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
katen-ka-za [31]
3 years ago
9

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

nd base length b of the box be so as to maximize its volume
Mathematics
1 answer:
kkurt [141]3 years ago
7 0

Answer:

b=h=\sqrt{6} m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box=2b^2+4bh

2b^2+4bh=36

b^2+2bh=18

2bh=18-b^2

h=\frac{18-b^2}{2b}

Volume of box, V=b^2h

Substitute the values

V=b^2\times \frac{18-b^2}{2b}

V=\frac{1}{2}(18b-b^3)

Differentiate w. r.t b

\frac{dV}{db}=\frac{1}{2}(18-3b^2)

\frac{dV}{db}=0

\frac{1}{2}(18-3b^2)=0

\implies 18-3b^2=0

\implies 3b^2=18

b^2=6

b=\pm \sqrt{6}

b=\sqrt{6}

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

\frac{d^2V}{db^2}=-3b

At  b=\sqrt{6}

\frac{d^2V}{db^2}=-3\sqrt{6}

Hence, the volume of box is maximum at b=\sqrt{6}.

h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}

h=\frac{18-6}{2\sqrt{6}}

h=\frac{12}{2\sqrt{6}}

h=\sqrt{6}

b=h=\sqrt{6} m

You might be interested in
Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear
Nikolay [14]

The graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

<h3>What is the slope?</h3>

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\rm m =\dfrac{y_2-y_1}{x_2-x_1}

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line m = 4

The slope of the line which is perpendicular to the above line:

M = -1/4 = -0.25

The graph second has a slope of -0.25

\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)

y - 2 = -0.25x - 1

y = -0.25x + 1

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

Learn more about the slope here:

brainly.com/question/3605446

#SPJ1

6 0
2 years ago
Please I need help in finding the diameter
Goshia [24]

Answer:

im pretty sure its 152, im sorry if im wrong, i took 180 and subtracted 180 - 16 - 12 and got that soooo

Step-by-step explanation:

5 0
2 years ago
Simplify this expression.
amm1812

Answer: 0.88

Step-by-step explanation:

Okay -5.37 + 8.14 = 2.77 ( you can simply plug this into the calculator or you could switch the problem around so it’s 8.14 - 5.37, either way you’ll get 2.77)

And then you take 2.77 -1.89 = 0.88

So 0.88 is your answer

7 0
2 years ago
The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determin
Oksana_A [137]

Answer:

um hola

Step-by-step explanation:

7 0
3 years ago
The figure above shows a square inscribed in a rectangle.
slava [35]

Step-by-step explanation:

first u must find the area of the rectangle.after that,find the area of the square.then you have tu subtract it so that u can get the orange area.

8 0
3 years ago
Other questions:
  • In this figure, AB and CD are parallel.
    8·1 answer
  • If a^1/n=r then which of the following statements are true
    11·2 answers
  • Write a explicit and recursive formula for -4,-6,-8,-10
    11·1 answer
  • What is the antiderivative of e^x^2?
    15·1 answer
  • 2. Suppose (220)_b and (251)_b are the squares of consecutive integers. Determine b.
    9·1 answer
  • Andrew sold $50 less than sarah did and evan sold $25 more than Sarah. these quantities can be communicated symbolically. if x=
    7·1 answer
  • Suki named a fraction that was not a multiple of. Which fraction could she have
    12·1 answer
  • Help help help help help help help
    5·1 answer
  • WILL MARK! <br> For parallelogram ABCD, find x.
    13·2 answers
  • Which equation has the correct sign on the product?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!