Mathematics: Determine the volume of the parallelopiped determined by the vectors a= −6,3,2 and b= −2,10,−5 and c= 1,10,−3 .

Determine the volume of the parallelopiped determined

Ответ:

allieballey0727

15.01.2022

Mathematics

The volume of the parallelopiped is 213 cubic units.

Step-by-step explanation:

The given vectors are A=<−6,3,2> and B=<−2,10,−5> and C=<1,10,−3>.

If three vectors a=,b=,c= are given then volume of the parallelopiped is

$V=|a\cdot (b\times c)|$

$a\cdot (b\times c)=\left|\begin{array}{ccc}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{array}\right|$

Using the above formula we get

$A\cdot (B\times C)=\left|\begin{array}{ccc}-6&3&2\\-2&10&-5\\1&10&-3\end{array}\right|$

Expand along row 1.

$A\cdot (B\times C)=|-6\cdot \det \begin{pmatrix}10&-5\\ 10&-3\end{pmatrix}-3\cdot \det \begin{pmatrix}-2&-5\\ 1&-3\end{pmatrix}+2\cdot \det \begin{pmatrix}-2&10\\ 1&10\end{pmatrix}|$

$A\cdot (B\times C)=-6\cdot (20)-3\cdot (11)+2\cdot (-30)$

$A\cdot (B\times C)=-213$

Volume of the parallelopiped is

$V=|A\cdot (B\times C)|$

V=|-213|

V=213

Therefore, the volume of the parallelopiped is 213 cubic units.

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Ответ:

kimlyn58p0wyn0

01.11.2021

Mathematics

To rent a certain meeting room, a college charges a reservation fee of $35 and an additional fee of $9.90 per hour.

Let t be the number of hours rented

charge for renting a meeting room is 9.90t +35

The chemistry club wants to spend at most $94.40 on renting the meeting room.

so charge is less than or equal to 94.40

The inequality becomes 9.90t + 35 <=94.40

Solve the inequality for t

9.90t + 35 <=94.40

Subtract both sides by 35

9.90t < = 59.4

Divide both sides by 9.90

t < = 6

So, they could rent the meeting room for maximum of 6 hours.

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Determine the volume of the parallelopiped determined by the vectors a=< −6,3,2> and b=< −2,10,−5> and c=< 1,10,−3> .

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