3 years ago

Simplify these expressions

Mathematics

1 answer:

svlad2 [7]3 years ago

4 0

Answer:

expressions.txt

Step-by-step explanation:

woah those were some hard expressions to simplify!!

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Answer:

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Step-by-step explanation:

An interior angle and its exterior angle are supplementary (they add up to 180°).

I would really appreciate it if you would mark me brainliest!

<em>Have a blessed day!</em>

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

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3 years ago

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if that 40% is how many are vacant then- 100 are vacant and 150 are occupied

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