KnockOut

Take a look:

https://web2.0calc.com/questions/help_53566

Take a look at:

https://artofproblemsolving.com/wiki/index.php/2006_AMC_12B_Problems/Problem_21

I think it's the problem you're looking for.

STEP 1.

So, we have a right triangle \(\triangle {ABC}\) with \(\angle B = 90^\circ\).

Let sides \({AC} = a\), \(AB = b\). and \(CB = c\).

\(2\sin A\) is equal to \(2(\frac{c}{a})\), and \(3\cos A \) is equal to \(3(\frac{b}{a})\)

Therfore, 

 \(2(\frac{c}{a}) = 3(\frac{b}{a})\),

\(\frac{2c}{a} = \frac{3b}{a}\),

\(2c = 3b\).

STEP 2.

\(\tan A\) is equal to \(\frac{c}{b}\).

We can substitute \(c\) for \(\frac{3b}{2}\).

\(\tan A\) \(=\) \(\frac{\frac{3b}{2}}{b}\),

\(\tan A\) \(=\) \(\frac{3b}{2} \times \frac{1}{b}\),

\(\tan A\) \(=\) \(\boxed{\frac{3}{2}}\)

So a square of a binomial would be in the form of \((a + b)^2\). In your case, we have \(4x^2 - 12x + a\), which is supposed to be the square of a binomial. 

So your binomial would probably be \((2x - 3)\). Squaring this would give us \(4x^2 - 12x + 9\).

So, \(\boxed{a = 9}\)

True.

The electronic configuration of \(Re^{7+}\) is\([Xe]\) \(5d^0\) \(6s^0\) and there is no unpaired electron in the outer shell to contribute in heat capacity.

I just realized. This question has also been answered b4. Just another thing to keep in mind. Hehe. 

Okay. I'm gonna attempt to explain how it works. 

The second and fourth rows of the pascal's triangle have only even digits (excluding the 1s).

If we look further down into Pascal's triangle, we can see that rows 8 and 16 are the next two rows with only even digits (excluding the 1).

Do you notice a pattern here?

The even digit rows in order are: \(2, 4, 8, 16...\)

The number of each subsequent row is twice the number of each preceding row.

Using this knowledge, we can find that the rows with only even numbers, less than 100 are:

\(2, 4, 8, 16, 32, 64\), which would give us an answer of \(\boxed 6 \) rows.

(P.S. When you are learning about Pasal's triangle, stuff like this is good to keep in mind)

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