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ddd [48]
3 years ago
8

the perimeter of a rectangle is twice the sum of its length and it width. The perimeter is 16 meters ans its length is 2 meters

more than twice its width. What is the length?
Mathematics
1 answer:
olganol [36]3 years ago
6 0

Answer:

The length is 6 meters.

Step-by-step explanation:

If its width is x meters  then its length is 2x + 2 meters and we have the equation:

2x + 2(2x + 2) = 16

2x + 4x + 4 = 16

6x = 16 - 4

6x = 12

x = 2 meters.

Thus x is the width and the length is 2(2) + 2 = 6 meters.

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Find a nonzero vector orthogonal to the plane through the points: ????=(0,0,1), ????=(−2,3,4), ????=(−2,2,0).
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Answer:

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

\overrightarrow {PQ}==

\overrightarrow {PR}==

The nonzero vector orthogonal to the plane through the points P,Q, and R is

\overrightarrow n=\overrightarrow {PQ}\times \overrightarrow {PR}

\overrightarrow n=\det \begin{pmatrix}i&j&k\\ \:\:\:\:\:-2&3&3\\ \:\:\:\:\:-2&2&-1\end{pmatrix}

Expand along row 1.

\overrightarrow n=i\det \begin{pmatrix}3&3\\ 2&-1\end{pmatrix}-j\det \begin{pmatrix}-2&3\\ -2&-1\end{pmatrix}+k\det \begin{pmatrix}-2&3\\ -2&2\end{pmatrix}

\overrightarrow n=i(-9)-j(8)+k(2)

\overrightarrow n=-9i-8j+2k

\overrightarrow n=

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