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lapo4ka [179]
3 years ago
10

A dog owner wants to use 200 ft of fencing to enclose the greatest possible area for his dog. he wants the fenced area to be rec

tangular. what dimensions should he use?
Mathematics
1 answer:
Fiesta28 [93]3 years ago
5 0
Perimeter (P) = 2 · Length(L) + 2 · Width (W) → P = 2L + 2W
Solve for either L or W (I am solving for L).
200 - 2W = 2L
(200 - 2W)/2 = L
100 - W = L

Area (A) = Length (L) · Width (W)
              = (100 - W) · W
              = 100W - W²

Find the derivative, set it equal to 0, and solve:
dA/dW = 100 - 2W
     0    = 100 - 2W
     W  = 50

refer to the equation above for L: 
100 - W = L
100 - 50 = L
        50  = L

Dimensions for the maximum Area are 50 ft x 50 ft
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Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in. Find
mr Goodwill [35]

Answer:

The volume in such a package is 27648 in³

Step-by-step explanation:

Consider the provided information.

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in.

Let the dimension are x by x by y.

Where x is the variable for the square base package and y is the variable for length.

Thus l=x, b=x and h=y

Then the volume of the box is: V(x)=x^2y (∵V=lbh)

The maximum combined length and girth is 144.

Therefore, 4x+y=144

y=144-4x

Substitute the value of y in volume of the box.

V(x)=x^2(144-4x)

V(x)=144x^2-4x^3

V'(x)=288x-12x^2

Substitute V'(x)=0.

0=288x-12x^2

12x(24-x)=0

x=0\ or\ x=24

Now apply second derivative test.

V''(x)=288-24x

V''(0)=288-24(0)>0 (Min)

V''(24)=288-24(24) (Max)

Hence, the maximum volume is at x=24

If x=24 then y=144-4(24)=48

Substituting value of x = 24 and y = 48 V(x)=x^2y gives 27648.

Hence, the volume in such a package is 27648 in³

5 0
3 years ago
I need to know the step by step on how to solve this question
cluponka [151]
My father taught me a method that I call, 'throwing some thing over the wall'. There is a sample equation for the first picture that shows you how it works. It's a great way to help isolate the variable and I hope that it works for you. The second picture contains the answers I got through the use of this method. I'm sorry for the messy handwriting; I was on a bus.

5 0
3 years ago
14. Phyllis wants to hire a clown to entertain at her daughter's birthday party.
kaheart [24]

Answer:

C=25+5.50n

Step-by-step explanation:

C=25+5.50n where c is the total cost and n is the number of hours the clown entertains.

3 0
3 years ago
Find the GCF of 56 and 46. 2 8 10
Sonbull [250]
Your GCF would be 2.
3 0
3 years ago
Read 2 more answers
2 math questions below!!!!
Radda [10]
Perimeter is 10 units while the area is 8 units I believe but that’s just by counting the boxes
3 0
3 years ago
Read 2 more answers
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