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

Gregoria borrowed $2,450, to be paid back at 3.5% simple interest. She repays $3221.75. How many years was the loan period?

Answers

Answer:

90.7yrs.  

Step-by-step explanation:

Given parameters:

Amount borrowed  = $2450

Interest rate  = 3.5%

Amount repaid = $3221.75

Unknown:

Number of years the load was paid  = ?

Solution:

The formula of simple interest;

    I = PRT

Where I is the interest

           P is the principal

          R is the rate

          T is the time

  To find the interest;

    Interest = Amount paid back - loan  = 3221.75 - 2450  = 771.75

Now;

     P = IRT

     2450  = 771.75 x [tex]\frac{3.5}{100}[/tex]  x T

     2450 = [tex]\frac{2701.25T}{100}[/tex]

    T = [tex]\frac{245000}{2701.125}[/tex]   = 90.7yrs

The number of years of the loan period was 90.7yrs.  

Write an expression meaning a number divided by 4 + 8.

Answers

Answer:

x/4+8

Step-by-step explanation:

....................................

Answer:

what i believe you are looking for:

[tex] \frac{x}{4 + 8} [/tex]

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

Triangle ABC is located in the third quadrant of a coordinate plane. If triangle ABC is reflected across the −axis to obtain triangle, A’B’C’, which statement is true? A. Triangle A’B’C’ lies in quadrant II and is congruent to Triangle ABC B. Triangle A’B’C’ lies in quadrant IV and is congruent to Triangle ABC C. Triangle A’B’C’ lies in quadrant II and is not congruent to Triangle ABC D. Triangle A’B’C’ lies in quadrant IV and is not congruent to Triangle ABC

Answers

Answer:

The answer is B

Step-by-step explanation:

Answer:

It’s Triangle A’B’C’ lies in quadrant II and is congruent to Triangle ABC

Step-by-step explanation:

I just took the test

What is sin 60 degrees?

Answers

Answer:

A

Step-by-step explanation:

(x + 1)(x - 3)(x - 4)

Answers

Answer:

Simplified:

x^3 - 6x^2 + 5x + 12

Roots:

-1

3

4

Your answer is x^3-6x^2+5x+12

(please help I will give brainlist) Twenty students tried out for the basketball team. Sever were selected. What is the ratio of students selected to those trying out?

Answers

Answer:

7:20

Step-by-step explanation:

35% of the students made the team

Answer:

7:20

Step-by-step explanation:

hope this helps :)

Evaluate the following algebraic expression for the given value of the variable ​

Answers

Answer:

[tex]\boxed{8}[/tex]

Step-by-step explanation:

-Solve the following expression when [tex]x = 4[/tex]:

[tex]\frac{5x + 12}{4}[/tex]

-Apply the value of [tex]x[/tex] onto the equation:

[tex]\frac{5x + 12}{4}[/tex]

[tex]\frac{5(4)+ 12}{4}[/tex]

-Multiply both the [tex]5[/tex] and [tex]4[/tex]:

[tex]\frac{5(4)+ 12}{4}[/tex]

[tex]\frac{20+ 12}{4}[/tex]

-Add both [tex]20[/tex] and [tex]12[/tex]:

[tex]\frac{20+ 12}{4}[/tex]

[tex]\frac{32}{4}[/tex]

-Divide [tex]32[/tex] by [tex]4[/tex]:

[tex]\frac{32}{4}[/tex]

[tex]\boxed{8}[/tex]

So, therefore, the final answer is [tex]8[/tex].

Answer:

Step-by-step explanation:

My answer is 8!!!

If x is equal to 4 then 5x4=20 because if there is no sign then that means that you have to multiply, then you add 20 and 12 which is equal to 32, And then you simplify 4 which equals 8, or you can think of dividing 32 and 4 which is also 8.

Which postulate or theorem proves that these two triangles are congruent?
A. ASA Congruence Postulate
B. AAS Congruence Theorem
C. HL Congruence Theorem
D. SAS Congruence Postulate

Answers

Answer:

Option (B)

Step-by-step explanation:

From the given picture,

Given:

Two lines PM and QR are intersecting each other at a point N.

∠NMR ≅ ∠NPQ

NR ≅ QN

To prove:

ΔMNR ≅ ΔPNQ

              Statements                               Reasons

1). NR ≅ QN                                 1). Given

2). ∠NMR ≅ ∠NPQ                     2). Given

3). ∠MNR ≅ ∠PNQ                     3). Definition of vertical angles

4). ΔMNR ≅ ΔPNQ                     4). AAS theorem of congruence

Therefore, Option (B) will be the correct option.

Answer:

B: AAS Congruence Theorem

In the function f (x) = = (x²-1) / (x-1), what happens if x takes the value of 1? Explain your answer.

Answers

Answer:

If x=1, then f(x)= undefined

Step-by-step explanation:

1*1=1

1-1=0

0/0

You can't divide by 0, so anything that is divided by 0 is undefined.

((1*1)-1)/(1-1)

(1-1)/(1-1)

0/0

0/0=Undefined

f(x)= undefined

What is 39% of 198? Percantage

Answers

Answer:

39% of 198 = 77.22

Have a nice day.

Answer:77.22Step-by-step explanation:

1: Calculate the percentage of a number.

For example: 39% of 198 = 77.22

2: Calculate a percentage based on 2 numbers.

For example: 77.22/198 = 39%

hope this help!

I need help solving these problems.

Answers

I can’t see the picture very well

MATH QUESTION PLS HELP!

Answers

Answer:

4) -14/5

Step-by-step explanation:

Answer is 4 -14/5 !!

what is 5.6 rounded to the nearest tenth

Answers

6? Cuz you have to round up due to it being 5.6

Answer:

it would be 5.60

Step-by-step explanation:

5.60 is the answer

674
x 38
Multiply by the ones.
Multiply by the tens.
+ Add the partial products.
+

Answers

Answer:

25612

Step-by-Step Explanation:

Simple multiplication

Find the missing side This is due in a hour

Answers

Answer:

The Arch is 630 ft tall

Step-by-step explanation:

Solve the system of equations..
y = 8x - 6
y= 5x +9

Answers

Answer:

x = 5

y = 34

Step-by-step explanation:

Sub y = 8x - 6 into second equation (y = 5x + 9)

8x - 6 = 5x + 9

Rearrange by collecting like terms

8x - 5x = 9 + 6

3x = 15

x = 5

Sub x = 5 into first equation (y = 8x - 6)  

y = (8*5) - 6

y = 40 - 6

y = 34

X=5 and y= 34 are the values

Jordan created a scale drawing of a rectangular room. The drawing is 8 inches long by 6 inches wide. He used a scale of 1 inch - 3 feet. What is the area, in square feet,

Answers

Answer: 144 feet

Step-by-step explanation:

Well solving for area you multiply length times wedth. So multiply 8 and 6 to get 48. Now you have to convert 48 inches into feet. So just multiply 48 times 3 to get 144.

A sign company charges $28 per yard for each custom-made banner. Ms.Gill orders two banners that are each 1 7/8 yards long, and one banner that is 2 5/8 yards long. What will Ms.Gill pay for all three banners?

Answers

Answer:

%178.50

Step-by-step explanation:

$52.50+$73.50=$126

$126+$52.50=

$178.50 for all three banners

Help it is for Geometry

Answers

Answer:

-3/4

Step-by-step explanation:

CHOP CHOP PLZ HURRRYYYYY I WILL POST ONE MORE QUESTION FOR 20 POINTS AND BRAILY CHOP CHOP PLZ

Answers

Answer:

given, verticals angle thm, definition of supplementary, {you need to see the pic for it}, substitution, and you need to see the pic for the rest so i can’t help

can you go answer my question tho

Step-by-step explanation:

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?

(A) 250 yards

(B) 300 yards

(C) 350 yards

(D) 400 yards

(E) 450 yards

Answers

Answer:

(C) 350 yards

Step-by-step explanation:

From available information

Mean = 790

1 running back = 1637 yards

Standard deviation above mean = 2.42

Using formula

z =( x - mean)/sd

2.42 = (1637-790)/sd

2.42 = 847/sd

We cross multiply

2.42sd = 847

Divide through by 2.42

Sd = 847/2.42

Sd = standard deviation = 350

So our answer is 350 and therefore option c.

what is the price of 29.99 after a 33 1/3 markdown?

Answers

Answer:

$29.99*0.6667%= $19.99= markdown price

Step-by-step explanation:

Mkae me the brainlist plssss

Answer:

$29.99*0.6667%= $19.99= markdown price

Step-by-step explanation:

Write an equation for the problem. Use n for the variable. *
$5 less than the amount Steven has is $25.

Answers

Answer:

[tex]the \:equation \: for \: the \: problem \: is : \\ n - 5 = 25. \\ and \: the \: value \: of \: n \: is \: 30.[/tex]

Step-by-step explanation:

[tex]if \: n \: is \: the \: variable, \: then : \\ n - 5 = 25 \\ n = 30.[/tex]

If a turtle walks 24 meters in 30 minutes, about how many minutes will it take the turtle to walk 36 meters?

Answers

30/24= 1.25m per min

= 1.25×36= 45 minutes

how do simplify -15.6/-4

Answers

In your question you want -15.6/-4?

The answer is -3.9

Step-by-step explanation:

A sandwich is 2 12 feet long. You decide to cut the sandwich into pieces that are 1 14 feet long. How many pieces will you cut?

Answers

Answer:

Im assuming you meant 2 1/2 and 1 1/4, so the answer would be 2 pieces

Step-by-step explanation:

2 1/2-1 1/4=1 1/4, so 2

Using the division operation, the number of pieces of sandwich that can be cut is 2

Given the Parameters :

Length of sandwich = 2.5 feets

Length per piece cut = 1.25 feets

The number of pieces that can be cut out of the sandwich can be calculated thus :

Length of sandwich ÷ Length per piece cut

Number of pieces = (2.5 ÷ 1.25) = 2

Therefore, there are 2 pieces of sandwich that can be cut.

Learn more : https://brainly.com/question/14429071


In the diagram, which of these must be true

Answers

Answer:

XYN is a right angle

explanation:

The correct answer is that Xyn is a right angle

find the equation of the line shown
how do you do this ?

Answers

Answer:

y=1/2x+0.5

Step-by-step explanation:

The slope is 1/2, which you can see by looking at the change of y/x. The y intercept is 0.5, which can be seen on the y axis.


If f(x) = 2x + 1 and
g(x) = -(x - 1)² + 3 what is the smallest solution for f(x)=g(x)?

Answers

Answer:

The smallest solution is x=-1

Step-by-step explanation:

Quadratic Equation

We have:

[tex]f(x)=2x+1[/tex]

[tex]g(x)=-(x-1)^2+3[/tex]

We'll find the solutions of f(x)=g(x), or:

[tex]2x+1=-(x-1)^2+3[/tex]

Operating:

[tex]2x+1=-(x^2-2x+1)+3[/tex]

[tex]2x+1=-x^2+2x-1+3[/tex]

Rearranging all terms on the left side:

[tex]2x+1+x^2-2x+1-3=0[/tex]

Simplifying:

[tex]x^2-1=0[/tex]

Since the term with the x is missing, we can solve for x:

[tex]x^2=1\qquad\Rightarrow x=\sqrt{1}=\pm 1[/tex]

There are two solutions:

x=1, x=-1

The smallest solution is x=-1

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