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Degree of Financial Leverage

n finance, leverage is a general term for any technique to multiply gains and losses. Most often it involves buying more of an asset by using borrowed ... more

Speeds and feeds - feed rate

The phrase speeds and feeds or feeds and speeds refers to two separate velocities in machine tool practice, cutting speed and feed rate. They are often ... more

Gompertz–Makeham Law of Mortality

The Gompertz–Makeham law states that the human death rate is the sum of an age-independent component (the Makeham term, named after William Makeham) and an ... more

Worksheet 334

In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.

To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.

Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:

Pythagorean theorem (right triangle)

To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get

Cosine function

While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.

Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point

For x axis:

Cosine function

For y axis:

Sine function

The coordinates of the character on the rotated map will be (-1.109, 5.725)

Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Nernst Equation - total cell potential

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... more

Solar Cell - Fill Factor

Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more

Software equation

In the study of software project estimation, the Software Equation is a model with multiple variables based on assumptions of a specific distribution of ... more

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

Worksheet 292

What is the cost of running a 0.600-kW computer 6.00 h per day for 30.0 d if the cost of electricity is $0.120 per kW ⋅ h ?


where t is the total consumption time, td is the days of consumption and th the hours of consumption per day

Power-average (related to Work)

where P is Power consumption rate, E is the energy supplied by the electricity company and t is consumption time



where C is the total cost and CkW is the cost per kilowatt hour

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Compound lens' focal length

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more

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