HELP IMMEDIATELY!!

[JCoupe]

My final is tomorrow. out of 50 questions i don't get these 4. can somebody help me out and show me how to do it..


What is equivalent to

4+i
------
2-3i


Simplify

(x^5y^3)^3
---------------------
x^3y^-2*x^8y^-6


In 1995, the population of Mexico was approximately 9.37*10^7 and the land area was 7.62*10^5 square miles. Find the average number of people per square mile in Mexico in 1995.


In the solution (x,y) to the system

{-2x+3y=0
{x-3y=-12

what is the value of x + y?

 

[tkhunny]

What is equivalent to

4+i
------
2-3i

Multiply numerator and denominator by the complex conjugate of the denominator, 2+3i in this case. Simplfy and be amazed.

Simplify

(x^5y^3)^3
---------------------
x^3y^-2*x^8y^-6

I'd do the numerator first: x^15*y^9
Then the denominator x^11*y^(-8)

Is it any easier, now?

In 1995, the population of Mexico was approximately 9.37*10^7 and the land area was 7.62*10^5 square miles. Find the average number of people per square mile in Mexico in 1995.

Division? (9.37*10^7) / (7.62*10^5) = 1.23*10^(7-5) = 1.23*10^2

In the solution (x,y) to the system

-2x+3y=0
x-3y=-12

what is the value of x + y?

Add the two equations;

-x = -12
x = 12

Substitute

12-3y = -12
-3y = -24
y = 8

x+y = ???

 

[JCoupe]

omg, thank you soooo much.. ur a lifesaver.... i went from to in a matter of seconds..

 

[soroban]

Hello, JCoupe!

What is equivalent to

4+i
------
2-3i

We must "rationalize" the denominator.
Multiply top and bottom by the conjugate of the denominator.

. . . .4 + i . .2 + 3i . . . . 8 + 12i + 2i + 3i² . . . . .8 + 14i - 3 . . . .5 + 14i
. . . ------- . -------- . = . ---------------------- . = . -------------- . = . ---------
. . . .2 - 3i . 2 + 3i. . . . . . 4 + 6i - 6i - 9i² . . . . . . . 4 + 9 . . . . . . . 13

Simplify

. . .(x⁵y³)³
-----------------
(x³y^-2)(x⁸y^-6)
.

. . . . . . . . . .(x⁵)³(y³)³ . . . . . x¹⁵y⁹
We have: . -------------- . = . --------- . = . x⁴y¹⁷
. . . . . . . . . . . x¹¹y^-8 . . . . . . x¹¹y^-8


Edit: Too fast for me (again), TK!

 

[JCoupe]

w00t, thx guys, i got an 88 on the exam..

 

[tkhunny]

Good call! What's the goal for the next one?

 

[JCoupe]

what do u mean??

 

[tkhunny]

Well, 88 is pretty good. What's next? Will you be shooting for 90?

 

[JCoupe]

sure, i always keep my goal high..