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3 years ago

✨42 POINTS✨PLEASE HELP 6th grade math!!! need answers for A B and C

Mathematics

1 answer:

Alex3 years ago

3 0

9514 1404 393

Answer:

A"(-6, 3)

B"(-9, 0)

C"(-5, -1)

Step-by-step explanation:

We presume the first transformation is a translation 4 units right and 1 unit up:

(x, y) ⇒ (x+4, y+1)

The second transformation negates the x-coordinate, so the two transformations together have the rule ...

(x, y) ⇒ (-(x+4), y+1)

Then the transformed points are ...

A"(-6, 3)

B"(-9, 0)

C"(-5, -1)

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3 years ago

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

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Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

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3 years ago