Gaming Project

module 5

100

log1,000,000

6

natural log base is 10

10^6=1,000,000

200

(2³)⁴

2¹²

multiply 3(4)=12

300

2⁹=512

9=log₂(512)

the mmber becomes the base and the exponent becomes the number

400

10^x=3162

x=3.5

x=log₁₀(3162)

500

what is the compound interest formula

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

module 6

100

simplify (a+b) (a+b)

a²+ab+ba+b²

multiply with FOIL, (first outer inner last)

(a)(a)=a²  (b)(b)=b²  (a)(b)=ab  (b)(a)=ba

200

predict the number of roots

a(x)=x²+3x-10

2

An n^th degree polynomial has n roots

300

find the zeros

f(x)=x²+20x=51

(-17,0) (-3,0)

(x+17)(x+3)

17+3=20

17(3)=51

400

simplify

3x/6x²

x/2x²

factor (3)(x)/(3)(2x²)

eliminate the common factor x/2x²

500

simplify

(3x(2x+7)(x-1)(6x-5))/(x(2x+7)(x-1)(6x-5))

3

remove common factors 3x/x

3x/x = 3/1 = 3

module 7

100

x+(2/x)=3 

2

get rid of the denominator x(x+(2/x))=x(3)

move it to one side x²-3x+2=0

(x-2) (x-1)

check for extranious, 2 works, 1 does not.

200

(x²+8x+12)/(x²+3x-18)

(x+2)/(x-3)

simplify (x+6)(x+2)/(x+6)(x-3)

eliminate the identical ones (x+2)/(x+3)

300

Identify actual solutions, -1 and 5/2

a-(3/(2a+1))=2

both work

plug in the answers as "a"

(-1)-(3/(2(-1)+1))=2 it works

(5/2)-(3/(2(5/2)+1))=2 it works

400

what is the verticle asymptote of 

y=(x+4)/(-2x-6)

-4

set the denominator equal to zero and solve

(x+4)/0=y

x+4=0

x=-4

500

how do you find the horizontal asymptote

• If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
• If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
• If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator