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What is the formula for eccentricity?

In general, the term eccentric refers to something being off center. Mathematicians calculate eccentricity to determine how close the resemblance is between a conic section and a circle. A circle's eccentricity is always zero and with an ellipse, the eccentricity is less than one, but greater than zero. The eccentricity of two conic sections must be equal for them to be similar.

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What is the sin2(x) identity?

The double-angle identity of sin2(x) is sin2(x) = cos2(x) - cos(2x). That identity can also be expressed as 1 - 2sin2(x) = 2cos2(x) - 1. Using the half-angle identity, sin2(x) can be expressed as ½[1 – cos(2x)]. In math, the identity of a trigonometric function, such as sine, is defined as rule that is always true for the function for any value of x.

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How many zeros are in one hundred million?

One thousand has three zeros, 10,000 has four (one for the 10 in "ten thousand" and three for the thousand) and 100,000 has five (two for the hundred in "one hundred thousand" and three for the thousand). Ten million has seven zeros. One billion is actually 1,000 millions and has nine zeros. One trillion is a thousand billion and contains 12 zeros. The number called a Googol has 100 zeros, and another number called a Googolplex is written as a one with a Googol of zeros after it.

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What are some scientific notation word problem examples?

Other scientific notation word problems include:\nThe speed of light is 3 x 10^8 meters/second. If the sun is 1.5x 10^11 meters from earth, how many seconds does it take light to reach the earth?\nThe half-life of Uranium 234 is 2.5 x 10^5 years and the half-life of Plutonium is 8.0 x 10^7 years. How many times greater is the half-life of Plutonium than Uranium 234?

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How is 3x + 2y = 8 solved?

These types of equations are most commonly used to find the slope and the y-intercept of a problem. To find these, the equation must always be transformed into slope intercept form. The slope of the line is always the number that is connected with x, while the y-intercept is always the number that is on its own in the equation.In the 3x + 2y = 8 equation, 8 is the y-intercept. The y-intercept is the point of the slope or the line where the line goes through the y-axis. The line will always pass through the y-axis only once in these types of equations because the line is constantly evolving and..

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What are some examples of reliability and validity in statistics?

Conclusion validity describes whether the variables being studied are actually related. A study might not have good conclusion validity if the researcher has a very small sample size because the relationship might be missed due to individual differences.\nInternal validity considers whether the study identifies a cause-effect relationship. If a group of researchers want to determine whether a tutorial session has an impact on grades, they need to confirm that the effect is not because the students who participate are more motivated to work or put in extra time rather than the tutorial itself.\..

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How do you find the surface area of a cube?

The surface area of any polyhedron is found by taking the area of each face and adding them all together. A cube is a special kind of rectangular prism in which each face is a square, meaning that every face has the same area. The cube is the only regular hexahedron, or six-sided regular polyhedron.

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What is the vector equation of a line?

Vectors provide a simple way to write down an equation to determine the position vector of any point on a given straight line. In order to write down the vector equation of any straight line, two known values must be present.\nIf the position vector of a specific point that lies on the line and a vector that gives the direction of the line, called a direction vector, are both present, then the position vector referred to as "r" of any general point P on the line is given by the equation: r = a + tb.\nFor example, suppose that Line A has the equation r = i + 3k + t(2i + j + k), so that line A i..

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Who invented the unit circle?

The unit circle is a circle with a radius of 1 and a diameter of 2. It is typically used in trigonometry and calculus. The origin of the unit circle is (0,0), with each zero denoting the values of "x" and "y." The unit circle is commonly learned by high school students in introductory calculus classes, as it is an important element in learning advanced calculus and trigonometry in a college setting.

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How many laps around a track is a mile?

One mile is equivalent to 1,609 meters, which is equal to 5,280 feet. The majority of outdoor tracks are built such that the inner lane (lane 1) is exactly 400 meters, which is equal to 1,312.3 feet. Track lanes have a standard width of 1.22 meters, so for every lane out from the center, the lap length increases by approximately 7.67 meters, or 25 feet.\nOn nonstandard tracks, some work must be done to determine the number of laps in a mile. Walk one circuit of the track, and count the number of paces. Multiply stride length, which is approximately 2.25 feet, by the number of paces to calculat..

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