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Marizza181 [45]
3 years ago
7

An open box is to be made from a flat piece of material 19 inches long and 4 inches wide by cutting equal squares of length x fr

om the corners and folding up the sides. Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors. V= If we write the domain of the box as an open interval in the form (a,b), then what is a=? a= and what is b=? b=
Mathematics
1 answer:
Aleksandr [31]3 years ago
7 0

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

x

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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Vlad [161]

Answer:

x < 7

Step-by-step explanation:

First apply the -2 onto each term that it is being multiplied onto.

-2x + 6 > - 8

Now subtract six from both sides.

-2x > -14

Now divide by -2.

x < 7

<u>REMEMBER</u>

When doing greater than and less than equations like this, if you divide by a negative you must flip the greater than/less than.

5 0
3 years ago
Two ships leave the same port at the same time. Two hours later ship A has traveled 12 miles and ship B has traveled 8 miles.
MakcuM [25]

Answer:

the angle between their paths is <em>100.8°</em>

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the <em>Cosine Rule</em> which is:

c² = b² + a² - 2 b c cos(θ)

where

  • c = 16 miles
  • b = 8 miles
  • a = 12 miles

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

<em>θ = 100.8°</em>

<em></em>

Therefore, the angle between their paths is <em>100.8°</em>

4 0
3 years ago
After dividing a piece of wood into four equal sections,each section is 4 in.long.How long was the piece of wood I started with
Cerrena [4.2K]

I'm going to out on a limb and say 16 in.

4 pieces * 4 in. = 16

5 0
3 years ago
Which values represent solutions to cos
shepuryov [24]

Answer:

C option

Step-by-step explanation:

C is the correct solution of to above equation

4 0
3 years ago
5x-4=-6x+4 then x=? please help!
7nadin3 [17]

Answer:

x = 8/11

Step-by-step explanation:

5x - 4 = -6x + 4

Collect like terms

5x + 6x = 4 + 4

11x = 8

x = 8/11

4 0
3 years ago
Read 2 more answers
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