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Dmitry_Shevchenko [17]
2 years ago
14

A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where

x is the height in inches.
What is the height of the box if the volume is 15 in.3?


There is a rectangular box with length x+2 in. , width x-2 in. , and height x in.


height = in.

Mathematics
1 answer:
marta [7]2 years ago
3 0

Answer:

Height =3

Step-by-step explanation:

Given

Length = x + 2

Width = x - 2

Height = x

Volume = 15

Required

Find the height

The volume is calculated as thus:

Volume = Length * Width * Height

This gives

15 = (x + 2) * (x - 2) * x

Apply difference of two squares

15 =(x^2 - 4 ) * x

15 = x^3 - 4x

Subtract 15 from both sides

x^3 - 4x - 15 = 0

Using a calculator to factorize, we have:

(x-3)(x^2+3x+5) = 0

Split

x - 3 = 0 or x^2 + 3x + 5 = 0

x = 3 or  x^2 + 3x + 5 = 0

x has complex roots for x^2 + 3x + 5 = 0

Hence:

x = 3

Recall that:

Height = x

Height =3

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max2010maxim [7]

Answer:

2 5/9 is less than 21/3;  2 5/9 < 21/3

Step-by-step explanation:

<u>Step 1:  Convert 2 5/9 into an improper fraction</u>

2 5/9 = 2 * 9/9 + 5/9 = 18/9 + 5/9 = 23/9

<u>Step 2:  Convert 21/3 so the denominator is 9</u>

21*3 / 3*3 = 63/9

<u>Step 3:  Compare</u>

<em>23/9 < 63/9</em>

<em />

Answer:  2 5/9 is less than 21/3;  2 5/9 < 21/3

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7 0
3 years ago
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Step-by-step explanation:

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The problem statement tells you that t represents minutes after lift off, so this solution means the altitude is 21000 feet 6 minutes after lift off.

The question is asking for the number of minutes after lift off that the plane reaches an altitude of 21000 feet, so this answers the question directly:

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