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3 years ago

Find x. (Use pic for more info)

Mathematics

1 answer:

V125BC [204]3 years ago

8 0

Answer:

x=75

Step-by-step explanation:

Hey There!

If you didn't know the exterior angle of a triangle is equal to the sum of the opposite interior angles of a triangle

So essentially what I'm saying is that

2x-5=70+x

step 1 add 5 to each side

-5+5 cancels out

70+5=75

now we have

2x=70+x

step 2 subtract x from each side

x-x cancels out

2x-x=x

we're left with

x=75

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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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