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Neko [114]
2 years ago
6

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three h

undred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?

The smaller dimension is

feet
Mathematics
1 answer:
neonofarm [45]2 years ago
6 0

Answer:

  • 50 ft by 75 ft
  • 3750 square feet

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

  y = (300 -2x)/3

And the enclosed area is ...

  A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

  50 ft by 75 ft

That maximum area is 3750 square feet.

_____

<em>Comment on the solution</em>

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).

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azamat

Answer:

x = 1

Step-by-step explanation:

Given equation:

\frac{x}{2}+\frac{1}{3}=\frac{5}{6}

Now,

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we get

⇒ \frac{x}{2}+\frac{1}{3}-\frac{1}{3}=\frac{5}{6}-\frac{1}{3}

or

⇒ \frac{x}{2}+0=\frac{5}{6}-\frac{1}{3}

or

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or

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or

\frac{x}{2}=\frac{1}{2}

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4 0
3 years ago
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Answer:

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Step-by-step explanation:

The calculation is presented in the attached images to this solution.

4 0
3 years ago
Miss watson runs a disatnce of 200 metres in 25 seconds.
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Step-by-step explanation:

ANSWER:

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8 0
2 years ago
Solve. Write the solution in interval notation. -2x&gt;-8 and -5x&lt;20.
Novosadov [1.4K]

Answer:

The interval notation of the solution is (-4 , 4)

Step-by-step explanation:

* Let us explain a very important point in solving inequality

- When you multiply or divide an inequality by negative number we

   must reverse the symbol of the inequality

- Ex:

∵ 2 < 3

- If we multiply the both sides of the inequality by -1, then the

  inequality will be -2 < -3 and this is completely wrong, so we must

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∴ -2 > -3

* Now let us solve the problem

∵ -2x > -8

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∴ x < 4

∵ -5x < 20

- Divide both sides by -5 and remember to reverse the symbol of the

  inequality

∴ x > -4

- From both solutions

∴ -4 < x < 4

∴ The solution is {x : -4 < x < 4}

- Interval notation is a way of writing the solutions of inequalities

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4 0
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Answer: The widths of Kyle and Myla's boxes is the same as 2 ft.

Step-by-step explanation:

Formula : Volume of cuboidal box = length x width x height

width=\dfrac{Volume}{length\times height}

Given: Kyle has a storage box that is 2 ft. Long, 3 ft. High, and has a volume of 12 ft³ .

width=\dfrac{12}{2\times3}=2\ ft.

Myla has a storage box that is 4 ft. High, 2 ft. Long, and has a volume of 16 ft³.

width=\dfrac{16}{4\times2}=2\ ft.

Hence, the widths of Kyle and Myla's boxes is the same as 2 ft.

4 0
3 years ago
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