Melody

(    (-sqrt(3)+x)*((1/8)*cos(   ((5*pi)/3)  )x(sin(((5*pi)/3))))

I know you have tried your best to put all the brackets in but I am still confused.

Is this what you want.  

\((     (-\sqrt{3}+x)   *    (\frac{1}{8}*cos   (\frac{5\pi}{3})    x(sin(\frac{5\pi}{3}))))\\~\\  =(-\sqrt{3}+x)       (\frac{1}{8}*cos   (\frac{5\pi}{3})    x(sin(\frac{5\pi}{3}))\\~\\  =(-\sqrt{3}+x)       (\frac{1}{8}*cos   (\frac{1\pi}{3})    x(-sin(\frac{1\pi}{3}))\\~\\  =(-\sqrt{3}+x)       (\frac{1}{8}*\frac{1}{2}   x(-\frac{\sqrt3}{2}))\\~\\  =(-\sqrt{3}+x)       (-\frac{\sqrt3 x}{32})\\~\\  =\frac{3x-\sqrt3 x^2}{32}\\~\\ \)

LaTex:

(     (-\sqrt{3}+x)   *    (\frac{1}{8}*cos   (\frac{5\pi}{3})    x(sin(\frac{5\pi}{3}))))\\~\\

 =(-\sqrt{3}+x)       (\frac{1}{8}*cos   (\frac{5\pi}{3})    x(sin(\frac{5\pi}{3}))\\~\\

 =(-\sqrt{3}+x)       (\frac{1}{8}*cos   (\frac{1\pi}{3})    x(-sin(\frac{1\pi}{3}))\\~\\

 =(-\sqrt{3}+x)       (\frac{1}{8}*\frac{1}{2}   x(-\frac{\sqrt3}{2}))\\~\\

 =(-\sqrt{3}+x)        (-\frac{\sqrt3 x}{32})\\~\\

 =\frac{3x-\sqrt3 x^2}{32}\\~\\

Next time please include the address of the original post, preferably as a link.   

there are 52C3=22100  ways to chose 3 cards

three in a row are

A23

234

345

456

567

678

789

89 10

9 10 J

10 JQ

JQK

QKA

there are 12 of them for each suit which makes 48 altogether.

48/22100 = 12 / 5525

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 800 pounds more than each of her trucks, but no more than 1/5 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?

My neighbour is a woman.

That is impossible.

If my truck holds less than 1/5 of her trucks combined then my truck holds less than one of her trucks.

If my truck holds less than one of her trucks then it cannot carry 800 pounds more than her truck.

It is a trick question.

The graph of (x - 3)^2 + (y - 5)^2 = 16     This is a circle    centre (3,5) radius 4

is reflected over the line y = x + 2.            

I will find the perpendicular distance of y=x+2 to (3,5)

x-y+2=9       (3,5)

\(d=\frac{|3*1+5*-1+2|}{\sqrt{1^2+1^2}}=0\)

So the line goes through the centre of the circle.

So you are refecting the circle over a diameter.  So what does this mean?

--------------------

The new graph is the graph of the equation x^2 + Bx + y^2 + Dy + F = 0  for some constants B, D, and F. 

Find B + D + F.

I take half of Jeremy's money and divide it into 7 equal piles. Six of these piles b**w away in the wind, but from the seventh pile, I take 2 dollars and hand Jeremy the rest, which is 8 dollars. How much money, in dollars, did Jeremy begin with?

Work backwards !

7th pile is   8+2=10  

So what now?

Thanks Amy  

BigBoi, next time you ask a repost question can you please give the address of the original post.

It is better that all the answers are together even if some are not good.   

x is at least twice as far from 5 than from 3

the distance between 5 and x is |5-x|     which is the same as  |x-5|

the distance between 3 and x is |3-x| 

5 is further away

so

\(|5-x| \ge 2*|3-x|\)

Very nice, thanks guys.    

ok, if you want me to work through it just ask but if you can do it yourself, (with mine or any other substitution) that is even better.

If you do it with a different substitution, and you get it out, please share that with us.  

I wanted to get rid of the square root off the bottom.

if 

 \(u^2=1+sin\theta\\ \text{then denominator becomes u}\)

It was a bit of a guess but I tried it and it appeared to work.

Do you want me to explain more?