How do I solve this problem

Mathematics

1 answer:

Vaselesa [24]3 years ago

4 0

C = 84 degrees

A = 2B
C = A + 20
A + B + C = 180

A = 2B
A/2 = B

A + (A/2) + (A+20) = 180
multiply each side by 2
2A + A + 2A + 40 = 360
combine like terms
5A + 40 = 360
subtract 40 from both sides
5A = 320
divide both sides by 5
A = 64

C = A + 20
C = 64 + 20
C = 84

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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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Answer:

The family of possible values for $p$ are:

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

Step-by-step explanation:

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: