Factor yz + 6 + y +6z. z + 1)(y + 6) (z - 1)(y + 6) (z + 6)(y - 1)

1 answer:

8 0

The answer is the first one: (z+1)(y+6).

Explanation:

yz + 6 + y + 6z

= yz + y + 6 + 6z

= y(z+1) + 6(1+z)

= (z+1)(y+6)

For (z+1), you can also write (1+z), it doesn’t matter.

Hope it helps!

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If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by

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The family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

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By Linear Algebra, we can calculate the angle by definition of dot product:

$\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}$ (1)

Where:

$\theta$ - Angle between vectors, in sexagesimal degrees.

$\|\vec a\|, \|\vec b \|$ - Norms of vectors $\vec {a}$ and $\vec{b}$

If $\theta$ is acute, then the cosine function is bounded between 0 a 1 and if we know that $\vec {a} = (p, 3, -7)$ and $\vec {b} = (p, -p, 4)$ , then the possible values for $p$ are: