A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 56 meters of fencing available, determine the dimensions that would create the garden of maximum area. You may enter an exact answer or round your answer to the nearest hundredth.

Answers

Answer 1

Answer:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

Step-by-step explanation:

Rectangular garden    A (r ) =  x * y

Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.

the perimeter of the rectangle is  p  =  2*x  +  2*y    ( but in this particular case only one side x will be fencing with wire

56   =   x    +  2*y      56   -  2*y  =  x

A(r)   =  ( 56  -  2*y ) * y

A(y ) =  56*y  -  2*y²

Tacking derivatives on both sides of the equation we get:

A´(y )  =  56  - 4 * y        A´(y) = 0     56  -  4*y  =  0    4*y  =  56

y =  14 m

and x  =  56  - 2*y    =  56 - 28  = 28 m

Then dimensions of the garden:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

How do we know that the area we found is a local maximum??

We find the second derivative

A´´(y)  = - 4     A´´(y)  <  0   then the function A(y) has a local maximum at y = 14 m


Related Questions

5/6 + 4/6

a) 1/6
b) 9/12
c)1 3/6
d) 1 2/6​

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Answer:

this is the answer Hope's it helps

solve for x:

x + 2 1/3 = 3 1/5

x-2 2/3 = 5/6 ​

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It is 3/15 because it was the only time that I’ve had the same problem in my class

Which three types of transformations result in congruent shapes?

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Answer:

There are three main types of congruence transformations: reflections (flips), rotations (turns), and translations (slides). These congruence transformations can be used to obtain congruent shapes or to verify that two shapes are congruent

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Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

[tex] \frac{2}{3} \times \frac{7}{4} \\ = \frac{2 \times 7}{3 \times 4} \\ = \frac{14}{12} \\ = \frac{7}{6} [/tex]

You'll get the answer as 7/6 which is equal to 1.16. 2/3 is equal to 0.66.

[tex]•°• \frac{7}{6} > \frac{2}{3} [/tex]

So, the answer is greater than 2/3.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

Suppose the population of the world now is 4 billion and its doubling period is
35 years, what will be the population of the world after 350 years, 700 years, 1050 years?
If the surface area of the earth is 1,860,000 billion square feet, how much space would
each person get after 1050 years?

Answers

Answer:

4096b after 350 years, 4194304b after 700 years, and 4294967296b after 1050 years. 0.000433065 sq ft. per person after 1050 years making earth uninhabitable.

4096b after 350 years, 4194304b after 700 years, 4294967296b after 1050 years, 0.000433065 sq ft. per person after 1050 years making earth  uninhabitable.

What is surface area?

The surface area of a solid object exists as a measure of the total area that the surface of the object inhabits.

The surface area of a figure (in square units) exists the numeral of unit squares it brings to cover the entire surface without gaps or overlaps. If a three-dimensional figure includes flat sides, the sides exist named faces. The surface area exists as the total of the areas of the faces.

4096b after 350 years, 4194304b after 700 years, 4294967296b after 1050 years, 0.000433065 sq ft. per person after 1050 years making earth  uninhabitable.

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g(x) = 3x^2 + 10x-8
Use the drop-down menus to factor the expression and find the zeros of g(x).

Answers

Answer:

g(x) = (3x - 2)(x + 4)

x = {-4, 2/3}

Step-by-step explanation:

g(x) = 3x^2 + 10x - 8

Factor

g(x) = (3x - 2)(x + 4)

Zero I

3x - 2= 0

3x = 2

x = 2/3

Zero II

x + 4 = 0

x = -4

x = {-4, 2/3}

Answer:

The answer is, [tex]x = {-4, 2/3}[/tex]

Explanation:

Definition of factor:

A factor is a number that divides another number by itself without leaving a residue. To put it another way, if multiplying two whole numbers produces a product, the numbers we're multiplying are factors of the product since they're divisible by it.

Factors can be found using two methods: multiplication and division. In addition, divisibility rules can be applied.

Step-by-step:

[tex]g(x) = 3x^2 + 10x - 8[/tex]

Factor:

[tex]g(x) = (3x - 2)(x + 4)[/tex]

Step 1:

Zero 1.

[tex]3x - 2= 03x = 2x = 2/3[/tex]

Step 2:

Zero 2.

[tex]x + 4 = 0x = -4[/tex]

[tex]x = {-4, 2/3}[/tex]

Hence, the g(x) zeros are [tex]x = {-4, 2/3}[/tex]

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find the exact value of cos A in simplest radical form

Answers

Answer:

cosA = 1/2

Step-by-step explanation:

cos = adj/hyp

cosA = 5 /10

cosA = 1/2

Enter the coordinates of the solution of these two linear equations.

Answers

Answer:

(-4,2) are solution coordinates

This is the point in which these two lines intersect

(1 point) Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 16 specimens of a particular species, 7 resprout after fire. Estimate with 99% confidence the proportion of all shrubs of this species that will resprout after fire.

Answers

Answer:

The answer is "[tex]0.45 \pm 0.18204[/tex]"

Step-by-step explanation:

For the +4 sample proportion[tex]= \frac{(7+2)}{(16+4)} = \frac{9}{20} = 0.45[/tex]

Sample percentage measurements estimated stdev

[tex]= \sqrt{\frac{[(0.45)(1-0.45)]}{[(16+4)]}}\\\\ = \sqrt{\frac{[(0.45)(0.55)]}{[(20)]}}\\\\ = \sqrt{\frac{0.2475}{20}}\\\\= \sqrt{0.012375}\\\\=0.111[/tex]

Calculating the critical z for a=0.1, two-tailed = 1.64

Calculating the confidence interval:

[tex]= 0.45 \pm 0.111 \times 1.64 \\\\= 0.45 \pm 0.18204[/tex]

HELP!!!!

5^m x (5^-7)^m = 5^12

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Answer:

not sure lol but, like it up

Step-by-step explanation:

Am I correct? K
Thanks for helping!
PLEASEEE CHECK ME WORK!

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Yes, these are all correct! Good job!!! :))

Answer:

yes you are correct on all of them good job

Pls help this is with 26 pt and brainlest

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Answer:

a) 1 only

Step-by-step explanation:

this is what I believe it is but 1 is for sure an answer

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Answer:

I don't know I'm sorry I tried to found answers but I couldn't

(-6, 10), (-6,1),(1, 10) What are the coordinates of the fourth vertex of the rectangle? Enter your answer by filling in the boxes.​

Answers

Answer:

(1,1)

Step-by-step explanation:

Happy To Help!

Consider a normal distribution of values with a mean of 32 and a standard
deviation of 1.5. Find the probability that a value is less than 36.8.


Anyone know?

Answers

Answer: The probability that a value is less than 36.8 is 0.9993.

Step-by-step explanation:

Let X be the random variable that normally distributed.

Given: [tex]\mu=32,\sigma=1.5[/tex]

The probability that a value is less than 36.8 = [tex]P(X<36.8)[/tex]

[tex]=P(\frac{X-\mu}{\sigma}<\frac{36.8-32}{1.5})\\\\=P(Z<3.2)\ \ \ [Z=\frac{X-\mu}{\sigma}]\\\\=0.9993[/tex][Using P-value calculator]

Therefore, The probability that a value is less than 36.8 is 0.9993.

HELP QUICK!!!!!!!! GIVING BRAINLIEST!!

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3x. =180-90

3x. =90

x. =30

Find the value of x . Round your answer to the nearest tenth.

Answers

the answer is 26

brainliest?

Answer:

The answer is 100 :D

Step-by-step explanation:

1: You would start by finding the sum of the two angles given (72 and 8) which is 80

2: You would then subtract the sum from 180

3: 180-80 = 100

Hope this helps :D

-3(_x + 4) = 9x – 12 Using the distributive property, what number would go in the blank in order for the given statement to be correct? ​

Answers

Answer:

-3(-3x + 4) = 9x - 12

Step-by-step explanation:

-3( Ax + 4) = 9x - 12

-3Ax -12 = 9x - 12

Equating coefficients of  x terms on both sides :

-3A = 9

A = -3

Therefore, -3(-3x + 4) = 9x - 12

what is 300 to the nearest ten

Answers

300 simply because the last 2 numbers of 300 are (00) therefore it can neither be rounded up or down

Answer:

300⇒ nearest ten

300 (rounded to the nearest ten)

Explanation:

We round the number up to the nearest ten if the last digit in the number is 1, 2, 3, 4, 5, 6, 7, 8, or 9.  If the last digit is 0, then we do not have to do any rounding, because it is already to the ten. Therefore 300 rounded to the nearest ten is 300.

ASAP pls wkkwmwkwnwnwwnwn

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Answer: Her highest score is on turn two because she used a negative number over a positive and a positive is more than a negative.

Step-by-step explanation:

10>-16

A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year

Answers

Answer:

mu = the population true mean time spent by teenagers playing computer game this year

Step-by-step explanation:

Dear student, there is no much information given to answer this question but we will try as much as possible to explain  (what is the parameter) of the true mean.

In 1990s;

μ = 10.2 hours/week

From the information given,we understand that the parameter is linked to the population, and we're looking for the population average time spent playing computer games by teens in the current situation.

In this situation, the population parameter is the population true mean mu = the population true mean.


What is the distance from the origin to point A graphed on the complex plane below?

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I’m pretty sure it’s b!

Correct me if I’m wrong
Have a nice day!

Answer:

B

Step-by-step explanation:

Edge

Identify a segment parallel to segment ZY

Answers

Answer:

UT

Step-by-step explanation:

Opposite sides of a rectangle are parallel

convert 1 2/5 x 2/3 into a mixed number

Answers

it simplifies to the proper fraction 14/15 so it cannot be a mix number

hope this helps !!

If x=-4 what is the value of the following expression?

2x^2 +3x -2

18
12
-22
-46

Answers

Answer:

2x^2 +3x -2

18

12

-22

-46

Step-by-step explanation:

Each week the manager of a coffee shop orders three more cases of soy milk than almond milk. Let x represent the cases of almond milk and lery
represent the cases of soy milk
Create a table to represent this relationship.
Move each necessary number to its appropriate row to complete the table.
1
5
4
7
12

Answers

Answer:

1 4

2 5

4 7

7 10

9 12

Step-by-step explanation:

Please answer what is 1 2 3 4 5 no links I forgot to do my homework

Answers

1. 40°

2. 50°

3. 45°

4. a. draw a line from angle P to downward but make it so it can cut angle OPQ from the half

b. 70°

c. angle TPQ = angle OPQ ÷2

angle TPQ = 140÷2= 70°

f(x)=10x-15 g(x)=2x-3 Find: (f/g)(x)

Answers

The function operation (f/g)(x) in the functions f(x) = 10x-15 and g(x) =2x-3 is 5.

What is the function operation (f/g)(x) in the given function?

A function is simply a relationship that maps one input to one output.

Given that;

f( x ) = 10x - 15g( x ) = 2x - 3( f / g )( x ) = ?

First, we replace the function designators in f/g with the actual functions.

(f / g )(x) = f(x) / g(x)

(f / g )(x) = ( 10x - 15 ) / ( 2x - 3 )

Now, factor out 5 from 10x and -15

(f / g )(x) = 5( 2x - 3 ) / ( 2x - 3 )

Cancel the common factor of 2x - 3

(f / g )(x) = 5( 1 ) / ( 1 )

(f / g )(x) = 5 / 1

(f / g )(x) = 5

Therefore, the function operation (f/g)(x) equals 5.

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A baby whale gains about 250 pounds a day. It was 250 pounds at birth. Find an equation to find the number of days it will take for a baby to weigh its first ton.

Answers

Answer:

8 days

Step-by-step explanation:

1 ton=2,000 pounds and If you divide 2,000÷250=8 days. It will talk 8 days for the baby whale to weigh his first ton.

1. How much salt and baking powder together is needed to make 36 cup cakes?

Answers

Answer:

too much salt will not bring taste to the cup cakes

Step-by-step explanation:

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