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
astraxan [27]
3 years ago
5

An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou

r corners and bending up the sides. Find the maximum volume that the box can have.
Mathematics
1 answer:
Burka [1]3 years ago
6 0

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

                              = 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

                            = 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

You might be interested in
A car weighs 2332 pounds. If 372 pounds of old parts are removed and replaced with 412 pounds of new parts, find new weights of
Makovka662 [10]

Answer:

2372

Step-by-step explanation:

You would do the equation 2332-372+412

5 0
3 years ago
Simplify (7x+42)/(x^2+13x+42)
Colt1911 [192]
\frac{7x+42}{x^2+13x+42}=  \frac{7(x+6)}{x^2+7x+6x+42}=   \frac{7(x+6)}{x(x+7)+6(x+7)}=  \frac{7(x+6)}{(x+6)(x+7)}=  \frac{7}{x+7}
7 0
3 years ago
Read 2 more answers
HELP ME PLZZZ
Usimov [2.4K]

True


If two polygons are similar, their corresponding angles are the same, while corresponding sides are all in the same ratio.

3 0
3 years ago
Help me asap show work ​
STatiana [176]

We want to find out how much it costs for each pound of feed

For chicken feed 12 divided by 8.40

$1.43 for 1 pound of chicken feed

For goat feed 75 divided by 60

$1.25 for 1 pound of goat feed

For dog feed 50 divided by 37.50

$1.33 for 1 pound of dog feed

For pig feed 80 divided by 62.80

$1.27 for 1 pound of pig feed

When reviewing all the answers per pound for feed, chicken feed is the most expensive per pound.

Hope this helps:)

5 0
3 years ago
PLEASE HELP
UkoKoshka [18]

Answer:

really easy its 180

Step-by-step explanation:

because you multiply 30 times 6 u get 180

3 0
3 years ago
Read 2 more answers
Other questions:
  • This one as well. Thanks! #22 a & b ​
    10·2 answers
  • A gallon of water weighs 8 1/3 pounds. how much does 7 gallons weigh
    12·2 answers
  • 50 is x% of 1000 <br>please help me with these
    7·1 answer
  • At the beach, Pancho and his sister both built sandcastles and then measured their heights. Pancho's sandcastle was 3/5 of a foo
    15·1 answer
  • Two consecutive odd numbers whose sum is 144 ?
    14·2 answers
  • a rectangular block is such that the sides of its base are of the length x cm and 3x cm. The sum of all the lengths of all its e
    14·1 answer
  • Helllllppppppppppppppp thank you
    9·2 answers
  • Find the missing side length
    11·1 answer
  • Can you help me pls i have 1 day
    10·1 answer
  • Perimeter of a equilateral triangle is 27cm. Find the length of each sides.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!