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Eduardwww [97]
3 years ago
14

Si juan tiene 7 manzanas y le da 5 a jose ¿cuantas manzanas le quedan a juan?​

Mathematics
1 answer:
ryzh [129]3 years ago
5 0

Answer:

2

Step-by-step explanation:

por que el le dio 5 manzanas a jose y le quedaron 2

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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​
PIT_PIT [208]

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:

Minimum (\cos \theta = 0)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0

Maximum (\cos \theta = 1)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1

With the help of a graphing tool we get the family of possible values for p are:

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

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