A box is 1 meter wider than its height and 2 meters longer than his width.
1 answer:
Let the height be
Hence, the width is $x+1$ and length is $(x+1)+2=x+3$
The volume is given to be 2 m³
Hence, $2=x(x+1)(x+3)$
Solving,
$x^3+4x^2+3x-2=0$
$(x+2)(x^2+2x-1)=0$
$\implies x+2=0$ or $x^2+2x-1=0$
But $x=-2$ cannot be possible
Hence, $x^2+2x-1=0$
$\implies x=-1-\sqrt 2$ or $x=-1+\sqrt 2$
Reject the negative solution.
Hence, the height is $\sqrt 2-1$,
width is $\sqrt 2$ and length is $\sqrt 2 +2$
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Using translation concepts, it is found that the correct option regarding the function is:
The function h(x) is decreasing on the interval (3, ∞).
<h3>What is a translation?</h3>A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
Which increases on (0, ∞).
The translated function is given by:
With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:
The function h(x) is decreasing on the interval (3, ∞).
More can be learned about translation concepts at brainly.com/question/4521517
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