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3 years ago

15

Rachel is packing up her room to move to a new city.Together,all the books on her bookshelf weigh 85 pounds.She wants to divide

the books among 4 boxes,so that each box will weigh the same amount.
How many pounds of books will be in each box?

1 answer:

attashe74 [19]3 years ago

3 0

Answer:

21.25

Step-by-step explanation:

85/4 = 80/4+5/4 = 20 + 1 + 1/4 = 21 + 0.25 = 21.25

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Acute angle between the two planes: approximately $43^\circ$ .

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Find the normal vector of each plane:

The normal vector of the plane $x - 2\, y + 5\, z = 3$ is $\displaystyle \begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix}$ .
The normal vector of the plane $2\, x + y - 3\, z = 15$ is $\displaystyle \begin{bmatrix}2 \\ 1\\ -3\end{bmatrix}$ .

As the name suggests, there is a $90^\circ$ angle between a plane and its normal vector. The following four angles will correspond to the vertices of a quadrilateral:

The $90^\circ$ angle between the first plane and its normal vector.
The angle between the normal vector of each plane.
The $90^\circ$ angle between the second plane and its normal vector.
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Make use of the dot product to find the angle between these two normal vectors. Let $\theta$ denote the angle between these two vectors.

$\displaystyle \cos \theta = \frac{\begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix} \cdot \begin{bmatrix}2 \\ 1 \\ -3\end{bmatrix}}{\sqrt{1^2 + (-2)^2 + 5^2} \cdot \sqrt{2^2 + 1^2 + (-3)^2}} \approx -0.73193$ .

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