Math 104

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Math 104

Chapter 7

Interest

Compound Interest

A=2,000(1+(0.015/4)^4*1

A=$2030.17

A=P(1+r/n)^nt

n=times it compound

Simple Interest

I=2,000*.015*1/4

I=$2038.17

I=Prt

t=time

r=rate

P=principle

Log & Expon Equations

log20(x+9)+log20(x+1)=1

X=-1,1

Final answer: x=1

4log6 x=log6 16

x=2,-2

Final Answer: x=2

"x cant be negative"

Laws Of Exponents

In X^2/(X-2)^4

InX^2-In(x-2)^4

"Express all powers as factors"

2Inx-4In(x-2)

Loga(x^2 √x+1), x>0

2logax+loga(x+1)^1/2

"Express All powers as factors"

All powers= Exponents

2logax+1/2loga(x+1)

Exponential Functions Property

Domain & Range

g(x)=log(5+x/5-x)

Interval Notation: (-5,5)

f(x)=log3(x+2)

Domain: {x|X>-2}

Interval Notation: (-2,∞)

Range

(∞,∞)

Domain

(0,∞)

Cant have zero so its not included

Log property

y=logx ↔ x=a^y

log3 81 ↔ y=log3 81

y=4

e^u=25 ↔ u=loge25

1.6^3= ↔ 3=log1.6

y=log7x ↔ x=7^y

a^u=a^v ↔ u=v

Trigonometr

Law Of Sines

SinA/a = SinB/b = SinC/c

Pythagorean Idebtites

1+cot^2Θ=csc^2Θ

1+tan^2Θ=sec^2Θ

sin^2Θ+cos^2Θ=1

Six Trig Functions

CotΘ

1/tanΘ

cosΘ/sinΘ

Adjacent/Opposite

CscΘ

1/sinΘ

Hypotenuse/Opposite

SecΘ

1/cosΘ

Hypotenuse/Adjacent

TanΘ

1/cotΘ

SinΘ/cosΘ

Opposite/Adjacent

CosΘ

1/secΘ

Adjacent/ Hypotenuse

SinΘ

1/cscΘ

Opposite/Hypotenuse

Law of Cosine

c^2=a^2+b^2ab cosC

b^2=a^2+c^2-2ac cosB

a^2=b^2+c^2-2bc cosA

Chapter8

Binomial Theorem

Expand

(x+3)^2=(x+3)(x+3)

Nonlinear Equations

Use Substitution or Elimination

Determinants

Cramer's Rules

3x3 Determinants

2x2 Determinats

Matrices

Row Echelon Form

Augmented Matrix

Systems Of Equations

Consistent, Inconsistent, And Dependent