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Makovka662 [10]
3 years ago
10

Is 4-heap Nim with heaps of sizes 22, 19, 14, and 11 balanced or unbalanced? Player I's first move is to remove 6 coins from the

heap of size 19. What should player II's first move be?
Mathematics
1 answer:
nadya68 [22]3 years ago
3 0

Answer:

Player II should remove 14 coins from the heap of size 22.

Step-by-step explanation:

To properly answer this this question, we need to understand the principle and what it is exactly is being asked.

This question revolves round a game of Nim

What is a game of Nim: This is a strategic mathematical game whereby,  two opposing sides or opponent take turns taking away objects from a load or piles. On each turn, a player remove at least an object and may remove any number of objects provided they all come from the same heap/pile.

Now, referring back to the question, we should first understand that:

                        22₂ = 1 0 1 1 0

                         19₂= 1 0 0 1 1

                         14₂= 0 1 1 1 0

                          11₂= 0 1 0 1 1

and also that the “bit sums” are all even, so this is a balanced game.

However, after Player I removes 6 coins from the heap of size 19, Player II should remove 14 coins from the heap of size 22.

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You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 500cm3. Determ
babymother [125]

Answer:

x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.

Step-by-step explanation:

V= x^2y = 500

Surface area A = x^2 + 4xy.

From the first equation y = 500/x^2

So substituting for y in the equation for the surface area:

A = x^2 + 4x * 500/x^2

A = x^2 + 2000/x

Finding the derivative:

dA/dx = 2x - 2000x^-2

dA/dx = 2x - 2000/x^2

This = 0 for a minimum/maximum value of A, so

2x - 2000/x^2  = 0

2x^3 - 2000 = 0

x^3 = 2000/ 2 = 1000

x = 10

Second derivative is  2 + 4000/x^3

when x = 10  this is positive so x = 10 gives a minimum value of A.

So y =  500/x^2

= 500/100

= 5.

6 0
3 years ago
A cone has a diameter of 4 cm and a height that is 6 times the diameter. Using 3.14 for pi, which of the following can be used t
Triss [41]

Answer:

1/3(3.14)2^2(24)

Step-by-step explanation:

The volume of a cone is given by the formula;

1/3πr³

Considering the radius is 2 cm and the height is 24 cm (4 times the diameter).

Therefore;

Volume = 1/2(3.14)2²(24)

            This can be used to calculate the volume.

3 0
3 years ago
A supporting goods store sells 2 fishing reels and 5 fishing rods for $243. Later, they still 8 fishing reels and 6 fishing rods
Gwar [14]
To answer this, you can set up a system of equations.  Solve for one of the variables and substitute this new equation into the 2nd equation.

2x + 5y = 243 - I'll solve this one for x.
8x + 6y = 538

2x + 5y = 243
2x = 243 - 5y
2          2
x = 121.5 - 2.5y ;  substitute this in for x in the second equation

8x + 6y = 538
8 (121.5 - 2.5y) + 6y = 538
972 - 20y + 6y = 538
972 - 14y = 538
-972            -972
-14y = -434
-14       -14
y = 31

<u><em>The cost of a rod (y) is $31.  </em></u>

x = 121.5 - 2.5y
x = 121.5 - 2.5 x 31
x = 44

<em><u>The cost of a reel(x) is $44.</u></em>

5 0
3 years ago
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Inga [223]
4x4=16. So think of it like this now..
3x-16=65

Add 16 in each side and you get 3x=81. Divide 3 with 81 and should be 27, or x=27.
Then you check it by putting in the #'s

3(27)-4(4)=65
81-16=65
65=65 ✔️
8 0
3 years ago
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