DAY 3 FORMULA Flashcards by Vince Rafael Candelaria

measure of an interior angle of a regular polygon

180 (n-2) /2

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number of diagonals of a polygon

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

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apothem

angle = 180/n

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perimeter of regular polygon

P=nx

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Area of a regular polygon

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

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area of trapezoid

[ (b1+b2) x h ] / 2

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angle between two lines

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

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binomial theorem expansion

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

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clock problem formula

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

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workers & working time

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

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upstream & downstream

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

upstream
(rboat - rcurrent) = d/t up

td + tu = 1

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area of a sector

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

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volume of a cylinder

V = pi r^2 h

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volume of a cone

V = pi r^2 h/3

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volume of a sphere

V = 4 pi r^3 / 3

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lateral area of cylinder

2 pi r L

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surface area of cylinder

2 pi r^2 + 2 pi r L

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lateral area of cone

pi r L

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surface area of cone

pi r L + pi r^2

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surface area of sphere

4 pi r^2

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poisson’s distribution

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

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interquartile and semiIQR

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

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odds (happening)

P/1-P

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odds (not happening)

1-P/P

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area of quadrilateral

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

effective rate of interest

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

compound interest

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

continuously compounding

F = Pe^rn

discount rate

d = r/1+r

ordinary annuity

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

deferred annuity

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

annuity due

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

perpetuity

P = A/i

depreciation: straight line method

A+Bx where b=slope=depreciation

depreciation: declining balance method

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

depreciation: sum of the yrs digit

_+Cx^2 dep charge during nth yr = BVprevious - BVnth yr

total depreciation formula

Dn = Co - BVn

relation of angular and translational quantities

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

angle of banking

tan (thetab + thetaf) = V^2/gr thetab = tan^-1coefficient

centripetal force

F = mV^2/r

total mechanical energy

TME = PE + KE

coefficient of restitution

e = -deltaVafter/deltaVbefore e=0 (perfectly inelastic) 0

normal stress

P/A

punching shear

P/piDt

tangential/circumferential/hoop stress

PD/2t

longitudinal stress

PD/4t

spherical shell

(Pi-Po)D / 4t

safety factor

ultimate stress / allowable stress

elongation

elongation = PL/AE P=mg

torsion (Tmax)

Tmax = 16T/piD^3

polar moment of inertia

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

angle of twist

theta = TL/JG (in radians)

power (torsion)

P = 2 pi f T

Tmax (helical spring)

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

spring deflection/elongation

elongation = 64PR^3n/Gd^4

moment of inertia: sphere

I = 2/5 mr^2

moment of inertia: cylinder

I = (1/2) mr^2

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

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

moment of inertia: rectangular plate

power formula

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

transformer: relation of N and V pri and sec

Npri/Nsec = Vpri/Vsec

transformer: relation of I and N pri and sec

I pri N pri = I sec N sec

transformer: relation of R and N pri and sec

Rpri/Rsec = (Npri/Nsec)^2

Pascal's principle

Pin = Pout Fin/Ain = Fout/Aout

Capacitance Series Formula for Q, V, and C

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

Formula of charge (Q)

Q = It

Capacitance Parallel Formula for Q, V, and C

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

differential equations: dilution/mixture formula

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

projectile: time

t = 2Vsin theta / g

index of refraction of water and air

nwater = 1.33 nair = 1