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Beta distribution (Harmonic mean)

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized ... 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
Drag force on a rigid cylinder when velocity is perpendicular to its axis(Slender-body theory)

n fluid dynamics and electrostatics, slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an ... more

Drag force on a rigid cylinder when velocity is parallel to its axis(Slender-body theory)

In fluid dynamics and electrostatics, slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an ... more

Binomial distribution

Binomial distribution, with parameters n and p, is the discrete probability distribution of the number of successes in a sequence of n independent yes/no ... more

Right triangle altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more

Logit function

The logit function is the inverse of the sigmoidal “logistic” function or logistic transform used in mathematics, especially in statistics. ... more

Reynolds number - Flow in a pipe with mass flow rate

For flow in a pipe or tube, the Reynolds number is generally defined as presented here.

For shapes such as squares, rectangular or annular ducts ... more

Specificity ( true negative rate)

For classification tasks, the terms true positives, true negatives, false positives, and false negatives compare the results of the classifier under test ... more

False Discovery Rate

For classification tasks, the terms true positives, true negatives, false positives, and false negatives compare the results of the classifier under test ... more

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