Liana has 320 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum​ area? A rectangle that maximizes the enclosed area has a length of nothing yards and a width of nothing yards

Answers

Answer 1

Answer:

Breadth = 60,  Length = 60

Step-by-step explanation

Let length & breadth of rectangular area be : L & B

As, Fencing Yards = 320. So, perimeter ie  2 (L + B) = 320

B = (320 - 2L)/2 → B =  160 - L (*)

Area of rectangle [A]  = L x B = L  (160 - L)  → A = 160L - L^2

Maximising Area, So first derivative d [A] / d [L] = 160 - 2L

d [A] / d [L] ] = 0  → 160 - 2L = 0  → L = 160/2  → L = 80

By (*) : B = 160 - L = 160 - 80 → B = 80

Checking maximising condition, double derivative d^2[A] / d[L]^2 = -2

As d^2[A] / d[L]^2 is negative, L & B values are maximising A


Related Questions

Which expression is equivalent to the given expression?
2x^2– 14x + 24

Answers

2(x-4)(x-3) I think not really

Answer:

2(x - 3)(x - 4)

Step-by-step explanation:

answer to all these in order please !

Answers

Answer:

?? 6363

Step-by-step explanation:

Anagha's mother bought an equal number of ladoos and pedas. She put 13 of the ladoos and 15 of the pedas into a packet and gave it to Anagha to distribute at school. If there were a total of 80 sweets in the packet, how many ladoos did Anagha's mother buy?

Answers

Answer:

150

Step-by-step explanation:

Anagha's mother bought an equal number of ladoos and pedas. Let there are x number of ladoos and pedas.

She puts x/3 of the ladoos and x/5 of the pedas into a packet and gave it to Anagha to distribute at school.

Total no of sweets in the packet = 80

[tex]\dfrac{x}{3}+\dfrac{x}{5}=80\\\\\dfrac{5x+3x}{15}=80\\\\\dfrac{8x}{15}=80\\\\x=\dfrac{80\times 15}{8}\\\\x=150[/tex]

So, there are 150 ladoos brought by Anagha's mother.

I need help plz I have a quiz and idk how to do these

Answers

Answer:

c

Step-by-step explanation:

You have to use pemdas and you should get c

whats the answer to number 4?
please and thank you

Answers

Answer:

90+55+x

145+x=180*

=35

answer: 35°

explanation: the sum of all the interior angles in a triangle will always equal 180°. in this triangle we have a right angle which is equal to 90°, a 55° angle, and x°. To find out x you would do 90 + 55 = 145. once you get that you would then do 180 - 145 = 35. So, X = 35°

I need this answer
5x + 10 = 6x – 20

Answers

Answer:

30

Step-by-step explanation:

Step 1:

5x + 10 = 6x - 20       Equation

Step 2:

10 = x - 20        Subtract 5x on both sides

Step 3:

10 + 20 = x        Add 20 on both sides

Answer:

x = 30

Hope This Helps :)

Answer: x=30

Step-by-step explanation:

What is 20 mulitpyed by 50

Answers

it is 1000 because 2 x 5 =10 then just add the extra 2 0s from 20 and 50

Answer:

1,000

Step-by-step explanation:

what is a rational algebraic expression?​

Answers

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions

PLEASE HURRY. An electrician charges $45 per hour plus a fixed charge of $30 which of these equations could be used to determine C, the cost an electrician charges for h hours of work?

Answers

$45 per hour plus a fixed change of $30

Marcos is baking a cake. He has a recipe for a large cake that calls for 6 cups of flour, 2 cups of sugar, and 1 cup of butter. Marcos only has ½ cup of sugar, so he's going to make a smaller cake. How much flour and butter should he use in his recipe?

Answers

Answer:

3/2 cups of flour

1/4 cups of butter

Step-by-step explanation:

Cups of flour = 6

Cups of sugar = 2

Cup of butter = 1

Marcos only has ½ cup of sugar, so he's going to make a smaller cake.

Cups of sugar for big cake = 2

Cups of sugar for small cake = 1/2

Ratio of cups of sugar for big cake to small cake is

= 2 : 1/2

= 2 ÷ 1/2

= 2 × 2/1

= 4

This means to make smaller cake, all recipes should be divided by 4

Flour for small cake = flour for big cake / 4

= 6 / 4

= 3/2 cups of flour

= 1.33

Butter for small cake = Butter for big cake / 4

= 1 / 4 cups of butter

= 0.25

the slopes of two lines are 8 and -1/8. because of this, we can conclude that these two lines are which of the following?

Answers

Answer:

perpendicular

Step-by-step explanation:

Two lines with opposite signs and reciprocals depict perpendicular lines

how would you write 8.235 E14 in standard form​

Answers

Answer:

what????

Step-by-step explanation:

If the temperature is 95 degree F,what is the temperatur in Celsius

Answers

Answer:

35 degree celcuis

Step-by-step explanation:

Josh's football team has never scored more than 31 points in a game.
Which inequality represents the number of points that they would need
to score to beat their record?

A. p 31
D. p ≥ 31

Answers

Answer:

p > 31

Step-by-step explanation:

If their record is 31, and they need to beat it, then it would mean his score needs to be greater than 31, which is written as:

p > 31

Hope this helps

wendy buys a dress that costs $30.00 she pays 8% sales tax
how much does she pay for the dress in tax

Answers

Answer:

She pays $2.40 in sales tax

Step-by-step explanation:

Answer:

it was 32.40 for me bro

Step-by-step explanation:

The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle?

Square root of 5
Square root of 7
5
7

Answers

Answer:

7

Step-by-step explanation:

let the other leg be x

Then using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 3² = 4²

x² + 9 = 16 ( subtract 9 from both sides )

x² = 7 ( take the square root of both sides )

x = 7

Answer:

7

Step-by-step explanation:

let the other leg be x

Then using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 3² = 4²

x² + 9 = 16 ( subtract 9 from both sides )

x² = 7 ( take the square root of both sides )

x = 7

calcula el 25%,35% y el 75% de 1255​

Answers

Answer:

25%=313.75  35 %=439.25  75%=941.25

Step-by-step explanation:

Solve for the value of q.
134°
(9q-8)

Answers

Answer:

If you mean that 134 degrees = (9q - 8), the answer is: q = 15.78 degrees

Step-by-step explanation:

134 degrees = 9q - 8

142 = 9q

142/9 = q

15.78 = q

q = 15.78 degrees

WILL GIVE BRAINLIEST! What is 24 written as a percent?

Answers

Answer:

24%

Step-by-step explanation:You divide it by a hundred percent and overall it equals 24% since 24 out of one hundred (24/100) it would be 24% of that.

Now you owe me brainly. Thanks.(:

A school orders 12 boxes of dice. Each box contains six bags of dice. Each bag contains
35 dice. How many dice do the school order in total?

Answers

Answer: 2520 Dice.

Step-by-step explanation:

1. Multiply 35 Dice by 6 Bags (You should get 210)

2. Multiply the amount of dice (210) by 12 Boxes (You should get 2520 Dice)

There ya go!

Any Questions?

The answer of this is 2520. You have to multiple 35 by 6 and that gives you 210. Then you multiply 210 by 12 and that gives you the answer of 2520

When you solve |2x+6|=4x it has one extraneous solution at x=-1
true or false

Answers

It’s true hope that helped have a good night

Can you Help me out?!

Answers

Answer:

3/4

Step-by-step explanation:

2/9 are lemon

Hope this helps ;)
Please mark me as the Brainliest ;)

Determine the slope

(4,12) and (6,20)

Answers

M=4 the slope to your equation is 4.

Answer:

4

Step-by-step explanation:

Is that the right answer ?

Answers

Answer:

Yes, that is correct

Step-by-step explanation:

The formula for the slope can be referred to as "rise over run", a fraction where the rise (change in the y direction) is divided by the run (change in the x direction).

We can get the rise and run by choosing two points on the slope and looking for the change in the x and y direction. In this case, let us use the points (-4,0) and (0,-5). The change in the y direction is from 0 to -5, thus the rise will be -5. Likewise, the change change in the x direction is from -4 to 0 and the run will be 4.

Going back to "rise over run", we divide the rise by the run, giving us -5/4

In a standard Normal distribution, what percentage of observations lie between z = –1.08 and z = 0.92?

Answers

Answer:

68.11

Step-by-step explanation:

i think


Which equation below shows a correct first step for solving 3x = -12
A 3x+ 3 = -12 + 3
B 3x- 3 = -12 - 3
C 3(3x) = 3(-12)
D 3x/3=-12/3

Answers

The answer is A. You just solve each one and you would find that it would be the same as 3x=-12.

PLSSSSS!!!!!! HELP ME!!!! I WIL MARK U!!!!!

Answers

Answer:

-44

Step-by-step explanation:

You multiply 11 times 2 to the second power then multiply negative 1

-44
That is bro it’s easy

por favor ayúdeme!!​

Answers

Answer:

CHEEEEEEEEESE

Step-by-step explanation:

What is 10/3(fraction) times 6/5(fraction)

Answers

Answer:

4

Step-by-step explanation:

When multiplying those fractions, you multiply the top (numerators) by each other and you'll get 60

Then when you divide the denominators you'll get 15.

60 divided by 15 is 4.

10/3 x 6/5 = 4

Step-by-step explanation:

You multiply the numerators together, same with the denominator. You get 60/15. You divide those numbers so you get 4 as your answer. Hope this helps!

Find the percent increase or decrease from Monday to Tuesday.
Miles Jan walked Monday: 12
Miles Jan walked Tuesday: 3

Answers

multiply 12 and 3 and your answer should b36.

Answer:

multiply 12 and 3 and your answer should b36.

Step-by-step explanation:

is this carret

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