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3 years ago

Eram Figure A4

Mathematics

1 answer:

arsen [322]3 years ago

8 0

Answer:

18 ft³

Step-by-step explanation:

Consider the given figure showing the steps to consists of 3 rectangle prism or cuboid.

The cubic feet of concrete necessary = sum of the volume of the 3 cuboid/rectangular prism

Volume = l*w*h

Dimension of each cuboid:

Note that 1 ft = 12 inches

First cuboid:

Length (l) = 48 in = 48/12 = 4 ft

Width (w) = 36 in = 36/12 = 3 ft

Height (h) = 9 in = 9/12 = 0.75 ft

Volume = 4*3*0.75 = 9 ft³

Second cuboid:

Length (l) = 48 in = 48/12 = 4 ft

Width (w) = 24 in = 24/12 = 2 ft

Height (h) = 9 in = 9/12 = 0.75 ft

Volume = 4*2*0.75 = 6 ft³

Third cuboid:

Length (l) = 48 in = 48/12 = 4 ft

Width (w) = 12 in = 12/12 = 1 ft

Height (h) = 9 in = 9/12 = 0.75 ft

Volume = 4*1*0.75 = 3 ft³

Cubic feet of concrete necessary for the steps = 9 + 6 + 3 = 18 ft³

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valkas [14]

For the matrix

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$\det \begin{bmatrix}{a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}}\end{bmatrix}=a_{31}\det \begin{bmatrix}{a_{12}} & {a_{13}} & {} \\ {a_{22}} & {a_{23}} & {} \\ {} & {} & {}\end{bmatrix}-a_{32}\det \begin{bmatrix}{a_{11}} & {a_{13}} & {} \\ {a_{21}} & {a_{23}} & {} \\ {} & {} & {}\end{bmatrix}+a_{33}\det \begin{bmatrix}{a_{12}} & {a_{12}} & {} \\ {a_{22}} & {a_{22}} & {} \\ {} & {} & {}\end{bmatrix}$

Answer:

First, we compute the determinants of the minors:

$\begin{gathered} \det \begin{bmatrix}{0} & {4} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}=0+4=4, \\ \det \begin{bmatrix}{1} & {4} & {} \\ {1} & {3} & {} \\ {} & {} & {}\end{bmatrix}=3-4=-1, \\ \det \begin{bmatrix}{1} & {0} & {} \\ {1} & {-1} & {} \\ {} & {} & {}\end{bmatrix}=-1-0=-1. \end{gathered}$

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