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
Naddika [18.5K]
3 years ago
12

Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter

. 1. Dimensions: equation editorEquation Editor 2. Minimum perimeter: equation editorEquation Editor Enter your result for the dimensions as a comma separated list of two numbers. Do not include the units.
Mathematics
1 answer:
mezya [45]3 years ago
4 0

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

You might be interested in
Simplify 3/4 - 1 1/4
lbvjy [14]
I think the answer is -7/4.
4 0
3 years ago
Read 2 more answers
What are the twin prime numbers of 99 -199​
Naddika [18.5K]

Answer:

Therefore, the pairs of twin-prime numbers are (101,103) , (107,109) , (137,139) , (149,151) , (179,181) , (191,193) , (197,199) . So, the correct answer is “ (101,103) , (107,109) , (137,139) , (149,151) , (179,181) , (191,193) , (197,199) ."

4 0
3 years ago
A sweater for 36.00 at 7% sales tax
blagie [28]
$36 x 1.07 = $38.52
The cost will be $38.52
Tax on this is $2.52
4 0
3 years ago
If a solution has a ( OH- )= 8.6 × 10-5 what is the pOH
riadik2000 [5.3K]
POH is the -log [ OH- ]. Using this equation, simply find the -log of the OH- concentration to find the pOH:

pOH = - log ( 0.000086 ) = 4.07


6 0
3 years ago
M<br>+ 8 = 15 <br>find the number m represent ​
leva [86]

Answer:

m=7

Step-by-step explanation:

15-8=7

therefore m=7

8 0
3 years ago
Read 2 more answers
Other questions:
  • The diagram shows rectangle ABCD on a pair of aces. The lengths of its sides are 20 units and 5 units. The coordinates of point
    8·1 answer
  • Susan paid $240 to have her house decorated. The materials used to decorate the house coast $115, and service was charged at $5
    13·1 answer
  • (PLZZZZ HELP ME its actually easy I am trying to check my work) Bob's family of three was driving to Washington D.C.. They were
    13·2 answers
  • What is the absolute value of [-2/3]
    7·1 answer
  • Kaylee opened an account with a deposit of $800. The bank pays 4% annual simple interest on this account. Kaylee makes no additi
    12·1 answer
  • What is the value of x?
    9·2 answers
  • Please answer my question correctly.<br><br>Nonsense/Plagiarized = Report​
    6·2 answers
  • A story owner wants to prepare 100 lb of a candy mix that she will she for $1.36 per lb. She mixes 20 lb of jelly beans that cos
    6·1 answer
  • The polynomial below is a perfect square trinomial of the form A^2 - 2AB + B^2
    15·1 answer
  • A company is started by four friends. The company was Erica’s idea, so she wants to fill 70% of the orders. Jen, Heather, and To
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!