Transformations

TRANSFORMATIONS

Linear Programming

Linear Programming

(Worksheet problems)

#4
Vertices:	(0,0)		(0,6)		(6,0)
Constraints	Objective Function: C= 3x+4y
x ≥ 0 y ≥ 0 x + y ≤ 6	C=3x+4y C=3(0)+4(0) C=0	C=3x+4y C=3(0)+4(6) C=24		C=3x=4y C=3(6)+4(0) C=18

#5
Vertices:	(-5,4)		(5, 4)		(5, 8)
Constraints	Objective Function: C=2x+5y
x ≤ 5 y ≥ 4 -2x +5 y ≤ 30	C=2x+5y C=2(-5)+5(4) C=10	C=2x+5y C=2(5)+5(4) C= 30		C=2x+5y C=2(5)+5(8) C=50

# 6
Vertices:	(1, 2)		(5,2)		(1,8)
Constraints	Objective Function: C= 7x+3y
x ≥ 1 y ≥ 2 6x +4 y ≤ 38	C= 7x+3y C=7(1)+3(2) C= 13	C=7x+3y C=7(5)+3(2) C= 41		C= 7x+3y C=7(1)+3(8) C= 31

#7
Vertices:	(0, 4)		(0, 8)		(6, 8)
Constraints	Objective Function: C= 4x+6y
x ≥ 0 y ≤ 8 -2x + 3y ≥ 12	C= 4x+6y C=4(0)+6(4) C= 24	C=4x+6y C=4(0)+6(8) C= 48		C= 4x+6y C=4(6)+6(8) C= 72

#8
Vertices:	(0,0)		(5,0)		(2,3)		(0,4)
Constraints	Objective Function: C= 8x+7y
x ≥ 0 y ≥ 0 x + y ≤ 5	C= 8x+7y C=8(0)+7(0) C=0	C=8x+7y C=8(5)+7(0) C=40		C= 8x+7y C=8(2)+7(3) C=37		C= 8x+7y C=8(0)+7(4) C=28

#9
Vertices:	(0,2)		(3,0)		(4,3)		(0,4)
Constraints	Objective Function: C= 3x+5y
x ≥ 0 y ≥ 0 x + y ≤ 5	C= 3x+5y C=3(0)+5(2) C=10	C=3x+5y C=3(3)+5(0) C= 9		C= 3x+5y  C=3(4)+5(3) C=27		C=3x+5y C=3(0)+5(4) C=20

Measures of Central Tendency (statistics test)

Measures Of Central Tendancy:

Statistics Test

Statistics

Statistics:

Statistics Powerpoint 

Statistics Data

Compound Interest Formula

Compound Interest Formula:

formula:

 

P= principal

A= amount

N= number of times per year, interest is compounded

T= time in years

R= rate of interest 

Graphing Exponential Growth/Decay

GRAPHING EXPONENTIAL GROWTH/DECAY: 

y= aŸb^x-h+k

a= multiplier

         a>1 = stretch 
         0<a<1 = compression 
         a<0 (negative) = flipped over x-axis 
b= base 
         b>1 = GROWTH (always increasing)
         0<b<1 = DECAY (always decreasing) 
h= left/right (opposite) 
k= up/down


Domain

(-∞,∞) = All Real numbers 

Range:     y>k (Positive)

                y<k (Negative) 

Asymptote

y=k

General Forms of a Sequence

General Forms Of A Sequence:

~Sequence: series (list) of numbers

~Arithmetic:  sequence of numbers such that the difference between the consecutive terms is constant.
            
             -example-  5,7,9,11,13,15... is an arithmetic sequence with a                               difference of 2.

             -formula-  a_n=  a₁+(n-1)d                    d=a_n-a_n-1

                                            _{d= common difference}

~Geometric: sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
             -example-  2,6,18,54... is a geometric sequence with a common                      ratio of 3.

             -formula-  a_n=a_{1 x} r^n-1                                  r= a_n ÷ a_n-1

                                                      _{r= common ratio}