All Answers 352881 Answers

The idea of a hammock made of rubber bands is  interesting also.  

Thanx , Melody ! 

The egg has to be exposed to the environment. It cannot be inside a full can or a full cardboard box.

The water and salt idea is interesting though.

i got 4800

x+1 = 2(y-1)

y+1 = x-1     or  y+2 = x

y+2+1 = 2(y-1)

y+3 = 2y-2

y = 5    x = 7

    x+y = 12  

1

a=10,b=3,c=29

just solve system of equations

\ [  (a + (  2n+1  ) d  ) ^2- (a + (2n  ) d  ) ^2 + (  a + (2n-1  ) d  ) ^2 - (a+ (  2n-2  ) d  ) ^2 + \cdots + (a+d  ) ^2 - a^2.\] 

\(\ [ (a + ( 2n+1 ) d ) ^2- (a + (2n ) d ) ^2 + ( a + (2n-1 ) d ) ^2 - (a+ ( 2n-2 ) d ) ^2 + \cdots + (a+d ) ^2 - a^2] \)

I have not finished this question but i have made a reasonable start.

I expanded each of these squared terms.

The a^2  terms all cancel out.

So you are left with 2 series.

   One of those series looks easy to deal with, the other looks a lot more tricky.

Have you tried this and made a good start for yourself ?

Thanks EP,

Yes i will verify that.

x=(180+360n) degrees    where n is an integer.

Use an oatmeal box instead of a coffee can, so you can staple inside it.  

Get a large balloon and cut it open so that you have a flat piece of soft rubber that will reach across the inside of the oatmeal box with some slack in it.   

Staple the rubber inside the oatmeal box to make a sort of sling, or hammock, for the egg to rest on.

Set the egg on the rubber and drop the oatmeal box.  Devise some way to maintain the box's orientation as it drops; you can't let it turn sideways. 

_.

The volume of the apparatus must be about the size of a coffee can, so use an actual coffee can.  Dropping the coffee can might damage it, so it would be prudent to have some spare cans on hand.

Fill the coffee can with water.  Dissolve salt into the water until an egg placed in it will float. 

Drop the water-filled coffee can with the egg floating in it from 4 meters and see if the egg survives.  Keep increasing the height of the drop until the egg breaks, then back off half the distance higher than 4 meters.  For example, if the egg finally breaks at 14 meters, then back off half of the extra 10 meters, for a total drop of 9 meters. 

You'll need to devise some way to maintain the orientation of the coffee can as it drops so it doesn't turn sideways; maybe you could glue some fins to it, or drop it inside a hollow tube, or... I'm sure you can think of something better than that, though.   

_.

And it would be the same probability if the question means between 8 and 15 inclusive. 

The numbers would be  8, 9, 10, 11, 12, 13, 14, 15   

                                      e  o    e    o    e    o    e    o    

4 evens out of a total 8 possibilities = 4/8 = 1/2            

_.

The numbers between 8 and 15    9 10 11 12 13 14      six choices  , three are even   3/6 = 1/2   

Can you please give some hints on how you got this answer? I get that you use difference of squares, but I couldn't find the last term. Thanks

The number of ways is 228.

The probability that both cards are numbers (2 through 10) totaling 12 is 3/34.

The number of residents is 58.

(a) You can get to the top in 112 ways.

(b) If you skip the 6th question, you can get to the top in 73 ways.

The range of g(x) is [-14,2].

x_0 + y_0 = 13 + 4 = 17.

OK.....that just seems like an odd answer....is the +7 portion correct too?

and yes im sure because x - 3 squared is the 3 to the right of zero on the x axis

thank you so much you really helped me

Second one

-1/5 (x-3)^2 +7                        (are you sure about the red part....did you enter it corrrectly?)

-1/5 [ (x-3)^2 -35]

-1/5  (x^2-6x+9-35)

-1/5 (x^2-6x-26)

-1/5 (x-8.92)(x+2.92)      using Quadratic Formula  (this is the reason why I question the red part)

-1/10  (x-3)^2 +10

-1/10 [ (x-3)^2-100]

-1/10 [  x^2 - 6x+9 -100 ]

-1/10 (x^2-6x-91)

-1/10 (X-13)(X+7)

8350(1+0.052/12)^10*12

Should be written as    8350(1+0.052/12)^(10*12)

The brackets around the 10*12 are important.   

Otherwise you would just take the power of 10   AND THEN   multiply by 12 afterwards

So what guest has done is most likely what you wanted   BUT  it is not what you wrote.