Tuesday, January 21, 2014

Sunday, January 5, 2014

Which of the points a. (0,1), b. (-1,2), c.(-3,2), d. (1,0) is a solution of 3x+4y < 2?

We test each ordered pair by checking if it results in a true statement when substituted into the inequality: 

a) 0+4 < 2, false
b) -3+8 < 2, False
c) -9+8 < 2, True
d) 3+0 < 2, False 

c. is correct

Solve the system: {A+B=140, B+C=160, C+D=130, D+A=110}

Writing in matrix form we get the augmented matrix:

After row operations the system can be transformed to:
 


using t we can write:

A=110-t
B=t+30
C=130-t
D=t

The first and last term of the arithmetic progression are 3 and 21 respectively and the sum of the series is 240. Find the number of terms.

S%5Bn%5D=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29
240=%28n%2F2%29%283%2B21%29
n=240%2F12=20

how do you simplify (5-2i)/(-4+i) ?

%285-2i%29%2F%28-4%2Bi%29=%28%285-2i%29%28-4-i%29%29%2F%28%28-4%2Bi%29%28-4-i%29%29 

simplifying...

%28-20-5i%2B8i-2%29%2F%2816%2B1%29=-22%2F17%2B%283%2F17%29i

Solve for x : 15^(2x)=36

15%5E%282x%29=36
log%2815%2C15%5E%282x%29%29=log%2815%2C36%29%0D%0A
2x%2F2=log%2815%2C36%29%2F2
x=log%2815%2C36%29%2F2

if the three sides of a triangle are 2, 5, and x units and area of triangle is x sq. units, what is the value of x ?

I used Heron's formula for the area and after some algebra we can see that there is no real solution for x: