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
mixer [17]
3 years ago
5

Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui

lding material possible.
Mathematics
1 answer:
Vesnalui [34]3 years ago
3 0
<h3>The dimensions of the given rectangular box are:</h3><h3>L  =   15.874 cm  , B  =  15.874 cm   , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box  

= Area of the base +  4 x ( Area of the adjacent faces)

=  S x S  +  4 ( S x H)   = S² +  4 SH   ..... (1)

Also, Area of the box  = S x S x H  =  S²H

⇒ S²H = 2000

\implies H = \frac{2000}{S^2}

Substituting the value of H in (1), we get:

A = S^2 + 4 SH =  S^2 + 4 S(\frac{2000}{S^2}) =  S^2 + (\frac{8000}{S})\\\implies A  =  S^2 + (\frac{8000}{S})

Now, to minimize the area put :

(\frac{dA}{dS} ) = 0 \implies 2S  - \frac{8000}{S^2}  = 0\\\implies S^3 = 4000\\\implies S  = 15.874 \approx 16 cm

Putting the value of S  = 15.874 cm in the value of H , we get:

\implies H = \frac{2000}{S^2}  =  \frac{2000}{(15.874)^2} = 7.8937 cm

Hence, the dimensions of the given rectangular box are:

L  =   15.874 cm

B  = 15.874 cm

H = 7.8937 cm

You might be interested in
Complete the table for the function
IgorLugansk [536]

Answer:

C

Step-by-step explanation:

y(x) = x^(1/3)+7

y(-8)=(-8)^(1/3)+7=5

y(-1)=(-1)^(1/3)+7=6

y(1)=(1)^(1/3)+7=8

y(8)=(8)^(1/3)+7=9

4 0
3 years ago
Peter tracks the goals he scores in 9 soccer games. In two games Peter scored 2 goals each, in one game he scored 0 goals, in tw
Lynna [10]
1.6 i think 
add all the goals and divide by the amount of games?
8 0
3 years ago
Read 2 more answers
Need help plz!!!!? Help would be appreciated
kolbaska11 [484]

Answer:

118•

Step-by-step explanation:

The interior side lengths are:

90

180-34

180-x

180-x

The sum of these are 360º

90 + 180-34 + 180-x + 180-x = 360

-2x = -236

x = 118º

3 0
3 years ago
PLEASE HELP ASAP
lesya692 [45]

Answer:

x^2+14x+49    ( it could be polynomial because it has 3 terms and each term has a whole number and a coefficient)

Step-by-step explanation:

(x+7)^2

(x+7)(x+7)

x^2+7x+7x+49

x^2+14x+49

I am not sure it's a polynomial or not

7 0
3 years ago
PLEASE HELP WITH MATH QUESTION!! EXPLANATION NEEDED TOO!
Dovator [93]

Answer:

Matt should have factored out the leading coefficient 2 on the second step before completing the square

Step-by-step explanation:

To complete the square, you must first factor the leading coefficient from the first two terms.

y = 2x² − 10x − 4

y = 2 (x² − 5x) − 4

y = 2 (x² − 5x + 25/4 − 25/4) − 4

y = 2 (x² − 5x + 25/4) − 25/2 − 4

y = 2 (x − 5/2)² − 33/4

8 0
3 years ago
Other questions:
  • What is the greatest common factor for 12,8 and 24
    14·2 answers
  • Look at the to equations _3X + 6 = 21, _3X + 6 &lt; 21. Which statement best describes the process used to solve the equations
    10·2 answers
  • Ab + c = d solve for B
    7·2 answers
  • What is negative 5 and 3/4 as a fraction
    9·1 answer
  • Tiembra bought a bag of 36 apples. She used 25% of the apples to make an apple cake and 1/3 of the apples to make an apple pie.
    8·1 answer
  • I need a equation please.
    11·1 answer
  • Someone finish this rq
    8·1 answer
  • Can you guys answer both of these questions
    13·2 answers
  • The distance from Earth to Pluto is about 5,750,000,000 km. How many light-years is this?
    14·1 answer
  • Help me to solve this ✨​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!