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Aris Law of Video Gaming Value for Money

Video Gaming Value for Money(VfM) according to Aris.

... more

Foivos Law of Video Gaming - f(Gt)

Video Gaming Value for Money(VfM) according to Foivos.

... more

Periodic compounding

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of ... 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

Pump energy (centrifugal pump)

Centrifugal pumps are a sub-class of dynamic axis-symmetric work-absorbing turbo-machinery.The rotational energy typically comes from an engine or electric ... more

Exponential decay

A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. If the decaying quantity, N(t), is the number of ... more

Pressure to depth (empirical formula - sea water)

In sea water, there is an approximate numerical equivalence between the change in pressure in decibars and the change in depth from the surface in meters. ... more

Quality Factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or ... 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
Subtraction

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
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Power gain (in nepers)

In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) to increase the power or amplitude of a signal from the input ... more

Worksheet 980

PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps

Using the Pythagorean theorem, for 3 different screen resolutions:

Diagonal Resolution - Pixels

Using the Diagonal Resolution from the previous formula we calculate the PPI for 3 corresponding screen sizes :

Pixels Per Inch (PPI)

Results:

10.1 inch tablet screen of resolution 1024×600 : 117.5PPI
21.5 inch PC monitor of 1080p resolution : 102.46PPI
27 inch PC monitor of 1440p resolution : 108.78PPI

Diagonal Resolution - Pixels

Pixels per inch (PPI) (or pixels per centimeter (PPCM)) is a measurement of the pixel density ... more

Pixels Per Inch (PPI)

Pixels per inch (PPI) (or pixels per centimeter (PPCM)) is a measurement of the pixel density ... more

Damping ratio (related to Quality factor)

Formula first contributed by:
trooper

In engineering, the damping ratio is a dimensionless measure describing how ... more

Properties of concrete - modulus of elasticity

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more

Eight foot pitch

The pipe organ is a musical instrument commonly used in churches or cathedrals that produces sound by driving pressurized air (called wind) through pipes ... more

Mean Time Between Failures - MTBF

Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation. ... more

Weighted arithmetic mean

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

Steering ratio

The steering ratio is the relationship between how far you turn a steering wheel and how far the actual wheels turn as a result. A higher steering ratio ... more

Optimum HDTV viewing distance

Optimum HDTV viewing distance is the distance that provides the viewer with the optimum immersive visual ... more

Total harmonic distortion

The total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ... more

Exact doubling time for an interest rate

For periodic compounding, the exact doubling time for an interest rate of r per period is a logarithmic formula, that can be used if we want to know the ... more

Arithmetic mean size - 1st moment

Calculates the arithmetic mean size (arithmetic method of moments) of the particles’ size distribution of a soil, in metric scale. In statistics, the ... more

Air-to-cloth ratio

The air-to-cloth ratio is the volumetric flow rate of air flowing through a dust collector’s inlet duct divided by the total cloth area in the ... more

Tortuosity

Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property. ... more

Anelastic Attenuation Factor

In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q (which is inversely proportional to attenuation ... more

Angular resolution

Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, ... 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 â‹… h ?

Multiplication

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

keywords:
ballistics

Multiplication

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

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

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