MATH FORMULAS AND CONCEPTS

1 Gal = 4 Quarts = 8 Pints = 16 cups = 128 ounces

Relation between Gallon and smaller units for cooking

halfway

Two tangent lines on a parabola always meet \__________________

2/3

The centroid of a triangle is \_______ of the line from the vertex to the median on the opposite side

4 minutes

Each degree difference in LONGITUDE is equal to a ___ time difference

A \= 2ab

Maximum area of a rectangle that can be inscribed in an ECLIPSE

V \= h/3 * [A1 + A2 + sqrt(A1*A2) ]

Frustum general formula

F + V \= E + 2

CODING: (Unsa na nga social media? FB, ITO)

Formula for FACES, VERTICES and EDGES

V \= sqrt(2)/12 * a^3

Volume of tetrahedron formula

V \= sqrt(2)/3 * a^3

Volume of Octahedron formula

sq[ (s-a) (s-b) (s-c) (s-d) - abcd*cos^2(θ) ]

Area of TRAPEZIUM GENERAL FORMULA

A = 1/2\*d1\*d2\*sin(θ)

Area of General Quadrilateral given diagonals

A = sqrt\[ (s-a)\*(s-b)\*(s-c)\*(s-d) \]

Area of cyclic quadrilateral

r = sqrt\[(ab+cd)\*(ac+bd)\*(ad+bc)\] / 4A

Radius of circle circumscribing QUADRILATERAL

0

The limit of [ (-1 to the nth power) * (2 to the - nth power)] as n approaches infinity

Period

It is the time that it takes to create 2 successive peaks in a wave.

Frequency

Inverse of period

pi/a

NOTE: tan ( 0 ) \= tan (pi) \= 0 ; hence, pi must be the argument to get the period.

What is the period of tan (ax) where a \= variable

R \= [ ( 1 + y'^2 ) ^3/2] / abs(y'')

Radius of Curvature formula

K \= 1/R

Curvature formula

x \= 3/5 b
y \= 3/8 h

CENTROID in PARABOLIC SEGMENT

x \= 4r/3pi
y \= 4r/3pi

CENTROID in QUARTER CIRCLE

x \= 4a/3pi
y \= 4b/3pi

measured from the intersection of vertical and horizontal lines

CENTROID in SPANDREL

V = h/6 \* (Atop + Abot + 4 Amid)

\
V = h\*(Aave)

Volume of PRISMATOID formula

r \= 2/3 R
h \= 1/3 H
V \= 4/9 Vcone

Maximum Volume CYLINDER inside a CONE

W \= (sp.wt)*pi*x^2*(s-y)dy

:integrate from 0 to Htank

s \= height above tank to be pumped
y \= height to centroid

Work required to pump liquid above tank

L^2/3 \= a ^ 2/3 + b ^ 2/3

Longest Ladder that can pass through two intersecting passages of widths a and b

A \= 1/2*(L + W)^2

Maximum area of rectangle that can circumscribe another rectangle of fixed length, L, and width, W

x \= sqrt(h1*h2)

h1 \= height to bottom of figure from eye level
h2 \= height to top of figure from eye level

Distance, x, for Maximum viewing angle formula

D \= sqrt(2) * L

and L \= W (length \= width)

Maximum length of diagonal of rectangle formula

theta \= 45 deg

Theta that will give maximum area and perimeter in a right triangle with given hypotenuse

L \= 1/2 h
W \= 1/2 b

b \= base of triangle
h \= height of triangle

Maximum area of rectangle that can be cut from a given right triangle

W \= b/2
L \= h/2

b \= side given
h \= altitude

Maximum area of rectangle inscribed in a triangle with altitude and one side given

y \= sqrt(3) * x

Stiffest beam that can be cut from a log of radius R if the stiffness of the beam is proportional to the breath and the cube of depth

A \= r^2

Largest rectangle cut from a semi-circle of given radius R

y \= x

Maximum rectangle inscribed in a circle

L \= a + b

a \= semi-major axis
b \= semi-minor axis

Minimum length of the line (L) tangent to ellipse intercepted by two axes

L \= sqrt(2) a
W \= sqrt(2) b

a \= semi-major axis
b \= semi-minor axis

Dimensions of biggest rectangle that can be inscribed in an ellipse

h \= y + x/2
h \= x
x \= 2y

x \= diameter of semi-circle above rectangle
x \= length of rectangle
y \= height of rectangle

Maximum light area of a NORMAN window if perimeter is given

x \= W/3
theta \= 60 deg

x \= length of sides of gutter.

Maximum capacity of trapezoidal gutter of given width (W)

x \= 2b* sqrt( 1/3 )
y \= 2a *sqrt (2/3)

a \> b
a \= semi major axis

Strongest beam that can be cut from an ellipse if the strength varies as the product of the breath and square of the depth

x \= y \= z

Maximum volume of rectangular parallelipiped

x^2 \= A/3

x \= 2y

A base \= x * x

Maximum volume if the area, A, of the material is known (open top)

Wcy \= W/sqrt(3)

Weight of the heaviest right circular cylinder that can be cut from the sphere having weight W

V cy \= Vsphere/sqrt(3)

Maximum volume of right circular cylinder that can be inscribed in a sphere of radius R

h \= sqrt(2) * R

Proportion of the cylinder that requires the least material if open at the top but closed at the bottom

H \= sqrt(2) * R

Least amount of canvass needed when the capacity of the conical tint is given; GIVE RELATION BETWEEN R and H

sin theta \= 1/3

where:
theta \= angle between h and s in the right triangle formed by h, s, r
h \= height
s \= slant height
r \= radius of cone

Minimum volume of the cone circumscribing a sphere of given radius R

h \= (4/3) R

Maximum volume of right circular cone inscribed in the given sphere of radius R

h \= s/ sqrt(3)
tan theta \= sqrt(2)

The altitude (h) and angle (theta) if the volume is maximum given slant height (s)

h \= (5/4) * R

Maximum surface area of the right circular cone inscribed in the given sphere

P \= (FC - SV) / (1 + i)^n - 1

If a machine has an economic life (n) with a salvage value (SV), first cost (FC), and with REPLACEMENT. What is its equivalent CAPITALIZED COST

P \= A/i

Present Worth of PERPETUITY formula

1 + ieff \= (1 + r/m) ^ m

Effective interest rate formula

P \= Fr * (1+i)^n - 1 / i * (1+i)^n + R / (1+i)^n

Present Worth of BONDS formula

D \= F - P

DISCOUNT formula

d \= D/F

RATE OF DISCOUNT formula

i \= d/1-d

Relation between rate of discount (d) and rate of interest (i)

BVm \= FC * (1 - 2/n)^m

n \= economic life

Double Declining Depreciation BOOK VALUE formula

dm \= (FC - SV) * Sum (reveresed)/Sum (n)

Sum (n) \= 1 + 2 + 3 + ... + n
Sum (reversed) \= n + (n-1) + ... (n-m)

Sum-of-years-Digit Depreciation at year (m) formula

Dm \= (FC-SV) * (Qm)/Qn

Qm \= Total Quantity produced during year m
Qn \= Total no. of units up to end of life n

Service output Method TOTAL DEPRECIATION (Dm) after m years

Dm \= (FC - SV) * Hm/Hn

Hm \= Total no. of hours during year m
Hn \= Total no of hours throughout life

WORKING HOURS METHOD Dm formula

B-C ratio \= (Arev - Acost)/C
C \= Annuity equivalent of (FC - SV)

Arev \= annual revenues
Acost \= annual cost

BENEFIT TO COST RATIO Formula

P(B|A) = P( A & B) / P(A)

\
Kung unsa ang after sa “|”, mao na ang denominator

Conditional Probability formula

Sum of coefficients formula in BINOMIAL EXPANSION

S = n\*(n+1)

Sum of exponents in BINOMIAL EXPANSION

\

rth term of BINOMIAL EXPANSION

D = AB/C+1

\
A = coeff of previous term

B = exponent x

C = exponent y

Coefficient of next term (D) in BINOMIAL EXPANSION

an = a1 + (n-1)\*d

Arithmetic Progression formula

Sn = (n/2)\*\[ 2a1 + (n-1)d\]

\
a1 = first term

d = common diff

Arithmetic SERIES Formula

Am = (a1 + … + an)/n

Arithmetic Mean

An = A1\*r ^ (n-1)

Geometric Sequence Formula

Sn = A1/(r-1)\*(r^n -1)

Geometric SERIES when r > 0

Geometric SERIES when r < 0

S = A1/(1-r)

Infinite Geometric SERIES formula

G.M = nth root (a1\*a...\*an)

Geometric Mean formula

nPn = (n-1)!

Cyclic Permutation formula

nPn = (1/2)\*(n-1)!

Cyclic Permutation for BRACELETS & NECKLACES

Sum = -B/A

SUM OF ROOTS of Quadratic Equation

Product = C/A

PRODUCT OF ROOTS of Quadratic Equation

B^2 - 4AC

Discriminant of Quadratic Eq.

Real and Equal

if Discriminant = 0,

Real and Unequal

if Discriminant > 0,

imaginary or complex

if Discriminant < 0

\

QUADRATIC FORMULA

theta = 60/11 \* H

\
H = hour hand w/c forms right, straight, etc.

Time on clock with given angle

(+/-) deg = 30H - 5.5 M

\
(+) = hour hand in front

(-) = minute hand in front

Angle on clock GENERAL FORMULA

Capital + Profit = Selling Price - Discount

Cost and Investment formula

Discounted Selling Price

The %profit is based on what?

A

In y = A\*sin(Bx + C) + D: amplitude?

\

2\*pi/B

In y = A\*sin(Bx + C) + D: period?

B

In y = A\*sin(Bx + C) + D: angular vel?

\-C/B

In y = A\*sin(Bx + C) + D: phase shift?

D

In y = A\*sin(Bx + C) + D: vertical shift?

a + b > c

SCHWARZ’s Inequality?

Centroid

Intersections of MEDIAN

Orthocenter

Intersections of ALTITUDE

Incenter

Intersections of ANGLE BISECTOR

Circumcenter

Intersections of PERPENDICULAR BISECTORS

PYTHAGOREAN RELATION in TRIGO

sinAcosB + cosAsinB

sin (A + B) =?