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BigorU [14]
3 years ago
14

You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board wi

th T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

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And we can round this to the nearest up integer and we got 110194.  

Step-by-step explanation:

The natural growth and decay model is given by:

\frac{dP}{dt}=kP   (1)

Where P represent the population and t the time in years since 1970.

If we integrate both sides from equation (1) we got:

\int \frac{dP}{P} =\int kdt

ln|P| =kt +c

And if we apply exponentials on both sides we got:

P= e^{kt} e^k

And we can assume e^k = P_o

And we have this model:

P(t) = P_o e^{kt}

And for this case we want to find P_o

By 1990 we have t=20 years since 1970 and we have this equation:

143000 = P_o e^{20k}

And we can solve for P_o like this:

P_o = \frac{143000}{e^{20k}}   (1)

By 2019 we have 49 years since 1970 the equation is given by:

98000 = P_o e^{49k}   (2)

And replacing P_o from equation (1) we got:

98000=\frac{143000}{e^{20k}} e^{49k} =143000 e^{29k}  

We can divide both sides by 143000 we got:

\frac{98000}{143000} =0.685 = e^{29k}

And if we apply ln on both sides we got:

ln(0.685) = 29k

And then k =-0.01303024661[/tex]

And replacing into equation (1) we got:

P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69

And we can round this to the nearest up integer and we got 110194.  

7 0
2 years ago
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