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
Marizza181 [45]
3 years ago
10

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by

cutting congruent squares from the corners and folding up the sides. Then find the volume. The dimensions of box of maximum volume are 17.66 comma 7.66 in.
Mathematics
1 answer:
faltersainse [42]3 years ago
8 0

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 in^3.

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

                                         =[(23-2x)(13-2x)x] in^3

                                         =(299x-72x² +4x^3) in^3

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here a=12, b=-144 , c=299

\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}

\Rightarrow x= 9.33, 2.67

If  we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

V''|_{x=2.67}=-144+(24\times 2.67)=-79.92

Therefore  at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

                                    =17.66 in

The width of the box =[13-(2×2.67)] in

                                  =7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) in^3

                                                            =361.19 in^3

You might be interested in
6n + 8 and 2(3n + 4)<br> Are the two expressions equivalent
lara [203]
Yes, they are equivalent
3 0
3 years ago
Read 2 more answers
2) The 114 students in the ninth grade at Mathville High are going on a field trip to the science
9966 [12]

Answer:

4 buses

Step-by-step explanation:

40b=114+114/10

40b=114+11.4

40b=125.4

b=3.135

The answer is 4 because you have to round up to get the remaining people.

5 0
3 years ago
What is the side lengths, in inches, of a cube with a volume of 1 1 cubic inch? Branliest
Mnenie [13.5K]

Answer:

34

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Can someone pleaseeee help and if you’re correct i’ll give brainliest
deff fn [24]

Answer:

The answer should be 13.

8 0
3 years ago
Read 2 more answers
Evaluate r(x)=−x−7 when x=−2,0, and 5.<br> Brainliest to right answer
HACTEHA [7]

Answer:

r(-2) = -5 , r(0) = -7 , r(5) = -12.

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is bigger 5 feet or 60 inches
    11·2 answers
  • What is the result when 4x^2-17x+36 is subtracted from 2 x^2-5x+25?
    13·2 answers
  • Find Is number 9 correct?
    5·1 answer
  • Trying to figure out 5n + 6 + (7n)<br><br> I have it written out but Im affraid it's wrong
    9·1 answer
  • What is the area of the label on a soup can that is 8 inches high and has a diameter of 4 inches? Round to the nearest hundredth
    5·1 answer
  • Y=-6x+10. Y=-6x+3<br><br> Solve the system of equations
    5·1 answer
  • Please help me! I will give brainly!
    8·2 answers
  • This one too I always get confused
    6·1 answer
  • Use green's theorem to find integral subscript c left parenthesis y space plus space e to the power of square root of x end expo
    7·1 answer
  • Which value of "b" will make the trinomial 4x^2 + bx + 36 a perfect square trinomial? 0 24 O 6 O 12 O 4​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!