Final exam question solutions

Jayvon Final exam Question solutions

1a) 3^5x+2=9^x+4

3^5x+2=3^2x+8

5x+2=2x+8

5x=2x+6

3x=6

x=2

1b) 5^x+3=7^x

ln5^x+3=ln7^x

(x+3)*ln5=x*ln7

x*ln5+3*ln5=x*ln7

xln5-xln7=3ln7

x(ln5-ln7)=3ln7

x=3ln5/(ln5-ln7)

2a) x^2-2x-3>=0

x^2-2x-3>=0

(x+1)=0  &.  (x-3)=0

x=-1  &    x=3

x>=-1    &    x>=3

(-inf,-1)U(3, inf)

2b) |x-4| >= 7

(x-4)>=7    &    -x+4>=7

x>=11      &      x=<-3

(-inf, -3) U (12, inf)

3) y=2*sin(4x-pi)

amplitude:2

period:1/2pi

phase shift:pi/4

minima:-2

maxima:2

pi/4+2*pi*n

4a) y=5+6x

x=5+6y

f^-1(x)=(x-5)/6

4b) y=2/(8x+5)

x=2/(8y+5)

f^-1(x)=(2/x-5)/8

5) f(x)=(x+2)/(3-x)

x-int:2

y-int:2/3

domain:(-inf, 3)U(3, inf)

vertical:3

horizontal:-2

6a) 3(cos315+I*sin315)/18(cos135+I*sin135)

3/18* cos(315-135)+I*sin(315-135)

1/6*cos(180)+I*sin(180)

1/6*(-1+0i)

-1/6

6b) ln* sqrt(x^3*4*sqrt(y))

ln x^3^1/2+ln y^1/4^1/2

sqrt(3)u+1/2v

7)a. a1:5

b. ratio:5

c. a_n*r^n-1=5*5^n-1

d. 5^n*5^10-1=9765625

8)2015-2003=12

80,000(1+.04)^13

=133205

3=(1+.04)^x

(ln3/ln1.04=x)

9a) sqrt((-5sqrt(3))^2+(5)^2)

sqrt(100)=10

magnitude=10

tan^-1(5/-5*sqrt(3))

tan^-1(5/-5*sqrt(3))=-30+180=

angle=(150 degrees)

10)sin(2a)=(-14*sqrt(113))/16)

cos(2a)=(-1)

tan(2a)=(sqrt(113)/-32)