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What are irrational numbers?

e, π, sqrt of 2

What are the equivalent values of i¹, i², i³, i⁴?

i, -1, -i, 1

Example of natural numbers

1, 2, 3, 4

Zero is included in whole numbers.

True

Numbers which can be expressed as a quotient of two numbers or a fraction.

rational numbers

The smallest natural number that have two natural numbers as a factor.

Least Common Multiple

The least common multiple of two or more denominators

Least Common Denominator

The largest number which is a factor of each of the given numbers.

Greatest Common Factor

The sum of roots X1+X2 is equal to

-B/A

The product of roots x1•x2 is equal to

C/A

If B²-4AC=0, the roots are

equal

B²-4AC>0, the roots are

real and unequal

B²-4AC<0, the roots are

imaginary

1 US gal is equal to

3.785 liters

1 liter is equal to

1.06 quarts

1 ton is equal to

2000 lbs

1 lb is equal to

16 oz

1 mile is equal to

5280 feet

All circles having the same center but with unequal radii are called

Concentric circles

The plane rectangular coordinate system is divided into four parts which are known as

quadrants

An angular unit equivalent to 1/400 of the circumference of a circle is called

Grad

1 is equal to

e^(2kπi)

cosh (jπ/4)

cos (π/4)

tan² (j0.78)

j tanh (0.78)²

Using power series expansion about 0, find cos x by differentiating from sin x.

1-(x²/2!)+(x⁴/4!)-(x⁶/6!)+...

Using power series expansion, find sinh x

x+(x³/3!)+(x⁵/5!)+(x⁷/7!)+...

Using power series expansion, find e^x

1+x+(x²/2!)+(x³/3!)+...

A periodic function has zero average value over a cycle and it's Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?

even quarter

cosh (x), sinh (x), tanh (x) is equal to

cos (ix), -isin (ix), -itan (ix)

cosh (ix), sinh (ix), tanh (ix) is equal to

cos (x), isin (x), itan (x)

A line is perpendicular to the y-axis has a slope equal to:

zero

It represents the distance of a point from the y-axis

abscissa

The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal is

parabola

A conic section whose eccentricity is equal to one (1) is known as:

parabola

The ____ of a parabola is the line which passes through the focus and is perpendicular to the directrix.

axis

The ____ of a parabola is the line which passes through the focus and is parallel to the directrix.

latus rectum

What curve is described by the equation y²+4y+x-1=0

parabola

What is the length of the latus rectum of the parabola y=4px²

The locus of a point which moves so that the sum of its distances between two fixed points is constant is called

ellipse

A conic section whose eccentricity is less than one (1) is known as:

ellipse

What curve is described by the equation 4x²-y²+8x+4y=15

hyperbola

In conic section, if the eccentricity is greater than one (1), the locus is

hyperbola

If the general equation of the conic is Ax²+Bxy+Cy²+Dx+Ey+F=0. If B^2-4AC>0, the equation describes a

hyperbola

A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as

inflection point

In the equation y=-x²+x+1, where is the curve facing?

downward

A given function f (t) can be represented by a Fourier series if it

all of the above

In a Fourier series expansion of a periodic function, the coefficient a0 represents its

DC value

If in the Fourier series of a periodic function, the coefficient a0, is zero, it means that the function has

any of the above

The axis of the hyperbola through its foci is known as

transverse axis

Describe the locus represented by |z+2i|+|z-2i|=6

ellipse

The product of the slopes of any two straight lines is negative 1, one of the lines are said to be

perpendicular

A normal to a given plane is

perpendicular to the plane

In the polar coordinate system, the distance from a point to the pole is

radius vector

A periodic function f (t) is said to possess odd quarter-wave symmetry if

both (b) and (c).

If the average value of a periodic function over one period is zero and it consists of only odd harmonics then it must be possessing _____ symmetry.

half-wave

If in the Fourier series of a periodic function, the coefficient a0 = 0 and an = 0, then it must be having ____ symmetry.

either (a) or (b).

In the case of a periodic function possessing half-wave symmetry, which Fourier coefficient is zero?

A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function.

even quarter-wave

Which of the following periodic function possesses even symmetry?

cos 3t

If the Fourier coefficient bn, of a periodic function is zero, then it must possess ______ symmetry.

either (a) and (b).

A complex voltage waveform is given by V = 120 sin wt + 36(3wt + pi/2)+12 sin (5wt + pi). It has a time period of T seconds. The percentage fifth harmonic contents in the waveform is

In the waveform of V = 120 sin wt + 36(3wt + pi/2)+12 sin (5wt + pi), the phase displacement of the third harmonic represents a time interval of _____ seconds.

T/12

When the negative half-cycle of a complex waveform is reversed, it becomes identical to its positive half-cycle. This feature indicates that the complex waveform is composed of

both (a) and (b)

A periodic waveform possessing half-wave symmetry has no

even harmonics

The Fourier series of a wave form possessing .even quarter-wave symmetry has only

odd cosine terms

The Fourier series of a waveform possessing odd quarter-wave symmetry contains only

odd sine terms

Give example of non-integers

1/2, 0.10 , 3/5

Classify 1 (one) in number system

neither prime nor composite

Classify 2 in number system

prime and even

Classify zero in number system

whole number and not a natural number

Describe the property of (a+b)+c=c+(a+b)

Commutative

Which of the following refers to a three dimensional figure having a polygon as its base and triangles for the rest of its faces meeting at a point

pyramid

Which of the following refers to an angle having a measure greater than 90° but less than 180°

obtuse angle

Which of the following refers to a quadrilateral with opposite sides parallel and each pairs of opposite sides and angles is congruent

parallelogram

1 yard is equal to

36 inches

1 dime is equal to

10 centavos

1 cup is equal to

8 oz

orthogonal trajectories is equal to

perpendicular slope

the equation of a limacon is

r = a + b cos theta

find the area enclosed by the lemniscate of bernoulli r² = a² cos 2 theta

a²

The mathematical expression (1+I)^n is referred to

compound amount factor

what is the factor name for the formula (1+I)^-n

single payment present worth

when using net present worth calculations to compare two objects, which of the following could invalidate the calculation

evaluating over a different period of time

which of the following corresponds to the meaning of annuity

a series of uniform amounts over a period of time

what is a borrower of a particular loan almost always required to do during repayment?

repay the loan over over-agreed upon amount of time

an interest earning fund in which equal deposits are made at equal intervals of time for the purpose of gradually accumulating a specific sum of money required at some future date

sinking fund

what is the formula for a straight line depreciation rate?

100 percent-percent net savage value/ estimated service life

it is an amount which a willing buyer will pay to a willing seller for the property where each has equal advantage and is under no compulsion to buy or sell

market value

what is "work in process" classified as?

an asset

which of the following does not affect owner's equity?

license to start operation

what is another term for acid test ratio

quick ratio

the ability to convert assets to cash quickly is known as

liquidity

In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a

latus rectum

what is the ratio of the sides of the triangle if the product of the sines of its angle is a maximum?

1:1:1

which of the following is a disadvantage of using the sample range to measure of spread or dispersion?

the largest or the smallest observation (or both) may be a mistake or an outlier

ESAS Lesson Objectives 1

ESAS Lesson Objectives 1

ESAS Lesson Objectives 2

ESAS Lesson Objectives 2

ESAS Lesson Objectives 3

ESAS Lesson Objectives 3

Other Terms for ESAS

Other Terms for ESAS

Hazel Lynn Ramos · 99問 · 2年前

ESAS Matlab

ESAS Matlab

99問 • 2年前

ESAS 200 objectives 1

ESAS 200 objectives 1

ESAS 200 objectives 2

ESAS 200 objectives 2

ESAS 350 objectives 1

ESAS 350 objectives 1

ESAS 350 objectives 2

ESAS 350 objectives 2

Hazel Lynn Ramos · 44問 · 2年前

ESAS 350 objectives 3

ESAS 350 objectives 3

44問 • 2年前

EE Lesson Objectives 1

EE Lesson Objectives 1

EE Lesson Objectives 2

EE Lesson Objectives 2

EE Lesson Objectives 3

EE Lesson Objectives 3

Hazel Lynn Ramos · 100問 · 1年前

EE Terms Additional

EE Terms Additional

100問 • 1年前