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Aleonysh [2.5K]
3 years ago
5

Patricia purchased x meters of fencing. She originally intended to use all of the fencing to enclose a square region, but later

decided to use all of the fencing to enclose a rectangular region with length y meters greater than its width. In square meters, what is the positive difference between the area of the square region and the area of the rectangular region?
Mathematics
1 answer:
sergejj [24]3 years ago
5 0

Answer:

  (y^2)/4 square meters

Step-by-step explanation:

For a perimeter length of x, the side of a square will be x/4 and its area will be (x/4)^2.

If one side of the square is shortened by y/2 and the adjacent side is lengthened by y/2, then the difference in side lengths will be y. The area of the resulting rectangle will be ...

  (x/4 -y/2)(x/4 +y/2) = (x/4)^2 -(y/2)^2

That is, the difference in area between the square and the rectangle is ...

  (x/4)^2 - ((x/4)^2 -(y/2)^2) = (y/2)^2 = y^2/4

The positive difference between the area of the square region and the area of the rectangular region is y^2/4 square meters.

You might be interested in
Find the mean and variance of the following data<br><br> 52,34,64,49,55,26,38,63
BlackZzzverrR [31]

Answer:

Mean = 47,625

Variance, ignoring the commas = 157

Explanation:

The mean is quite simple: is the mid value of an amount (m') of numbers.

Examples:

Mean of 2, 4:  2 + 4/2 = 3

Mean of 5, 6 and 8: 1+6+8/3 = 15/3 = 5

Generalizing: M' = An + Bn-1 + Cn-2 +... + Y1/ n

So, for the enunciated, we have:

M = 52 + 34 + 64 + 49 + 55 + 26 + 38 + 63/8

M = 47,625

Variance is quite harder.

The mathematics definition is also quite harder:

∑n, i=1 (Xi - X')²/n

Traduction: the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, divided by the number of observed terms is the square of the standard deviation, that is, the variance.

Don't worry, you don't need to understand that. I'll do the question, then you will see in practice what that means.

First, we need the mean of the observerd terms. We already have done that.

M = 47,625.

Next, we will do the the difference o<em>f the square </em>of the dispersion measures by the arithmetic mean of them. Which are:

A.52 - 47,625 = (4,375)²

B.34 - 47,625 = (-13,625)² - <em>Because of a value like that, you know see why</em>

C.64 - 47,625 = (16,375)²

D.49 - 47,625 = (1,375)²

E.55 - 47,625 = (7,375)²

F.26 - 47,625 = (-21,625)² - <em>we need to square everything: because a negati</em>

G.38 - 47,625 = (-9,625)² - <em>ve result doest not help in the statisc.</em>

K.63 - 47,625 = (15,375)²

I am using a calculator, but really with that, I'll aproximately the values. If you need a accurate measure, just square them all the way.

A = 16     D  = 1     G = 100

B = 169    E = 49    K = 225

C = 256   F = 441

The last part is the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, dividing them by the number of observations.

16 + 169 + 256 + 1 + 49 + 441 + 100 + 225/ 8 = 157,125

8 is the number of observations.

___________________________

But why we do the variance? The variance serves to us for know how much the mean is precise.

So, the lower is the variance, the better is the mean.

Take a look on this example:

Imagine three persons, A, B and C.

They are in pub, talking about how much they receive. A gets, per month, 1000US$, b 2000 and C 3000US$.

So, their mean are 3000US$.

Now imagine that Bill Gates joins the group. And Bill, last month, got 100 milion US$.

Now the mean will be almost 25 milions of dollars.  So, she is VERY far from the reality of the major part of the group. And is in there that cames the variance. Looking to the variance, we will see that there is a big discrepancy for each observed term.

5 0
3 years ago
Least to greatest<br> 3/4,5/8,3/7,1/3,2/5
tangare [24]

Answer:

1/3 < 2/5 < 3/7 < 5/8 < 3/4

Step-by-step explanation:

Using the given inputs:  

3/4 5/8 3/7 1/3 2/5

The least common denominator (LCD) is: 840.

Rewriting as equivalent fractions with the LCD:

3/4= 630/840

5/8= 525/840

3/7= 360/840

1/3= 280/840

2/5=  336/840  

Sorting this by the numerators of the equivalent fractions in order from least to greatest:

1/3= 280/840=       < 2/5=  336/840=    <     3/7= 360/840=      <    5/8= 525/840=       <     3/4 = 630/840

Therefore, the sorted inputs in order from least to greatest is:

1/3 < 2/5 < 3/7 < 5/8 < 3/4

Hopes this helps!

Have a good evening! :)

5 0
3 years ago
What is the value of n in this equation 1/2(n-4)-3=3-(2n+3)?
alexdok [17]

Answer:

n = 2

Step-by-step explanation:

Given

\frac{1}{2}(n - 4) - 3 = 3 - (2n + 3)

Multiply through by 2 to clear the fraction

n - 4 - 6 = 6 - 2(2n + 3) ← distribute

n - 10 = 6 - 4n - 6 ( add 4n to both sides )

5n - 10 = 0 ( add 10 to both sides )

5n = 10 ( divide both sides by 5 )

n = 2

6 0
3 years ago
Linda, Aldo, and bob have a total of 70 in their wallets. Bob has 3 times what Linda has. Linda has 5 more than Aldo. How much d
yanalaym [24]
L, A, B = the amount of money each person has.
L + A + B = 70
B = 3L
L = A +5 or A = L-5 
Set up an equation in L only:
L + L - 5 +3L =70
5L -5 = 70
5L =75
L = 15
follows
B=3*15 =45
A = 15 - 5 = 10
7 0
3 years ago
If y = 2x3 – 4x and dx, dt equals 4, find dy, dt when x = 1. give only the numerical answer. for example, if dy, dt = 3, type on
Rufina [12.5K]
<span>y= 2*3-4x;
    differentiate with respect to t we get dy = -4xdt; -- eqn 1
   given dt = 4 substitute in eqn 1 we get , dy =-4 x( 4) = -16x; --eqn2
  given x=1 then sub then the value of x in eqn 2 we get dy = -16(1)=-16
   ie Ans dy = -16</span>
4 0
3 years ago
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