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Good to know that you're not dead yet DS...pls let me know if you do anytime...i dont want to miss your funeral feast...lol.....just kidding....

How have you been? 

I dont use any special app to upload pics, its works fine for me,...

are you having any trouble uploading?

hows everything going on for you!

Glad to see you!!!

Hi DS it is wonderful to see you again!

I only use this site on my computer (not on my phone) but I don't need any special app to upload the pics. 

I actually do use Gyazo becasue I find it convenient and it is a free download BUT you it is not necessary.  People can still use the uploader that is included in the normal picture insertion on the forum. 

If we choose  any four numbers from the first thousand integers, we will have

C(1000, 4)    different  sets of four numbers

And each can be arranged in 4!  ways  =  24 ways

But only one arrangement  of each of these sets is in the desired order

So....the probability  of the correct arrangement is just   1 / 24

DS!!!!!....good to see you , my man!!!!

Where have you been keeping yourself   ???

The 19 foot ladder forms the hypotenuse.

One leg is 5 ft     the other leg is the side of the wall

Pythagorean theorem (for right triangles ONLY)

a^2 + b^2 = c^2      where c = hypot    a  and b are legs

5^2 + b^2 = 19^2

b^2  = 19^2 - 5^2

b = height up the wall = sqrt(19^2-5^2) = 18.33 ft

Thanx! for the 'fix' !    I amke almost as mnay typos as I do math mistkaes

Your numbers are STILL the best! You just made a typo of 842 should be 824:

10468 x 23579 =246,824,972

Hmmmmm.... Assuming no leading zeroes

1 0 4 6 8                     x     2 3 5 7 9   =  246 842 972

my guess

The area covered will be  (3/4)  of the area of a circle with a radius  of 15 plus a  the area of half circle with a radius of 3

So....the total area is

(3/4)*pi * (15^2)  + (1/2*)pi*(3)^2  ≈  530.14 m^2

You where right on your setup, but the fianl answer ended up being 109 years.

The equation is

y  = m(x - h)  + k

Where m is the slope of the perpendicular bisector.....and ( h, k)  = ( 4, 6)  which is a point on the perpedicular bisector....in this case, it's the midpoint of AB

I'm not sure, then.....maybe someone else can spot my error  or have another way to solve this...

Can you explain where the x-4 came from please

Okay thanks I'm following how you solved but I type that answer in and it said it was wrong. In the back of my textbook they have the same problem only difffernce is 48 hours instead of 49.  They got 28 years. They do not show any work in the book though.

We need to find the mid-point of AB....this is :

[  (2 + 6)/2, (5 + 7) /2)  =   ( 8 / 2, 12 / 2)   = (4, 6)   

The perpendicular bisector will go through this point...and it will have a slope of -2

So .....its equation is

y  =  -2 ( x - 4)   + 6  

y = -2x + 8 + 6

y = -2x + 14

The number of possible "faces"  is

4^12  = 16,777,216

The number of minutes spent each year is 

 49 hours per week* 60 minutes per hour * 52 weeks per year   =  152880 min per yr

So...the number of years is :

16777216 / 152880  ≈  109.7 years  =  110 years

There may be other ways to do this, but....one way is to position B at the origin  and position the other points accordingly

So A  becomes  ( -2 + 1, 1 - 4)  =  ( - 1, - 3)

And C becomes ( 5 + 1, 0  - 4)  =  (6, - 4)

The slope of A  from the origin is  ( -3/ -1)  =  (3/1)

Rotated 90° counter-clockwise  produces     (-1/3)  = (-3, 1)

The slope of C from the origin produces ( -4/6)

Rotated 90° counter=clockwise prouduces ( 6/4)  =  (6, 4)

So......re-positioning the points, we have

B = ( -1 , 4)

A =  ( -3- 1, 1 + 4)  =  ( -4, 5)

C = (6 - 1, 4 + 4)  =  ( 5, 8)

Here is my guess: 23789 * 10456 = 248,737,784

i'm assuming that you mean   a + b  =  44

a^2  - b^2  =  (a + b)  (a - b)

So

704  =   44  ( a - b)

16  =  a - b

For the last one....i'll let you do the caclulation

The radius  is  6/2  =  3 in

So....the volume of the cone =

V  =  (1/3) pi (radius)^2 * (height)  =

(1/3) (3.14)(3)^2 ( 15)

Don't forget that this is in  in^3   !!!!

2)  Square Pyramid.....base = 12.....height  = 18

The volume  is  given by:

(1/3) (base length)^2 (height) =

(1/3) (12)^2 (18)  =   864 cm^3

Haha that's because I was logged out when I started to answer! I'm just glad you got the same thing!

1)

For the first figure,  we can divide it into  two triangles on either end and a rectangle in the middle

The  triangle  on the left  has a base of 3  and a height of 6

So....its area is  (3 * 6)/2  =  9 units^2

The rectangle in the middle has a base of 4 and a height of 2

So.....its area is  4 * 2  =  8 units^2

The triangle on the right has a base (at the top) of   4  and a height of 2

So...its area is   (4 * 2)  / 2  =    4 units^2

So......the total  area is   [ 9 + 8 + 4 ]  =   21 units^2

Sorry, hectictar....I was working on this and then I saw your answer when I submitted mine....at least we agree !!!

Here's my take on this....

The sum of the roots is  r + s  = 2m   .....so....

(r + s)^2  = 

r^2 + 2rs + s^2   = 4m^2    (1)

The product of the roots is  r * s   =  m^2 + 2m + 3   (2)  

Manipulating (1), we have that

r^2 + s^2  =  4m^2 - 2rs

Sub (2)  into this

r^2 + s^2  = 

4m^2  - 2(m^2 + 2m + 3)   =  

4m^2 - 2m^2 - 4m - 6

2m^2 - 4m - 6         (3)

(3)  is minimized when  m = 

4/ (2*2)   =  4 / 4   =  1

And the minimum value is  2(1)^2 - 4(1) - 6  =  2 - 4 - 6  =  -8  

So......

The minimum  of   r^2 + s^2   = [ min ] 2m^2 - 4m - 6  =  - 8