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Equation of exchange ( in transactions form)

The quantity theory of money, says that any change in the amount of money in a system will change the price level. The equation of exchange is the ... more

Bose–Einstein statistics ( εi > μ)

In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting ... more

Weighted average cost of capital

The weighted average cost of capital is the rate that a company is expected to pay on average to all its security holders to finance its assets. It is the ... more

Preload (cardiac)

Preload is described as the stretching of a single cardiac myocyte immediately prior to contraction and is, therefore, related to the sarcomere length. ... more

Near branch of a hyperbola in polar coordinates with respect to a focal point

In mathematics, a hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution ... more

Machinability Index

The term machinability refers to the ease with which a metal can be cut (machined) permitting the removal of the material with a satisfactory finish at low ... more

Beta distribution (mean)

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized ... more

Corner sight distance

Corner sight distance (CSD) is the road alignment specification which provides a substantially clear line of sight so that the ... 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
Menzerath's Law

Menzerath’s law, or Menzerath–Altmann law (named after Paul Menzerath and Gabriel Altmann), is a linguistic law according to which the increase of a ... more

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