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Thanks very much guest#2 for digging that post out.   

Well i can see no thank you or interaction from out poster at all. 

I also have not noticed and difference in the wording.

So unless demonstrated otherwise, ... well you can all fill in this blank ....... 

Perhaps you, guest#1 would like to point out this 'crucial typo'

Here's his previous post:

Did you say thank you to anyone, or appologize for the incorrect posting  on the original.

I do not think I ever witness either of those events.

What have you changed anyway?

Perhaps you could give us a link to the original post so that we can see what you have changed AND so that we can see your good manners displayed too. 

"What is the value of k if point P(k, k sqrt(3)) is 4 units from the line 5x+3y=12?"

.

\(\text{Oh, my bad it's }-25 - 2i \\ 2(x+i y) + 3 (x - i y ) = -25 - 2i \\ 5x - i y = -25 - 2i \\ x = -5, ~y=2 \\ z= -5 +2 i \)

In your question, y varies inversly to sqrtx

so you must start with:

\(y=\frac{k}{\sqrt{x}}\)

then sub in (2,4) to determine the value of k

Once you have k then you have a formula that you can use for determining the y value of any x value.

Yes you use this fact

Let k be a constant that you will often need to find using information from the question.

If y is directly proportional to x then    

\(y=kx\)

If you graph x agains y you will get a straight line.  

The y interept is 0

aand the gradient is k

OR

If y is inversely proportional to x then 

\(y=\frac{k}{x}\)

This time if you graph it it will be a hyperbola. 

If k is positive it will be in the first and 3rd quad

and if k is neg it will be in the 2nd and 4th quads.

Now consider the case there k is +1

If x=2    y=1/2

If x=4     y=1/4

See, as x gets bigger, y gets smaller.   (that is when k is positive)

Hi Rom, this was my initial answer, but it is apparently wrong.

\(2z+3z^* = -25 - 2i \\ \text{let }z=x+i y \\ 2(x+i y) + 3(x - i y) = 25 -2i \\ 5x - i y = 25-2i\\ x=5, y=2 \\ z = 5 + 2i \\\)

2 digit multiples of 19 are (19, 38, 57, 76, 95)

2 digit multiples of 31 are (31, 62, 93)

1 -> 19

19 -> 193 or 195

193 -> 1931 or 1938

195 -> 1957

1931 -> 19319

1938 -> X

1957 -> 19576

19319 -> 193193 or 193195

19576 -> 195762

193193 -> 1931931 or 1931938

193195 -> 1931957

195762 -> X

1931931 -> 19319319

1931938 -> X

1931957 -> 19319576

continuing this way for a bit we see the following pattern

strings of (4+3k) digits will have the last digit in the set (1,7,8)

strings of (5+3k) digits will have the last digit in the set (6, 9)

strings of (6+3k) digits will have the last digit in the set (2, 3, 5)

2002 = 4 + 3(666)

so the possible last digits in the string will be 1, 7, or 8

8 is the largest of these

there are 2 0 point tiles out of 100

thus the probability of choosing a 0 point tile is 2/100 = 1/50

similarly there are 10 4 point tiles so the probability of choosing one is 10/100 = 1/10

there are 2 tiles worth 10 points and again the probability is 2/100=1/50 of choosing a 10 point tile

the probability of choosing a tile worth at least 4 point is that of choosing either a 4, 5, 8, or 10 point tile.

I leave you to figure out what that probability is.  (Hint: sum the number of tiles 4 points and greater)

I think it is: OEIS A003754

I'm seeing it's 425.

I don't have a suggestion on how to find that though.

I guess you could start at 400 and add 1 for every square or cube you encounter in the list

There are 20 squares <= 400, 1-20,

There are 7 cubes <= 400, 1-7

But you seem to be excluding 1 from the series and that's counted here twice so we only have 25 squares and cubes.

Thus the 400th element is 425.

there are 5 ways for 1 drawer to be open

there are 3+2+1=6 ways for 2 drawers to be open

there is 1 way for 3 drawers to be open

5+6+1 = 12 ways total

pretty simple to list these out

(0,0,25)

(0,1,20)

(0,2,15)

(0,3,10)

(0,4,5)

(0,5,0)

(1,0,15)

(1,1,10)

(1,2,5)

(1,3,0)

(2,0,5)

(2,1,0)

12 ways

Idk. It depends where you are.

Thanks.

How did it get smaller? How does this get smaller: y = k/sqrt(x). So this is how I am suppose to solve inverse problems? Doing/using this formula/work?

Another NON-Caculus method:

Minimum pt of the parabola   =   - b / 2a  = 12000/182500 = t = .032876 hr

Then substitute this value of 't' in to the d equation to get the same answer...

[-4,4] x [-3,3] = 9 x 7 = 63 integer coordinate points are strictly in the interior

no 2x2 squares have 4 black squares

all 3x3 squares have at least 4 black squares, as do all 4x4, 5x5, 6x6, 7x7, and 8x8 squares.

there are 6x6=36 3x3 squares

there are 5x5=25 4x4 squares

there are 4x4=16 5x5 squares

there are 3x3=9  6x6 squares

there are 2x2=4  7x7 squares

there is   1          8x8 square

Summing we get 91 squares

3)
Find the volume of one bead: 4/3*pi*r^3=4/3*pi*3^3=36pi
27 x 36pi =972pi - combined volume of 27 beads
972pi =4/3*pi*r^3, solve for r
r = 9 - units - radius of  new larger gold sphere.

4)
Volume of cylinder =Pi x r^2 x h
Volume of pizza =Pi x 6^2 x 1/3 =12pi 
Volume of 1 slice =12pi/12 =pi - cubic inches

For Question 3, I'm getting two different answers. 9, is my first take.