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Suction head coefficient

NPSH characterize the potential for cavitation. The suction head coefficient is a dimensionless measure of ... more

Hydraulic conductivity (as a function of water)

By definition, hydraulic conductivity is the ratio of velocity to hydraulic gradient indicating permeability of porous media.

Civil engineers ... more

Velocity of a falling object

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Fluid Thread Breakup - Linear Stability of Inviscid Liquids

Fluid thread breakup is the process by which a single mass of fluid breaks into several smaller fluid masses. The process is characterized by the ... more

Black-Scholes formula - value of a call option for a non-dividend-paying underlying stock

The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. ... more

Linear equation (Slope–intercept form)

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

... more

Time-domain reflectometry ( reflection coefficient-resistive load)

Time-domain reflectometry or TDR is a measurement technique used to determine the characteristics of electrical lines by ... more

Concentric tube heat exchanger - Required length

Concentric Tube (or Pipe) Heat Exchangers are used in a variety of industries for purposes such as material processing, food preparation, and ... 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/

Exchanged Heat in a Heat Exchanger

The logarithmic mean temperature difference (also known as log mean temperature difference or simply by its initialism LMTD) is ... more

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