Find the dimensions of a rectangle (in m) with area 2,197 m2 whose perimeter is as small as possible. (enter the dimensions as a comma separated list. ).

Answers

Answer 1

The dimensions of a rectangle with an area 2,197 m² whose perimeter is as small as possible are 46.9m by 46.9m

What is area?

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of a rectangle is expressed as A = xy

Perimeter of the rectangle = 2(x + y)

Since A = 2,197m²

xy = 2197..............1

2(x+y) = Minimum ....................2

From 1,

x = 2197/y

Substitute into equation 2,

2(2197/y + y) = minimum

4394/y + 2y = P(y)

If the perimeter is at minimum, hence dP/dy = 0

-4394/y² + 2 = 0

-4394/y² = -2

2y² = 4394

y² = 2197

y =√2197

y = 46.9m

Since xy = 2197

x = 2197/y

x = 2197/46.9

x = 46.9m

Hence the dimensions of a rectangle with an area 2,197 m² whose perimeter is as small as possible are 46.9m by 46.9m

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Related Questions

HELP ME PLEASE THANKS GOOD NIGHT☺️

HELP ME PLEASE THANKS GOOD NIGHT

Answers

Y = -2x + 6
Slope is -2
Y intercept is 6

Answer:

y= -2x+6

Step-by-step explanation:

y=mx+b

b is the y intercept (what is y when x is 0) in this case it is positive 6

m is slope which is rise/run, in this case down 2 and over 1 so that would be -2/1 which is the same as -2

y = -2x+6

I WILL GIVE BRANLIEST PLS HELP
What is the contrapositive of the following conditional statement?

"If it is summer, then it is sunny."

If it is not sunny, then it is not summer.
If it is sunny, then it is summer.
If it is not summer, then it is not sunny.
It is summer if and only if it is sunny.

Answers

Answer:

The contrapositive of the given conditional statement "If it is summer, then it is sunny" is "If it is not sunny, then it is not summer."

Step-by-step explanation:

In logic, a conditional statement takes the form "if p then q", where p is the hypothesis or antecedent, and q is the conclusion or consequent. The contrapositive of a conditional statement involves negating both the hypothesis and conclusion and reversing their order. So, the contrapositive of "if p then q" is "if not q then not p".

In the given conditional statement "If it is summer, then it is sunny", the hypothesis is "it is summer", and the conclusion is "it is sunny". The negation of the hypothesis is "it is not summer", and the negation of the conclusion is "it is not sunny". Therefore, the contrapositive of the given conditional statement is "If it is not sunny, then it is not summer".

h. How many yards are there in 255ft? (3 ft = 1 yd)

Answers

Answer:

85

Step-by-step explanation:

Answer:

85 yards

Step-by-step explanation:

You just go online to find the answer.

plsss helpp meeee!!!!!!!

plsss helpp meeee!!!!!!!

Answers

Answer:

is that geometry

Step-by-step explanation:

A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 31 batteries of each type. (a) How many ways can a total inventory of 31 batteries be distributed among the eight different types

Answers

Answer: 12,620,256

Step-by-step explanation:

Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.

Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is \(^{n+r-1}C_r=\ ^{31+8-1}C_{31}\)

\(=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256\)

Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256

Which of the following titles is most likely a compare-and-contrast essay?
A. Living on the West Coast and Why I Like It
B. East Meets West: Natives’ Perspectives
C. Traveling on the West Coast
D. Problems with Living on the East Coast

Answers

B. East Meets West: Natives’ Perspectives is most likely a compare-and-contrast essay because it is directly comparing the perspectives of people from the East and West coasts. The other titles are more descriptive or subjective in nature, rather than focused on comparing and contrasting two different things.

East Meets West: Natives’ Perspectives

Notice how it already compares two things in the title, East and West

On the map below, 1 cam represents 50 km. The distance between sommerwile and Linden is 2.5 cm.

On the map below, 1 cam represents 50 km. The distance between sommerwile and Linden is 2.5 cm.

Answers

Answer:

125

Step-by-step explanation:

Answer:   I think it's D

Step-by-step explanation: I say the answer is (B) because  in the full question, it's asking how much would 2.5 means, therefore, you're multiplying, to get 125.

If 1cm=50km Then 2.5 is 50km, 50km, 25

50+50+25=125, or simply just multiply. 25 is half of 50, so with the 2.5 there, doesn't make it a whole number, therefore, making the 25 in it's place, because of the 2.5.

HELP PLEASE!!!!

The 10 largest soccer and football stadiums have a capacity of at least of 1 x 105 people. Each stadium has 8 events each year for 10 years.

How many total people attended these events if every event was seated to capacity? Select ALL that apply

A

at least 80,000,000 people

B

at least 800,000,000 people

С

at least 0.8 x 107 people

D

at least 8 x 107

people

E

at least 80 x 107 people

Answers

We have 10 stadiums each holding 105 people.
If each stadium has 8 events each year that’s 80 events per year in total.
So there is 800 events throughout the 10 years (each year holding 80 events).
To find the total number of people that attended the event we multiply the number of people that attended each event by how many events we had in total (105x800=84000)
So, C,D and E apply.

Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 1/3.

Draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/3.

Answers

Answer:

Here you gooooo

Step-by-step explanation:

Draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/3.

Answer:

khan

Step-by-step explanation:

Draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/3.

a variable has a normal distribution with a mean of 100 and a standard deviation of 15. what percent of the data is less than 105? round to the nearest 10th of a percent.

Answers

Rounding to the nearest tenth of a percent, we find that approximately 65.5% of the data is less than 105.

To find the percentage of the data that is less than 105 in a normal distribution with a mean of 100 and a standard deviation of 15, we can use the standard normal distribution table or a statistical calculator.

Using a standard normal distribution table, we need to calculate the z-score for the value 105, which represents the number of standard deviations away from the mean:

z = (x - μ) / σ,

where x is the value (105), μ is the mean (100), and σ is the standard deviation (15).

Substituting the values:

z = (105 - 100) / 15 = 5 / 15 = 1/3.

Looking up the z-score of 1/3 in the standard normal distribution table, we find that it corresponds to approximately 0.6293.

The percentage of the data that is less than 105 can be calculated by converting the z-score to a percentile:

Percentile = (0.5 + 0.5 * erf(z / √2)) * 100,

where erf is the error function.

Substituting the z-score into the formula:

Percentile = (0.5 + 0.5 * erf(1/3 / √2)) * 100 = (0.5 + 0.5 * erf(1/3 / 1.414)) * 100.

Calculating this value gives us approximately 65.48.

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f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6​​​​​​​
where c is constant

Answers

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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5 pts! (Yall I really need help) How much does a video game cost per in:
America
Great Britain
Japan

Answers

Answer:

there are millions of video games, ranging from all different prices, so it all depends on what game.

Step-by-step explanation:

Depends really on how new or old the game is and what game it is

is 7-y=5x+11 a linear equation

Answers

Yes. As long as it is y = mx+b.

In geriatrics, why is it MOST important not to be too focused on one aspect of care?




The patient may have multiple medical problems.



The family may not want to focus on the illness.



The patient may want to talk about other things.



There may not be a good chance for a recovery

Answers

In geriatrics, it is crucial not to be overly focused on one aspect of care because elderly patients often have multiple medical problems. By taking a holistic approach to care, healthcare providers can address the comprehensive needs of the patient and improve overall well-being.

Elderly patients frequently experience various health conditions concurrently, such as chronic illnesses, cognitive impairment, and physical limitations. Focusing solely on one aspect of care may neglect other critical issues, leading to inadequate treatment and potentially worsening the patient's overall health status.

Furthermore, being too narrowly focused on one aspect of care may not align with the preferences and priorities of the patient and their family. It is essential to engage in open communication and consider the patient's desires, allowing them to express their thoughts and concerns. This person-centered approach ensures that care is tailored to their individual needs and preferences.

Lastly, geriatric patients may have limited chances for a complete recovery due to the presence of chronic conditions or age-related decline. Instead of aiming for cure or complete reversal of the illness, the focus should shift towards improving quality of life, managing symptoms, and providing comfort and support.

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Find the total surface area of a cylinder. Use 3.14 for pi

1. 228.49 ft
2. 1,005.9 ft
3. 954 ft
4. 847.80 ft
5. 610.11 ft
6. 740.96 ft

Find the total surface area of a cylinder. Use 3.14 for pi1. 228.49 ft2. 1,005.9 ft3. 954 ft4. 847.80

Answers

Answer:

it is 847.80 ft

i done the quiz

what is this answer? ​

what is this answer?

Answers

Shidd I couldn’t tell you but like this

Choose the graph that represents the following set.
the whole numbers greater than 3

Choose the graph that represents the following set.the whole numbers greater than 3

Answers

The answer is C. !! ITS CCCCC

Answer:

The last graph or

Graph C

Step-by-step explanation:

what number is a solution of the inequality 3<3x-15

Answers

Answer:

x > 6

{7, 8, 9, 10...}

Step-by-step explanation:

\(3<3x-15\\\\3x-15>3\\\\3x-15+15>3+15\\\\3x>18\\\\\frac{3x>18}{3}\\\\\boxed{x>6}\)

Any number will be a solution if it's value is greater than 6.

Hope this helps.

( help me please ) ….

( help me please ) .

Answers

Answer:

The slope is 6/5, ;)))))))

The speed at which a ball bits the ground is proportional to the
height to which the ball rebounds. If the ball hits the ground at
a speed of 20 miles per hour and rebounds to a height of 10 feet,
then how fast must it be traveling (in miles per hour) to rebound
to a height of 15 feet?

Answers

Answer:

30 mph

Step-by-step explanation:

let s represent speed and h represent rebound.

Given that s is proportional to h then the equation relating them is

s = kh ← k is the constant of proportion

To find k use the condition s = 20, h = 10, then

20 = 10k ( divide both sides by 10 )

2 = k

s = 2h ← equation of proportionality

When h = 15 , then

s = 2 × 15 = 30 mph

Convert fraction to equaivlent
17
__
6

Answers

Answer:

\(\frac{34}{12}\) , \(\frac{51}{18}\) , \(\frac{68}{24}\) , \(\frac{85}{30}\)

some equivalent fraction examples of \(\frac{17}{6}\):

\(\dfrac{17}{6} *\dfrac{2}{2} = \dfrac{34}{12}\)

\(\dfrac{17}{6} *\dfrac{3}{3} = \dfrac{51}{18}\)

\(\dfrac{17}{6} *\dfrac{4}{4} = \dfrac{68}{24}\)

\(\dfrac{17}{6} *\dfrac{5}{5} = \dfrac{85}{30}\)

Therefore the equivalent fractions are \(\frac{34}{12}\) , \(\frac{51}{18}\) , \(\frac{68}{24}\) , \(\frac{85}{30}\)

A group of friends are going to see a movie. The admission cost is $8 per person. The table below represents the number of friends and the total cost. Movie Costs Number of Friends, (x) 2 3 4 5 Total Cost in Dollars, (y) Which set of ordered pairs can be written from the table? (2, 10), (3, 11), (4, 12), (5, 13) (2, 16), (3, 24), (4, 32), (5, 40) (10, 2), (11, 3), (12, 4), (13, 5) (16, 2), (24, 3), (32, 4), (40, 5)

Answers

Answer:

B) (2, 16), (3, 24), (4, 32), (5, 40)

Step-by-step explanation:

1 ticket costs $8. 8 x 2 = 16, so 2 tickets cost $16. 8 x 3 = 24, so 3 tickets cost $24. The same thing goes for 4 tickets, and 5 tickets.

Answer:

It should be (b) on edge 2020.

Step-by-step explanation:

Use the Intermediate Value Theorem to show that at least one zero lies in the given interval for the given polynomial. f (x) = x^3 - 6x + 1, between x = 2 and x = 3 Substitute x = 2 and x = 3 into the function and simplify. f (2) = f (3) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since f (2) it and f (3) is, there is at least one real zero between x = 2 and x =

Answers

Proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

The polynomial is given by

f(x) = \(x^3\) - 6x + 1

We have to show that at least one zero lies in the given interval for the given polynomial using the intermediate value theorem

When the value of x = 2

Substitute the value of x in the polynomial

f(2) = (2)^3 - 6(2) + 1

= 8 - 12 + 1

= -3

When the value of x = 3

Substitute the value of x in the polynomial

f(3) = (3)^3 - 6(3) + 1

= 27 - 18 + 1

= 10

Here the value of f(2) is negative and the value of f(3)  is positive therefore there is at least one real zero between x = 1and x = 2

Hence, proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

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Marie transforms △TZP to create △VQK. She translates △TZP 1 inch down and 1.5 inches to the right. She then dilates △TZP using a scale factor of ⁹⁄₅. Select the true statements below regarding the dimensions of △VQK.

Answers

The true statements regarding the dimensions of △VQK, the transformation of △TZP, are as follows:

△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.

The side lengths of △VQK are not equal to the corresponding side lengths of △TZP.

The corresponding angles of △VQK and △TZP are congruent.

△VQK is larger or smaller in size compared to △TZP due to the dilation.

Explanation:

The transformation of △TZP to △VQK involves a translation and a dilation. Firstly, △TZP is translated 1 inch down and 1.5 inches to the right. This means that every point of △TZP is moved 1 inch downwards and 1.5 inches to the right to obtain the corresponding points in △VQK. The translation affects the position of the vertices, but it does not alter the shape or size of the triangle.

Secondly, △TZP is dilated using a scale factor of ⁹⁄₅. This means that every side length of △TZP is multiplied by ⁹⁄₅ to obtain the corresponding side lengths in △VQK. The dilation changes the size of the triangle, making it larger or smaller depending on the scale factor.

Based on these transformations, we can conclude the following true statements:

△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.

The side lengths of △VQK are not equal to the corresponding side lengths of △TZP due to the dilation.

The corresponding angles of △VQK and △TZP are congruent, as angles are preserved under both translation and dilation.

△VQK is larger or smaller in size compared to △TZP due to the dilation.

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15 of the 25 students Brought their own lunch. What percent of the students brought their own lunch?

Answers

Answer:

60%

Step-by-step explanation:

1: 15 divided by 25 to get 0.6

2: multiple 0.6 by 100 to get 60%

john cleans the house for two hours more than jane. if they work together they clean the house for 2 hours and 24 minutes. for how many hours does john clean the house? can you write the solution as well

Answers

John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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Which number is bigger 25% or 0.025

Answers

50%

The website told me

25% should be bigger. If the decimal was 0.25 then it would be equal, but since it’s 0.025 that makes 25% bigger.

how many solutions are there to square root x =9

Answers

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Nina can ride her bike 63,360 feet in 3,400 seconds, how fast is she going?

Answers

Answer:

18.64 ft/s

Step-by-step explanation:

Use the formula for speed, speed = distance/time or s = d/t

Here, Distance = 63,360 Feet and Time = 3400 Seconds

Therefore, using the formula with these specifications we get speed = 63360/3400 = 18.64 ft/s

Nina Travels at 18.64 ft/s

Which graph shows the fastest rate of change in the velocity of Ross' car?
Change in Velocity
1234
Time (seconds)
Change in Velocity
1234S
Time (seconds)
Change in Velocity
12345
Time (seconds)
Change in Velocity
12345
Time (seconds)
Velocity
(leet per second)
Velocity
(feet per second)
Velocity
(feet per second)
Velocity
BOT
...

Which graph shows the fastest rate of change in the velocity of Ross' car?Change in Velocity1234Time

Answers

Answer:

B

i’m not 100 percent sure but i think it’s b

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