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mr Goodwill [35]
3 years ago
9

Help please asap!!!!!!!!!

Mathematics
1 answer:
goldenfox [79]3 years ago
3 0
Try C but im not 100% sure though
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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t
Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be F=L+2W.

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

LW=80,000...(1)

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be C=20L+5(2W)\Rightarrow 20L+10W.

From equation (1), we will get:

L=\frac{80,000}{W}

Upon substituting this value in cost equation, we will get:

C=20(\frac{80,000}{W})+10W

C=\frac{1600,000}{W}+10W

C=1600,000W^{-1}+10W

To minimize the cost, we need to find critical points of the the derivative of cost function as:

C'=-1600,000W^{-2}+10

-1600,000W^{-2}+10=0

-1600,000W^{-2}=-10

-\frac{1600,000}{W^2}=-10

-10W^2=-1,600,000

W^2=160,000

\sqrt{W^2}=\pm\sqrt{160,000}  

W=\pm 400

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

C''=-2(-1600,000)W^{-3}

C''=3200,000W^{-3}

C''=\frac{3200,000}{W^3}

Now, we will substitute W=400 in 2nd derivative as:

C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05

Since 2nd derivative is positive at W=400, therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting W=400 in L=\frac{80,000}{W}, we will get:

L=\frac{80,000}{400}\\\\L=200

Therefore, the side parallel to the river will be 200 feet.

4 0
3 years ago
When g ( t ) = 3 t 2 + 2 t + 1 , evaluate g ( − 4 )
Luda [366]

Answer:

Just substitue every 't' with -4

Step-by-step explanation:

g(-4) = 3*(-4)*(-4) + 2*(-4) + 1

g(-4) = 64-8+1

g(-4) = 57

7 0
3 years ago
Read 2 more answers
Find the sides of a triangle if 2 sides of it are equal, the third side is 1 1/3, and the perimeter is 5 2/5
Kaylis [27]
Both of the sides are 2 and 1/30
7 0
3 years ago
60 cars to 20 cars indenify percent of change
Margaret [11]

Answer: -66.67%, but if the answer is supposed to positive then the answer is 66.67%.

<em>* Hopefully this helps:) </em>

7 0
2 years ago
Parallelogram PQRS is shown. m/S=(3x), m/R=120, and m/Q=(2y). Find the value of y.A.
fomenos

Option B. From the parallelogram PQRS the value of y is given to be 30

<h3>How to solve for the value of y from the parallelogram</h3>

In order to get the value of y we have to use the formula

2y + 120 = 80

where the value 120 is the angle that is stated as 120 from the question

2y = 180 - 120

2y = 60

y = 60 / 2

y = 30

Hence the value of y = 30

We can go ahead to get the value of x as well

3x + 120 = 180

take the like terms

3x = 180 - 120

3x = 60

divide through by 3 to get x

60 / 3 = x

20 = x

Read more on parallelograms here: brainly.com/question/24056495

#SPJ1

7 0
1 year ago
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