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3 years ago

Help me solve the question in the picture (pls show working)

Mathematics

2 answers:

Bess [88]3 years ago

5 0

Answer:

92.75 cm²

Step-by-step explanation:

area of polygon = area of ∆EDA + area of ∆ADC +area of ∆ACB.

area of triangles is ½×base×height.

area of ∆EDA=½×EF×AD

=½×4.5×12

=27 cm². -------->(1)

area of ∆ADC=½×AD×DC

=½×12×5

=30 cm². --------->(2)

area of ∆ACB=½×AC×BG

=½×AC×5.5

from pythagorean theorem

(AC)²=(AD)²+(CD)²

= 25+144

= 169 cm then. AC= 13 cm

then area of ∆ACB=½×5.5×13

=35.75 cm² ---------->(3)

from equation (1), (2) and (3):

then the area of polygon = 27 + 30 + 35.75

=92.75 cm²

Dima020 [189]3 years ago

4 0

Add all the numbers

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Vinvika [58]

Answer:

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Step-by-step explanation:

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.

Since in total there are 303 hours for electronics work, then:

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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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My name is Ann [436]

Answer:

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Step-by-step explanation:

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