DAY 3 FORMULA Flashcards
measure of an interior angle of a regular polygon
180 (n-2) /2
number of diagonals of a polygon
n(n-3)/2 or nC2-n
apothem
angle = 180/n
perimeter of regular polygon
P=nx
Area of a regular polygon
Apolygon = n x Atriangle
Atriangle = (1/2) x ax
area of trapezoid
[ (b1+b2) x h ] / 2
angle between two lines
tan@ = abs |(m2-m1)/(1+m2m1)|
binomial theorem expansion
nCr (a)^n-r (b)^r where r=nth term - 1
clock problem formula
angle = |30h - 5.5m|
x = (60/11) (initial + hr spaces)
workers & working time
constant = # workers x total time / # of units (1 default)
upstream & downstream
downstream:
(rboat + rcurrent) = d/t down
upstream
(rboat - rcurrent) = d/t up
td + tu = 1
area of a sector
A = 1/2 r^2 theta = Lr/2
L = r theta
volume of a cylinder
V = pi r^2 h
volume of a cone
V = pi r^2 h/3
volume of a sphere
V = 4 pi r^3 / 3
lateral area of cylinder
2 pi r L
surface area of cylinder
2 pi r^2 + 2 pi r L
lateral area of cone
pi r L
surface area of cone
pi r L + pi r^2
surface area of sphere
4 pi r^2
poisson’s distribution
P = e^-lambda x lambda^n / n!
interquartile and semiIQR
IQR = Q3-Q1 semi = Q3-Q1/2
odds (happening)
P/1-P
odds (not happening)
1-P/P
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<e<1 (inelastic/partially elastic)
e=1 (perfectly elastic)
hrn = e^2n x ho
hr = rebound height
ho = original height
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
