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
lesantik [10]
3 years ago
8

box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am

ount of material used. sides of base
Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

You might be interested in
A rectangular balcony has an area of 32 square feet. its perimeter is 24 feet. what are the dimensions of the balcony?
Paul [167]

Answer:

Step-by-step explanation:

8 ft by 4 ft

8ft x 4ft = 32 ft

8ft + 8 ft = 16 ft  4 ft + 4 ft = 8 ft

16ft + 8 ft = 24 ft

5 0
3 years ago
ANSWER ASAP Which of the following best describes the graph shown below?
Thepotemich [5.8K]

Answer:

C. This is the graph of a linear function.

Step-by-step explanation:

Linear function because it's not touching each other.

4 0
3 years ago
Read 2 more answers
How is 6/10 written as a decimal?
BARSIC [14]
It’s written as 0.6 in decimal form
6 0
3 years ago
Read 2 more answers
What is the area of a trapezoid? 47,45,65
Masteriza [31]
Area = 2,520m^2
(47+65)/2 = 56
56x45 = 2,520
8 0
2 years ago
What decimal is greater 0.732 or 0.75
BARSIC [14]
0.732
0.750

If you have trouble with decimals, then multiply both numbers by a constant number to get rid of the decimals. In this case, we would multiply by 1000.

0.732 x 1000 = 732
0.750 x 1000 = 750

Obviously, 750 is bigger than 732. Therefore, 0.75 is bigger than 7.32.

By the way, this is a property: 
If a \ \textgreater \  b, then a \cdot c ~\ \textgreater \ ~ b\cdot c
5 0
3 years ago
Read 2 more answers
Other questions:
  • Lorena is driving a truck that is painting the lines on a new road. The lines she paints are 0.152 meters wide, and she will pai
    14·1 answer
  • What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
    9·2 answers
  • Evaluate the following: 3 Squared ÷ (2 + 1). 2 3 4 5
    12·2 answers
  • Luther takes 45 bottles of water on a camping trip. If he drinks 80 % of them how many does he have left?
    10·1 answer
  • A grocery store clerk is putting cans of soup on the shelves. She has 12 boxes, which each contain 24 cans of soup. Altogether,
    6·2 answers
  • 9 < 11, so 9(5) < 11(5) true or false?
    14·1 answer
  • Which angle is included angle forJL and KL
    10·1 answer
  • Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1
    15·1 answer
  • (2n-9)-5(2.4n+4) does anyone know the answer to this?
    10·1 answer
  • Find the EXACT distance between the two points.<br><br><br><br> (4,7) and (−4,9)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!