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Formulas/Concepts > Day 3 > Flashcards

Day 3 Flashcards

1
Q

Discriminant

A

B²-4AC

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2
Q

Sum of roots of quadratic formula

A

-B/A

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3
Q

Pdt of roots of quadratic formula

A

C/A

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4
Q

rth term of (x+y)^n

A

nCr-1 (x)^n-r+1 (y)^r-1

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5
Q

Term involving y^r in (x+y)^n

A

nCr (x)^n-r y^r

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6
Q

Coefficient of any term

A

(C of past term)(exponent of X) ÷ exponent y + 1

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7
Q

Sum of coefficients

A

Subs 1 to variables
If with k, -(k)^n

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8
Q

3 variables expansion

A

n!/a!b!c! (x^a y^b z^c)

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9
Q

nth term of arithmetic progression

A

a1 + (n-1)d

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10
Q

nth term of geometric progression

A

g1 r^(n-1)

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11
Q

Sum of infinity numerical progression

A

g1/(1-r)

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12
Q

Reference angle

A

sin^-1 (Abs (sin theta))

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13
Q

Radius of right triangle

A

(a+b-c) / 2

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14
Q

1/cos theta

A

Sec theta

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15
Q

1/ sin theta

A

Csc theta

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16
Q

Sine law

A

a/sin A = b/sin B = c/sin C

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17
Q

Cosine law

A

c² = a² + b² -2ab cosC

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18
Q

Area of right triangle

A

1/2 bh

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19
Q

Area of triangle SAS

A

1/2 ab sin C

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20
Q

Area of triangle SSS

A

sqrt ((S) (S-A) (S-B) (S-C))

S = (a+b+c) / 2

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21
Q

Area of interperpendicular bisector

A

abc/4r

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22
Q

Area of interperpendicular angle bisector

A

rs

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23
Q

Area of triangle escribed in a circle

A

ra(s-a)
rb(s-b)
rc(s-c)

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24
Q

Area of triangles AAS

A

(a² sinB sinC) / 2 sinA

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25
Q

Median of triangle

A

½ sqrt (2 (adj1² + adj2²) - op²)

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26
Q

Perimeter or circumference of circle

A

2 pi r

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27
Q

Area of circle

A

pi r²

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28
Q

Arc length

A

r x theta rad

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29
Q

Area of sector

A

1/2 r² theta rad

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30
Q

Perimeter of sector

A

2r + r(theta)

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31
Q

Area of segment

A

1/2 r² (2 theta rad - sin 2 theta)

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32
Q

Sum and theta of interior angles

A

S = (n-2)(180°)
Theta = (n-2)(180)/n

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33
Q

Sum and theta of exterior angles

A

S= 360
Theta = 360/n

34
Q

Diagonals

A

d = (n/2)(n-3) = nC2-n

35
Q

Area (with R) of polygon

A

1/2 nR² sin (360°/n)

36
Q

Perimeter and Area of semi-circle

A

P = 1/2 pi r² + 2r
A = 1/2 pi r²

37
Q

Area of trapezoid

A

1/2 (b1 + b2)(h)

38
Q

Area of rhombus

A

xh
x² sin theta
1/2 (d1)(d2)

39
Q

Area of parallelogram

A

bh
ab sin theta
1/2 (d1)(d2) sin theta

40
Q

Area of trapezium/ quadrilateral

A

sqrt (s-a)(s-b)(s-c)(s-d) - abcd cos² theta

Theta = (A+C)/2 or (B+D)/2

S = (a+b+c+d) / 2

41
Q

Area of cyclic quadrilateral

A

sqrt (s-a)(s-b)(s-c)(s-d)

42
Q

Ptolemy’s theorem

A

d1d2 = ac + bd

43
Q

Area of circle inscribed in quadrilateral

A

sqrt abcd
rs

44
Q

Area of equilateral triangle

A

1/2 x² sin 60

45
Q

Axial stress

A

σ = P/A

46
Q

Single or Double shear stress

A

σ = P/na

n = 2 (single) or 3 (double)

47
Q

Punching shear

A

σ = P/ (pi)(d)(t)

48
Q

ksi

A

lbs/in² x103

49
Q

Tangential stress

A

σt = PiD / 2t

50
Q

Longitudinal stress

A

σL = PiD/4t

2 long = tangential

51
Q

Thermal stress

A

σT = E (alpha) delta T

σyield = σ - σT

52
Q

Max shearing stress/ Torsional shearing stress

A

Tmax = Tr/J

53
Q

Polar moment of inertia of solid shaft

A

J = pi/32 D⁴

54
Q

Polar moment of inertia of hollow shaft

A

J = pi/32 (Do⁴ - Di⁴)

55
Q

Angle of twist

A

Theta rad = TL/JG

56
Q

Power through shaft

A

P = Tw = 2 pi f T

57
Q

Hooke’s Law

A

σ = E epsilon

58
Q

Factor of Safety

A

FoS = σu / σa

59
Q

Elongation

A

PL/AE

60
Q

Elongation due to its weight

A

rho g L² / 2E

mgL / 2AE

61
Q

Area of star

A

1.123r^2

62
Q

Simple Interest

A

I = Pin

F = P(1+in)

63
Q

Kinds of year

A

Banker’s year - 360
Ordinary year - 365
Leap year - 366

64
Q

Rate of discount

A

d = r/ r+1
d = discounted deduction/ original price

65
Q

Nominal Rate of Interest

A

r = im

66
Q

Effective Rate of Interest

A

r
ERI = ( 1 + — ) ^m - 1
m

67
Q

Compound Interest

A

F = P(1+i) ^n

    P( 1+ r    ) ^mt F =            —
             m
68
Q

Continuously Compounding

A

F = Pe^rt

ERI = e^r - 1

69
Q

Perpetuity

A

P = A/i

70
Q

Present amount gradients

A

P = Σ (xý (1+i)^-x ,1,n)

71
Q

Capitalized Cost

A

A P
CC = FC + — + —————
i (1+i)^n -1

72
Q

Book Value

A

BVn = Co-Dn

73
Q

Annual depreciation

A

dn = BVn-1 - BVn

74
Q

Types of depreciation

A

Straight Line - Mode 3-2

Declining Balance/ const. % - Mode 3-6

Sum of Year’s Digit - Mode 3-3

75
Q

Annual depreciation of sinking fund

A

(Co-SV) i
d = —————
(1+i)^n -1

76
Q

Total depreciation of sinking fund

A

(1+i)^n - 1
Dn = d ( ————— )
i

77
Q

Bonds

A

Fr
P = —— (1- (1+i)^-n + C (1+i)^-n )
i

78
Q

Altering of transverse waves so that vibration occurs in one direction perpendicular to the direction of propagation

A

Polarization

79
Q

Formation of a rainbow occurs as a result of

A

Dispersion

80
Q

Moment of inertia is

A

Tensor

Formulas/Concepts (3 decks)

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