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

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!

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:

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!

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?

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:


!! 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

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

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:)

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

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

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

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

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

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

I need help please.​

Answers

Answer:

e

Step-by-step explanation:

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:

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.

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:

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

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:

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:

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

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.



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

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

Find the area of this

Answers

Answer:

616

Step-by-step explanation:

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
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