By using determinant method solve following questions 3x+4y+5z=18. 2x-y-8z=13. 5x-2y+7z=20

Mathematics

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Sauron [17]3 years ago

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Pavel [41]3 years ago

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3x+4y+5z=18,2x−y+8z=13,5x−2y+7z=20 D= ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 3 2 5 4 −1 −2 5 8 7 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =3(−7+16)−4(14−40)+5(−4+5) =3(9)−4(−26)+5(1)=27+104+5=136 D 1 = ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 18 13 20 4 −1 −2 5 8 7 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =18(−7+16)−4(91−160)+5(−26+20) =18(9)−4(−69)+5(−6)=162+276−30=408 D 2 = ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 3 2 5 18 13 20 5 8 7 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =3(91−160)−18(14−40)+5(40−65) =3(−69)−18(−26)+5(−25)=−207+468−125=136 D 3 = ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 3 2 5 4 −1 −2 18 13 20 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =3(−20+26)−4(40−65)+18(−4+5) =3(6)−4(−25)+18(1)=18+100+18=136 Now, x= D D 1 = 136 408 =3 y= D D 2 = 136 136 =1 z= D D 3 = 136 136 =1 Hence, the solution for the system is (3,1,1).

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Sienna used the scale drawing above to create a pool that is 14 ft wide x 22 ft long. She then decided to make pool with a final

Bond [772]

A scale factor allows a shape to be changes into another shape by changing the linear dimensions to the multiples of the initial dimension and a constant

The expression that finds the change in scale factor for the longer pool with a final length of 33 ft. Sierra is building is the option;

$\dfrac{2 \, ft.}{3 \, ft.}$

Reason:

Known parameters are;

Dimensions of the pool created = 14 ft. wide × 22 ft. long

Final length of the pool = 33 ft.

Let x represent the length of the drawing using the initial scale factor, we have;

$The \ initial \ scale \ factor = \dfrac{22 \, ft.}{x \, in.}$

The scale factor of the drawing following a final length of 33 ft. is therefore;

$New \ scale \ factor = \dfrac{33 \, ft.}{x \, in.}$

The change in scale factor is given as follows;

$Change \ in \ scale \ factor = \dfrac{Initial \, scale \, factor}{Final \, scale \, factor}$

Therefore;

$Change \ in \ scale \ factor = \frac{\left( \dfrac{22 \, ft.}{x \, in.} \right)}{\left( \dfrac{33 \, ft.}{x \, in.} \right)} = \dfrac{2 \, ft.}{3 \, ft.}$