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CHE BOARD EXAM > DAY 3 FORMULA > Flashcards

DAY 3 FORMULA Flashcards

1
Q

measure of an interior angle of a regular polygon

A

180 (n-2) /2

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2
Q

number of diagonals of a polygon

A

n(n-3)/2 or nC2-n

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3
Q

apothem

A

angle = 180/n

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4
Q

perimeter of regular polygon

A

P=nx

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5
Q

Area of a regular polygon

A

Apolygon = n x Atriangle
Atriangle = (1/2) x ax

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6
Q

area of trapezoid

A

[ (b1+b2) x h ] / 2

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7
Q

angle between two lines

A

tan@ = abs |(m2-m1)/(1+m2m1)|

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8
Q

binomial theorem expansion

A

nCr (a)^n-r (b)^r where r=nth term - 1

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9
Q

clock problem formula

A

angle = |30h - 5.5m|
x = (60/11) (initial + hr spaces)

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10
Q

workers & working time

A

constant = # workers x total time / # of units (1 default)

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11
Q

upstream & downstream

A

downstream:
(rboat + rcurrent) = d/t down

upstream
(rboat - rcurrent) = d/t up

td + tu = 1

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12
Q

area of a sector

A

A = 1/2 r^2 theta = Lr/2
L = r theta

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13
Q

volume of a cylinder

A

V = pi r^2 h

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14
Q

volume of a cone

A

V = pi r^2 h/3

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15
Q

volume of a sphere

A

V = 4 pi r^3 / 3

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16
Q

lateral area of cylinder

A

2 pi r L

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17
Q

surface area of cylinder

A

2 pi r^2 + 2 pi r L

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18
Q

lateral area of cone

A

pi r L

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19
Q

surface area of cone

A

pi r L + pi r^2

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20
Q

surface area of sphere

A

4 pi r^2

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21
Q

poisson’s distribution

A

P = e^-lambda x lambda^n / n!

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22
Q

interquartile and semiIQR

A

IQR = Q3-Q1 semi = Q3-Q1/2

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23
Q

odds (happening)

A

P/1-P

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24
Q

odds (not happening)

A

1-P/P

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25
Q

area of quadrilateral

A

A = 1/2 (sume of lower - sum of upper)

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26
Q

effective rate of interest

A

ERI = (1+r/m)^m - 1

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27
Q

compound interest

A

F = P (1+r/m)^mt

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28
Q

continuously compounding

A

F = Pe^rn

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29
Q

discount rate

A

d = r/1+r

30
Q

ordinary annuity

A

P = A [ 1 - (1+i)^-n / i ]
F = A [ (1+i)^n - 1 / i ]

31
Q

deferred annuity

A

P = A [ 1 - (1+i)^-n / i ] x (1+i)^-m

32
Q

annuity due

A

P = A [ 1 - (1+i)^-n / i ] x (1+i)

33
Q

perpetuity

A

P = A/i

34
Q

depreciation: straight line method

A

A+Bx where b=slope=depreciation

34
Q

depreciation: declining balance method

A

AB^x where rate of dep = 1-B
dep charge during nth yr = BVprevious - BVnth yr

35
Q

depreciation: sum of the yrs digit

A

_+Cx^2

dep charge during nth yr = BVprevious - BVnth yr

36
Q

total depreciation formula

A

Dn = Co - BVn

37
Q

relation of angular and translational quantities

A

S=r tehta
V = r W
a = r alpha

38
Q

angle of banking

A

tan (thetab + thetaf) = V^2/gr

thetab = tan^-1coefficient

39
Q

centripetal force

A

F = mV^2/r

40
Q

total mechanical energy

A

TME = PE + KE

41
Q

coefficient of restitution

A

e = -deltaVafter/deltaVbefore
e=0 (perfectly inelastic)
0<e<1 (inelastic/partially elastic)
e=1 (perfectly elastic)

hrn = e^2n x ho
hr = rebound height
ho = original height

42
Q

normal stress

A

P/A

43
Q

punching shear

A

P/piDt

44
Q

tangential/circumferential/hoop stress

A

PD/2t

45
Q

longitudinal stress

A

PD/4t

46
Q

spherical shell

A

(Pi-Po)D / 4t

47
Q

safety factor

A

ultimate stress / allowable stress

48
Q

elongation

A

elongation = PL/AE
P=mg

49
Q

torsion (Tmax)

A

Tmax = 16T/piD^3

50
Q

polar moment of inertia

A

solid shaft: J = piD^4/32
hollow shaft: J = pi (D^4-d^4) / 32

51
Q

angle of twist

A

theta = TL/JG (in radians)

52
Q

power (torsion)

A

P = 2 pi f T

53
Q

Tmax (helical spring)

A

Approx method:
Tmax = (16PR / pi d^3) (1+d/4R)

AM Wahls formula
Tmax = (16PR/pi d^3) (4m-1/4m-4 + 0.615/m)
m = 2R/d

54
Q

spring deflection/elongation

A

elongation = 64PR^3n/Gd^4

55
Q

moment of inertia: sphere

A

I = 2/5 mr^2

56
Q

moment of inertia: cylinder

A

I = (1/2) mr^2

57
Q

moment of inertia: thin rod (centroidal axis and at one end)

A

centroidal I = (1/12) mL^2
at one end I = (1/3) mL^2

58
Q

moment of inertia: rectangular plate

A
59
Q

power formula

A

P = IV = I^2R = V^2/R

60
Q

transformer: relation of N and V pri and sec

A

Npri/Nsec = Vpri/Vsec

61
Q

transformer: relation of I and N pri and sec

A

I pri N pri = I sec N sec

62
Q

transformer: relation of R and N pri and sec

A

Rpri/Rsec = (Npri/Nsec)^2

63
Q

Pascal’s principle

A

Pin = Pout

Fin/Ain = Fout/Aout

64
Q

Capacitance Series Formula for Q, V, and C

A

Qt = Q1 = Q2
Vt = V1+V2
1/Ct = 1/C1 + 1/C2

65
Q

Formula of charge (Q)

A

Q = It

66
Q

Capacitance Parallel Formula for Q, V, and C

A

Vt = V1 = V2
Qt = Q1+Q2
Ct = C1+C2

67
Q

differential equations: dilution/mixture formula

A

dS / dt = Sinrin - Sout rout
Sout = S / vol + rin t - rout t

68
Q

projectile: time

A

t = 2Vsin theta / g

69
Q

index of refraction of water and air

A

nwater = 1.33
nair = 1

CHE BOARD EXAM (34 decks)

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