I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]
ft (smaller value) ? ft (larger value)
ft2

Answers

Answer 1

Answer:

Length = [tex]5\ \text{ft}[/tex]

Breadth = [tex]5\ \text{ft}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the length of the garden

and [tex]y[/tex] be the width of the garden

From the details of the cost in the question we get

[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]

Now area of the garden is

[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dA}{dx}=10-2x[/tex]

Equating with 0

[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]

Double derivative of the area is

[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]

So, area is maximum at [tex]x=5[/tex]

[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]

So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].


Related Questions


!! please help timed

If the value of "y" varies directly with "x"
and y = -8 when x = 20, find "y" if x = -4.
Enter the number that belongs in the green box.
Reduce to simplest form.

Answers

Answer:

Step-by-step explanation:

Y= -2/5 x -4/1 so the answer is Y=8/5

If f(x) = x, find the simplified form for the following inputs:


b) f(x) + 2

c) 1/2f(x)

d) 2( f (x) ) +3

Answers

Answer:

Step-by-step explanation:

Is there another part to the question? Maybe the original function?

answer and show work

Answers

Answer:

3x+2/4>-20

3x+2>-80

3x>-80-2

3x>-82

x>-82/3

Also simplified to, x>-27 1/3
B is the correct answer

help me please click link to go to question

brainly.com/question/19566932?answeringSource=feedPublic%2FhomePage%2F2

Answers

Answer:

okay thank you. ummmm yes well it's not loading

I just need a walkthrough or step by step process on how to get it so i can understand :)

Answers

Answer:

The answer and explanation  is located in the screenshot.

Step-by-step explanation:

Hope this helped! And have a wonderful day!

A bus traveled on a level road for 2 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on level road of the entire trip was 310 miles

Answers

Answer:

The average speed on level road is 65 mph

Step-by-step explanation:

Let the speed on the winding road be x mph

So the speed on the straight road will be x +20 mph

Mathematically, distance = speed * time

Distance on level road will be;

(x + 20)2

Distance on winding road will be;

x* 4 = 4x

Thus, we have;

2(x + 20) + 4x = 310

2x + 40 + 4x = 310

6x + 40 = 310

6x = 310 - 40

6x = 270

x = 270/6

x = 45 mph

The average speed on the level road is x + 20

That will be 45 + 20 = 65 mph

Find the area of this

Answers

Answer:

616

Step-by-step explanation:

subtract -2/3- (-2/5)

Answers

Answer:

- 4/15

Step-by-step explanation:

The  - and - make a + so -2/3 + 2/5

HOPE THIS HELPS

PLZ MARK BRAINLIEST

6. Explain why 4 tens is greater than 4 tenths. (2 marks)​

Answers

Answer:

One is greater than zero, one is less than zero because one is on the right of the decimal and the other one is on the left of the decimal/

Step-by-step explanation:

Answer: because 4 tenths, is another way of saying 4/10 and in decimal form it's 0.4 and 4 tens is 10 10 10 10 which will = 40 a whole number

Step-by-step explanation:

Find the equation of a line that passes through the points (-1,-3) and (1,-5).
Leave your answer in the form y = mx + c​

Answers

Answer:

Y= -1x - 4

Step-by-step explanation:

How do you divide 10.5 divided by2.5?

Answers

Answer:

4.2

Step-by-step explanation:

10.5/2.5= 4.2

Move the decimal in 10.5 over one to the right to get 105.0

Answer:

Divide how you normally would, without the decimals, then put the decimal back in its orginal position; this would result in 4.2.

Step-by-step explanation:

when the Dixon family traded in their old car, it had 53,790 miles on it. they had the car for 8.25 years. on average, how many miles did they drive per year?​

Answers

Answer:

6,520 miles per year

Step-by-step explanation:

53,790 divided by 8.25 equals 6,520

NEED HELP 45 POINTS PLZ

Is there enough information to prove that the triangles are congruent?

If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.

If no, justify your answer.

Answers

Answer:

I have given the answer in the chat box as i was not able to post officialy

Step-by-step explanation:

the number if baskets nikki can make varies directy with the time she spends making the baskets she can make 4 baskets in 1/2 an hour how many baskets can nikki make in 5 hours

Answers

Answer:

40 baskets

Step-by-step explanation:

Find out how many baskets she can make in an hour. Since she makes 4 in 1/2 an hour, multiply 4 by 2 to find out how much she makes in an hour. She makes 8 baskets an hour, so multiply 8 by 5. 8 x 5 = 40.

Answer:

40 Baskets

Step-by-step explanation:

4 x half an hour = 8 baskets an hour. 8 x 5 = 40

I need help please.​

Answers

Answer:

e

Step-by-step explanation:

Please help me it due today at 11:59pm please help me will mark the brainiest please

Answers

first, i’d put the fraction into a decimal, then distribute, for example the fraction would be multiplied by y and 3 separately. then equal that to 40. it should now be a simple equation

Answer:

y = 69

Step-by-step explanation:

start with the distributive property:

5/9 * y and 5/9 * 3

and now you have: 5/9y + 15/9 = 40

and we have to isolate y so subtract 15/9 from both sides:

5/9y + 15/9 = 40

        - 15/9     -15/9

and now you have 5/9y = 345/9

and now divide both sides by 5/9 so: 5/9y divided by 5/9 = y

and 345/9 divided by 5/9 = 345/5 and lets simplify....

y= 69

hope this helps luv

82 added to a number is the same as 36

Answers

Answer:

-46

Step-by-step explanation:

You’re answer will be -46 I’m pretty sure

My teacher doesnt really explain stuff good cause of her accent. May someone please explain how to do the problem and the correct answer? (no Trolls please) the problem is in the pic below

Answers

Answer:

hey sisters

Step-by-step explanation:

I’ll mark you brainliest .
It’s either B,C,or D

Answers

Is the letter B I think

Answer:

I believe it may be C or D.

C and D are the exact same, but I don't think it is B, seeing as it is an absolute value function. If I'm wrong, please forgive me.

Step-by-step explanation:

complete the statements,extra points!!! please don't answer if you don't know ​

Answers

Answer:

1. 0.08703 killograms

2. Decameters

3. Liters

Step-by-step explanation:

convert.

On Friday, a local hamburger shop sold a combined total of 436 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number
of hamburgers sold. How many hamburgers were sold on Friday?

Answers

115 hamburgers were sold

The classroom has 12 9/10 meters of tape in one area of the building, and 8 3/5 meters of tape in another part. How much tape does the classroom have in all

Answers

Answer: 32

Step-by-step explanation: 45wheeej5t

Answer: 21 1/2

Step-by-step explanation:

12 9/10 + 8 3/5 = 21 1/2

hope this helps!

Help stat please.Brainlist for the best ansmwer

Answers

Answer:

(-9/8)x-7=-25
Multiply both sides by 8
-9x-56=-200
Move the constant to the right
-9x=-200+56
-9x=-144
-9x/-9=-144/9
x=16

1.2x-2.4=84

Pls show work...

Answers

Answer:

x=72

Step-by-step explanation:

1.2x−2.4=84

Step 1: Add 2.4 to both sides.

1.2x−2.4+2.4=84+2.4

1.2x=86.4

Step 2: Divide both sides by 1.2.

x=72

Answer: x=72

Step-by-step explanation:

Please help if u get these all right i will mark brainliest

Answers

Answer:

1.

5x+2+3x
8x+2

2.

3+17x+8
11+17x

3.

19+6x+2x
19+8x

4.

4x+5^2+5x+10^2
4x+25+5x+100
9x+125

5.

5x+18+13y+12x+8y
17x+18+21y

It wasn’t specified in regard to how, it should be solved. So I just simplified them all.



12 time 10 times 10 times 10

Answers

Answer:i used a calculator 12000

Step-by-step explanation:12 × 10 × 10 × 10 = 12000

and have a nice Day :)

Answer:

12000

Step-by-step explanation:

If you multiply 12 by 10 its 120, if you add 2 more 0's to the end of the number, it will be 12000, so, basically, any time you multiply a number by 10, you add a 0 to the end of the number your multiplying 10 by, hope this helps:)

Write the LCD (Least Common Denominator I think) for each pair of fractions.
1/3, 1/5 | 2/7, 1/4 | 3/4, 3/5 | 2/9, 5/12 | 1/3, 3/7 | 1/6, 4/9

Please help. ASAP​

Answers

Answer:

answer: 15, 28, 20, 36, 21, 18

9. The temperature outside Jeff's house is 14 °C at midday.
By midnight, the temperature has fallen by 27 °C.
What is the temperature at midnight?
Section 1 – Number and Proportion

Answers

Answer:

-13ºC

Step-by-step explanation:

The temperature has fallen, so you subtract.

14ºC-27ºC=-13ºC

Amy's car gets 32 miles per gallon. If her car's tank holds 15 gallons of gas, and she wants to keep a minimum of 1 gallon of gas in the tank for safety, how far (in miles) can Amy drive after filling up before she needs to fill up again?

Answers

Answer:

478miles

Step-by-step explanation:

32=1gallons 32×15 = 510miles

15g

510- 32= 478miles

Which set of side lengths cannot make a triangle?
1.) 3 cm, 3 cm, 6 cm
2.) 3 cm, 4 cm, 5 cm
3.) 3 cm, 5 cm, 7 cm
4.) 3 cm, 6 cm, 6 cm

Answers

Answer:

Option "A" is correct answer to the following question.

Step-by-step explanation:

We know that, in triangle sum of two smaller lines ≥ largest side

So,

3 cm + 3 cm < 6 cm   [Not correct to the given situation.]

3 cm + 4 cm > 5 cm [Correct]

3 cm + 5 cm > 7 cm [Correct]

3 cm + 6 cm > 6 cm [Correct]

Answer:

A  The one that says 3 cm, 3 cm, 6 cm.

Step-by-step explanation:

Other Questions
A student who is training for a distance race jogged for thirty minutes and covered a distance of 7.5 km. What is the average speed of the student? Escoge la respuesta correcta.Hace diez aos visit a un amigo en Yucatn.presentepasado futuro How pandemic affects your studies ? our community and to the world? plz help me I dont want to fail Under which type of Middle Eastern government does a parliament choose government leaders, such as a prime minister?A.a democracyB.a monarchyC.a republicD.a theocracy\ALSO ADD ME>>>>>>>FIRST ONE ALSO GETS BRAINLIEST Brainliest...dont need an explanation I have a question, about trends in the periodic table. Mostly focusing on ionization energy. From going from right to left it increases as the atom's size decreases. Can someone explain why this happens? Like why does it increase as the size decreases Thank you. What is the correct order for the levels of organization?celltissuesorganssystemsorganismsBcellorganstissuesorganismsorgansOccellsystemstissuesorganismsorganscellorganismstissuesorganssystems Select the correct answer.Which sentence best explains the authors choice for structuring this passage? The equation y=1.35x+10 models the cost of a cab ride, where y is the total cost of the ride in dollars and x is the number of miles driven. Which statement describes this model?A. Customers pay $1.35 per-mile for the first x miles, and then $10 per mile afterwards.B. Customers pay 10$ per-mile, and then $1.35 per mile afterwardsC. Customers pay $1.35 initially, and then another $10 for every mile traveled.D. Customers pay $10 initially, and then another $1.35 for every mile travled A line passes through the point (4, -8) and has a slope of -5/4. Write an equation in slope-intercept form for this line. Escoje las conjugaciones correctas del verbo decir en el tiempo futuro.1. decir, decirs, decir, deciremos, deciris, decirn2. dira, diras, dira, diramos, dirais, diran3. dir, dirs, dir, diremos, diris, dirn4. dije, dijiste, dijo, dijimos, dijisteis, dijeron HELLPP. ITS URGENT.50 PTSPlease show working.Question : If and are roots of the quadratic equation : 4x-5x-1=0, find the quadratic equation whose roots are :(See image for full question . No (IV) and (v)) HELP PLEASE ME IS DUMB In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in and then =, the symbolic entry option will automatically convert that to .Be sure to use decimal numbers in your answer (such as using 0.40 for 40%). What type of figurative language are they SPANISH SPEAKERS (DON'T JUST PUT IT IN GOOGLE TRANSLATE PLEASE) Translate this into Spanish please!!!In the morning I will get out of bed at around 7:00am and sometime I will sleep in. Then I usually go and get my self ready for the day. Then I will go get some coffee or tea, depending on how I feel at the moment. And if it's a school day I will get my computer and start to do some school work. If its the weekend then I will sometimes do some school work but if I don't have any I will just sleep in until I have to get out of bed. SOMEONE PLEASE HELP I WILL MARK BRANLIEST!!!!!! NEED DONE QUICK!!!! 20 POINTS!!!Now think of how you could sell the region you chose to a customer at the Time Travel Agency. You will write a short sales pitch, including the text for a travel brochure that encourages someone to visit that region.Check that your sales pitch includes the following:several aspects of the region that would attract a travelerlikely dangers the customer might encounter (these may sound like negative traits but they add adventure to your pitch)descriptive wording that highlights the regions physical and cultural attractionsfun and engaging writing that will persuade someone to visit the regiona good argument with logical reasoning and solid evidence that will convince people to visit the regioninteresting images of artifacts, monuments, and geographical featuresVisuals such as photographs, paintings, and illustrations will make your sales pitch more appealing to a potential customer. Make sure the pictures you use are of good quality. They shouldnt look fuzzy or grainy. They should be visually appealing.Write a short pitch of about 150 words.also make it about WESTERN EUROPE . What lessons can you learn from the Wright brothers about problem solving? A hemispherical bowl is made of brass has an inner diameter 35 cm. What is the inner surface area? URGENT