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)
I don’t know how to link my answers to the person.
I don’t know how to link my answers to the person.