But if the plane had a prevailing wind from the west blowing at 10 miles per hour, it would end up 5 miles to the east of the airport, as the wind has blown the airplane off course.\nThink of the plane's speed and direction as vector A, and the wind's speed and direction as vector B. Add them head to foot, then draw a line from the plane's starting point to the end ..

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Who invented percentages?

The word percent comes from the Latin phrase per centum, and it means "for each hundred." According to Cut the Knot, in 17th century Europe, the symbol o o was often used as an abbreviation for percent. This ancient symbol has evolved into the % symbol, which is commonly used today. For instance, 1 percent can be written as 1%, and it is the same as the fraction 1/100. Ten percent can be written as 10%, which is the same as the fraction 10/100. Likewise, a penny is 1 percent of a dollar, and a dime is 10 percent of a dollar.

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What is the triangle angle bisector theorem?

To give the result of the angle bisector theorem more precisely, it is necessary to label the parts of a triangle. If one calls the points of a triangle x, y and z, one can say that a line bisects the angle with its vertex at point x and that this line goes through the opposite side of the triangle at point w. The line segments on the triangle are named according to their endpoints, so the side of the triangle between points x and y is termed segment XY, for example.\nAccording to the angle bisector theorem, the length of segment YW divided by the length of segment WZ is equal to the length of..

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What is scientific sampling?

Simple random sampling is a term used to describe the method of selecting the sample to be examined. The sample has the same probability as the rest of the data to be selected.\nScientific sampling is not a reliable source when a high level of accuracy is desired. An advantage of scientific sampling is that it is cost effective to gain an overall perspective of a large group of data.

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What are some examples of the reflective property of equality?

There are more equality properties for real numbers, such as symmetric, transitive, addition, division, substitution and distributive properties. The transitive, reflective and symmetric properties give equivalence relations between real numbers. The other equality properties are useful for solving equations with real numbers. For example, the substitution property states that if a = b, then 'b' can be substituted for a in an expression. This is a useful property when solving a problem, such as if x = 3, then solve for x + 25 = ?. Through the substitution property, the answer is 28..

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Does a rectangle have rotational symmetry?

The number of ways a shape can be rotated and yield a shape that exactly resembles the original shape is known as the order of rotational symmetry. A standard six-pointed snowflake shape has rotational symmetry of order six. A regular hexagon also features rotational symmetry of order six, as the shape may be rotated in 60-degree increments six times before undergoing a complete turn.

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What is the identity function in math?

Casting the identity function as a linear function of the form y = mx + b, where m = 1 and b = 0 for all real numbers, more properties of the identity function become easier to see. All linear functions are combinations of the identity function and two constant functions. For example, the linear function y = 3x + 2 breaks down into the identity function multiplied by the constant function y = 3, then added to the constant function y = 2. Conversely, the identity function is a special case of all linear functions.\nAlthough there are not many practical real-world applications of the identity fu..

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What is the derivative of cross product?

The cross product formula is commonly used to find a vector that is orthogonal to two other vectors, both of which have been computed into the formula. It is also used to find areas of triangles or parallelograms that are formed by the initial two vectors as they join together.\nIf the vectors have the same direction or one has a length equal to zero, the cross product is zero. The magnitude of the product equals the area of a parallelogram with the vectors for sides. For perpendicular vectors, this is a rectangle, and the magnitude of the product is the product of their lengths. The cross pro..

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What is MyMathLab?

MyMathLab is entirely browser based. Although MML does not require downloading, students must purchase an access code to use it. As of 2015, classes that use MML are very standardized. Students anywhere in the country that use MML receive the same resources and materials for a given math subject. Some of these materials include tutorial videos and online quizzes. MML also provides grades for students at the completion of the course.

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How do you calculate jelly beans in a jar?

Another way to estimate the number of jellybeans in a jar is to make a guess based on the volume of the jar. There are approximately 930 jellybeans in a gallon. Look at the jar to estimate its volume, and make a guess accordingly. For instance, if the jar is about the size of a quart, there would be approximately 233 jellybeans in the jar. This is because a quart is 1/4 gallon, and 930 jellybeans divided by four is roughly 233.\nJellybeans can be irregularly shaped, and therefore, they may not fill the jar tightly. Rather, there may be air holes or gaps in the jar. If estimating the number of ..

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