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
Given that sin theta = 1/4, 0
GaryK [48]
Answer: cos(Θ) = (√15) / 4

Explanation:

The question states:

1) sin(Θ) = 1/4

2) 0 < Θ < π / 2

3) find cos(Θ)

This is how you solve it.

1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

(cos \alpha )^2 + (sin \alpha )^2 =1

2) From which you can find:

(cos \alpha )^2 = 1 - (sin \alpha )^2

3) Replace sin(α) with 1/4

=> (cos \alpha )^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16

=> cos \alpha =+/- \sqrt{15/16} = +/- (\sqrt{15} )/4

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:

cos(Θ) = \sqrt{15} /4.

And that is the answer.
6 0
3 years ago
Convert the following into scientific notation:<br> 70.2 = _____ x 10 ____
ElenaW [278]

Answer:

7.02 x 10^1

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
PLEASEE HELP AGAINNNN!!!!<br> If a1 = 4 and an = -4an - 1 then find the value of a6
sertanlavr [38]

The 6th term of the geometric sequence is of -4096.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

For this problem, we have that:

  • The first term is a_1 = 4.
  • a_n = -4a_{n - 1}, hence the common ratio is q = -4.

Thus the 6th term of the sequence is found as follows:

a_6 = a_1q^5 = 4(-4)^5 = -4096

More can be learned about geometric sequences at brainly.com/question/11847927

#SPJ1

6 0
1 year ago
An online ticket seller charges $44 for each ticket ton concert, plus a fixed handling fee of $12. Define the unknown variables
enot [183]

Answer:

x= number of tickets bought

y= total

44x+12=y

8 0
3 years ago
The sum of first 'n' terms. Sn of a particular Arithmetic Progression is given by Sn=12n-2n^2. Find the first term and the commo
Vitek1552 [10]

Answer:

d=-4 and a=10

Step-by-step explanation:

The sum of a arithmetic sequence is given by (n/2)*(2a+(n-1)d). Comparing coefficients with the given Sn, we have; a-d/2=12 and d/2=-2, d=-4 and a=10.

4 0
3 years ago
Other questions:
  • During a sale, every item in a store is 80% of its regular price. The regular prices of five items are shown here find the sale
    13·1 answer
  • 2. Solve 9 = 1 + 8x – 8. A. x = 2 B. x = 10
    7·2 answers
  • What do the graphs of all arithmetic sequences have in common
    5·1 answer
  • Find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)
    9·1 answer
  • Factor 5x^2+26x+24 ?
    13·1 answer
  • One week, you tell two of your friends a secret. The next week, each of them tell two people the secret, and the next week, each
    11·2 answers
  • The perimeter of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle. Ravi says he can find the width usin
    5·1 answer
  • When I click the camera option here it just says the two things you can do at the bottom but you can’t take a pic someone plz te
    15·1 answer
  • C.18 of the houses are for sale How many houses are for sale?​
    13·1 answer
  • What is the ratio of ounces of<br> peanuts to ounces of almonds?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!