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Dividend discount model ( Gordon growth model)

The dividend discount model is a method of valuing a company’s stock price based on the theory that its stock is worth the sum of all of its future ... more

Distance to exsphere center from a vertex of a regular tetrahedron

The exsphere of a face of a regular tetrahedron is the sphere outside the tetrahedron which touches the face and the planes defined by extending the ... more

Standard Error

The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that ... more

Auger electron spectroscopy - electron impact cross-section

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more

Solute sieving coefficient

The selection of synthetic membranes for a targeted separation process is usually based on few requirements. Membranes have to provide enough mass transfer ... more

Sears–Haack body (cross sectional area)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume.The mathematical ... 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
Auger electron spectroscopy - Total yield

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more

Regular Icosahedron (Surface Area)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Nose cone Spherically blunted tangent ogive( X- coordinate of the tangency point )

The nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet) is ... more

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