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
daser333 [38]
3 years ago
9

onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutti

ng 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 volumes of several such boxes

Mathematics
1 answer:
Sholpan [36]3 years ago
5 0

Answer:

V (max)  = 2 ft³

and x side of the base is  x  =  0,5 feet

Step-by-step explanation:  See annex ( two different cubes)

We have a square piece of cardboard of  3 inches wide

Let  x be lenght of side to cut in each corner

Then the base of the (future cube) is    3  -  2x,  and the area is  

( 3 - 2x )²

And  the height   is x  Then volume of the cube as a function of x is:

V(x)  =  ( 3 - 2x )² *x   or       V(x)  =    ( 9 + 4x² - 12x )*x

V(x)  =  4x³  -  12x²  + 9x

Taking derivatives on both sides of the equation

V´(x)  =  12x² - 24x  + 9

V´(x)  =  0       12x² - 24x  + 9  =  0   simplifying   4x² - 8x  + 3  =  0

Second degree equation solving for x

x₁,₂ =  [ 24 ± √( 576) - 432  /24

x₁,₂ =  [24 ±√144 ]/24

x₁,₂ = ( 24 ± 12) /24         x₁  =  1.5 feet        x₂  = 0,5 feet

Of these two values we have to dismiss x₁  because if  x = 1.5 we don´t have a cube ( 0 height )

Then we take x  = 0,5  feet

And

V (max)  =  (2)²*0,5   =  4*0,5

V (max)  = 2 ft³

You might be interested in
What number is 12 and a half percent of 64
Mkey [24]
<span>12.5% of 64=8 Would be the answer to this.</span>
8 0
3 years ago
Read 2 more answers
Lori is running in a marathon, which is 26.2 miles long. So far, she has run one-tenth of the marathon. How far has Lori run
Mila [183]

Answer:

lori has run 2.62 miles

Step-by-step explanation:

Do 26.2/10

4 0
2 years ago
Pharmacy Technician Rolando received a prescription for 150 calcium carbonate tablets for the patient. Rolando used 1/3 of the s
Feliz [49]
450

If he used 1/3 of the stock bottle, then you have
150=1/3x

Now, you multiply both sides by 3, which gives you

450=x

So, originally there were 450 bottles in the stock bottle
7 0
3 years ago
Find the equation 3x-1=11
g100num [7]

Answer:

x = 4

Step-by-step explanation:

3x - 1 = 11

3x = 1 + 11

3x = 12

x = 12/3

x = 4

Thus, The value of x is 4

<u>-</u><u>T</u><u>h</u><u>e</u><u>U</u><u>n</u><u>k</u><u>n</u><u>o</u><u>w</u><u>n</u><u>S</u><u>c</u><u>i</u><u>e</u><u>n</u><u>t</u><u>i</u><u>s</u><u>t</u>

8 0
2 years ago
Read 2 more answers
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s
earnstyle [38]
According to the Fundamental Theorem of Algebra, the number of zeros or roots of the equation is equal to the highest degree among the terms. So with the given real roots 4, and  -8 <span>the order should be 2 or a binomial. We expound (x-4) * (x+8)  to give </span><span> x2 + 4x - 32 = 0</span>
5 0
3 years ago
Other questions:
  • The standard trampoline has a circumference of about 41 feet. When Jenna's dad lays with his feet at the center of the trampolin
    12·1 answer
  • The cost of joining a DVD club and buying DVDs is a linear function of the number of DVDs bought. The cost of 3, 5, and 7 DVDs i
    7·1 answer
  • Which term means that you receive a fixed amount of pay for a job on a weekly, bi-weekly, or monthly basis?
    14·1 answer
  • A gardener has 2 bags of potting soil and several flower pots. Each flower pot needs 1/8 bag of potting soil for the
    6·1 answer
  • There are a total of 63 bikes in a store. If the ratio of blue bikes to red bikes is 4 to 5, how many of the bikes are blue?
    9·1 answer
  • Need help with maths ASAP
    13·1 answer
  • What are the potential solutions of
    15·1 answer
  • Find product 5 (-2/3)=
    15·2 answers
  • An escalator 152 feet in length rises to a platform and makes a 31° angle with the ground. Find the height of the
    13·1 answer
  • What times 1/11 equals 1?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!