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
Alex Ar [27]
2 years ago
13

Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cu

tting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volume of each configuration. Does it appear that there is a maximum volume
Mathematics
1 answer:
Alecsey [184]2 years ago
7 0

Answer:

) See annex

b) See annex

x  =  0,5 ft

y =  2 ft   and

V = 2 ft³

Step-by-step explanation:  See annex

c) V = y*y*x

d-1) y = 3 - 2x

d-2) V = (3-2x)* ( 3-2x)* x   ⇒ V = (3-2x)²*x    

V(x) =( 9 + 4x² - 12x )*x    ⇒   V(x) = 9x + 4x³ - 12x²

Taking derivatives

V¨(x) = 9 + 12x² - 24x

V¨(x) = 0              ⇒   12x² -24x +9 = 0     ⇒  4x² - 8x + 3 = 0

Solving for x (second degree equation)

x =[ -b ± √b²- 4ac ] / 2a

we get    x₁  =  1,5       and    x₂ =  0,5

We look at y = 3 - 2x    and see that the value x₂ is the only valid root

then

x  =  0,5 ft

y =    2 ft   and

V = 0,5*2*2

V = 2 ft³

You might be interested in
a baseball pitcher won 80% of the games he played. if he pitched 35 games, how many games did he win?
andrey2020 [161]

Answer:

28 games

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Simplify the following: (25 ×−716 ) + ( 25 × 28)
kvv77 [185]

Answer:

- 17900 + 700

answer to the equation would be -17,200

7 0
2 years ago
Read 2 more answers
Which would be included in a probability model for rolling a cube with faces numbered 1 through 6. Select all that apply.
Inessa [10]

Answer:

it's b.

Step-by-step explanation:

3 0
3 years ago
Solve for I when 3/5 +I-1/15
Ugo [173]

Answer:

23 over 15 or 1.533

Step-by-step explanation:

Group like terms:

1+(3/5+-1/15)

Find LCD:

1+9/15+-1/15

Combine numerators:

15/15+8/15

And you get 23/15

Simplified:1 8/15

Decimal: 1.533

4 0
2 years ago
Describe and correct the error below.
statuscvo [17]

Step-by-step explanation:

It is given that,

-2.2 × 3.7 = 8.14

The first number is -2.2

The second number is 3.7

We know that, (-) × (+) = - (the answer is a negative)

If we multiply -2.2 and 3.7, we will get -8.14.

But in the given case, the answer is 8.18 instead of -8.14. Hence, this is the only error.

8 0
2 years ago
Other questions:
  • What is the ratio for the volumes of two similar Pyramids, given that the ratio of the edge lengths is 8:3?
    7·2 answers
  • There are 40 tables in a library, with 30% of them seating 4 people. The tables remaining only seat 2 people. How many seats are
    9·1 answer
  • There are 128 fluid ounces in gallon and 16 fluid ounces in a pint. Shelby wants to find the number of pints in a gallon. She wr
    11·1 answer
  • What is y=x^2-12x+99^12 if x=32
    15·1 answer
  • Please answer this correctly
    12·2 answers
  • Please help needed!!! Help me!!!
    11·1 answer
  • Find the measure of major<br> arc<br> OQN.<br> M<br> K<br> IN<br> 38<br> 6<br> P
    8·1 answer
  • A. A cylinder just fits into a cube of side length 36 m Calculate the percentage
    10·1 answer
  • 12 = 6x + 3y, find the solution for y
    8·2 answers
  • Need help now please please
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!