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
kotegsom [21]
2 years ago
14

A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

s. Find the dimensions of the tank with minimum weight.
Mathematics
1 answer:
ira [324]2 years ago
8 0

Answer:

The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft

Step-by-step explanation:

We were given the volume of the tank as, 2048 cubic feet.

Form minimum weight, the surface area must be minimum.

Let the height be h and the lengths be x

the volume will be: V=x²h then substitute the value of volume, we have

2048=hx²

hence

h=2048/x²

Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.

The surface area of the box described is

A=x²+4xh

Then substitute h into the Area equation we have

A= x² + 4x(2048/x²)

A= x² + 8192/x

We want to minimize

A

dA/dx = -8192/x² + 2 x= 0 for max or min

when dA/dx=0

dA/dx= 2x-8192/x²=0

2x=8192/x²

Hence

2x³=8192

x³=4096

x=₃√(4096)

X=16ft

Then h=2048/x²

h=2048/16²

h=8ft

The box should have base 16ft by 16ft and height 8ft

Hence the dimensions are 16 ft by 16 ft by 8 ft

You might be interested in
A line with a negative slope is perpendicular to one of the lines shown. What is its slope? Use the graph shown below. The Slope
goblinko [34]

Answer:

  • The slope for the red line is decreasing and hence the slope must be negative. -1x or simply -x
  • The slope of the blue line is increasing and hence positive: 1/2x
  • The solution to the equation is the intercept (2,3)
  • Rate positively and give brainlist
7 0
3 years ago
Please answer !!!!!!!!!
xxMikexx [17]

Answer:

answer is b

Step-by-step explanation:

look at the picture

3 0
3 years ago
Read 2 more answers
Xiao bought ​ 4310 ​ gallons of gas that cost $2.50 per gallon.
Vikentia [17]

Answer:

$10775

Step-by-step explanation:

If 1 gallon of gas is $2.50, then the cost of 4310 gallons of gas will be:

4310 * 2.50

= $10775

Hope this answer was helpful!!

8 0
3 years ago
Read 2 more answers
 The distance between city A and B is 600 km. The first train left A and headed towards B at the speed of 60 km/hour. The secon
hoa [83]
\bf \begin{array}{ccccllll}
&distance&rate(km/hr)&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
A&d&60&t\\
B&600-d&v&t+3
\end{array}

\bf \textit{meaning}\implies 
\begin{cases}
d=(60)(t)
\\ \quad \\
600-d=(v)(t+3)\\
------------\\
d=\boxed{60t}\qquad thus
\\ \quad \\
600-\boxed{60t}=v(t+3)\leftarrow \textit{solve for "t"}
\end{cases}

keep in mind, that "t" is the time when the train at A station, left towards B station

they met, at some time "t", and by the time that happened, train from A
which started 3 hours earlier, had already covered "d" distance,
whatever that is
and the train coming from B, covered, 600-d, or the difference
8 0
2 years ago
Timed test please help. Can someone please help me explain how you graph the circle from the equation below and how you find the
ryzh [129]
Well, you have the radius and the center already. So all you have to do is graph the center point, then count from that center point out 5 units, then draw the circle.
5 0
3 years ago
Read 2 more answers
Other questions:
  • For the rhombus ABCD, diagonal BD = 18 and diagonal AC = 24. What is the side length of the rhombus? A) 15 2 B) 21 2 C) 15 D) 21
    9·1 answer
  • At an airport restaurant, 2 sodas and 4 hamburgers cost $12.00. An order of 4 sodas and 2 hamburgers costs $9.00. How much does
    11·2 answers
  • 9 is 10% of what number
    5·2 answers
  • 5th grade math; convert & write an equation with an exponent 108 cm to meters. 108 cm = _m
    5·1 answer
  • On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angl
    13·1 answer
  • An angle measures 40° less than the measure of its supplementary angle. What is the measure of each angle? please hlpppppp
    9·1 answer
  • ASAP help me please!!!!!!!!!!!!!!!!!!
    14·1 answer
  • At Burger Barn, each burger is made with 5/12 pounds of beef.If the chef has 3 1/3 pounds of ground beef, how many burgers can b
    13·1 answer
  • A student has passed 60 percent of the 20 quizzes he has written so far successfully. If the student writes 50 quizzes during th
    13·2 answers
  • An amusement park charges $25 per adult ticket and $15 per child ticket. A group of 10 people paid $180 to enter the park. How m
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!