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
amid [387]
3 years ago
9

Find the dimensions of a right-circular cylinder that is open on the top and closed on the bottom, so that the can holds 1 liter

and uses the least amount of material? ...?
Mathematics
1 answer:
anzhelika [568]3 years ago
5 0
Volume of cylinder:
V = πr²h
The desired volume is 1 Liter = 1000 cm³
1000 = πr²h
h = 1000/πr²

Surface area of cylinder:
S.A = 2πr² + 2πr²h
We substitute the value of h from the first equation:
S.A = 2πr² + 2πr(1/πr²)
S.A = 2πr² + 2/r
Now, to minimize surface area, we differentiate the expression with respect to r and equate to 0.
0 = 4πr - 1000/r²
4πr³ - 1000 = 0
r = 4.3 cm
h = 17.2 cm
You might be interested in
Find the range f(x) =-2x-5 for the domain (-2,-1,1,2).
iVinArrow [24]

Answer:

{ - 9, - 7, - 3, - 1 }

Step-by-step explanation:

To obtain the range substitute the values of x from the domain into f(x)

f(- 2) = - 2(- 2) - 5 = 4 - 5 = - 1

f(- 1) = - 2(- 1) - 5 = 2 - 5 = - 3

f(1) = - 2(1) - 5 = - 2 - 5 = - 7

f(2) = - 2(2) - 5 = - 4 - 5 = - 9

range is { - 9, - 7, - 3, - 1 }

8 0
2 years ago
Berta, Maya, and Zach are in different checkout lanes at a store. Berta has 3 more people in front of her than are in front of M
erica [24]
Maya=2
Berta=5
Zach=4
Total=11
4 0
3 years ago
A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and rig
givi [52]

An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, A_p=(x-2)(y-8)

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}

Equate the differentiated function with 0,

0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

Learn more about Equation:

brainly.com/question/2263981

#SPJ1

4 0
2 years ago
Ali wants to buy a piano. The piano measures 19/4 ft long. She has a space 5ft long for the piano in her house. Does she have en
KATRIN_1 [288]
19/4 = 4 3/4 ft which is less than 5ft
Yes she has room
6 0
2 years ago
Read 2 more answers
Name the independent variable (IV) and the dependant variable (DV) for the hypothesis. There will be one IV and one DV for the h
Fittoniya [83]

Answer:B

Step-by-step explanation:

21

8 0
3 years ago
Other questions:
  • How to write this question as an algebraic expression the sum of 4x by A and 5x by B?
    14·2 answers
  • In Minneapolis, it is 20 degrees colder than it is in Houston
    14·1 answer
  • If f(x) =6x -4,whats is f(x) when x =8?
    7·1 answer
  • An isosceles triangle has area of 110 ft. If the base is 14 ft, what is the length of each leg? Round your
    12·1 answer
  • At Henry's yearly physical, he measured 5 feet 8 inches tall. If there are 2.54 centimeters in 1 inch, what is Henry's height in
    5·1 answer
  • Solve 2^x =3 round to the nearest ten-thousand
    9·2 answers
  • Really need help!<br> 2 1/2 = 1 2/3 ÷y<br> The thing I usually use isn't giving me an answer!!
    9·1 answer
  • Find the value of x and y
    14·2 answers
  • SOMEONE PLEASE HELP ME IT'S DUE TODAY AT 11:59 PM:(​
    8·1 answer
  • Problem below<br><br> Please show full work <br><br> Thx
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!