Melody

1)  The most obvious one is that you cannot divide by 0

mmm

2) you cannot take the log of a negative number.

3) A positive  number raised to any power must be greater than 0

there is a couple.

This is not the algebraic answer that I am sure you need, but....

How would one calculate percent with ppm and promille, for example
What is 11% in parts per milion

I am not sure if there is something I do not understand in this question but I would say.

\(\frac{x}{1000000}=0.11\\ x=0.11*1000000\\ x=110000 \)

11% = 110000ppm

ok So Phil is going to do one exercise from each of 56 cards. 

Each card has just one exercise.

The only thing differnt between the workouts is the ORDER that the exercises are done in.

so there is   

56! ways that the cards can be ordered.   

56! =

=710998587804863451854045647463724949736497978881168458687447040000000000000 = 7.1099858780486345e74

so

56!   is about    7.1 x  10^74    ways to order the cards.     That is way more than 3 trillion orders.

You question needs to be fixed. You have used the wrong letter, the first pqrs should be abcd.

\(3x + 3 (x-1) < 7 - 2x + 6\\ 3x + 3x-3 < 13 - 2x\\ 6x-3 < 13 - 2x\\ 8x<16\\ x<2 \)

Use the cosline rule.

I have a drawer with 6 forks, 6 spoons, and 6 knives in it. If I reach in and randomly remove three pieces of silverware, what is the probability that I get one fork, one spoon, and one knife?

6/18*(6/17)*(6/16)*3! = \(\frac{9}{34}\)

(Edited as an error was pointed out - thanks )

How do you find the exact answer to this problem? sin(90°-acsc(3))

Lets see.....

\(sin(90°-acsc(3))\\ sin(90°-asin(\frac{1}{3}))\\\)

Remember that asin or inverse sin of a ratio is an ANGLE so we have

\(sin(90-\theta)=cos\theta\)

\(sin(90°-asin(\frac{1}{3}))\\ =cos(asin(\frac{1}{3}))\\ =\frac{2\sqrt2}{3}\\ \)

check:

sin(90-acsc(3)) = 0.942809041582

2*sqrt(2)/3 = 0.9428090415820634

Thanks Chris :)