chase1869

chase1869

26.03.2021 •

Mathematics

Can you help me figure this out?

Can you help me figure this out?

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Ответ:

asalimanoucha2v

23.04.2022

Answer with Step-by-step explanation:

We are given that

Length of flat piece of material =19 inches

Width of flat piece=4 inches

An open box is to be made from a flat piece by cutting equal squares of length x from the corners and folding up the sides

Therefore, length of open box= (19-2x) inches

Width of open box= 4-2x inches

Height of box= x inches

Volume of box= $l\times b\times h$

Substitute the values then we get

Volume of box= x(19-2x)(4-2x)

x(19-2x)(4-2x) 0

Because volume of open box is always greater than zero.

Then , x 0

Substitute

19-2x 0

2x-19 < 0

2x < 19 By adding 19 on both sides

Dividing by 2 on both sides

$x< \frac{19}{2}=9.5$

It means $x\in (0,9.5)$

Substitute 4-2x 0

2x-4< 0

Adding 4 on both sides then we get

2x < 4

Dividing by 2 on both sides

$x< \frac{4}{2}=2$

Then, $x\in (0,2)$

Therefore, domain of the box = $(0,2)\cap (0,9.5)=(0,2)$

Then ,a=0 and b=2

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