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Taya2010 [7]
3 years ago
7

Which of the following is a perfect square trinomial?

Mathematics
1 answer:
shutvik [7]3 years ago
5 0

Answer:

A.

Step-by-step explanation:

Take a look at what happens when squaring either of these...

(ax-by)^2=(ax-by)(ax-by)=a^2x^2-2abxy+b^2y^2\\\\(ax+by)^2=(ax+by)(ax+by)=a^2x^2+2abxy+b^2y^2\\

Notice a couple of patterns.

1.  The last term has a positive coefficient.  That rules out answer choices C and D.

2.  The coefficient of the middle term is either +2ab \text{ or } -2ab .  So what are <em>a</em>  and <em>b</em>?  <em>a</em> is the square root of the x^2 term and <em>b</em> is the square root of the y^2 term.

25x^2 \Rightarrow a=5\\\\9y^2 \Rightarrow b=3\\\\ab=15\\\\2ab=30

The middle coefficient needs to be either +30 or -30.  The answer is choice A.

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The answer is A. $15.00

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A system contains n atoms, each of which can only have zero or one quanta of energy. How many ways can you arrange r quanta of e
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Answer:

\mathbf{a)} 2\\ \\ \mathbf{b)} 184 \; 756 \\ \\\mathbf{c)}  \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}

Step-by-step explanation:

If the system contains n atoms, we can arrange r quanta of energy in

                         \binom{n}{r} = \dfrac{n!}{r!(n-r)!}

ways.

\mathbf{a)}

In this case,

                                n  = 2, r=1.

Therefore,

                    \binom{n}{r} = \binom{2}{1} = \dfrac{2!}{1!(2-1)!} = \frac{2 \cdot 1}{1 \cdot 1} = 2

which means that we can arrange 1 quanta of energy in 2 ways.

\mathbf{b)}

In this case,

                                n  = 20, r=10.

Therefore,

                    \binom{n}{r} = \binom{20}{10} = \dfrac{20!}{10!(20-10)!} = \frac{10! \cdot 11 \cdot 12 \cdot \ldots \cdot 20}{10!10!} = \frac{11 \cdot 12 \cdot \ldots \cdot 20}{10 \cdot 9 \cdot \ldots \cdot 1} = 184 \; 756

which means that we can arrange 10 quanta of energy in 184 756 ways.

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In this case,

                                n = 2 \times 10^{23}, r = 10^{23}.

Therefore, we obtain that the number of ways is

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66

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