CPhill

Move the decimal point to the right of the first non-zero digit....

So we have

5.696

Then, mutiply this by 10 raised to a (negative) exponent indicating how many places we moved the decimal → i.e., -1   ...   so we have

5.696 x 10^-1

(3x-4)+6<10      simplify

3x + 2 < 10       subtract 2 from both sides

3x < 8               divide both sides by 3

x < 8/3

31, 37  are prime

32 only has one prime factor ..... 2

33 = 3 x 11

34 = 17 x 2

35 = 7 x 5

38 = 19 x 2

39 = 13 x 3

This leaves only 36 = 2^2 x 3^2

So...the prime factors are 2 and 3....and these, indeed, sum to 5  !!!!

y=axsin(bx)+1.2

We need to solve the system  (if there is a solution)

5.5  = (9a)sin(9b) + 1.2   →       4.3 = (9a)sin(9b)

3.25 = (12a)sin(12b) + 1.2  →    2.05 = (12a)sin(12b)

WolframAlpha couldn't generate a solution for the above.......nor could it generate a solution  when the first "x" was a "times".......as Melody might have rightly assumed.

(3i+1)(1)+(3i+1)(2)+(3i+1)(3) =

(1 + 2 + 3)(3i + 1)=

6(3i + 1) =

18i + 6

cos^2(345)  means the same thing as [cos(345)]^2 =  cos(345) * cos(345)

cos(345^2)  means  cos(345 * 345) = cos(119025)

We'd have to know how many apples were on the tree to start with.

Yeah......now that I reconsider it, I like Melody's answer, too.......

Very nice, Alan

The distance between the 8cm sides is just 12 cm...

Here's a picture....

Notice that the distance between BD and AC (the two 12 cm sides) is just 4. And the distance between AB  and CD (the two 8 cm sides) is just 12.