CPhill

Hey, BJ....no cursing on here.......LOL!!!!

Man, SevenSins...that went right past me.....!!!!.....

Since I live in the Southern part of the US, we don't usually have to worry about this. The end of Winter for us sometimes comes in March...!!!!!

The multiplicative inverse of a = 1/a   so we have...

-5/4   =    1/(-5/4) =  -4/5

Basically, the muliplicative inverse is a number such that  a*n = 1

So.....n = 1/a = -4/5

I'm still trying to figure that one out, too, h7.....(???)

Let x  be the number she started with

Then

(x - 1) - (1/2)(x - 1) - 1 - (1/3)[(x-1) - (1/2)(x-1) -1] = 6   simplify

x -1 - (1/2)x + 1/2 - 1 - (1/3)x + (1/3) + (1/6)x - (1/6) +1/3  = 6  

x - (5/6)x + (1/6)x - 2 +1/2 +1/3 - 1/6 + 1/3 = 6

(1/3)x - 1 = 6   add 1 to both sides

(1/3)x = 7        multiply both sides by 3

x = 21

Check

21 - 1  = 20

Then 20 - (1/2)(21 - 1)  = 20 - 10  = 10 to her sister

Then 10 - 1 = 9

And 9 - (1/3)(9)  = 9 - [3 to her brother]  = 6    (√√√)

cot^2x * sinx = cot^2x    converting to sines and cosines, we have

(cos^2x / sin^2 x) * sinx  =  cos^2x/sin^2x

cos^2x/ sinx  = cos^2x/sin^2x     rearrange

cos^2x/sin^2x - cos^2x/sin^2x = 0

(cos^2x/sinx)(1/sinx - 1) = 0     setting each factor to 0 we have

cos^2x/sinx = 0        this is only = 0  where cosx = 0  = pi/2 and 3pi/2  on [0, 2pi]

And

(1/sinx - 1) = 0

cscx  -  1  = 0

cscx = 1     and this occurs at pi/2  on   [0, 2pi]

So, the solutions are (pi/2, 0) and (3pi/2, 0)

Here's the graph on [0, 2pi].....

Thanks, Melody.....

42 / 100   =   (2 x 21) / (2 x 50) .... "cancel' the 2's...... =  21 / 50

Does that help ???

Let x be the smallest number, and let y and z be the larger numbers....therefore, we have..

(y + z) = 4x

And

x + (y + z) = 85       substitute for (y + z)

x +  4x   = 85

5x  = 85       divide by 5 on both sides

x = 17

And (y + z) = 4(17) = 68

Unfortunately, we cannot determine the exact values for y and z....there are infinite possibilities.....!!!

42%  = .42   = 42/100

And "of" means "multiply"

Therefore, 42% of 50  = 42/100 x 50

But 50 = 50/1    so we have

42/100 x  50/1     and, swapping denominators, this equals the same thing as

42/1 x 50/100      but 50/100 = 1/2    ...so we have

42 x 1/2  =   42/2   = 21

And that's it....!!!