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
harkovskaia [24]
3 years ago
12

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

cents/cm2 and the top and bottom cost 4 cents/cm2. Find the dimensions of the box that minimize the total cost of the materials used.
Mathematics
1 answer:
Charra [1.4K]3 years ago
6 0

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

h=\frac{504}{lw}

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides C_{s}= 3[2(l + w)h] = 6(l + w)h

C_{s}= 3[2(l + w)h]

C_{s}=6(l+w)(\frac{504}{lw} )

Cost of the top and the bottom C_{(t,p)}= 4(2lw) = 8lw

Total cost of the box C = 3024\frac{(l+w)}{lw} + 8lw

                                      = 3024[\frac{1}{l}+\frac{1}{w}] + 8lw

To minimize the cost of the sides

\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0

\frac{3024}{l^{2}}=8w

\frac{378}{l^{2}}=w ---------(1)

\frac{dC}{dw}=3024(-w^{-2})+8l=0

\frac{3024}{w^{2}}=8l

\frac{378}{w^{2}}=l

w^{2}=\frac{378}{l}-------(2)

Now place the value of w from equation (1) to equation (2)

(\frac{378}{l^{2}})^{2}=\frac{378}{l}

\frac{(378)^{2} }{l^{4}}=\frac{378}{l}

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

w^{2}=\frac{378}{7.23}

w^{2}=52.28

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

h=\frac{504}{(7.23)^{2}}

h = 9.64 cm                        

You might be interested in
Easy math question please help
kondaur [170]

Answer:

B

Step-by-step explanation:

2x-3=7

Add 3 to both sides:

2x=10

Divide both sides by 2:

x=5

Hope this helps!

5 0
3 years ago
Read 2 more answers
What are the prime factors of 4,725
PtichkaEL [24]
Prime factors of 4,725 are 3, 5 and 7
5 0
3 years ago
HELP PLZZZZ DOING
Natasha_Volkova [10]
Hi,
The answer would be unit C. The distance between -80 & 0 is 80. The distance from 0 to 15 is 15. So 80+15=95. Hope this helps.
6 0
3 years ago
_____ have congruent corresponding parts.
aniked [119]

Answer:

Two congruent figures

Step-by-step explanation:

Here we have to use the definition of congruent.

Congruent means equal to each other.

Example.

If the two triangles said be congruent, their corresponding angles and corresponding sides are equal.

They will have to same size of the sides and same measure of angles.

Two equal polygons, that is two congruent figures.

Hope this will help you.

Thank you.

4 0
2 years ago
A jewelry store sells necklaces in lengths that vary from 16 inches to 22 inches. Any necklaces outside of this criteria are rej
Art [367]

Answer:

16-22

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • I need help<br><br> -5 = 3/4x -2<br><br> -7 + 1/2x =12<br><br> -7 -5/6x =18
    13·1 answer
  • Explain how you can tell that 31/33 is in simplest form
    7·2 answers
  • (75 POINTS) BRAINLIEST Graph g(x), where f(x) = 2x − 5 and g(x) = f(x + 1).
    15·1 answer
  • Arrange these units from smallest to largest: cm,um,km,mm,m,nm,dm,pm.
    5·1 answer
  • You plan to go skiing this weekend in Tennessee. The ski resort charges $18.50 per hour in addition to a $100 deposit to rent sk
    10·2 answers
  • the cost of admission to a history museum is $3.25 per person over the age of three , kids three and under get in for free. If t
    15·2 answers
  • Find the probobiboibility of pulling out a blue marbel ​
    12·1 answer
  • 7. A square has an area of 20 square feet. What is the length of a side of<br> the square, in feet?
    12·2 answers
  • Evaluate |3x| +4 when x=-5
    9·1 answer
  • What is negative 3 over 4 multiple by negative 2 over 5
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!