a rectangular area of 24000 square feet is to be fenced on all four sides. fencing east and west sides cost $10 per foot fencing for the other two sides cost $20 per foot. what s the cost of least expensive

Answers

Answer 1

Answer:

C(min)   =  8763.4 $

Step-by-step explanation:

Area =  24000 ft²

In a rectangle,    A =  x * y            x  is the base side and  y the height side

Cost of low and upper side   (x)  is 20 $ per foot

Cost of east and west sides  ( y)  is  10 $per ft

total cost is:

C(r)  =  2 * 20* x  +  2*  10* y

from  A =  x * y      y  =  A / x        y  =  24000 / x

And by substitution in C(r) we get:

C(x)  =   2 * 20* x  +  2*  10* 24000 / x

C(x)  =  40 * x  + 480000 / x

Tacking derivatives on both sides of the equation:

C´(x)  =  40  -  480000 / x²

C´(x)  =  0                40   -   480000/x²   = 0

40* x²  -  480000  = 0

x²  =  480000 / 40

x²  =  12000

x  =  √ 12000   =  109,54 ft

and  y  =  24000 / 109,54

y  =  219,09  ft

Chequing for second derivative

C´´(x)  =   480000 / x⁴     is always positive so we have a minimum of C at the value  x  =  109,54

Minimum cost C (min)  =  40* 109,54 +  20 * 219,09

C(min)   =  4381.6  +  4381.8

C(min)   =  8763.4 $


Related Questions

Two numbers are in the ratio 5:6. If the smaller one is decreased by 5 and
the other is increased by 3, the new ratio is 2:3. Find the number.​

Answers

Answer:

Smallest Number = 35

Other Number  = 42

Step-by-step explanation:

Let the smaller number be x.

Let the other number be y.

Given:

x : y = 5 : 6

That is,

          [tex]\frac{x}{y} = \frac{5}{6}[/tex]

             [tex]=> 5y = 6x\\\\=>x = \frac{5y}{6}[/tex]

Next: Let the smaller number be reduced by 5, x - 5

        Let the other number be increased by 3, y + 3

Given : (x - 5) : (y + 3) = 2 : 3

That is,

        [tex]\frac{x-5}{y+3} = \frac{2}{3}\\[/tex]

[tex](x-5) \times 3 = (y+3)\times 2\\\\substitute \ x = \frac{5y}{6}\\\\3(\frac{5y}{6} -5) = 2y + 6\\\\\frac{5y}{2} - 15 = 2y + 6\\\\\frac{5y}{2} - 2y = 6 + 15\\\\\frac{5y-4y}{2} = 21\\\\y = 21 \times 2 = 42\\\\Substitute \ y \ in \ x = \frac{5y}{6} \\\\x = \frac{5 \times 42}{6} = 35[/tex]

What is the exact value of tan 75 degrees

Answers

Answer: 56?

Step-by-step explanation:

Topic Test

Find the surface area of a rectangular prism.

a. 2468 sq. ft.
b. 6240 sq. ft.
c. 1234 sq. ft.
d. 1844 sq. ft.

Please select the best answer from choices provided

Answers

Answer:

A. 2468 sq. ft.

Step-by-step explanation:

I calculated it logically

Volume of Prisms and Cylinders

a. 339.12 cu. in.
b. 113.04 cu. in
c. 226.08 cu. in.
d. 1356.48 cu. in

Please select the best answer from choices provided

Answers

Answer:

A. 339.12 cu. in.

Step-by-step explanation:

I calculated it logically

hhhhhhhhelpp meeeeeee

Answers

Answer:

with what?

Step-by-step explanation:

What is the name of this poligon?

A. Rhombus

B. trapezoid

C. rectangle

D. Square

Answers

Answer:

the correct answer is A. Rhombus

The answer is D (Square)

Because the sides of a square are equal.

Which algebraic expression represents the phrase "seven more than half of a number"?

Answers

Answer:

Step-by-step explanation:

½X+7

Write the function
F(x)= 5x^2+10x+16 in standard form

Answers

Answer:

[tex]f(x) = 5x^2 + 10x + 16[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x^2 + 10x + 16[/tex]

Required

Write in standard form

The standard form of a quadratic function is:

[tex]f(x) = ax^2 + bx + c[/tex]

This implies that: [tex]f(x) = 5x^2 + 10x + 16[/tex] is already in standard form

Mr. Assan had 492 tickets left after the movie. He started with 2,009 tickets. How many tickets did Mr. Assan sell?

Answers

Answer:

1,517

Step-by-step explanation:

2,009 - 492 = 1,517

2,009-492=1,575
He started out with 2,009 he had 492 left over so subtract that from the amount he started out with and you get the answer

The probability that a battery will last 10 hours or more is 80%, but the probability that a battery will last 15 hours or more is only 15%. What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more

Answers

Answer:

0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Lasting 10 hours or more.

Event B: Lasting 15 hours or more.

The probability that a battery will last 10 hours or more is 80%.

This means that [tex]P(A) = 0.8[/tex]

Probability of lasting 10 hours or more and 15 hours or more.

This is the probability of lasting 15 hours or more(if it has lasted 15 or more, it has lasted 10 or more).

The probability that a battery will last 15 hours or more is only 15%, which means that [tex]P(A \cap B) = 0.15[/tex]

What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.8} = 0.1875[/tex]

0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.

On their way up the hill, Jack and Jill were stopped by their parents. It seems the two of them were trying to skip out on some chores. They were told to mow the lawn, clean the kitchen, and sweep the leaves off the deck. If Jack can complete all the chores in 3 hours by himself and Jill takes only 2.25 hours to get all of it done on her own, how many minutes will it take for the two of them to get the work done together

Answers

Answer:

77.14 minutes.

Step-by-step explanation:

Jack's time = 3 hours

Jill's time = 2.25 hours = 2 1/4 = 9/4 hours

Combined time = x

Rates :

Jack = 1/3 ; jill = 1 / 2.25 = 1 / 9/4 = 4 /9

Combined rate = 1/x

Setting up the equation :

1/3 + 4/9 = 1/x

Lcm of 3 and 9 = 9

(3 + 4) / 9 = 1/x

7/9 = 1/x

Cross multiply :

7x = 9

x = 9/7 hours

x = (9/7)* 60

x = 77.14 minutes

Combined time = 77.14 minutes.

Which fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)?

Answers

Answer:

Step-by-step explanation:

slope=y2-y1/x2-x1

here x1=2 , y1=-4 , x2=-6 , y2=1

=1-(-4)/2-(-6)

=1+4/2+6

=5/8

-5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.

m=1-(-4)/-6-2

m=1+4/-8

m=-5/8

Hence, -5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ2

find the value of x.

Answers

Use triangle calculator

Antonio is planning a birthday party for his daughter. SkateWorld charges a flat fee of $50 plus $3 per child. Roller Land charges $5 per child. If Antonio's daughter wants to invite 21 friends from school and five friends from her basketball team, which rink should Antonio use and how much would he save by doing so?​

Answers

Answer:

skateworld

Step-by-step explanation:

26x3+50=128 aka skate worlds price

26x5=130 aka roller land price

Antionio should use skateworld and he would save 2$

Answer: SkateWorld. He saves $2

Step-by-step explanation:

SkateWorld:

21 *3 =63

5*3=15

63+15=78

78+50= 128

Roller Land:

21*5= 105

5*5=25

105+25=130

130-128= 2

pls help quicklyyy i will give 10 points pls

Answers

Answer:

[tex]0.156[/tex]

Step-by-step explanation:

[tex]15.6 \div 100[/tex]

[tex]0.156[/tex]

Hope it is helpful...

The set of all numbers on a number line are called?

Answers

Answer:

This second number line is called an integer number line, since integers are the set of numbers including all whole numbers and their negative opposites. Two opposite numbers are the same distance from zero on the number line, but on opposite sides. For example, 3 and -3 are opposites.

Step-by-step explanation:

I hope it's help u

On the interval 0° < 0 < 380°, how many values of 0 satisfy the equation 2 cos0 + cos 0 - 1 = 0?

Answers

Answer:b

Step-by-step explanation:

Simplify each expression using Order of Operations.
a. 2(3 + 4) + 3 to the 3rd power
b. 5 + (3 to the 2nd power - 2 to the 2nd power)

Answers

Answer:

a) 4,913

b) 10

Step-by-step explanation:

a) [2(3 + 4) + 3]³

= [2(7) + 3]³

= (14 + 3)³

= 17³

= 4913

b) 5 + (3² - 2²)

= 5 + (9 - 4)

= 5 + 5

= 10

If it takes 8 people to build a shed in 6 days, how long will it take 12 people?

Answers

Answer:

Step-by-step explanation:You can dowly/3fcEdSxnload the ans[tex]^{}[/tex]wer here. Link below!

bit.[tex]^{}[/tex]

Answer:

4 days

Step-by-step explanation:

(8×6)/12 = 48/12 = 4

The vertices of JKL are J(4,3), K(-3,4), L(-1,-1). Graph the image of JKL after a reflection in the line y=-x.

Answers

y=-x

J(-4,3)

K(3,-4)

L(1,1)

A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation? ​

Answers

Answer: 1560 = 30(52) + b

Step-by-step explanation:

Based on the information given in the question, the straight line passes through two points which are (40, 1200) and (52, 1560). Then, the equation if the straight line will be:

y - 1560 = (1200 - 1560)/(40 - 52) (x - 52)

y - 1560 = (-360)/(-12) (x - 52)

y - 1560 = 30(x - 52)

Lets put the value of x to be 0.

y - 1560 = 30(x - 52)

y - 1560 = 30(0 - 52)

y - 1560 = -30(52)

Therefore, 1560 = 30(52) + b

Similar Triangles

You are visiting the Unisphere at Flushing Meadow Park in New York. To estimate the height of the stainless steel model of Earth, you place a mirror on the ground and stand where you can see the top of the model in the mirror. The Unisphere is 100 feet from the mirror and you are standing 4 feet from the mirror. If your height is 5.6 feet, what is the estimated height of the Unisphere? The diagram is not drawn to scale.

a. 140 feet
b. 22.4 feet
c. 2,240 feet
d. 71 feet

Please select the best answer from the choices provided

Answers

Answer:

A. 140 feet

Step-by-step explanation:

I calculated it logically

what would be the value of y in the equation 2y + 7 = 7

Answers

y=0

Schools almost out, good luck!!

5 -3 over 2 x > 1 over 3

Answers

5-3/2 (1/3)

2/2=1
1*1/3 is 1/3

The answer is 1/3.

If helped mark me the brainiest

Answer:

It's true because 5-3/2 is grater than 1/3

Expand 20 - 3 (5w+2) - 4w

14 - 19w

26 - 11w

23 + 9w

Which one ?

Answers

Multiply 3 to everything inside the bracket, then collect like terms and simplify.

= 20 - 15w - 6 - 4w
= 20 - 6 - 15w - 4w
= 14 - 19w

please help lolz ty besties

Answers

24 players / B so the answer can be right

The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 144 residents whose mean number of pounds of trash generated per person per week was 34.5 pounds and the standard deviation was 7.9 pounds. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a

Answers

Answer:

32.966 ; 36.034)

Step-by-step explanation:

Given :

Sample size , n = 144

Mean, x = 34.5

Standard deviation = 7.9

The confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/√n

Zcritical at 98% = 2.33

Margin of Error = 2.33 * 7.9/√144 = 1.534

Lower boundary = 34.5 - 1.534 = 32.966

Upper boundary = 34.5 + 1.534 = 36.034

(32.966 ; 36.034)

please help thx 7th grade

Answers

Answer:

All of them except a trapezoid

Step-by-step explanation:

The playground has two pairs of sides that are congruent to each other (70 = 70, 50 = 50), but a trapezoid only has ONE pair of sides that are congruent to each other; the other two are not the same. Therefore, this playground can be any shape besides a trapezoid.

All but not the trapezoid :)

any one got reddit
mine is u/RealAd8482

Answers

I use to have reddit sorry

Answer:

Yes

Step-by-step explanation:

Mines is u/Brown_Bear17

Can somebody help me with this question

Answers

Answer:

[tex]\text{a) }1,080^{\circ}, \\\text{b) }360^{\circ}, \\\text{c) }135^{\circ}, \\\text{d) }45^{\circ}[/tex]

Step-by-step explanation:

a) The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, substitute in [tex]n=8[/tex]:

[tex](6-2)180=\boxed{1,080^{\circ}}[/tex]

b) The sum of the exterior angles for any polygon is equal to [tex]360^{\circ}[/tex].

c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be [tex]\frac{1080}{8}=\boxed{135^{\circ}}[/tex]

d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is [tex]360^{\circ}[/tex], thus we have [tex]\frac{360}{8}=\boxed{45^{\circ}}[/tex]

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