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
weqwewe [10]
3 years ago
7

An open box is to be made from a square piece of cardboard measuring 15 inches on a side by cutting a square from each corner an

d folding up the sides. Find the dimensions of the resulting box with maximum volume.
Mathematics
1 answer:
vodomira [7]3 years ago
6 0

Answer:

Dimensions are;

2.5 inches height

Base: 10 inches by 10 inches

Max volume; 250 Sq.in

Step-by-step explanation:

Let each side of the square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60

Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

You might be interested in
need a lot of help
marishachu [46]
2.60 x 12 3/4

2.60 x 12.75 (convert to decimal)

= $33.15, which is not listed.
3 0
2 years ago
PLEASE HELP!!!
pogonyaev

Step-by-step explanation:

Part A:

Let m be the number of mittens and s be the number of scarves. Then we have the inequalities:

s+m\leq 30. <em>This says Nivyana and Ana cannot make more than 30 scarves</em>

50s+25m\geq 1000. <em>This says that</em> <em>Nivyana and Ana have to earn at least $1000.</em>

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region<em> (I picked those points to stress that the lines bounding the dark region are also solutions.)</em>

8 0
3 years ago
!!!!!URGENT!!!!!!
nasty-shy [4]

Answer:

hope this helps

Step-by-step explanation:

If you break the fraction into a whole number it would be 5 and 10 minus 5 is 5. so x=5

8 0
2 years ago
Which statements are true about the place values in the number 99.999?
allsm [11]
Answers A. and B. Are correct
5 0
3 years ago
List sides and angle from smallest to largest
irinina [24]

Answer: C,A,B

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Please help me,
    13·1 answer
  • Zarina is scuba diving. She will not give below -30 meters relative to the surface of the water. Write an inequality that repres
    13·1 answer
  • A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $5 each, but only 3,600 shower c
    8·1 answer
  • Please help!!!!!!!!!!!!
    8·1 answer
  • Can someone help me please ASAP
    5·1 answer
  • En un festival para niños se cobraron $50 por niño y $100 por adulto, si el total de dinero recaudado por boleto pagado fue de $
    12·1 answer
  • Can someone pleaseee help me i’ll give you brainliest
    8·1 answer
  • If a x b = a/b - 1, then 7 x 28
    8·1 answer
  • What is the value of f(4) in the function below? f(x) = -1/1·2x A. 16 OB. 8 C. 2 OD. 4​
    13·1 answer
  • Question 2 of 10
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!