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
If 9 people can drink 15 water bottles how many can 45 people drink
shutvik [7]
They can drink 51. Is my answer
5 0
3 years ago
NEED HELP ASAP!!!!!!!!!! Melissa rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that t
Masteriza [31]

Answer:

1\6

Step-by-step explanation:

You have one sixth

7 0
3 years ago
Read 2 more answers
find a number such that 8 times the number is 36 greater than the opposite of the number. Explain also please. ♥
lukranit [14]
Let's turn this sentence into an equation:

8n = -n + 36

Then solve:

9n = 36 => n=4
6 0
3 years ago
Read 2 more answers
Are the points U, H, and L collinear?<br> U<br> E<br> S<br> H
butalik [34]

Answer:

Yes

Step-by-step explanation:

Collinear means points are lying on the same straight line. U, H, and L are all lying on the line l.

4 0
3 years ago
A line with an undefined slope that has an x-intercept of 9
lesantik [10]
A vertical line has an undefined slope.
vertical lines are X= something
in this case it needs to intercept 9.
so it is X=9
7 0
3 years ago
Read 2 more answers
Other questions:
  • The lengths of a particular snake are approximately normally distributed with a given mean mc025-1.jpg = 15 in. and standard dev
    11·2 answers
  • find the common ratio of the following geometric sequence. 2.512, 11.304, 50.868, 228.906, 1,030.077, ...
    9·1 answer
  • Calculate 1/4+(-5/12)+(-2/3)
    15·2 answers
  • I need help with solving this quadratic equation by factoring. the problem I need help with is number 5.
    9·1 answer
  • The standard deviation of a probability distribution table is 26.6 and the mean is 674.0. During an event, you receive the resul
    7·2 answers
  • Let: u, v, w \varepsilon R3<br><br> Prove: (u x v) * [(v x w) x (w x u)] = [u * (v x w)]2
    8·1 answer
  • Is 11 1/3 greater than 34/3
    6·1 answer
  • Rewrite the function f(x)=4(x-2)²-8 in the form f(x)=ax²+bx+c.
    15·1 answer
  • Help me pls, will mark brainliest (just 1-7)
    13·1 answer
  • .<br> What number is<br> 1/10<br> of 300
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!