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Heronian mean

The Heronian mean of two non-negative real numbers is a weighted mean of their arithmetic and geometric means.The weighted mean is similar to an ... more

Weighted geometric mean

In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the ... more

Superformula - Polar Equation

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Superformula - Parametric Equation for X Axis

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Superformula - Parametric Equation for Y Axis

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Fβ-score (in terms of Type I and type II errors)

In statistical analysis of binary classification, the F1 score (also F-score or F-measure) is a measure of a test’s accuracy. ( a type I error is ... more

Critical Hall parameter (fully ionized gas)

The electrothermal instability (also known as the ionization instability) is a magnetohydrodynamic (MHD) instability appearing in ... more

Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average. The harmonic mean is the reciprocal of the ... more

Mean angular motion - function of gravitational parameter

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... more

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