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
Determine the value of f (4) if f (x) = 3x -- 1
sleet_krkn [62]

Answer: 11

Step-by-step explanation: plug in 4 for x

3(4) - 1 = 12 - 1 = 11

4 0
3 years ago
Here are Xavier's bowling scores:
SpyIntel [72]

Answer:

151

Step-by-step explanation:

Given the following scores

132,140,130,190,112,200,185, 172,163,151,149 . What isn’t the median ?

Median can be gotten whenever we arrange a set of scores in ascending or descending order.

Arranging the above scores in the ascending order, we have

112,130,132,140,149,151,163, 172,185,190 and 200

Median = 151

6 0
2 years ago
Read 2 more answers
Gcf of 6w square - 14w
melamori03 [73]
GCF of them is 2w.

Hope this helps :)
7 0
3 years ago
Your family has a second car that takes 1 gallon per 25 miles and has 10 gallons to start. Write an equation, identify the y int
PSYCHO15rus [73]

Answer:

Let's use the slope-intercept form of the equation of a line describe the slope and the y-intercept:

y = mx + b where m=slope and b=y-intercept

6 0
2 years ago
Read 2 more answers
Anthony's weight is nine pounds more than twice his brothers weight. Anthony's weighs 59 pounds. how much does his brother weigh
ahrayia [7]
A = Anthony's weight
B = Anthony's brother's weight

  A = 2B + 9   Plug in Anthony's weight
59 = 2B + 9   Subtract 9 from both sides
50 = 2B   DIvide both sides by B
25 = B   Switch the sides to make it easier to read
  B = 25

Anthony's brother weighs 25 pounds. 

8 0
3 years ago
Read 2 more answers
Other questions:
  • Use the distributive property to express 36 +48
    10·1 answer
  • I NEED HELP ASAP PLZZZZZZZZ
    6·1 answer
  • 4.9 g = kg convert answer it plz
    14·2 answers
  • What is the square of 20
    14·2 answers
  • Which of these is the algebraic expression for the verbal expression "five times the difference of a number and six
    6·1 answer
  • Use the properties of equality to solve the equation 3x+2-x=11x+9. State which property justifies your first step and why you ch
    15·1 answer
  • Part A
    12·1 answer
  • The roof of a home rises vertically at a distance of 8 ft through a horizontal distance of 15 ft. Find the pitch (slope) of the
    15·1 answer
  • charles had a sheet cake for his birthday when 9/12 remained charles took 1/3 of the remaining cake to wrap and save for later w
    6·1 answer
  • Evaluate ( 75 − 3/17 + 1 ) 2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!