1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seropon [69]
2 years ago
14

An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by removing a small square from each corner

and folding up the flaps to form the sides. What are the dimensions of the box of greatest volume that can be constructed in this way
Mathematics
1 answer:
seraphim [82]2 years ago
6 0

The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.

<h3>How to solve the dimension?</h3>

Let x be the side of the square to remove. Then the volume of the box is:

V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³

To find the maximum volume, differentiate and set it to 0:

V'(x) = 324 - 144x + 12x²

0 = x² - 12x + 27

0 = (x - 9)(x - 3)

x = 3 or 9

When x = 3,

V"(x) =-144+24x

V"(3) =-144+72=-72<0

so volume is maximum at x=3

Therefore the box is 12x12x3 and the volume is 432.

Learn more about dimension on:

brainly.com/question/26740257

You might be interested in
Solve the inequality -12≤2x-4&lt;10
tia_tia [17]
I hope this answers your question !

4 0
3 years ago
What am I doing wrong
stiv31 [10]
For this answer it is:

12 inches = 36 feet
7 0
3 years ago
-3 greater then or equal to &gt; -1
enot [183]
-3 is actually less than -1    

it can't be equal because they are 2 different values 

and it can't be greater than because if you place -3 and -1 in a number Line, -1 is closer to 0 which equals that -1 is greater than -3
5 0
4 years ago
PLEEEEEEEEEEASSEEEEEEE ANSWER QUESTION IS DOWN BELOW WORTH 15 POINTS each
Svetllana [295]

A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.

<h3>What is a Ratio?</h3>

A ratio shows us the number of times a number contains another number.

Given that the scale factor is 3:14. Therefore, the ratios can be written as,

(a) The ratio of the surface area of the model to the surface area of the original  is,

Surface area Ratio = (3/14)² = 9/196

(b) The ratio of the volume of the model to the volume of the original.

Volume Ratio = (3/14)³ = 27/2744

(c) The ratio of the width of the model to the width of the original.

Width Ratio = 3/14

Learn more about Ratios:

brainly.com/question/1504221

#SPJ1

3 0
2 years ago
5^2 + 12^2 = c^2 please show work I dont quite know how to finish the ending part off help.
Pavel [41]
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
take the square root of both sides
+ - 13 = c
3 0
3 years ago
Other questions:
  • Jean bought a $1,980 snow thrower on the installment plan. The installment agreement included a 10% down payment and 18 monthly
    10·1 answer
  • A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and tes
    6·1 answer
  • 1.05+2.24= x-3.12 ????????//
    6·1 answer
  • Solve the following quadratic equation for all values of x in simplest form !! Please answer this !!
    9·1 answer
  • A trapezoid has an area of 24 square meters. The length of the bases of the trapezoid are 5 meters and 7 meters. What is the hei
    5·1 answer
  • Ca someone plzzz help me with this problem?
    12·1 answer
  • Please help me . i will help you whenever you want
    6·1 answer
  • Help plssssss this is due today! This composite figure is made up of three simpler shapes. What is the area of the figure?
    11·2 answers
  • Ayo help pls help medee:&gt;
    10·1 answer
  • You are putting together your first post-graduation budget. Your take-home pay will be $2,500 per month. You estimate your month
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!