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
Aloiza [94]
3 years ago
14

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an op

en box may be made. If the cardboard is 15 in. long and 7 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.) smallest value in in largest value in
Mathematics
1 answer:
fgiga [73]3 years ago
7 0

Answer:

Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in

Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in

Height h = x = 1.50 in

Step-by-step explanation:

The volume of a box can be written as;

V = l×b×h

Where;

Length = l

Breadth = b

Height = h

Let x represent the length of the cube cut out of the four edges.

Using the attached image;

Length l = 15 - 2x

Breadth b = 7 - 2x

Height h = x

Substituting the values to the volume equation;

V = (15-2x)(7-2x)(x)

V = 105x - 30x^2 - 14x^2 + 4x^3

V = 105x - 44x^2 + 4x^3

At Maximum volume, V' = dV/dx = 0

V' = 105 - 88x + 12x^2 = 0

Solving the quadratic equation, we have;

x = 5.83 or x = 1.50

x cannot be 5.83 since 2x > 7 (greater than the breadth of cardboard)

Therefore ;

Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in

Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in

Height h = x = 1.50 in

You might be interested in
Dilations PLEASE HELP ME PLEASE
AURORKA [14]

Answer:

D' (6, - 6 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin then multiply the coordinates of D by 3, that is

D (2, - 2 ) → D'(3 × 2, 3 × - 2 ) → D' (6, - 6 )

6 0
3 years ago
19. 7 * 645 =<br> What does it equal
lutik1710 [3]

Answer:

4515

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Help will give the branniest
Naily [24]

The answer is C... Hope it helps

4 0
3 years ago
Please help with math question
Naddik [55]
1- Solution using graphs:
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.

2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II

Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.

Hope this helps :)

3 0
3 years ago
Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Expr
Anarel [89]

Answer:

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school.

a) It is the intersection A ∩ B

b) This is the difference A − B.

c) It is the union A ∪ B.

                                   ---    ---

d) It can be shown as A ∪ B. (bar over A and B both)

5 0
3 years ago
Other questions:
  • Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−5t
    8·1 answer
  • Help please! show work thanks
    11·1 answer
  • If u can't see, 2 is 1/5, 2/3, 5/8....... 3 is 1/2, 2/5, 6/10........ 4 is 4/6, 7/12, 5/10 and 5 is 1/4, 5/8, 1/2 and the Instru
    11·2 answers
  • How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F
    12·1 answer
  • What is 38.88 divided by 8
    10·2 answers
  • Two cards are drawn from a standard deck of 52 cards. A king is drawn first and not replaced. Find the probability of drawing a
    13·2 answers
  • Please help ill give brainliest
    7·2 answers
  • The volume of a cylindrical container is 226 cubic centimeters. The radius of the container is 6 centimeters. Find the height of
    6·1 answer
  • Find an equation for the line perpendicular to 4 x + 12 y = 96 and goes through the point ( − 3 , 4 ) . Write your answer in the
    5·1 answer
  • The table shows the heights y (in feet) of a baseball x seconds after it was hit. Predict the height after 5 seconds
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!