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have a good and happy day :)

congrats!

Why are you posting that on a math website?

I have tons of homework today so thank you it made me smile and is going to help me get through it.

Thanks Alan :)

I don't know what Guest #1's answer was, but here's a possible derivation (I've assumed Dx[...] means differentiate [...] with respect to x):

Ben throws four identical darts. Each hits one of four identical dartboards on the wall. After throwing the four darts, he lists the number of darts that hit each board, from greatest to least. How many different lists are possible?

It depends on what is imortant in the count. I mean is each board classed seperately of is is just the number of darts one any board that matters.

I'll assume it is just the number of darts that matter

Here are the possible answers

0004

0013

0022

0211

1111

That is 5 posiblilities :)

Never mind

LOL Time to re-tire or at least change the air [error] hahahaha!

I am interested for sure. Both my regular science (earth science) and political classes have discussions on this subject.  My science professor is doubtful, but my political professor is adamant that global warming is here now.  Most of my classmates in both classes think it happening now. I do to and always have, though after listening to my earth science professor Im not so sure anymore. 

I didn’t really expect you to reply to my post at all. I shouldn’t have wrote it so rudely. Sorry.  

25 / 2   is correct

The new coordinates are  given by :

[Vertex of triangle  - Center of Dilation  ] * (scale factor) + Center of Dilation 

So we have

[ ( -8, - 2 )  - ( 1, - 2 ) ] (1/3)  +  ( 1, -2 )  =

[   ( -9, 0 ) ] (1/3) +  ( 1, - 2 )     =

( -3, 0 )  +  (1, - 2 )   =    ( -2, -2 )

[ ( -8, 4 ) - ( 1, - 2 ) ] (1/3)  + (1, - 2)   =

[ ( -9, 6) ] (1/3)  + ( 1, - 2 )  =

( -3, 2 )  +  ( 1, -2 )  =    ( -2, 0 )

[ ( 4, 7 )  -  ( 1, - 2 )  ] (1/3)   +  ( 1 , -2 )   =

[  ( 3 , 9 ) ] (1/3)  +  (1, - 2 )   =

( 1 , 3 )  +  ( 1, - 2 )  =  (2, 1) 

Here are the pre and post images of the coordinates : 

https://www.desmos.com/calculator/jahlfxvluy

(x^3+250x^2+100x) / (1\2x^2+25x+9)  =

(2x^3 + 500x^2   + 200x)  / ( x^2 + 50x  + 18 )

                                      2x  +  400

x^2 + 50x   +  18  [   2x^3   +  500x^2    +  200x  ]

                                 2x^3   + 100x^2    +    36x

                                     _______________________

                                                   400x^2  + 164x

                                                   400x^2 +   20000x  + 7200

                                                   ____________________

                                                                    -19836x -  7200

This line will be perpendicular to the radial line drawn from the center to (5,5)

And the slope of this radial line is   [ 5 - 2 ] / [5 - 3 ]  =  3/2

And the slope of the line perpendicular to this will   be the negative reciprocal

=  - 2/3

We have a right triangle here

The length of the rope, 20 ft, is the hypotenuse and one of the legs  is  5 ft

And the height is the other leg  and is given by :

√[ 20^2  -  5^2  ]   =  √ [400 - 25 ]  =  √ 375  ≈ 19.365  ft   =  19 ft

The semi-perimeter, s, of this triangle  is    [ 6 + 7 + 11 ] / 2  =  12

The area, K  =     √  [ s  (s - a) (s - b) (s -c)  ]    where a,b, c are the sides...so we have

K  = √  [ 12  ( 12 - 11) (12 - 7) (12 - 6) ]  =  √ [12 * 5 * 6 ]  = √ 360  = 6√10

And we can solve for the  inradius, r, as  :

K  =  r * s

6√10  =  r  *  12         divide both sides by 12

√10 / 2   =  r     = the inradius

And the diameter is twice this  =  √10  units

Guest, please DO NOT delete your answer unless you really believe it is totally incorrect.

If that is the case then leave a note saying so. Thanks.

I have no idea what you are on about Splatmaster.

(x^3+250x^2+100x) / (1\2x^2+25x+9)

The meaning of the question is not clear.

What is the backwards slash for?

If it is a divide sign is the 1 divided by everything after it or is it only divided by the 2 or perhaps by only the 2x^2   ??

Thank you so much!!!!

The ladder will lean against the house.

The base of the ladder will be  8  feet from the house.

The house is  15  feet tall.

What is the length of the ladder? Let's call it  x .

From the Pythagorean theorem, we know

8² + 15²  =  x²

64 + 225  =  x²

289  =  x²           Take the positive square root of both sides of this equation.

17  =  x

So the exact length is 17 feet.

We want a ladder that is 1 foot longer...  17 ft  +  1 ft  =  18 ft    

h  =  -16t² + 36t + 7

We want to find the time when the height is  0  .

So plug in  0  for  h  and solve for  t .

0  =  -16t² + 36t + 7       Let's use the quadratic formula to solve this.

t  =  \(\frac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}\)

t  =  \(\frac{-36\pm\sqrt{1296+448}}{-32}\)

t  =  \(\frac{-36\pm\sqrt{1744}}{-32}\)

t  =  \(\frac{-36+\sqrt{1744}}{-32}\)  ≈  -0.18              or              t  =  \(\frac{-36-\sqrt{1744}}{-32}\)  ≈  2.43

It will take about  2.43 seconds for the ball to hit the ground.

Think about this Splatmaster,

A pack of  9  sweatshirts cost  $88.77 .

How much would it cost to buy a pack of  18  sweatshirts?

It would cost twice as much, right?

A pack of  9 * 2  sweatshirts costs  $88.77 * 2 .

So..likewise...

A pack of  9 / 9  sweatshirts costs  $88.77 / 9

A pack of    1     sweatshirts costs        ...  ?         Can you finish it?

The price of  1  sweatshirt is the unit price.  

y  =  f(x)  =  4 * 5^x

5  >  1 , so  y  will get bigger as  x  gets bigger.  That rules out the fourth graph.

And...

f(0)  =  4 * 5⁰  =  4 * 1  =  4       So the graph passes through the point  (0, 4) .

That rules out the first and third graph.

The second one has to be the right graph.