I don't have enough time right now, but if you can tell me if any of these are approximations that will help.  I will try to do these on Sunday night or Monday.  Sorry I can't help you today.

5 + 10 + 15 + 20 + ... 1995

mr.jones has a great explaination about sequences in the following link

http://www.math-magic.com/sequences/add_seq_geo.htm

24 x 65 x 62

are you sure this one is not an approximation...? if not, i really don't know a trick to this...

441 * 841

this is the way i'd do it...

441 is 21 squared

841 is 29 squared

change the problem to the following

21*19*21*19

then....the problem becomes 399*399, which is (399) squared

and change the problem to (400-1) squared, and do 400^2-400*2*1+1, cuz (n-1)^2=n^2-2n+1

the answer is 159201

If (1 - i) / (1 + i) = a + bi, then b =

here is another link, sorry i am really sick so i can't do much typing...

http://www.math-magic.com/algebra/imaginary.htm

if you have any questions just pm and i'll try to answer it, hope that helps

good luck

quincy

yeah, i checked again, the 25 * 65 * 62 isn't an approximation.  I checked it, it's number 29.  But what I don't get about the sequences is :

How do you find the number of terms?

Thanks a lot for your help, langris5

Let me try to explain some of the math behind the trig question you had, although trig is by no means my strong point. 

First off, there is a basic formula, or identity:

- sin (x) = cos ( 90 - x), and vice versa

this is true for all cofunctions, that is sin and cosine, tangent and cotangent, and secant and cosecant. 

So, in your problem, if sin (4x) is cos (x), then 4x = 90-x. So 5x = 90, etc.

If you want to know the explanation for why this works, here goes:

Consider a right triangle, ABC, with B as the right angle.  The hypotenuse in this case would be AC, and the legs would be AB and BC.  So the sine of angle A would be (BC)/(AC), and cosine of angle B would be the same (BC)/(AC). The relationship between angle A and B is (A + B = 90), because it is a right triangle.

So, sin(x) = cos (y) only if x + y = 90.

Hope that helps,

Vinay

Hey everybody, howz it hangin?  I wasn't sure if i should start a new thread for this or not, so ill just add it to this one.  I've been lookin at my old #sense tests, and there's a couple problems i always have trouble with.  Most of the tests are TMSCA, but the problems might be on the UIL tests too..

This first one, i know there's got to be a trick for it, because the answer is always a square, but i couldn't figure out how to get the number to square.

If f(x)= (x^2)-6x+9, then f (4.4) = (answer is 1.96)

this is basically the same type of problem-

If x+2 = 15, then (x^2)+4x+4 = (answer is 225)

This next one is probably really simple, i just don't know it-

7*7 7/8= ?

Im also finding questions about the roots, which i don't know how to do too well.

Find k, so that the roots of (3x^2)+kx+48=0 are equal. k=?

sorry, i lost my answer key for that one.  I know sum and product of the roots, but any help on any other problems envolving roots would be appreciated.

Thanks Everybody,  Cole