If a = (4, 3, 9), b = (2, 8, 5) and c = (0, 7, 1) Calculate the magnitude of 2a - 5b + 3c

2a - 5b + 3c =
2(4, 3, 9)-
5(2, 8, 5)+
3(0, 7, 1) =
(8,6,18)-
(10,40,25)+
(0,21,3) =
(8-10+0,6-40+21,18-25+3)=
(-2,-13,-4)
magnitude :

:)

Timmy enjoys playing old-fashioned video games. He found 3 game systems on eBay and wants to purchase a Nintendo game system, an Atari game system, and a Sega arcade game system. The Sega system costs $600 more than the sum of the Atari and the Nintendo systems. All together, the three game systems cost $11,000. The Atari system costs $1100 less than the Nintendo. Determine how much Timmy paid for each game system.

1 S=N+A+600
2 N+S+A=11000
3 A=N-1100 

A=2050
N=3150
S=5800

How would you go about solving this inequality? x^3>1

x^3>1 
x^3-1>0 
(x-1)(x^2+x+1)>0 
but this is always true: x^2+x+1>0 

so we only need look at 

x-1>0 
and thus x>1 

:)

Convert to augmented matrix. x+y+z=1 -x=2+z-3y z=x+y

x+y+z=1
-x=2+z-3y
z=x+y 

x+y+z=1
-2=x+z-3y
0=x+y-z 


 

with a vertical bar between columns 3 and 4


:)

My overall grade is an 86% I want to figure out what I need to score on my exam to get an A. My exam is worth 25% of my grade.

Solve this inequality: 
 


to get
x>102 
It is impossible to get an A 

:( 

Find the determinant of [-2 1 4][ 6 3 -4][ 1 -1 5]

[-2 1 4]
[ 6 3 -4]
[ 1 -1 5] 

expand about row 3 to get: 
det =1(-4-12)+1(8-24)+5(-6-6)=-92

log5(4x +1) = log5 (2x+7)

log5(4x +1) = log5 (2x+7) 
5^log5(4x +1) =5^log5 (2x+7) 
4x+1=2x+7 
2x=6 
x=3