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Neko [114]
3 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]3 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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Use the standard normal table to find P(z ≥ 1.06). Round to the nearest percent.
umka2103 [35]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
What is the value of x when Rq=3x+2 ,QN =2x and SM=3x?
Andru [333]

The value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

<h3>What is the triangle?</h3>

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

RQ = 3x+2 ,QN = 2x and SM=3x

In the figure, the TM, Rn, and SL are medians of the triangle SRT and Q is the centroid.

The centroid of the triangle divides each median in the ratio 2:1

RQ/QN = 2/1

(3x+2)/2x = 2/1

After solving:

3x + 2 = 4x

x = 2

Thus, the value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

5 0
2 years ago
I need help I don’t know how to Solve for 50=6.2x
tensa zangetsu [6.8K]

divide 50 by 6.2, because 6.2 and x are entangled by multiplication. once you do that, you will have your answer. it should be 8.06

4 0
3 years ago
Read 2 more answers
Simplifying an Expression with the Numerator and the Denominator Raised to a Power
slamgirl [31]

Answer:

The answer to your question is    the second option     \frac{1}{x^{48}y^{36}z^{6}}

Step-by-step explanation:

Expression

                       [\frac{(x^{2}y^{3})^{-2}}{(x^{6}y^{3}z)^{2}}]^{3}

Process

1.- Divide the fraction in numerator and denominator

a) Numerator  

 [(x²y³)⁻²]³ = (x⁻⁴y⁻⁶)³ = x⁻¹²y⁻¹⁸

b) Denominator

 [(x⁶y³z)²]²= (x¹²y⁶z²)³ = x³⁶y¹⁸z⁶

2.- Simplify like terms

a) x⁻¹²x⁻³⁶ = x⁻⁴⁸

b) y⁻¹⁸y⁻¹⁸= y⁻³⁶

c) z⁻⁶

3.- Write the fraction

        \frac{1}{x^{48}y^{36}z^{6}}

6 0
3 years ago
ASAP work pls answer
maxonik [38]
C because i did it and got it right
4 0
3 years ago
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