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
Alex17521 [72]
3 years ago
14

A box with a square base and an open top is being constructed out of A cm2 of material. If the volume of the box is to be maximi

zed, what should the side length of the base be? What should the height of the box be? What is the maximal volume of the box? Your answers should be in terms of A.
FInd: Side length(cm), Height(cm), and Volume(cm)
Mathematics
1 answer:
viktelen [127]3 years ago
8 0

Answer:

Side length = \sqrt{\frac{A}{3} } cm ,   Height =  \frac{1}{2} \sqrt{\frac{A}{3} } cm  ,  Volume = \frac{A\sqrt{A}}{6\sqrt{3} }  cm³

Step-by-step explanation:

Assume

Side length of base = x

Height of box = y

total material required to construct box = A ( given in question)

So it can be written as

A = x² + 4xy

4xy = A - x²

  1. y = \frac{A - x^{2} }{4x}

Volume of box = Area x height

V = x² ₓ y

V = x² ₓ ( \frac{A - x^{2} }{4x} )

V =  \frac{Ax - x^{3} }{4}

To find max volume put V' = 0

So taking derivative equation becomes

\frac{A - 3 x^{2} }{4} = 0

A = 3 x^{2}

x^{2} = \frac{A}{3}

x = \sqrt{\frac{A}{3\\} }

put value of x in equation 1

y = \frac{A - \frac{A}{3} }{4\sqrt{\frac{A}{3} } }  

y = \frac{2 \sqrt{\frac{A}{3} } }{4 \sqrt{\frac{A}{3} } }

y = \frac{1}{2} \sqrt{\frac{A}{3} }

So the volume will be

V = x^{2} × y

Put values of x and y from equation 2 & 3

V = \frac{A}{3} (\frac{1}{2} \sqrt{\frac{A}{3} } )

V = \frac{A\sqrt{A}}{6\sqrt{3} }

You might be interested in
Use quadratic regression to find
vovangra [49]

Answer:

y = 6x² -13x -5

Step-by-step explanation:

(1,-12) (2,-7) (5,80)

y = ax² + bx + c

-12 = a*1² + b*1 + c = a+b+c    (1)

-7 = 4a + 2b + c    (2)

80 = 25a + 5b + c   (3)

(2)-(1): 3a + b = 5    (4)

(3)-(2): 21a + 3b = 87   (5)

(4)*3:     9a + 3b = 15    (6)

(5)-(6):  12a = 72      a = 6

(4)                             b = -13

(2)                             c = -5

4 0
3 years ago
Solve the inequality
Alex17521 [72]
Isolate c by subtracting all sides by 4

Then divide all sides by -5

You should get


5 less than or equal to c less than or equal to 4



Hope this helped :)
8 0
1 year ago
1) Find AB<br> round answer to the nearest tenth
Lynna [10]

Answer: 23.6

Step-by-step explanation:

3 0
2 years ago
an airplane flies 105 miles and 1/2 hour how far can you fly on a 1/4 hours at the same rate of speed
nexus9112 [7]
1/2 hour = 105 miles

Divide by 1/2 on both sides :
1/4 hour = 52.5 miles
4 0
3 years ago
PLS SOLVE THIS<br> I WILL MARK BRAINLIEST
Paraphin [41]

Answer:

AB = 25 units

Step-by-step explanation:

In right triangle ACB, CD\perp AB

Therefore, by geometric mean property:

CD^{2} ={AD\times DB}  \\  \\  {10}^{2}  = AD\times 5 \\  \\ 100 = 5AD \\  \\  AD =  \frac{100}{5}  \\  \\ AD = 20

AB = AD + DB

AB = 20 + 5

AB = 25 units

3 0
2 years ago
Other questions:
  • Please help :c How do I convert 19.3g/mL to lb/in^3? (manually) I tried to so 19.3g (453.592lb)/1g but I'm not sure how to chang
    15·1 answer
  • A line has a slope of -2 and contains the point (1,-1). What is the equation of this line
    9·1 answer
  • May I have help on b. and can someone tell me if a is right?
    12·2 answers
  • Tina wants to save money for school. Tina invests $1,000 in an account that pays an interest rate of 6.75%. How many years will
    12·1 answer
  • What properties allow transformations to be used as problem-solving tools​
    8·1 answer
  • If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the e
    9·1 answer
  • Evaluate b^2 for b= -4
    7·2 answers
  • 2. Gerald was given the following problem to solve for the length of the "?". He has made a mistake in his work.
    12·1 answer
  • How do you verify this trig identity?
    10·2 answers
  • I need help plsssssss
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!