# QR Questions

#### razblo

##### Full Member
10+ Year Member
I have 3 QR questions from DAT Destroyer (2008 editon) that I'd like someone to explain to me if possible.

#72

Evaluate the following: 600e^-x = 300

I get to the part where it's -x=ln(1/2) but the correct answer is x=ln(2/1).

Could someone explain to me why it changes from 1/2 to 2/1?

#81

What is Cos(495 degrees)?

I understand the Quadrant thing where you go around 450 degrees which leaves the angle at 45 degrees.

The answer is -Cos(45 degrees) = -(&#8730;2/2)

It says it's a reference angle. Is that something we can figure out or is that something we have to memorize somewhere?

#87

This could be taken from a lot of problems (like #86 even).

6 people are running for 4 positions. How many different combinations can there be?

This is an easy problem. 6x5x4x3 = 360.

The part that I don't get, which almost seems irrelevant, is that in the answer it shows (6x5x4x3x2)/(2) and the 2s just cancel out.

Why do they have those extra "2s" and is there kind of example where they actually are significant?

Thanks! #### joonkimdds

##### Senior Member
10+ Year Member
7+ Year Member
I will answer them one by one.
Cos 495 is same as 135 degree.
What I did was 495 - 360.
And 135 degree is same as 45 degree in 2nd quadrant because 180 - 135 is 45.
45 degree right triangle has 1-1-square root of 2
cos of t his is 1/root(2). this is same as root(2) / 2

#### joonkimdds

##### Senior Member
10+ Year Member
7+ Year Member
6 ppl, fighting for 4 limited spots.
The question is not specifying it but I would guess that all 4 positions are diff, thus diff awards.

In this case, we use permutation
and that's 6!/2! = 6x5x4x3

#### joonkimdds

##### Senior Member
10+ Year Member
7+ Year Member
(1/2) ^ -1 is same as 2/1 = 2

For example, 10^-1 = 1/10 = 0.1

#### razblo

##### Full Member
10+ Year Member
(1/2) ^ -1 is same as 2/1 = 2

For example, 10^-1 = 1/10 = 0.1

You lost me on this one. If you take (1/2) and do this --> (1/2)^-1 --> ln(2/1), I get that.

Wouldn't you have to do that to the other side and which would make -x = (-1/x)?

I will answer them one by one.
Cos 495 is same as 135 degree.
What I did was 495 - 360.
And 135 degree is same as 45 degree in 2nd quadrant because 180 - 135 is 45.
45 degree right triangle has 1-1-square root of 2
cos of t his is 1/root(2). this is same as root(2) / 2

Good explanation!

#### UCB05

##### Full Member
(1/2) ^ -1 is same as 2/1 = 2

For example, 10^-1 = 1/10 = 0.1

and to go a step further, y ln(x) = ln (x^y). In this case, y = -1

-x=ln(1/2) --> x = -ln(1/2) = ln (1/2)^-1 = ln (2/1)

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