$8750 at 12.25% for 2 years

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

#SPJ1

7 0

1 year ago

Will give brainliest 1. What is the formula for experimental probability? 2. What is a trial?

Mariulka [41]

Answer:

1) Formula for experimental probability:

Experimental Probability = $\frac{No.OfFavourableOutcomes}{No.OfPossibleOutcomes}$

2) Any performance or a random experiment is called a trial.

5 0

3 years ago

Dana is making a seating chart for an awards banquet. There are 184 people coming to the banquet. If 8 people can be seated at e

FromTheMoon [43]

There are 184 people
there are 8 people in each table.
184÷8= 23 tables
she need 23 tables

6 0

3 years ago

Read 2 more answers

In Bangor it’s -3 F in Fairbanks it’s -12 F in Fargo it’s -8 F and in Calgary it’s -15 F in which city is to the coldest?

jonny [76]

Answer:

Calgary is the coldest

Step-by-step explanation:

The simple way to determine this will be to change the value of temperatures given in Fahrenheit to Celsius

32 F = 0°C

Formula to apply will be (T-32)×5/9 -------------where T is temperatures in Fahrenheit

Bangor is -3F-------------------change to Celsius

(-3-32)×5/9 =-35 × 5/9 = -19.44°C

Fairbanks is -12 ------------------------change to Celsius

(-12-32)×5/9 = -44 × 5/9 = -24.44°C

Fargo is -8 F ---------------------Change to Celsius

(-8-32)×5/9= -40×5/9 = -22.22°C

Calgary is -15 F-------------------------Change to Celsius

(-15-32)×5/9 = -47×5/9 = -26.11°C--------------coldest

3 0

3 years ago

Are is the Triangle SWT and triangle SVU similar? What would be the answer?

kondaur [170]

Answer:

A) Yes the 2 triangles are similar by SSS Similarity and SAS Similarity

Step-by-step explanation:

SSS:

ST/SU = SW/SV = WT/VU

60/70 = 48/56 = 30/35

6/7 = 6/7 = 6/7

SAS:

ST/SU = SW/SV = 6/7 (look at SSS proving)

Angle S = Angle S because they are reflexive or the same angles

4 0

3 years ago