Second Period Math Applications Flashcards
What is BEDMAS?
The standard sequence of mathematical operations. B-rackets E-xponents D-ivision } From left to right M-ultiplication / A-ddition } From left to right S-ubtraction /
What is accomplished when transposing an equation?
Change in the position of “parts” of the equation, while maintaining the equality.
What is an equation?
It is a statement of equality between two quantities.
When transposing, could you only apply a mathematical procedure to one side of the equation and still maintain equality?
No.
You must always apply the same procedure to both sides to maintain equality.
What is meant by squaring a number?
It is a process of multiplying the number by itself.
e.g. 9^2=9x9.
What is meant by square rooting a number?
It is the opposite process of squaring a number. It can be represented as SQRT(x)=x^0.5.
Why is scientific notation adopted en masse?
Because it is a simple way to express either a very large or very small number.
What is scientific notation?
It is a method of describing a number through powers of 10.
If a number has a scientific notation of a POSITIVE power of 10, which way will the decimal point move, when converting to a whole/decimal number?
To the right.
A positive power results in a larger number than 1, and a negative power results in a smaller number than 1.
What is meant by engineering notation?
A method of describing a number by powers of 10 which are divisible by 3.
e.g. 10^3, 10^6, 10^9, etc…
What multiplication factor is applied when given an SI prefix of Giga(G)?
It is 10^9 or 1 billion.
What are the SI prefixes (in order) associated with multiplication factors from 1 Trillionth, to 1 Billion?
Pico (p) 10^-12 = 1 Trillionth Nano (n) 10^-9 = 1 Billionth Micro (mu) 10^-6 = 1 Millionth Milli (m) 10^-3 = 1 Thousandth Centi (c) 10^-2 = 1 Hundredth Deci (d) 10^-1 = 1 Tenth Deka (da) 10^1 = Ten Hecto (h) 10^2 = 1 Hundred Kilo (k) 10^3 = 1 Thousand Mega (M) 10^6 = 1 Million Giga (G) 10^9 = 1 Billion
What symbol is commonly used to express an angle?
Theta.
What is the sum of all angles in any triangle?
180 degrees.
What is a “right triangle”?
One which contains a right angle (90 degrees), usually represented by a little square.
What is the vertical side of a right triangle called?
The altitude.
The longest side of a right triangle has a name, what is it?
The hypotenuse.
What does the Pythagorean Theorem state?
The hypotenuse squared is the sum of the base squared and the altitude squared.
There are three major trigonometric functions, what are these?
Sine (sin)
Cosine (cos)
Tangent (tan).
How does the Sine function relate the sides of a triangle if applied to one of the (non right) angles?
It equals a ratio between the side opposite from the angle and the hypotenuse.
How does the Cosine function relate the sides of a triangle if applied to one of the (non right) angles?
It equals a ratio between the side adjacent to the angle and the hypotenuse.
How does the Tangent function relate the sides of a triangle if applied to one of the (non right) angles?
It equals a ratio between the side opposite from the angle and the side adjacent to the angle.
If you are given the values of the sides of a triangle and are asked to find the angles, what functions must be used?
Inverse trigonometric functions, such as:
Arcsine (sin^-1)
Arccosine (cos^-1)
Arctangent (tan^-1)
What is a phasor? What does it represent?
A graphical representation of a complex number used to analyze a circuit.
Voltage or current and a time relationship between other phasors.
The tail of a phasor must always be fixed to the _____.
Origin.
What is a Cartesian plane?
A horizontal vertical axis crossing at a point called the origin. Right and up from the origin are positive values, left and down will be negative values.
What does the length of a phasor represent?
The RMS value of current or voltage.
Are phasors always drawn to a scale?
Yes, this makes it easy to see the relationships.
What is represented by the angle between phasors?
A time relationship, measured in electrical degrees.
What kind of arrowheads would you use if representing current with a phasor?
Closed arrowheads.
You would use open arrowheads for Voltage.
In a phasor diagram, what is considered to be the reference axis?
The positive horizontal axis (To the right from the origin).
Phasors can be expressed in two forms, what are these?
Polar(magnitude @ angle),
Rectangular(Horizontal component, Vertical component)
When adding two or more phasors together it is imperative to first convert them to _________ form.
Rectangular.
This is so we can add components easily.
What method is greatly efficient for adding two or more phasors?
Using an H/V chart.
What is a ratio?
A comparison between two like quantities.
e.g. 5 kg of salt : 10 kg of salt => 1:2.
A ratio must always have the same units.
Would a ratio be the same, regardless of the order it was represented in?
No, it is essential to use the correct order.
10:5 is not the same as 5:10.
What is a proportion?
It is a statement which says two ratios are equal.
What is the difference between a direct and indirect proportion?
A direct proportion has related quantities, either both on the top or both on the bottom.
(e.g. small heater/large heater = small ampacity/large ampacity)
Whereas an indirect proportion will have related quantities on opposite sides of the divisor line.
(e.g. small crew/large crew = small hours/large hours)
[small crew will be large hours, see how they are on opposite sides of the divisor?]
