Which calculation be used to find the value of p in the equation p^3=8?

I'm have some issues with the problem shown in the screenshot and would love some help.

KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

$\frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0$

Which gives;

$\frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0$

6•x² - 106•x + 315 = 0

$x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}$

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

Width ≈ 18 - 2×4.55 in. = 8.89 in.

Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

Height = x ≈ 4.55 in.

The maximum volume of the box, V ≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

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7 0

1 year ago

Your computer server recently crashed and you need to make changes to a large manual. The manual contains approximately 16,000 w

tensa zangetsu [6.8K]

Answer:

The manual cost that will take to recreate by the firm is $ 90.51

Step-by-step explanation:

Given:

Number of words the manual contains= 16000

Number of words typed by a clerk in one hour and 20 minutes = 4160

To Find:

The total cost for recreating the manual = ?

Solution:

Step 1: Finding the Number of hours is need to type 4160 words :

= $1\frac{20}{60}$ hours

$\\\\=1\frac{1}{3}$ hours

$\\\\=\frac{4}{3}$ hours

So it takes $\frac{4}{3}$ hours to type 4160 word

Step 2 : Finding the Number of hours is needed to type 1 word

= $\frac{4160}{\frac{4}{3}}$

= $4160 \times \frac{3}{4}$

= 3120 words per hour

Step 3 : Finding the Number of hours is needed to type 16000 words

= $\frac{\text{ total number of words}} {\text{ number of words written per hour}}$

Substituting the values

= $\frac{16000}{3120}$

= 5.1282 hours

Step 4 : Finding the cost for recreating the manual.

= number of hours x cost per hour

= 5.1282 x $17.65

= 90.51

5 0

3 years ago

I don't understand rational and irrational numbers

PSYCHO15rus [73]

A rational number is a number which can be expressed as a fraction whose numerator and denominator are both integers and whose denominator is not equal to zero. Rational numbers include all integers, fractions, mixed numbers, and some decimal numbers.

Note : All terminating and repeating decimal numbers are rational numbers because those numbers can be expressed as a fraction. On the other hand, a non repeating number and non terminating decimal, like square root of 2, is an irrational number.

$\dfrac{7}{16} \ as \ a \ decimal = 0.4375$