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3 years ago

6

Frances wants to paint rectangular wall that has a width of 8 feet and a height of 9 ft.She has a quart of paint that will cover

85 square ft.what is the area of the wall?

2 answers:

deff fn [24]3 years ago

8 0

Area is length times width
so you 8 x 9 =72 sq ft

VladimirAG [237]3 years ago

6 0

The area of the wall is 72 feet squared.

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Let x be the amount of type A mp3 produced, and the amount of model B mp3's produced and z the amount of model C mp3 produced.

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Since in total there are 393 hours for assembly, then:

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Since in total there are 416 hours for quality assurance, then:

$4.4x+3.4y+4.8z=416$

Then, the linear system associated to the problem is

$3.2x+5.4y+2.2z=303\\2.8x+2.4y+5.8z=393\\4.4x+3.4y+4.8z=416$

with coefficient matrix $A=\left[\begin{array}{ccc}3.2&5.4&2.2\\2.8&2.4&5.8\\4.4&3.4&4.8\end{array}\right]$ and vector of constant terms $b=\left[\begin{array}{ccc}303\\393\\416\end{array}\right]$

Since the determinant of A is equal to 36.704 then A is invertible.

Then for solve the system $Ax=b$ , is enough find the inverse of A and operate

$Ax=b\\A^{-1}Ax=A^{-1}b\\x=A^{-1}b$

Using Octave we obtain that

$A^{-1}=\left[\begin{array}{ccc}-0.22&-0.50 &0.71\\0.33&0.15&-0.34\\-0.028& 0.35&-0.20\end{array}\right]$

Then

$x=A^{-1}b=\left[\begin{array}{ccc}30\\20\\45\end{array}\right]$

This means that 30 mp3's of model A, 20 of model B and 45 of model C must be produced

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